title: Spectral Evolution of the Universe

abstract:
  We derive the evolution equations for the spectra of the Universe.
  Here "spectra" means the eigenvalues of the Laplacian defined on a space,
which contain the geometrical information on the space.
  These equations are expected to be useful to analyze the evolution of the
geometrical structures of the Universe.
  As an application, we investigate the time evolution of the spectral distance
between two Universes that are very close to each other; it is the first
necessary step for the detailed analysis of the model-fitting problem in
cosmology with the spectral scheme.
  We find out a universal formula for the spectral distance between two very
close Universes, which turns out to be independent of the detailed form of the
distance nor the gravity theory. Then we investigate its time evolution with
the help of the evolution equations we derive.
  We also formulate the criteria for a good cosmological model in terms of the
spectral distance.


title: Indications of causal set cosmology

abstract:
  Within the context of a recently proposed family of stochastic dynamical laws
for causal sets, one can ask whether the universe might have emerged from the
quantum-gravity era with a large enough size and with sufficient homogeneity to
explain its present-day large-scale structure. In general, such a scenario
would be expected to require the introduction of very large or very small
fundamental parameters into the theory. However, there are indications that
such ``fine tuning'' is not necessary, and a large homogeneous and isotropic
cosmos can emerge naturally, thanks to the action of a kind of renormalization
group associated with cosmic cycles of expansion and re-contraction.


title: Naked Singularities in the Charged Vaidya-deSitter Spacetime

abstract:
  We study the occurrence of naked singularities in the spherically symmetric
collapse of a charged null fluid in an expanding deSitter background - a piece
of charged Vaidya-deSitter spacetime. The necessary conditions for the
formation of a naked singularity are found. The results for the uncharged
solutions can be recovered from our analysis.


title:
Gravitational conformal invariance and coupling constants in
  Kaluza-Klein theory

abstract:
  We introduce a generalized gravitational conformal invariance in the context
of non-compactified 5D Kaluza-Klein theory. It is done by assuming the 4D
metric to be dependent on the extra non-compactified dimension. It is then
shown that the conformal invariance in 5D is broken by taking an absolute
cosmological scale $R_0$ over which the 4D metric is assumed to be dependent
weakly on the 5th dimension. This is equivalent to Deser's model for the
breakdown of the conformal invariance in 4D by taking a constant cosmological
mass term $\mu^2\sim R_0^{-2}$ in the theory. We set the scalar field to its
background cosmological value leading to Einstein equation with the
gravitational constant $G_N$ and a small cosmological constant. A dual Einstein
equation is also introduced in which the matter is coupled to the higher
dimensional geometry by the coupling $G_N^{-1}$. Relevant interpretations of
the results are also discussed.


title:
Solutions of the spherically symmetric SU(2) Einstein-Yang-Mills
  equations defined in the far field

abstract:
  It is shown analytically that every static, spherically symmetric solution to
the Einstein Yang Mills equations with SU(2) gauge group that is defined in the
far field has finite ADM mass. Moreover, there can be at most two horizons for
such solutions. The three types of solutions possible, Bartnik-McKinnon
particle-like solutions, Reissner-Nordstrom-like solutions, and black hole
solutions having only one horizon are distinguished by the behavior of the
metric coefficients at the origin.


title: Black Hole Decay and Quantum Instantons

abstract:
  We study the analytic structure of the S-matrix which is obtained from the
reduced Wheeler-DeWitt wave function describing spherically symmetric
gravitational collapse of massless scalar fields. The complex simple poles in
the S-matrix lead to the wave functions that satisfy the same boundary
condition as quasi-normal modes of a black hole, and correspond to the bounded
states of the Euclidean Wheeler-DeWitt equation. These wave function are
interpreted as quantum instantons.


title: Double Scalar-Tensor Gravity Cosmologies

abstract:
  We investigate homogeneous and isotropic cosmological models in scalar-tensor
theories of gravity where two scalar fields are nonminimally coupled to the
geometry. Exact solutions are found, by Noether symmetries, