title: The effective sigma-model of multidimensional gravity

abstract:
  The properties of the effective sigma-model for D-dimensional Einstein
gravity based on multidimensional geometries is analyzed. Besides pure
geometry, additional minimally coupled scalars and (p+2)-forms are considered
which yield an extended target space after reduction to the effective
D_0-dimensional geometry.
  In any case the target space is a homogeneous space. The orthobrane condition
guarantees the existence of exact solutions. Geometrically, it makes the target
space a locally symmetric one.
  New solutions with scalar fields are found, which may inflate not only in
time-like but in also in additional spatial directions of the effective
geometry.
  Static spherically symmetric solutions with a particular configuration of
intersecting electric and magnetic branes are investigated both, for the
orthobrane case and for degenerated charges. In both cases T_H depends
critically on the intersection dimension of the p-branes.
  Finally, the role of the Einstein frame for 4-geometries is addressed, and
the physical frame transformation for cosmological geometries is given.


title: Bounds on negative energy densities in static space-times

abstract:
  Certain exotic phenomena in general relativity, such as backward time travel,
appear to require the presence of matter with negative energy. While quantum
fields are a possible source of negative energy densities, there are lower
bounds - known as quantum inequalities - that constrain their duration and
magnitude. In this paper, we derive new quantum inequalities for scalar fields
in static space-times, as measured by static observers with a choice of
sampling function. Unlike those previously derived by Pfenning and Ford, our
results do not assume any specific sampling function. We then calculate these
bounds in static three- and four-dimensional Robertson-Walker universes, the de
Sitter universe, and the Schwarzschild black hole. In each case, the new
inequality is stronger than that of Pfenning and Ford for their particular
choice of sampling function.


title: On Accelerated Inertial Frames in Gravity and Electromagnetism

abstract:
  When a charged insulating spherical shell is uniformly accelerated, an
oppositely directed electric field is produced inside. Outside the field is the
Born field of a uniformly accelerated charge, modified by a dipole. Radiation
is produced. When the acceleration is annulled by the nearly uniform gravity
field of an external shell with a 1 + beta cos theta surface distribution of
mass, the differently viewed Born field is static and joins a static field
outside the external shell; no radiation is produced. We discuss gravitational
analogues of these phenomena. When a massive spherical shell is accelerated, an
untouched test mass inside experiences a uniform gravity field and accelerates
parallelly to the surrounding shell. In the strong gravity regime we illustrate
these effects using exact conformastatic solutions of the Einstein-Maxwell
equations with charged dust. We consider a massive charged shell on which the
forces due to nearly uniform electrical and gravitational fields balance. Both
fields are reduced inside by the ratio of the g_00 inside the shell to that
away from it. The acceleration of a free test particle, relative to a static
observer, is reduced correspondingly. We give physical explanations of these
effects.


title:
Fluctuations in a Thermal Field and Dissipation of a Black Hole
  Spacetime: Far-Field Limit

abstract:
  We study the back reaction of a thermal field in a weak gravitational
background depicting the far-field limit of a black hole enclosed in a box by
the Close Time Path (CTP) effective action and the influence functional method.
We derive the noise and dissipation kernels of this system in terms of
quantities in quasi-equilibrium, and formally prove the existence of a
Fluctuation-Dissipation Relation (FDR) at all temperatures between the quantum
fluctuations of the thermal radiance and the dissipation of the gravitational
field. This dynamical self-consistent interplay between the quantum field and
the classical spacetime is, we believe, the correct way to treat back-reaction
problems. To emphasize this point we derive an Einstein-Langevin equation which
describes the non-equilibrium dynamics of the gravitational perturbations under
the influence of the thermal field. We show the connection between our method
and the linear response theory (LRT), and indicate how the functional method
can provide more accurate results than prior derivations of FDRs via LRT in the
test-field, static conditions. This method is in principle useful for treating
fully non-equilibrium cases such as back reaction in black hole collapse.


title: Global foliations of matter spacetimes with Gowdy symmetry

abstract:
  A global existence theorem, with respect to a geometrically defined time, is
shown for Gowdy symmetric globally hyperbolic solutions of the Einstein-Vlasov
system for arbitrary (in size) initial data. The spacetimes being studied
contain both matter and gravitational waves.


title: Domain walls and torsion potentials

abstract:
  A Lagrangian for flat domain walls in spaces with Cartan torsion and
electromagnetic fields is proposed.The Lagrangian is very similar to a recently
proposed Lagrangian for domain walls in a Chern-Simons electrodynamics in 2+1
dimensions.We show that in the first approximation of the torsion scalar
potential the field equations are reduced to a Klein-Gordon type field equation
for the torsion potential and the electromagnetic wave equation.A planar
symmetric solution representing a parallel plates electric capacitor
interacting with the electric field is given.The photon mass is proportional to
the torsion potential and in the time dependent case the angular momentum is
computed and is shown to be connected with torsion in analogy with the
spin-torsion relation which appears in Einstein-Cartan gravity.When the
curvature Ricci scalar is introduced we are able to show that the torsion
potential can be associated with Higgs massive vectorial bosons.


title: Spurious Effects in perturbative Calculations

abstract:
  We show spurious effects in perturbative calculations due to different
orderings of inhomogeneous terms while computing corrections to Green functions
for two different metrics. These effects are not carried over to physically
measurable quantities like the renormalized value of the vacuum expectation
value of the stress-energy tensor.


title: Quantum to classical transition in quantum field theory

abstract:
  We study the quatum to classical transition process in the context of quantum
field theory. Extending the influence functional formalism of Feynman and
Vernon, we study the decoherence process for self-interacting quantum fields in
flat space. We also use this formalism for arbitrary geometries to analyze the
quantum to classical transition in quantum gravity. After summarizing the main
results known for the quantum Brownian motion, we consider a self-interacting
field theory in Minkowski spacetime. We compute a coarse grained effective
action by integrating out the field modes with wavelength shorter than a
critical value. From this effective action we obtain the evolution equation for
the reduced density matrix (master equation). We compute the diffusion
coefficients for this equation and analyze the decoherence induced on the
long-wavelength modes. We generalize the results to the case of a conformally
coupled scalar field in de Sitter spacetime. We show that the decoherence is
effective as long as the critical wavelength is taken to be not shorter than
the Hubble radius. On the other hand, we study the classical limit for
scalar-tensorial models in two dimensions. We consider different couplings
between the dilaton and the scalar field. We discuss the Hawking radiation
process and, from an exact evaluation of the influence functional, we study the
conditions by which decoherence ensures the validity of the semiclassical
approximation in cosmological metrics. Finally we consider four dimensional
models with massive scalar fields, arbitrary coupled to the geometry. We
compute the Einstein-Langevin equations in order to study the effect of the
fluctuations induced by the quantum fields on the classical geometry.


title:
Exterior Differential System for Cosmological G2 Perfect Fluids and
  Geodesic Completeness

abstract:
  In this paper a new formalism based on exterior differential systems is
derived for perfect-fluid spacetimes endowed with an abelian orthogonally
transitive G2 group of motions acting on spacelike surfaces. This formulation
allows simplifications of Einstein equations and it can be applied for
different purposes. As an example a singularity-free metric is rederived in
this framework. A sufficient condition for a diagonal metric to be geodesically
complete is also provided.


title: Field theory simulation of Abelian-Higgs cosmic string cusps

abstract:
  We have performed a lattice field theory simulation of cusps in Abelian-Higgs
cosmic strings. The results are in accord with the theory that the portion of
the strings which overlaps near the cusp is released as radiation. The radius
of the string cores which must touch to produce the evaporation is
approximately $r = 1$ in natural units. In general, the modifications to the
string shape due to the cusp may produce many cusps later in the evolution of a
string loop, but these later cusps will be much smaller in magnitude and more
closely resemble kinks.


title:
Quasistationary binary inspiral. I. Einstein equations for the two
  Killing vector spacetime

abstract:
  The geometry of two infinitely long lines of mass moving in a fixed circular
orbit is considered as a toy model for the inspiral of a binary system of
compact objects due to gravitational radiation. The two Killing fields in the
toy model are used, according to a formalism introduced by Geroch, to describe
the geometry entirely in terms of a set of tensor fields on the two-manifold of
Killing vector orbits. Geroch's derivation of the Einstein equations in this
formalism is streamlined and generalized. The explicit Einstein equations for
the toy model spacetime are derived in terms of the degrees of freedom which
remain after a particular choice of gauge.


title: A spacetime dual to the NUT spacetime

abstract:
  By decomposing the Riemann curvature into electric and magnetic parts, a
duality transformation, which involves interchange of active and passive
electric parts, has recently been proposed. It was shown that the Schwarzschild
solution is dual to the one that describes the Schwarzschild particle with
cloud of string dust or a global monopole. Following the same procedure we
obtain the solution dual to the NUT spacetime.


title: Decoherence in quantum cosmology at the onset of inflation

abstract:
  We calculate the reduced density matrix for the inflaton field in a model of
chaotic inflation by tracing out degrees of freedom corresponding to various
bosonic fields. We find a qualitatively new contribution to the density matrix
given by the Euclidean effective action of quantum fields. We regularise the
ultraviolet divergences in the decoherence factor. Dimensional regularisation
is shown to violate the consistency conditions for a density matrix as a
bounded operator. A physically motivated conformal redefinition of the
environmental fields leads to well-defined expressions. They show that due to
bosonic fields the Universe acquires classical properties near the onset of
inflation.


title: A New Family of Gauges in Linearized General Relativity

abstract:
  For vacuum Maxwell theory in four dimensions, a supplementary condition
exists (due to Eastwood and Singer) which is invariant under conformal
rescalings of the metric, in agreement with the conformal symmetry of the
Maxwell equations. Thus, starting from the de Donder gauge, which is not
conformally invariant but is the gravitational counterpart of the Lorenz gauge,
one can consider, led by formal analogy, a new family of gauges in general
relativity, which involve fifth-order covariant derivatives of metric
perturbations. The admissibility of such gauges in the classical theory is
first proven in the cases of linearized theory about flat Euclidean space or
flat Minkowski space-time. In the former, the general solution of the equation
for the fulfillment of the gauge condition after infinitesimal diffeomorphisms
involves a 3-harmonic 1-form and an inverse Fourier transform. In the latter,
one needs instead the kernel of powers of the wave operator, and a contour
integral. The analysis is also used to put restrictions on the dimensionless
parameter occurring in the DeWitt supermetric, while the proof of admissibility
is generalized to a suitable class of curved Riemannian backgrounds.
Eventually, a non-local construction is obtained of the tensor field which
makes it possible to achieve conformal invariance of the above gauges.


title: Unitary and non-unitary evolution in quantum cosmology

abstract:
  We analyse when and why unitarity violations might occur in quantum cosmology
restricted to minisuperspace. To this end we discuss in detail backscattering
transitions between expanding and contracting solutions of the Wheeler-DeWitt
equation. We first show that upon neglecting only backscattering, one obtains
an intermediate regime in which matter evolves unitarily but which does not
correspond to any Schr\"odinger equation in a given geometry since
gravitational backreaction effects are taken into account at the quantum level.
We then show that backscattering amplitudes are exponentially smaller than
matter transition amplitudes. Both results follow from an adiabatic treatment
valid for macroscopic universes. To understand how backscattering and the
intermediate regime should be interpreted, we review the problem of electronic
transitions induced by nuclear motion since it is mathematically very similar.
In this problem, transition amplitudes are obtained from the conserved current.
The same applies to quantum cosmology and shows that the unique consistent
interpretation is based on the current when backscattering is neglected. We
then review why, in a relativistic context, backscattering is interpreted as
pair production whereas it is not in the non relativistic case. In each example
the correct interpretation is obtained by coupling the system to an external
quantum device. From the absence of such external systems in cosmology, we
conclude that backscattering does not have a unique consistent interpretation
in quantum cosmology.


title: Cosmological models (Carg\`{e}se lectures 1998)

abstract:
  The aim of this set of lectures is a systematic presentation of a 1+3
covariant approach to studying the geometry, dynamics, and observational
properties of relativistic cosmological models. In giving (i) the basic 1+3
covariant relations for a cosmological fluid, the present lectures cover some
of the same ground as a previous set of Carg\`{e}se lectures \cite{ell73}, but
they then go on to give (ii) the full set of corresponding tetrad equations,
(iii) a classification of cosmological models with exact symmetries, (iv) a
brief discussion of some of the most useful exact models and their
observational properties, and (v) an introduction to the gauge-invariant and
1+3 covariant perturbation theory of
almost-Friedmann-Lema\^{\i}tre-Robertson-Walker universes, with a fluid
description for the matter and a kinetic theory description of the radiation.


title: Origin of Classical Singularities

abstract:
  We briefly review some results concerning the problem of classical
singularities in general relativity, obtained with the help of the theory of
differential spaces. In this theory one studies a given space in terms of
functional algebras defined on it. Then we present a generalization of this
method consisting in changing from functional (commutative) algebras to
noncommutative algebras. By representing such an algebra as a space of
operators on a Hilbert space we study the existence and properties of various
kinds of singular space-times. The obtained results suggest that in the
noncommutative regime, supposedly reigning in the pre-Planck era, there is no
distinction between singular and non-singular states of the universe, and that
classical singularities are produced in the transition process from
noncommutative geometry to the standard space-time physics.


title:
Isometric invariance of the positive-frequency kernel in generalized
  FRW-like spacetimes

abstract:
  Klein-Gordon equation with minimal coupling in FRW-like spacetimes with
compact but not necessarily isotropic neither homogeneous space sections.
Beside exceptional cases, the kernel is invariant under continuous isometries.


title:
Cosmological models with bulk viscosity in presence of adiabatic matter
  creation and with G, c and Lambda variables

abstract:
  Some properties of cosmological models with a time variable bulk viscous
coefficient in presence of adiabatic mater creation and G, c, Lambda variables
are investigated in the framework of flat FRW line element. We trivially find a
set of solutions through Dimensional Analysis. In all the studied cases it is
found that the behaviour of these constants is inversely prportional to the
cosmic time.


title: A Spinorial Hamiltonian Approach to Gravity

abstract:
  We give a spinorial set of Hamiltonian variables for General Relativity in
any dimension greater than 2. This approach involves a study of the algebraic
properties of spinors in higher dimension, and of the elimination of
second-class constraints from the Hamiltonian theory. In four dimensions, when
restricted to the positive spin-bundle, these variables reduce to the standard
Ashtekar variables. In higher dimensions, the theory can either be reduced to a
spinorial version of the ADM formalism, or can be left in a more general form
which seems useful for the investigation of some spinorial problems such as
Riemannian manifolds with reduced holonomy group. In dimensions $0 \pmod 4$,
the theory may be recast solely in terms of structures on the positive
spin-bundle $\mathbb{V}^+$, but such a reduction does not seem possible in
dimensions $2 \pmod 4$, due to algebraic properties of spinors in these
dimensions.


title: Entropy of Constrained Gravitational Instanton

abstract:
  The seeds for quantum creations of universes are constrained gravitational
instantons. For all compact constrained instantons with U(1) isometry, the
period $\beta$ of the group parameter $\tau$ is identified as the reciprocal of
the temperature. If $\beta$ remains a free parameter under the constraints,
then the Euclidean action becomes the negative of the "entropy". As examples,
we perform the calculations for the Taub-NUT and Taub-bolt-type models and
study the quantum creation of the Taub-NUT universe.


title:
Nonextreme black holes near the extreme state and acceleration horizons:
  thermodynamics and quantum-corrected geometry

abstract:
  We consider the class of metrics that can be obtained from those of
nonextreme black holes by limiting transitions to the extreme state such that
the near-horizon geometry expands into a whole manifold. These metrics include,
in particular, the Rindler and Bertotti - Robinson spacetimes. The general
formula for the entropy of massless radiation valid either for black-hole or
for acceleration horizons is derived. It is argued that, as a black hole
horizon in the limit under consideration turns into an acceleration one, the
thermodynamic entropy $S_{q}$ of quantum radiation is due to the Unruh effect
entirely and $S_{q}=0$ exactly. The contribution to the quasilocal energy from
a given curved spacetime is equal to zero and the only nonvanishing term stems
from a reference metric. In the variation procedure necessary for the
derivation of the general first law, the metric on a horizon surface changes
along with the boundary one, and the account for gravitational and matter
stresses is an essential ingredient of the first law. This law confirms the
property $S_{q}=0$. The quantum-corrected geometry of the Bertotti - Robinson
spacetime is found and it is argued that backreaction of quantum fields mimics
the effect of the cosmological constant $\Lambda_{eff\text{}}$ and can
drastically change the character of spacetime depending on the sign of $\Lambda
_{eff}$ --- for instance, turn $AdS_{2}\times S_{2}$ into $dS_{2}\times S_{2}$
or $Rindler_{2}\times S_{2}$. Two latter solutions can be thought of as the
quantum versions of the cold and ultracold limits of the Reissner-Nordstrom-de
Sitter metric.


title: Critical phenomena in perfect fluids

abstract:
  We investigate the gravitational collapse of a spherically symmetric, perfect
fluid with equation of state P = (Gamma -1)rho. We restrict attention to the
ultrarelativistic (``kinetic-energy-dominated'', ``scale-free'') limit where
black hole formation is anticipated to turn on at infinitesimal black hole mass
(Type II behavior). Critical solutions (those which sit at the threshold of
black hole formation in parametrized families of collapse) are found by solving
the system of ODEs which result from a self-similar ansatz, and by solving the
full Einstein/fluid PDEs in spherical symmetry. These latter PDE solutions
(``simulations'') extend the pioneering work of Evans and Coleman (Gamma = 4/3)
and verify that the continuously self-similar solutions previously found by
Maison and Hara et al for $1.05 < Gamma < 1.89 are (locally) unique critical
solutions. In addition, we find strong evidence that globally regular critical
solutions do exist for 1.89 < Gamma <= 2$, that the sonic point for Gamma_dn =
1.8896244 is a degenerate node, and that the sonic points for Gamma >Gamma_dn
are nodal points rather than focal points as previously reported. We also find
a critical solution for Gamma = 2, and present evidence that it is continuously
self-similar and Type II. Mass-scaling exponents for all of the critical
solutions are calculated by evolving near-critical initial data, with results
which confirm and extend previous calculations based on linear perturbation
theory. Finally, we comment on critical solutions generated with an ideal-gas
equation of state.


title: A Way to 3D Numerical Relativity --- Coalescing Binary Neutron Stars ---

abstract:
  One of the most promising sources of gravitational radiation is coalescence
of binary neutron stars or black holes. In order to study gravitational
radiation at the merging phase of coalescing binary neutron stars which is
called the last three-milliseconds, full general relativistic simulations are
required. Since coalescence of binary stars is a completely non-axisymmetric
and 3 dimensional (in space) event, which needs great powers of computers, we
have to develop a method of 3D numerical relativity using a vector-parallel
supercomputer. As a first step of this final goal, we started simulations using
post-Newtonian hydrodynamics including radiation reaction of gravitational
waves from 1989. They gave a lot of perspectives on coalescing events and
gravitational radiation from them. Next we started to attack 3D, fully
relativistic simulations. First, basic equations on the (3+1)-formalism of the
Einstein equations are shown. As for gauge conditions, we use conformal time
slicing and psuedo minimal distortion condtions at present. For these
conditions as well as to solve initial value equations, we should solve some
elliptic partial differential equations. It consumes the greatest part of CPU
time. We show recent results of test simulations on coalescing binary neutron
stars.


title: Characteristic hypersurfaces in a relativistic superfluid theory

abstract:
  By discussing the Cauchy problem, we determine the covariant equation of the
characteristic hypersurfaces in a relativistic superfluid theory.


title:
The exponential law: Monopole detectors, Bogoliubov transformations, and
  the thermal nature of the Euclidean vacuum in RP^3 de Sitter spacetime

abstract:
  We consider scalar field theory on the RP^3 de Sitter spacetime (RP3dS),
which is locally isometric to de Sitter space (dS) but has spatial topology
RP^3. We compare the Euclidean vacua on RP3dS and dS in terms of three
quantities that are relevant for an inertial observer: (i) the stress-energy
tensor; (ii) the response of an inertial monopole particle detector; (iii) the
expansion of the Euclidean vacuum in terms of many-particle states associated
with static coordinates centered at an inertial world line. In all these
quantities, the differences between RP3dS and dS turn out to fall off
exponentially at early and late proper times along the inertial trajectory. In
particular, (ii) and (iii) yield at early and late proper times in RP3dS the
usual thermal result in the de Sitter Hawking temperature. This conforms to
what one might call an exponential law: in expanding locally de Sitter
spacetimes, differences due to global topology should fall off exponentially in
the proper time.


title: Apparent horizons in simplicial Brill wave initial data

abstract:
  We construct initial data for a particular class of Brill wave metrics using
Regge calculus, and compare the results to a corresponding continuum solution,
finding excellent agreement. We then search for trapped surfaces in both sets
of initial data, and provide an independent verification of the existence of an
apparent horizon once a critical gravitational wave amplitude is passed. Our
estimate of this critical value, using both the Regge and continuum solutions,
supports other recent findings.


title: Open inflation from quantum cosmology with a strong nonminimal coupling

abstract:
  We propose the mechanism of quantum creation of the open Universe in the
observable range of values of $\Omega$. This mechanism is based on the
no-boundary quantum state with the Hawking-Turok instanton applied to the model
with a strong nonminimal coupling of the inflaton field. We develop the slow
roll perturbation expansion for the instanton solution and obtain a nontrivial
contribution to the classical instanton action. The interplay of this classical
contribution with the loop effects due to quantum effective action generates
the probability distribution peak with necessary parameters of the inflation
stage without invoking any anthropic considerations. In contrast with a similar
mechanism for closed models, existing only for the tunneling quantum state of
the Universe, the observationally justified open inflation originates from the
no-boundary cosmological wavefunction.


title: String Spreading on Black Hole Horizon

abstract:
  The phenomenon of string spreading on the black hole horizon, as originally
discussed by Susskind, is considered in the {\it exact} curved Schwarzschild
background. We consider an oscillating string encircling the black hole and
contracting towards the horizon. We then compute the angular and radial
spreading of the string, as seen by a static observer at spatial infinity using
fixed finite resolution time.
  Within our case study we find that there is indeed a spreading of the string
in the angular direction, such that the string eventually covers the whole
horizon. However, regarding the radial direction, we find that
Lorentz-contraction suppresses the radial string spreading.


title: Radiation of Charged Particles by Charged Black Hole

abstract:
  The probability of a charged particle production by the electric field of a
charged black hole depends essentially on the particle energy. This probability
is found in the nonrelativistic and ultrarelativistic limits. The range of
values for the mass and charge of a black hole is indicated where the discussed
mechanism of radiation is dominating over the Hawking one.


title:
Compact support of spherically symmetric equilibria in non-relativistic
  and relativistic galactic dynamics

abstract:
  Equilibrium states in galactic dynamics can be described as stationary
solutions of the Vlasov-Poisson system, which is the non-relativistic case, or
of the Vlasov-Einstein system, which is the relativistic case. To obtain
spherically symmetric stationary solutions the distribution function of the
particles (stars) on phase space is taken to be a function of the particle
energy and angular momentum. We give a new condition on this function which
guarantees that the resulting steady state has finite mass and compact support
both for the non-relativistic and the relativistic case. The condition is local
in the sense that only the asymptotic behaviour for energy values close to the
maximal energy value in the particle distribution needs to be prescribed.


title: Frames of Reference and Some of its Applications

abstract:
  We define a Frame of reference as a two ingredients concept: A meta-rigid
motion, which is a generalization of a Born motion, and a chorodesic
synchronization, which is an adapted foliation. At the end of the line we
uncover a low-level 3-dimensional geometry with constant curvature and a
corresponding coordinated proper-time scale. We discuss all these aspects both
from the geometrical point of view as from the point of view of some of the
physical applications derived from them.


title: An effective stochastic semiclassical theory for the gravitational field

abstract:
  Assuming that the mechanism proposed by Gell-Mann and Hartle works as a
mechanism for decoherence and classicalization of the metric field, we formally
derive the form of an effective theory for the gravitational field in a
semiclassical regime. This effective theory takes the form of the usual
semiclassical theory of gravity, based on the semiclassical Einstein equation,
plus a stochastic correction which accounts for the back reaction of the lowest
order matter stress-energy fluctuations.


title:
Existence of stable hairy black holes in su(2) Einstein-Yang-Mills
  theory with a negative cosmological constant

abstract:
  We consider black holes in EYM theory with a negative cosmological constant.
The solutions obtained are somewhat different from those for which the
cosmological constant is either positive or zero. Firstly, regular black hole
solutions exist for continuous intervals of the parameter space, rather than
discrete points. Secondly, there are non-trivial solutions in which the gauge
field has no nodes. We show that these solutions are linearly stable.


title: Isolated Horizons: A Generalization of Black Hole Mechanics

abstract:
  A set of boundary conditions defining a non-rotating isolated horizon are
given in Einstein-Maxwell theory. A space-time representing a black hole which
itself is in equilibrium but whose exterior contains radiation admits such a
horizon . Physically motivated, (quasi-)local definitions of the mass and
surface gravity of an isolated horizon are introduced. Although these
definitions do not refer to infinity, the quantities assume their standard
values in Reissner-Nordstrom solutions. Finally, using these definitions, the
zeroth and first laws of black hole mechanics are established for isolated
horizons.


title: Chern-Simons electrodynamics in (2+1)-spacetime with torsion

abstract:
  Chern-Simons electrodynamics in 2+1-spacetimes with torsion is investigated.
We start from the usual Chern-Simons (CS) electrodynamics Lagrangian and Cartan
torsion is introduced in the covariant derivative and by a direct coupling of
torsion vector to the CS field. Variation of the Lagrangian with respect to
torsion shows that Chern-Simons field is proportional to the product of the
square of the scalar field and torsion. The electric field is proportional to
torsion vector and the magnetic flux is computed in terms of the time-component
of the two dimensional torsion. Contrary to early massive electrodynamics in
the present model the photon mass does not depend on torsion.


title: Speed Limits in General Relativity

abstract:
  Some standard results on the initial value problem of general relativity in
matter are reviewed. These results are applied first to show that in a well
defined sense, finite perturbations in the gravitational field travel no faster
than light, and second to show that it is impossible to construct a warp drive
as considered by Alcubierre (1994) in the absence of exotic matter.


title: Relativistic dust disks and the Wilson-Mathews approach

abstract:
  Treating problems in full general relativity is highly complex and frequently
approximate methods are employed to simplify the solution. We present
comparative solutions of a infinitesimally thin relativistic, stationary,
rigidly rotating disk obtained using the full equations and the approximate
approach suggested by Wilson & Mathews. We find that the Wilson-Mathews method
has about the same accuracy as the first post-Newtonian approximation.


title: G1 Cosmologies with Gravitational and Scalar Waves

abstract:
  I present here a new algorithm to generate families of inhomogeneous massless
scalar field cosmologies. New spacetimes, having a single isometry, are
generated by breaking the homogeneity of massless scalar field $G_2$ models
along one direction. As an illustration of the technique I construct
cosmological models which in their late time limit represent perturbations in
the form of gravitational and scalar waves propagating on a non-static
inhomogeneous background. Several features of the obtained metrics are
discussed, such as their early and late time limits, structure of singularities
and physical interpretation.


title: The Universe With Bulk Viscosity

abstract:
  Exact solutions for a model with variable $G$, $\Lambda$ and bulk viscosity
are obtained. Inflationary solutions with constant (de Sitter-type) and
variable energy density are found. An expanding anisotropic universe is found
to isotropize during its course of expansion but a static universe is not. The
gravitational constant is found to increase with time and the cosmological
constant decreases with time as $\Lambda \propto t^{-2}$.


title: Critical phenomena in gravitational collapse

abstract:
  This article reviews classical and quantum aspects of critical phenomena in
gravitational collapse. We pay special attention to the origin of the scaling
law for black hole mass, and to phase transitions in which black hole formation
turns on at finite mass. We present some new results for perfect fluids with
pressure proportional to density.


title: A Model of Curvature-Induced Phase Transitions in Inflationary Universe

abstract:
  Chiral phase transitions driven by space-time curvature effects are
investigated in de Sitter space in the supersymmetric Nambu-Jona-Lasinio model
with soft supersymmetry breaking. The model is considered to be suitable for
the analysis of possible phase transitions in inflationary universe. It is
found that a restoration of the broken chiral symmetry takes place in two
patterns for increasing curvature : the first order and second order phase
transition respectively depending on initial settings of the four-body
interaction parameter and the soft supersymmetry breaking parameter. The
critical curves expressing the phase boundaries in these parameters are
obtained. Cosmological implications of the result are discussed in connection
with bubble formations and the creation of cosmic strings during the
inflationary era.


title: The Quantization of Gravity. Dynamic Approach

abstract:
  On the basis of dynamic quantization method we build in this paper a new
mathematically correct quantization scheme of gravity.
  In the frame of this scheme we develop a canonical formalism in
tetrad-connection variables in 4-D theory of pure gravity.
  In this formalism the regularized quantized fields corresponding to the
classical tetrad and connection fields are constructed. It is shown, that the
regularized fields satisfy to general covariant equations of motion, which have
the classical form. In order to solve these equations the iterative procedure
is offered.


title: The anomaly-free quantization of two-dimensional relativistic string. I

abstract:
  An anomaly-free quantum theory of a relativistic string is constructed in
two-dimensional space-time. The states of the string are found to be similar to
the states of a massless chiral quantum particle. This result is obtained by
generalizing the concept of an ``operator'' in quantum field theory.


title: How to interpret black hole entropy?

abstract:
  We consider a possibility that the entropy of a Schwarzschild black hole has
two different interpretations: The black hole entropy can be understood either
as an outcome of a huge degeneracy in the mass eigenstates of the hole, or as a
consequence of the fact that the interior region of black hole spacetime is
separated from the exterior region by a horizon. In the latter case, no
degeneracy in the mass eigenstates needs to be assumed. Our investigation is
based on calculations performed with Lorentzian partition functions obtained
for a whole maximally extended Schwarzschild spacetime, and for its
right-hand-side exterior region. To check the correctness of our analysis we
reproduce, in the leading order approximation, the Bekenstein--Hawking entropy
of the Schwarzschild black hole.


title: Metric Fluctuation Corrections to Hawking Radiation

abstract:
  We study how fluctuations of the black hole geometry affect the properties of
Hawking radiation. Even though we treat the fluctuations classically, we
believe that the results so obtained indicate what might be the effects induced
by quantum fluctuations in a self consistent treatment. To characterize the
fluctuations, we use the model introduced by York in which they are described
by an advanced Vaidya metric with a fluctuating mass. Under the assumption of
spherical symmetry, we solve the equation of null outgoing rays. Then, by
neglecting the greybody factor, we calculate the late time corrections to the
s-wave contributions of the energy flux and the asymptotic spectrum. We find
three kind of modifications. Firstly, the energy flux fluctuates around its
average value with amplitudes and frequencies determined by those of the metric
fluctuations. Secondly, this average value receives two positive contributions
one of which can be reinterpreted as due to the `renormalisation' of the
surface gravity induced by the metric fluctuations. Finally, the asymptotic
spectrum is modified by the addition of terms containing thermal factors in
which the frequency of the metric fluctuations acts as a chemical potential.


title: Cosmological Birefringence and the Microwave Background

abstract:
  We show that significant anisotropy in electromagnetic propagation generates
a distinctive signature in the microwave background. The anisotropy may be
determined by looking at the cross correlator of the $E$-mode and $B$-mode
polarisation spectrum.


title:
Collapsing shells of radiation in anti-de Sitter spacetimes and the hoop
  and cosmic censorship conjectures

abstract:
  Gravitational collapse of radiation in an anti-de Sitter background is
studied. For the spherical case, the collapse proceeds in much the same way as
in the Minkowski background, i.e., massless naked singularities may form for a
highly inhomogeneous collapse, violating the cosmic censorship, but not the
hoop conjecture. The toroidal, cylindrical and planar collapses can be treated
together. In these cases no naked singularity ever forms, in accordance with
the cosmic censorship. However, since the collapse proceeds to form toroidal,
cylindrical or planar black holes, the hoop conjecture in an anti-de Sitter
spacetime is violated.


title: The origin of black hole entropy

abstract:
  In this thesis properties and the origin of black hole entropy are
investigated from various points of view. First, laws of black hole
thermodynamics are reviewed. In particular, the first and generalized second
laws are investigated in detail. It is in these laws that the black hole
entropy plays key roles. Next, three candidates for the origin of the black
hole entropy are analyzed: the D-brane statistical-mechanics, the brick wall
model, and the entanglement thermodynamics. Finally, discussions are given on
semiclassical consistencies of the brick wall model and the entanglement
thermodynamics and on the information loss problem.


title:
Discrete Approaches Towards the Definition of a Quantum Theory of
  Gravity

abstract:
  We study the elongated phase of 4-D Dynamical Triangulations. In the case of
the sphere topology by using the Walkup's theorem we show that the dominating
configurations are stacked spheres. These stacked spheres can be mapped into
tree-like graphs (branched polymers). By using Baby-Universes arguments and an
antsatz on the universality class between the stacked spheres and a model
coming from the theory of random surfaces we argument that this elongated phase
is a trivial phase. The numerical evidence for a first order phase transition
and the triviality of the elongated phase suggest that a new approach to
simplicial quantum gravity might be useful. Along this line following the work
of various authors we study a first order version of Regge calculus formulated
as a local theory of the Poincare` group. This first order formalism has the
effects of smoothing out some pathological configurations, like "spikes", which
prevent the theory from having a smooth continuum limit. These confingurations
are in fact in the region of large deficit angles where the first order
formalism and the secon order formalism are not equivalent on lattice.
  We derive the first order field equations in the approximation of "small
deficit angles" and prove that (second order) Regge calculus is a solution.
Successively we derive the general first order field equations by taking into
account the constraints of the theory. An invariant measure for the
path-integral of this theory is defined. The coupling with matter, in
particular fermions, is also discussed in analogy to the continuum theory.


title:
General Solutions of The Spherically Symmetric Vacuum Einstein Field
  Equations

abstract:
  According to Birkhoff's theorem the only spherically symmetric solution of
the vacuum Einstein field equations is the Schwarzschild solution. Inspite of
imposing asymptotically flatness and staticness as initial conditions we obtain
that these equations have general solutions with the Schwarzschild metric as
merely a special and simplest form of them. It is possible to have perfect and
smooth metrics with the same Newtonian and post-Newtonian limits of
Schwarzschild by a convenient and correct selection.


title: Qualitative evolution in higher-loop string cosmology

abstract:
  We investigate the evolution of the homogeneous and isotropic universe within
the framework of the effective string gravity with string-loop modifications of
dilaton couplings. In the case of barotropic perfect fluid as a
nongravitational source the set of cosmological equations is presented in the
form of the third-order autonomous dynamical system. The cases are considered
when this system is integrable in terms of integrals depending on dilaton
coupling functions. Without specifying these functions we describe generic
evolution of the universe, using dynamical systems methods. The critical points
and their stability are found for all regions of the parameters. The
qualitatively different phase space diagrams are presented for the
spatially-flat, closed and open universes. The case of the tree-level models is
considered separately. The issue of dilaton stabilization is discussed within
the framework of Damour-Polyakov mechanism.


title: Self-Referential Noise and the Synthesis of Three-Dimensional Space

abstract:
  Generalising results from Godel and Chaitin in mathematics suggests that
self-referential systems contain intrinsic randomness. We argue that this is
relevant to modelling the universe and show how three-dimensional space may
arise from a non-geometric order-disorder model driven by self-referential
noise.


title: Quantum Mechanics in Riemannian Space-Times. I. The Canonical Approach

abstract:
  This paper is the first of two papers devoted to formulation of quantum
mechanics of a particle in a normal geodesic frame of reference in the general
Riemannian space-time. Here canonical quantization of geodesic motion in the
1+3-formalism is considered, the result of which will be compared in the
subsequent paper II with that of the field-theoretical approach, see also
gr-qc/9807030. The Schr\"odinger representation of quantum-mechanical
kinematics and dynamics is presented in the general-covariant form and a
physical interpretation of the state vectors and the position operators is
discussed.


title: Quantum Interference of Thermal Neutrons and Spin-Torsion Interaction

abstract:
  The discrepancy of $0.8 %$ between theory and the COW-experiment is
interpreted. This is done by using a new path equation other than the geodesic
one. It is shown that this discrepancy is possibly due to a type of interaction
between the torsion, of space-time generated by the background field, and the
spin of the moving neutron. The results obtained are discussed and compared
with the experimental interpretation suggested by Arif et al. in 1994. As a
byproduct, an upper limit is imposed on the free parameter of the new path
equation used.


title:
Hamilton's principle and the Generalized Field Theory : A comparative
  study

abstract:
  The field equations of the generalized field theory (GFT) are derived from an
action principle. A comparison between (GFT), M\o ller's tetrad theory of
gravitation (MTT), and general relativity is carried out regarding the
Lagrangian of each theory. The results of solutions of the field equations, of
each theory, are compared in case of spherical symmetry. The differences
between the results are discussed and interpreted.


title: Doing it with Mirrors: Classical analogues for Black Hole radiation

abstract:
  We construct analogues for the quantum phenomena of black hole radiation in
the context of {\it classical field theory}. Hawking radiation from a
(radially) collapsing star is mathematically equivalent to radiation from a
mirror moving along a specific trajectory in Minkowski spacetime. We construct
a classical analogue for this quantum phenomenon and use it to construct a
classical analogue for black hole radiation. The radiation spectrum in quantum
field theory has the power spectrum as its classical analogue. Monochromatic
light is continually reflected off a moving mirror or the silvered surface of a
collapsing star.The reflected light is fourier analysed by the observer and the
power spectrum is constructed. For a mirror moving along the standard black
hole trajectory,it is seen that the power spectrum has a ``thermal'' nature.
Mirror-observer configurations like an inertial mirror observed in an
accelerated observer's frame and an accelerated mirror observed in a Rindler
frame are investigated and conditions for obtaining a ``thermal'' power
spectrum are derived.The corresponding results in the black hole case are then
elucidated.It is seen that a ``thermal'' spectrum can arise either due to the
collapse of the star or due to the motion of the observer in the Schwarzchild
spacetime. The ``temperature'' of the Planckian spectrum seen is therefore
dependent on whether the star or the observer is in motion.In the latter case
it is possible to obtain a ``temperature'' which is entirely independent of the
mass of the star.


title: The classical essence of black hole radiation

abstract:
  We show that the mathematics of Hawking process can be interpreted
classically as the Fourier analysis of an exponentially redshifted wave mode
which scatters off the black hole and travels to infinity at late times. We use
this method to derive the Planckian power spectrum for Schwarzchild,
Reissner-Nordstrom and Kerr black holes.


title: A theorem on topologically massive gravity

abstract:
  We show that for three dimensional space-times admitting a hypersurface
orthogonal Killing vector field Deser, Jackiw and Templeton's vacuum field
equations of topologically massive gravity allow only the trivial flat
space-time solution. Thus spin is necessary to support topological mass.


title: Spinor formulation of topologically massive gravity

abstract:
  In the framework of real 2-component spinors in three dimensional space-time
we present a description of topologically massive gravity (TMG) in terms of
differential forms with triad scalar coefficients. This is essentially a real
version of the Newman-Penrose formalism in general relativity. A triad
formulation of TMG was considered earlier by Hall, Morgan and Perjes, however,
due to an unfortunate choice of signature some of the spinors underlying the
Hall-Morgan-Perjes formalism are real, while others are pure imaginary. We
obtain the basic geometrical identities as well as the TMG field equations
including a cosmological constant for the appropriate signature. As an
application of this formalism we discuss the Bianchi Type $VIII - IX$ exact
solutions of TMG and point out that they are parallelizable manifolds. We also
consider various re-identifications of these homogeneous spaces that result in
black hole solutions of TMG.


title: Non Metric Mass

abstract:
  In general relativity g_ab;c=0 implies that the wave equation
(\Box^2-M)g_ab=0 always has M=0. If the underlying geometry is generalized to
include non-metricity this incurs M \neq 0, and the above wave equation can be
rewritten as M(x)+\td{\na}_a Q_.^a+(\ep+\fr{d}{2}-2)Q_a Q_.^a=0, where \ep=0,
1, 2, or 3, d is the dimension of the spacetime, and Q is the object of
non-metricity. The consequences of this equation and the properties of M are
investigated.


title: Test of Comoving Coordinate Frame by Low Magnitude-Redshift Relation

abstract:
  Observational evidence from variety of sources points at an accelerating
universewhich is approximately spatially flat and with
$(\Omega_M,\Omega_{\Lambda})_0\approx(0.3,0.7)$. We have shown that for low
redshifts, $z\leq 0.2$, the metric of this cosmological model is equivalant to
the de Sitter metric within one percent error. Among various coordinate
descriptions for the flat de Sitter model two are most widely used, one yields
a non-static and FRW type, while the other gives a static and Schwarzschild
type metric. We have obtained the magnitude-redshift relation in the second
coordinate frame. Our result indicates a slope of 2.5 for small z. This is in
disagreement with observation which is close to the slope of 5. this test
discards the second and confirms the first coordinate frame as a comoving
reference frame for matter in de Sitter space. We anticipate this test
disqualifies any other solution of the field equations which asymptotically
approaches to the static de Sitter metric, e.g. the Schwarzschild-de Sitter
metric for space around a point mass m.


title: Is the Strong Anthropic Principle Too Weak?

abstract:
  We discuss the Carter's formula about the mankind evolution probability
following the derivation proposed by Barrow and Tipler. We stress the relation
between the existence of billions of galaxies and the evolution of at least one
intelligent life, whose living time is not trivial, all over the Universe. We
show that the existence probability and the lifetime of a civilization depend
not only on the evolutionary critical steps, but also on the number of places
where the life can arise. In the light of these results, we propose a stronger
version of Anthropic Principle.


title: Gravomagnetic Lensing by NUT Space

abstract:
  Using the fact that the null geodesics in NUT space lie on spatial cones, we
consider the gravomagnetic lens effect on light rays passing a NUT deflector.
We show that this effect changes the observed shape, size and orientation of a
source. Compared to the Schwarzschild lens, there is an extra shear (a
differential twist around the lens axis) due to the gravomagnetic field which
shears the shape of the source. Gravomagnetic monopoles can thus be recognized
by the spirality that they produce in the lensing pattern. All the results
obtained in this case (magnification factor, orientation of images,
multiplicity of images, etc.) depend on $Q$, the strength of the gravomagnetic
monopole represented by NUT metric. One recovers the results of the usual
Schwarzschild lens effect by putting this factor equal to zero.


title: A Matrix Formulation of Einstein's Vacuum Field Equations

abstract:
  We develop a correspondence between arbitrary tensors and matrices based on
the use of Kronecker products and associated identities.
  Utilizing the rules of matrix differentiation we derive the vacuum Einstein
field equations as a differential-matrix equation. This formulation may
facilitate their efficient use in numerical relativistic models.


title: Cosmological Constant in de-Sitter Spacetime

abstract:
  With the basic cosmological relations that agree with the recent
observations, simple expressions are suggested concerning the value of
cosmological constant($\Lambda$). A large contribution of quantum vacuum to the
energy momentum tensor does not agree with the observed cosmos. However,one
requires the presence of positive $\Lambda$ to make the various observations
consistent. After a review of the effect of cosmological constant on the
geodetic motions in the Schwarzschild de Sitter spacetime, some approaches to
its solutions are briefly discussed. Also suggested is the very weak limit on
$\Lambda$ from the planetary perturbations.


title:
Multidimensional cosmological and spherically symmetric solutions with
  intersecting p-branes

abstract:
  Multidimensional model describing the "cosmological" and/or spherically
symmetric configuration with n+1 Einstein spaces in the theory with several
scalar fields and forms is considered. When electro-magnetic composite p-brane
ansatz is adopted, n "internal" spaces are Ricci-flat, one space M_0 has a
non-zero curvature, and all p-branes do not "live" in M_0, a class of exact
solutions is obtained if certain block-orthogonality relations on p-brane
vectors are imposed. A subclass of spherically-symmetric solutions containing
non-extremal p-brane black holes is considered. Post-Newtonian parameters are
calculated and some examples are considered.


title:
Cosmic Solenoids: Minimal Cross-Section and Generalized Flux
  Quantization

abstract:
  A self-consistent general relativistic configuration describing a finite
cross-section magnetic flux tube is constructed. The cosmic solenoid is modeled
by an elastic superconductive surface which separates the Melvin core from the
surrounding flat conic structure. We show that a given amount $\Phi$ of
magnetic flux cannot be confined within a cosmic solenoid of circumferential
radius smaller than $\frac{\sqrt{3G}}{2\pi c^2}\Phi$ without creating a conic
singularity. Gauss-Codazzi matching conditions are derived by means of a
self-consistent action. The source term, representing the surface currents, is
sandwiched between internal and external gravitational surface terms. Surface
superconductivity is realized by means of a Higgs scalar minimally coupled to
projective electromagnetism. Trading the 'magnetic' London phase for a dual
'electric' surface vector potential, the generalized quantization condition
reads: $e/{hc} \Phi + 1/e Q=n$ with $Q$ denoting some dual 'electric' charge,
thereby allowing for a non-trivial Aharonov-Bohm effect. Our conclusions
persist for dilaton gravity provided the dilaton coupling is sub-critical.


title: Wave Function of a Brane-like Universe

abstract:
  Within the mini-superspace model, brane-like cosmology means performing the
variation with respect to the embedding (Minkowski) time $\tau$ before fixing
the cosmic (Einstein) time $t$. The departure from Einstein limit is
parameterized by the 'energy' conjugate to $\tau$, and characterized by a
classically disconnected Embryonic epoch. In contrast with canonical quantum
gravity, the wave-function of the brane-like Universe is (i) $\tau$-dependent,
and (ii) vanishes at the Big Bang. Hartle-Hawking and Linde proposals dictate
discrete 'energy' levels, whereas Vilenkin proposal resembles $\alpha$-particle
disintegration.


title: Quantum Gravity of a Brane-like Universe

abstract:
  Quantum gravity of a brane-like Universe is formulated, and its Einstein
limit is approached. Regge-Teitelboim embedding of Arnowitt-Deser-Misner
formalism is carried out. Invoking a novel Lagrange multiplier, accompanying
the lapse function and the shift vector, we derive the quadratic Hamiltonian
and the corresponding bifurcated Wheeler-Dewitt-like equation. The inclusion of
arbitrary matter resembles minimal coupling.


title: On non-Riemannian Superconductors and torsion loops

abstract:
  The geometrization of electrodynamics is obtained by performing the complex
extension of the covariant derivative operator to include the Cartan torsion
vector and applying this derivative to the Ginzburg-Landau equation of
superfluids and Superconductors.It is shown that the introduction of torsion
makes a shift in the symmetry breaking vacuum.Torsion loops are computed from
geometrical phases outside the superconductor.Inside the superconductor the
torsion vanishes which represents the Meissner effect for torsion geometry.
Torsion in general equals the London supercurrent.It is possible to place a
limit on the size of superconductor needed to give an estimate to torsion.


title: Scalar radiation emitted from a source rotating around a black hole

abstract:
  We analyze the scalar radiation emitted from a source rotating around a
Schwarzschild black hole using the framework of quantum field theory at the
tree level. We show that for relativistic circular orbits the emitted power is
about 20% to 30% smaller than what would be obtained in Minkowski spacetime. We
also show that most of the emitted energy escapes to infinity. Our formalism
can readily be adapted to investigate similar processes.


title: The Immortal Bel-Robinson Tensor

abstract:
  We present some generalizations, and novel properties, of the Bel-Robinson
tensor, in the context of constructing local invariants in D=11 supergravity.


title: Decay of protons and neutrons induced by acceleration

abstract:
  We investigate the decay of accelerated protons and neutrons. Calculations
are carried out in the inertial and coaccelerated frames. Particle
interpretation of these processes are quite different in each frame but the
decay rates are verified to agree in both cases. For sake of simplicity our
calculations are performed in a two-dimensional spacetime since our conclusions
are not conceptually affected by this.


title:
Charging Symmetries and Linearizing Potentials for Gravity Models with
  Symplectic Symmetry

abstract:
  In this paper we continue to study a class of four-dimensional gravity models
with n Abelian vector fields and Sp(2n)/U(n) coset of scalar fields. This class
contains General Relativity (n=0) and Einstein-Maxwell dilaton-axion theory
(n=1), which arizes in the low-energy limit of heterotic string theory. We
perform reduction of the model with arbitrary $n$ to three dimensions and study
the subgroup of non-gauge symmetries of the resulting theory. First, we find an
explicit form these symmetries using Ernst matrix potential formulation.
Second, we construct new matrix variable which linearly transforms under the
action of the non-gauge transformations. Finally, we establish one general
invariant of the non-gauge symmetry subgroup, which allow us to clarify this
subgroup structure.


title: Notes on Black Hole Fluctuations and Backreaction

abstract:
  In these notes we prepare the ground for a systematic investigation into the
issues of black hole fluctuations and backreaction by discussing the
formulation of the problem, commenting on possible advantages and shortcomings
of existing works, and introducing our own approach via a stochastic
semiclassical theory of gravity based on the Einstein-Langevin equation and the
fluctuation-dissipation relation for a self-consistent description of metric
fluctuations and dissipative dynamics of the black hole with backreaction of
its Hawking radiance.


title:
Gravoelectromagnetic approach to the gravitational Faraday rotation in
  stationary spacetimes

abstract:
  Using the 1+3 formulation of stationary spacetimes we show, in the context of
gravoelectromagnetism, that the plane of the polarization of light rays passing
close to a black hole undergoes a rotation. We show that this rotation has the
same integral form as the usual Faraday effect, i.e. it is proportional to the
integral of the component of the gravomagnetic field along the propagation
path. We apply this integral formula to calculate the Faraday rotation induced
by the Kerr and NUT spaces using the quasi-Maxwell form of the vacuum Einstein
equations.


title: Perdurance of multiply connected de Sitter space

abstract:
  This paper deals with a study of the effects that spherically symmetric
first-order metric perturbations and vacuum quantum fluctuations have on the
stability of the multiply connected de Sitter spacetime recently proposed by
Gott and Li. It is the main conclusion of this study that although such a
spacetime is stable to the classical metric perturbations for any size of the
nonchronal region, it is only stable against the quantum fluctuations of vacuum
if the size of the multiply connected region is of the order the Planck scale.
Therefore, boundary conditions for the state of the universe based on the
notion that the universe created itself in a regime where closed timelike
curves were operative and stable, still appear to be physically and
philosophically so well supported as are those boundary conditions relying on
the notion that the universe was created out of nothing.


title:
Data analysis of gravitational-wave signals from spinning neutron stars.
  III. Detection statistics and computational requirements

abstract:
  We develop the analytic and numerical tools for data analysis of the
gravitational-wave signals from spinning neutron stars for ground-based laser
interferometric detectors. We study in detail the statistical properties of the
optimum functional that need to be calculated in order to detect the
gravitational-wave signal from a spinning neutron star and estimate its
parameters. We derive formulae for false alarm and detection probabilities both
for the optimal and the suboptimal filters. We assess the computational
requirements needed to do the signal search. We compare a number of criteria to
build sufficiently accurate templates for our data analysis scheme. We verify
the validity of our concepts and formulae by means of the Monte Carlo
simulations. We present algorithms by which one can estimate the parameters of
the continuous signals accurately.


title: Scaling Solutions in Robertson-Walker Spacetimes

abstract:
  We investigate the stability of cosmological scaling solutions describing a
barotropic fluid with $p=(\gamma-1)\rho$ and a non-interacting scalar field
$\phi$ with an exponential potential $V(\phi)=V_0\e^{-\kappa\phi}$. We study
homogeneous and isotropic spacetimes with non-zero spatial curvature and find
three possible asymptotic future attractors in an ever-expanding universe. One
is the zero-curvature power-law inflation solution where $\Omega_\phi=1$
($\gamma<2/3,\kappa^2<3\gamma$ and $\gamma>2/3,\kappa^2<2$). Another is the
zero-curvature scaling solution, first identified by Wetterich, where the
energy density of the scalar field is proportional to that of matter with
$\Omega_\phi=3\gamma/\kappa^2$ ($\gamma<2/3,\kappa^2>3\gamma$). We find that
this matter scaling solution is unstable to curvature perturbations for
$\gamma>2/3$. The third possible future asymptotic attractor is a solution with
negative spatial curvature where the scalar field energy density remains
proportional to the curvature with $\Omega_\phi=2/\kappa^2$
($\gamma>2/3,\kappa^2>2$). We find that solutions with $\Omega_\phi=0$ are
never late-time attractors.


title:
Diffeomorphism invariant Quantum Field Theories of Connections in terms
  of webs

abstract:
  In the canonical quantization of gravity in terms of the Ashtekar variables
one uses paths in the 3-space to construct the quantum states. Usually, one
restricts oneself to families of paths admitting only finite number of isolated
intersections. This assumption implies a limitation on the diffeomorphisms
invariance of the introduced structures. In this work, using the previous
results of Baez and Sawin, we extend the existing results to a theory admitting
all the possible piecewise smooth finite paths and loops. In particular, we
$(i)$ characterize the spectrum of the Ashtekar-Isham configuration space,
$(ii)$ introduce spin-web states, a generalization of the spin-network states,
$(iii)$ extend the diffeomorphism averaging to the spin-web states and derive a
large class of diffeomorphism invariant states and finally $(iv)$ extend the
3-geometry operators and the Hamiltonian operator.


title: Nonorientable spacetime tunneling

abstract:
  Misner space is generalized to have the nonorientable topology of a Klein
bottle, and it is shown that in a classical spacetime with multiply connected
space slices having such a topology, closed timelike curves are formed.
Different regions on the Klein bottle surface can be distinguished which are
separated by apparent horizons fixed at particular values of the two angular
variables that eneter the metric. Around the throat of this tunnel (which we
denote a Klein bottlehole), the position of these horizons dictates an ordinary
and exotic matter distribution such that, in addition to the known diverging
lensing action of wormholes, a converging lensing action is also present at the
mouths. Associated with this matter distribution, the accelerating version of
this Klein bottlehole shows four distinct chronology horizons, each with its
own nonchronal region. A calculation of the quantum vacuum fluctuations
performed by using the regularized two-point Hadamard function shows that each
chronology horizon nests a set of polarized hypersurfaces where the
renormalized momentum-energy tensor diverges. This quantum instability can be
prevented if we take the accelerating Klein bottlehole to be a generalization
of a modified Misner space in which the period of the closed spatial direction
is time-dependent. In this case, the nonchronal regions and closed timelike
curves cannot exceed a minimum size of the order the Planck scale.


title: Scale invariance, new inflation and decaying Lambda terms

abstract:
  Realizations of scale invariance are studied in the context of a
gravitational theory where the action (in the first order formalism) is of the
form $S = \int L_{1} \Phi d^{4}x$ + $\int L_{2}\sqrt{-g}d^{4}x$ where $\Phi$ is
a density built out of degrees of freedom, the "measure fields" independent of
$g_{\mu\nu}$ and matter fields appearing in $L_{1}$, $L_{2}$. If $L_{1}$
contains the curvature, scalar potential $V(\phi)$ and kinetic term for $\phi$,
$L_{2}$ another potential for $\phi$, $U(\phi)$, then the true vacuum state has
zero energy density, when theory is analyzed in the conformal Einstein frame
(CEF), where the equations assume the Einstein form. Global Scale invariance is
realized when $V(\phi)$ = $f_{1}e^{\alpha\phi}$ and $U(\phi)$ =
$f_{2}e^{2\alpha\phi}$. In the CEF the scalar field potential energy
$V_{eff}(\phi)$ has in, addition to a minimum at zero, a flat region for
$\alpha\phi \to\infty$, with non zero vacuum energy, which is suitable for
either a New Inflationary scenario for the Early Universe or for a slowly
rolling decaying $\Lambda$-scenario for the late universe, where the smallness
of the vacuum energy can be understood as a kind of see-saw mechanism.


title:
Global structure of Robinson-Trautman radiative space-times with
  cosmological constant

abstract:
  Robinson-Trautman radiative space-times of Petrov type II with a
non-vanishing cosmological constant Lambda and mass parameter m>0 are studied
using analytical methods. They are shown to approach the corresponding
spherically symmetric Schwarzschild-de Sitter or Schwarzschild-anti-de Sitter
solution at large retarded times. Their global structure is analyzed, and it is
demonstrated that the smoothness of the extension of the metrics across the
horizon, as compared with the case Lambda=0, is increased for Lambda>0 and
decreased for Lambda<0. For the extreme value 9Lambda m^2=1, the extension is
smooth but not analytic. This case appears to be the first example of a smooth
but not analytic horizon. The models with Lambda>0 exhibit explicitly the
cosmic no-hair conjecture under the presence of gravitational waves.


title: Remarks on Superenergy Tensors

abstract:
  We define super-energy tensors for arbitrary physical fields, including the
gravitational, electromagnetic and massless scalar fields. We also define
super-super-energy tensors, and so on. All these tensors satisfy the so-called
"Dominant Superenergy Property" among other interesting and good properties.
The possibility of interchange of superenergy between gravitational and other
fields is considered.


title: General Dynamic Wormholes and Violation of the Null Energy Condition

abstract:
  Although wormholes can be treated as topological objects in spacetime and
from a global point-of-view, a precise definition of what a wormhole throat is
and where it can be located can be developed and treated entirely in terms of
local geometry. This has the advantage of being free from unnecesary technical
assumptions about asymptotic flatness, and other global properties of the
spacetime containing the wormhole. We discuss our recent work proving that the
violation of the null energy condition (NEC) is a generic feature of all
wormholes, whether they be time-dependent or static, and demonstrate that
time-dependent wormholes have two throats, one for each direction through the
wormhole, which coalesce only in the static limit.


title: Fixing Einstein's equations

abstract:
  Einstein's equations for general relativity, when viewed as a dynamical
system for evolving initial data, have a serious flaw: they cannot be proven to
be well-posed (except in special coordinates). That is, they do not produce
unique solutions that depend smoothly on the initial data. To remedy this
failing, there has been widespread interest recently in reformulating
Einstein's theory as a hyperbolic system of differential equations. The
physical and geometrical content of the original theory remain unchanged, but
dynamical evolution is made sound. Here we present a new hyperbolic formulation
in terms of $g_{ij}$, $K_{ij}$, and $\bGam_{kij}$ that is strikingly close to
the space-plus-time (``3+1'') form of Einstein's original equations. Indeed,
the familiarity of its constituents make the existence of this formulation all
the more unexpected. This is the most economical first-order symmetrizable
hyperbolic formulation presently known to us that has only physical
characteristic speeds, either zero or the speed of light, for all (non-matter)
variables. This system clarifies the relationships between Einstein's original
equations and the Einstein-Ricci and Frittelli-Reula hyperbolic formulations of
general relativity and establishes links to other hyperbolic formulations.


title: Program Universe and Recent Cosmological Results

abstract:
  Recent improvements in astronomical observations lead to the conclusion that
the Hubble constant lies between 60 and 80 Mpc km$^{-1}$ sec$^{-1}$ and the age
of the universe between 11 and 14 Gigayears. Taken together with recent
observations of distant type Ia supernovae and the cosmic background radiation,
these limits allow a check of the consequences of predictions made a decade ago
using program universe and the combinatorial hierarchy that the ratio of
baryons to photons is $1/256^4$ and of dark to baryonic matter is 12.7. We find
that the restrictions on the matter content of the universe and the
cosmological constant are within, and much tighter than, the limits established
by conventional means. The situation is further improved if we invoke an
estimate of the normalized cosmological constant made by E. D. Jones of
$\Omega_{\Lambda} \sim 0.6$. This opens a ``window of opportunity'' to get the
predictions of the ANPA program in front of the relevant professional community
{\it before} precise observations lead to a consensus. We urge ANPA members to
join us in the assault on this breach in the walls of establishment thinking.


title: Quantum Mechanics of Geometry

abstract:
  Over the past six years, a detailed framework has been constructed to unravel
the quantum nature of the Riemannian geometry of physical space. A review of
these developments is presented at a level which should be accessible to
graduate students in physics. As an illustrative application, I indicate how
some of the detailed features of the micro-structure of geometry can be tested
using black hole thermodynamics. Current and future directions of research in
this area are discussed.


title: On the Emergence of Time in Quantum Gravity

abstract:
  We discuss from a philosophical perspective the way in which the normal
concept of time might be said to `emerge' in a quantum theory of gravity. After
an introduction, we briefly discuss the notion of emergence, without regard to
time (Section 2). We then introduce the search for a quantum theory of gravity
(Section 3); and review some general interpretative issues about space, time
and matter Section 4). We then discuss the emergence of time in simple quantum
geometrodynamics, and in the Euclidean approach (Section 5). Section 6
concludes.


title: On the Topological Nature of Fundamental Interactions

abstract:
  A thought experiment is proposed to unify quantum mechanics and general
relativity. The central paradigm is that space-time {\it topology} is
ultimately responsible for the Heisenberg uncertaintly principle. It is found
that Plankian space-time exhibits a complicated, but also definite, multiply
connected character. In this framework, an analysis of the interactions in
Nature is presented.
  I. The Universal ground state of the constructed theory derives from the
properties of the topological manifold $Q=2T^3\oplus 3S^1\times S^2$, which has
23 intrinsic degrees of freedom, discrete $Z_3$ and $Z_2\times Z_3$ internal
groups, an SU(5) gauge group, and leads to a U(1) symmetry on a lattice. The
structure of $Q$ provides a unique equation motion for the mass-energy and
particle rest mass wave functions. In its excited state the Universe is
characterized by a lattice of three-tori, $L(T^3)$. The topological
identifications present in this structure, a direct reflection of the
Heisenberg uncertainty principle, provide the boundary conditions for solutions
to the equation of motion, and suggest an interpretation for the conceptually
difficult concept of quantum mechanical entanglement. II. In the second half of
the paper the (observable) properties of $Q$ and $L(T^3)$ are investigated. One
reproduces the standard model, and the theory naturally contains a Higgs field
with possible inflation. The electron and its neutrino are identified as
particle ground states and their masses, together with those of all other known
particles, are predicted. A mass of $m_{\rm H}=131.6$ GeV is found for the
Higgs boson. [Abridged]


title: Critical behavior in black hole thermodynamics

abstract:
  In this talk I introduce the critical behavior occurring at the extremal
limit of black holes. The extremal limit of black holes is a critical point and
a phase transition takes place from the extremal black holes to their
nonextremal counterparts. Some critical exponents satisfying the scaling laws
are obtained. From the scaling laws we introduce the concept of the effective
dimension of black holes and discuss the relationship between the critical
behavior and the statistical interpretation of black hole entropy.


title: Geodesic Motions in 2+1 Dimensional Charged Black Holes

abstract:
  We study the geodesic motions of a test particle around 2+1 dimensional
charged black holes. We obtain a class of exact geodesic motions for the
massless test particle when the ratio of its energy and angular momentum is
given by square root of cosmological constant. The other geodesic motions for
both massless and massive test particles are analyzed by use of numerical
method.


title: Quantum Creation of Black Hole by Tunneling in Scalar Field Collapse

abstract:
  Continuously self-similar solution of spherically symmetric gravitational
collapse of a scalar field is studied to investigate quantum mechanical black
hole formation by tunneling in the subcritical case where, classically, the
collapse does not produce a black hole.


title:
On Further Generalization of the Rigidity Theorem for Spacetimes with a
  Stationary Event Horizon or a Compact Cauchy Horizon

abstract:
  A rigidity theorem that applies to smooth electrovac spacetimes which
represent either (A) an asymptotically flat stationary black hole or (B) a
cosmological spacetime with a compact Cauchy horizon ruled by closed null
geodesics was given in a recent work \cite{frw}. Here we enlarge the framework
of the corresponding investigations by allowing the presence of other type of
matter fields. In the first part the matter fields are involved merely
implicitly via the assumption that the dominant energy condition is satisfied.
In the second part Einstein-Klein-Gordon (EKG), Einstein-[non-Abelian] Higgs
(E[nA]H), Einstein-[Maxwell]-Yang-Mills-dilaton (E[M]YMd) and
Einstein-Yang-Mills-Higgs (EYMH) systems are studied. The black hole event
horizon or, respectively, the compact Cauchy horizon of the considered
spacetimes is assumed to be a smooth non-degenerate null hypersurface. It is
proven that there exists a Killing vector field in a one-sided neighborhood of
the horizon in EKG, E[nA]H, E[M]YMd and EYMH spacetimes. This Killing vector
field is normal to the horizon, moreover, the associated matter fields are also
shown to be invariant with respect to it. The presented results provide
generalizations of the rigidity theorems of Hawking (for case A) and of
Moncrief and Isenberg (for case B) and, in turn, they strengthen the validity
of both the black hole rigidity scenario and the strong cosmic censor
conjecture of classical general relativity.


title: Mass-Generation by Weyl-Symmetry Breaking

abstract:
  A massless electroweak theory for leptons is formulated in a Weyl space, W_4,
yielding a Weyl invariant gauge dynamics allowing for conformal rescalings of
the metric and all fields with nonvanishing Weyl weight together with the
corresponding transformations of the Weyl vector fields representing the D(1)
or dilatation gauge fields. To study the appearance of nonzero masses this
theory is explicitly broken by a term in the Lagrangean involving the curvature
scalar R of the W_4 and a mass term for the scalar field. Thereby also the
gauge fields as well as the charged fermion field acquire a mass as in the
standard electroweak theory. The symmetry breaking is governed by the relation
D Phi^2=0, where Phi is the modulus of the scalar field and D denotes the
Weyl-covariant derivative. This true symmetry reduction, establishing a scale
of length in the theory, is compared to the so-called spontanous symmetry
breaking in the standard electroweak theory which is, actually, the choice of a
particular (nonlinear) gauge obtained by adopting an origin in the coset space
representing the scalar field which is invariant under the electromagnetic
gauge group. Particular attention is devoted to the appearance of Einstein's
equations for the metric after the Weyl-symmetry breaking yielding a
pseudo-Riemannian space V_4 from a W_4 and a scalar field with a constant
modulus which in turn affects Einstein's gravitational constant in a manner
comparable to the Brans-Dicke theory.


title:
Critical phenomena and a new class of self-similar spherically symmetric
  perfect-fluid solutions

abstract:
  We consider the self-similar solutions associated with the critical behavior
observed in the gravitational collapse of spherically symmetric perfect fluids
with equation of state $p=\alpha\mu$. We identify for the first time the global
nature of these solutions and show that it is sensitive to the value of
$\alpha$. In particular, for $\alpha>0.28$, we show that the critical solution
is associated with a new class of asymptotically Minkowski self-similar
spacetimes. We discuss some of the implications of this for critical phenomena.


title: Comment on entropy bounds and the generalized second law

abstract:
  In a gedanken experiment in which a box initially containing energy $E$ and
entropy $S$ is lowered toward a black hole and then dropped in, it was shown by
Unruh and Wald that the generalized second law of black hole thermodynamics
holds, without the need to assume any bounds on $S$ other than the bound that
arises from the fact that entropy at a given energy and volume is bounded by
that of unconstrained thermal matter. The original analysis by Unruh and Wald
made the approximation that the box was ``thin'', but they later generalized
their analysis to thick boxes (in the context of a slightly different process).
Nevertheless, Bekenstein has argued that, for a certain class of thick boxes,
the buoyancy force of the ``thermal atmosphere'' of the black hole is
negligible, and that his previously postulated bound on $S/E$ is necessary for
the validity of the generalized second law. In arguing for these conclusions,
Bekenstein made some assumptions about the nature of unconstrained thermal
matter and the location of the ``floating point'' of the box. We show here that
under these assumptions, Bekenstein's bound on $S/E$ follows automatically from
the fact that $S$ is bounded by the entropy of unconstrained thermal matter.
Thus, a box of matter which violates Bekenstein's bound would violate the
assumptions made in his analysis, rather than violate the generalized second
law. Indeed, we prove here that no universal entropy bound need be hypothesized
in order to ensure the validity of the generalized second law in this process.


title: Gravitation, Thermodynamics, and Quantum Theory

abstract:
  During the past 30 years, research in general relativity has brought to light
strong hints of a very deep and fundamental relationship between gravitation,
thermodynamics, and quantum theory. The most striking indication of such a
relationship comes from black hole thermodynamics, where it appears that
certain laws of black hole mechanics are, in fact, simply the ordinary laws of
thermodynamics applied to a system containing a black hole. This article will
review the present status of black hole thermodynamics and will discuss some of
the related unresolved issues concerning gravitation, thermodynamics, and
quantum theory.


title: Two-Fluid Atmosphere for Relativistic Stars

abstract:
  We have extended the Vaidya radiating metric to include both a radiation
fluid and a string fluid. This paper expands our brief introduction to
extensions of the Schwarzschild vacuum which appeared in 1998 Phys. Rev. D Vol
57, R5945. Assuming diffusive transport for the string fluid, we find new
analytic solutions of Einstein's field equations.


title: Universal Entropy Bound for Rotating Systems

abstract:
  We conjecture a universal upper bound to the entropy of a rotating system.
The entropy bound follows from application of the generalized second law of
thermodynamics to an idealized gedanken experiment in which an entropy-bearing
rotating system falls into a black hole. This bound is stronger than the
Bekenstein entropy bound for non-rotating systems.


title: Quantum scalar field in D-dimensional static black hole space-times

abstract:
  An Euclidean approach for investigating quantum aspects of a scalar field
living on a class of D-dimensional static black hole space-times, including the
extremal ones, is reviewed. The method makes use of a near horizon
approximation of the metric and $\zeta$-function formalism for evaluating the
partition function and the expectation value of the field fluctuations
$<\phi^2(x)>$. After a review of the non-extreme black hole case, the extreme
one is considered in some details. In this case, there is no conical
singularity, but the finite imaginary time compactification introduces a cusp
singularity. It is found that the $\zeta$-function regularized partition
function can be defined, and the quantum fluctuations are finite on the
horizon, as soon as the cusp singularity is absent, and the corresponding
temperature is T=0.


title:
The imprint of the equation of state on the axial w-modes of oscillating
  neutron stars

abstract:
  We discuss the dependence of the pulsation frequencies of the axial
quasi-normal modes of a nonrotating neutron star upon the equation of state
describing the star interior. The continued fraction method has been used to
compute the complex frequencies for a set of equations of state based on
different physical assumptions and spanning a wide range of stiffness. The
numerical results show that the detection of axial gravitational waves would
allow to discriminate between the models underlying the different equation of
states, thus providing relevant information on both the structure of neutron
star matter and the nature of the hadronic interactions.


title: Renormalization of Black Hole Entropy

abstract:
  We review the renormalization of one-loop effective action for gravity
coupled to a scalar field and that of the Bekenstein-Hawking entropy of a black
hole plus the statistical entropy of the scalar field. It is found that the
total entropy of the black hole's geometric entropy and the statistical entropy
yields the renormalized Bekenstein-Hawking area-law of black hole entropy only
for even dimensional Reissner-N\"{o}rdstrom (Schwarzschild) black holes. We
discuss the problem of the microscopic origin of black hole entropy in
connection with the renormalization of black hole entropy.


title: On Equivalence of Critical Collapse of Non-Abelian Fields

abstract:
  We continue our study of the gravitational collapse of spherically symmetric
skyrmions. For certain families of initial data, we find the discretely
self-similar Type II critical transition characterized by the mass scaling
exponent $\gamma \approx 0.20$ and the echoing period $\Delta \approx 0.74$. We
argue that the coincidence of these critical exponents with those found
previously in the Einstein-Yang-Mills model is not accidental but, in fact, the
two models belong to the same universality class.


title:
Gravitational waves from a test particle scattered by a neutron star:
  Axial mode case

abstract:
  Using a metric perturbation method, we study gravitational waves from a test
particle scattered by a spherically symmetric relativistic star. We calculate
the energy spectrum and the waveform of gravitational waves for axial modes.
Since metric perturbations in axial modes do not couple to the matter fluid of
the star, emitted waves for a normal neutron star show only one peak in the
spectrum, which corresponds to the orbital frequency at the turning point,
where the gravitational field is strongest. However, for an ultracompact star
(the radius $R \lesssim 3M$), another type of resonant periodic peak appears in
the spectrum. This is just because of an excitation by a scattered particle of
axial quasinormal modes, which were found by Chandrasekhar and Ferrari. This
excitation comes from the existence of the potential minimum inside of a star.
We also find for an ultracompact star many small periodic peaks at the
frequency region beyond the maximum of the potential, which would be due to a
resonance of two waves reflected by two potential barriers (Regge-Wheeler type
and one at the center of the star). Such resonant peaks appear neither for a
normal neutron star nor for a Schwarzschild black hole. Consequently, even if
we analyze the energy spectrum of gravitational waves only for axial modes, it
would be possible to distinguish between an ultracompact star and a normal
neutron star (or a Schwarzschild black hole).


title: Seed Magnetic Fields from the Breaking of Lorentz Invariance

abstract:
  Spontaneous breaking of Lorentz invariance may take place in string theories,
possibly endowing the photon with a mass. This leads to the breaking of the
conformal symmetry of the electromagnetic action allowing for the generation
within inflationary scenarios of magnetic fields over $Mpc$ scales. We show
that the generated fields are consistent with amplification by the galactic
dynamo processes and can be as large as to explain the observed galactic
magnetic fields through the collapse of protogalactic clouds.


title: Stability and size of galaxies from Planck's constant

abstract:
  Stability and characterisitic geometrical and kinematical sizes of galaxies
are strictly related to a minimal characteristic action whose value is of order
$h$, the Planck constant. We infer that quantum mechanics, in some sense,
determines the structure and the size of galaxies.


title: H-projectively Equivalent Kahler Manifolds and Gravitational Instantons

abstract:
  The goal of the present paper is to investigate four dimensional Kahler
manifolds admitting H-projective mappings with special attention to
Einstein-Kahler manifolds of this type which can be interpreted as field
configurations of the gravitational instantons.


title:
Critical collapse in tensor-multi-scalar and non-linear gravity
  theories: A universal class

abstract:
  Critical collapse in tensor-multi-scalar gravity theories is studied, and
found that for any given target space all the theories conformally related
belong to the same universal class. When only one scalar field is present, the
universality is extended to include a class of non-linear gravity theories.


title: The origin of the difference between space and time

abstract:
  All differences between the role of space and time in nature are explained by
proposing the principles in which none of the space-time coordinates has an
{\it a priori} special role. Spacetime is treated as a nondynamical manifold,
with a fixed global ${\bf R}^D$ topology. Dynamical theory of gravity
determines only the metric tensor on a fixed manifold. All dynamics is treated
as a Cauchy problem, so it {\em follows} that one coordinate takes a special
role. It is proposed that {\em any} boundary condition that is finite
everywhere leads to a solution which is also finite everywhere. This explains
the $(1,D-1)$ signature of the metric, the boundedness of energy from below,
the absence of tachyons, and other related properties of nature. The time arrow
is explained by proposing that the boundary condition should be ordered. The
quantization is considered as a boundary condition for field operators. Only
the physical degrees of freedom are quantized.


title: The theoretical significance of G

abstract:
  The quantization of gravity, and its unification with the other interactions,
is one of the greatest challenges of theoretical physics. Current ideas suggest
that the value of G might be related to the other fundamental constants of
physics, and that gravity might be richer than the standard Newton-Einstein
description. This gives added significance to measurements of G and to
Cavendish-type experiments.


title: Acoustic black holes

abstract:
  Acoustic propagation in a moving fluid provides a conceptually clean and
powerful analogy for understanding black hole physics. As a teaching tool, the
analogy is useful for introducing students to both General Relativity and fluid
mechanics. As a research tool, the analogy helps clarify what aspects of the
physics are kinematics and what aspects are dynamics. In particular, Hawking
radiation is a purely kinematical effect, whereas black hole entropy is
intrinsically dynamical. Finally, I discuss the fact that with present
technology acoustic Hawking radiation is almost experimentally testable.


title:
Irrotational and Incompressible Binary Systems in the First
  Post-Newtonian Approximation of General Relativity

abstract:
  The first post-Newtonian (PN) hydrostatic equations for an irrotational fluid
are solved for an incompressible binary system. The equilibrium configuration
of the binary system is given by a small deformation from the irrotational
Darwin-Riemann ellipsoid which is the solution at Newtonian order. It is found
that the orbital separation at the innermost stable circular orbit (ISCO)
decreases when one increases the compactness parameter $M_{\ast}/c^2 a_{\ast}$,
in which $M_{\ast}$ and $a_{\ast}$ denote the mass and the radius of a star,
respectively. If we compare the 1PN angular velocity of the binary system at
the ISCO in units of $\sqrt{M_{\ast}/a_{\ast}^3}$ with that of Newtonian order,
the angular velocity at the ISCO is almost the same value as that at Newtonian
order when one increases the compactness parameter. Also, we do not find the
instability point driven by the deformation at 1PN order, where a new sequence
bifurcates throughout the equilibrium sequence of the binary system until the
ISCO.
  We also investigate the validity of an ellipsoidal approximation, in which a
1PN solution is obtained assuming an ellipsoidal figure and neglecting the
deformation. It is found that the ellipsoidal approximation gives a fairly
accurate result for the total energy, total angular momentum and angular
velocity. However, if we neglect the velocity potential of 1PN order, we tend
to overestimate the angular velocity at the ISCO regardless of the shape of the
star (ellipsoidal figure or deformed figure).


title:
Dynamics of a relativistic Rankine vortex for a two-constituent
  superfluid in a weak perturbation of cylindrical symmetry

abstract:
  From a recent study of a stationary cylindrical solution for a relativistic
two-constituent superfluid at low temperature limit, we propose to specify this
solution under the form of a relativistic generalisation of a Rankine vortex
(Potential vortex whose the core has a solid body rotation).Then we establish
the dynamics of the central line of this vortex by supposing that the deviation
from the cylindrical configuration is weak in the neighbourhood of the core of
the vortex. In "stiff" material the Nambu-Goto equations are obtained.


title:
A complete classification of spherically symmetric perfect fluid
  similarity solutions

abstract:
  We classify all spherically symmetric perfect fluid solutions of Einstein's
equations with equation of state p/mu=a which are self-similar in the sense
that all dimensionless variables depend only upon z=r/t. For a given value of
a, such solutions are described by two parameters and they can be classified in
terms of their behaviour at large and small distances from the origin; this
usually corresponds to large and small values of z but (due to a coordinate
anomaly) it may also correspond to finite z. We base our analysis on the
demonstration that all similarity solutions must be asymptotic to solutions
which depend on either powers of z or powers of lnz. We show that there are
only three similarity solutions which have an exact power-law dependence on z:
the flat Friedmann solution, a static solution and a Kantowski-Sachs solution
(although the latter is probably only physical for a<0). For a>1/5, there are
also two families of solutions which are asymptotically (but not exactly)
Minkowski: the first is asymptotically Minkowski as z tends to infinity and is
described by one parameter; the second is asymptotically Minkowski at a finite
value of z and is described by two parameters. A complete analysis of the dust
solutions is given, since these can be written down explicitly and elucidate
the link between the z>0 and z<0 solutions. Solutions with pressure are then
discussed in detail; these share many of the characteristics of the dust
solutions but they also exhibit new features.


title:
Nonminimal Derivative Coupling and the Recovering of Cosmological
  Constant

abstract:
  We show that the existence of the cosmological constant can be connected to a
nonminimal derivative coupling, in the action of gravity, between the geometry
and the kinetic part of a given scalar field without introducing any effective
potential of scalar fields. Exact solutions are given.


title: Cosmological Solutions of Type II Superstrings

abstract:
  We study maximally symmetric cosmological solutions of type II supersymmetric
strings in the presence of the exact quartic curvature corrections to the
lowest order effective action, including loop and D-instanton effects. We find
that, unlike the case of type IIA theories, de Sitter solutions exist for type
IIB superstrings, a conclusion that remains valid when higher-curvature
corrections are included on the basis of SL(2,Z) invariance.


title:
Constructing hyperbolic systems in the Ashtekar formulation of general
  relativity

abstract:
  Hyperbolic formulations of the equations of motion are essential technique
for proving the well-posedness of the Cauchy problem of a system, and are also
helpful for implementing stable long time evolution in numerical applications.
We, here, present three kinds of hyperbolic systems in the Ashtekar formulation
of general relativity for Lorentzian vacuum spacetime. We exhibit several (I)
weakly hyperbolic, (II) diagonalizable hyperbolic, and (III) symmetric
hyperbolic systems, with each their eigenvalues. We demonstrate that Ashtekar's
original equations form a weakly hyperbolic system. We discuss how gauge
conditions and reality conditions are constrained during each step toward
constructing a symmetric hyperbolic system.


title: A simple derivation of the naked singularity in spherical dust collapse

abstract:
  We describe a simple method of determining whether the singularity that forms
in the spherically symmetric collapse of inhomogeneous dust is naked or
covered. This derivation considerably simplifies the analysis given in the
earlier literature, while giving the same results as have been obtained before.


title: Effective action and decoherence by fermions in quantum cosmology

abstract:
  We develop the formalism for the one-loop no-boundary state in a cosmological
model with fermions. We use it to calculate the reduced density matrix for an
inflaton field by tracing out the fermionic degrees of freedom, yielding both
the fermionic effective action and the standard decoherence factor. We show
that dimensional regularisation of ultraviolet divergences would lead to an
inconsistent density matrix. Suppression of these divergences to zero is
instead performed through a nonlocal Bogoliubov transformation of the fermionic
variables, which leads to a consistent density matrix. The resulting degree of
decoherence is less than in the case of bosonic fields.


title: The incorporation of matter into characteristic numerical relativity

abstract:
  A code that implements Einstein equations in the characteristic formulation
in 3D has been developed and thoroughly tested for the vacuum case. Here, we
describe how to incorporate matter, in the form of a perfect fluid, into the
code. The extended code has been written and validated in a number of cases. It
is stable and capable of contributing towards an understanding of a number of
problems in black hole astrophysics.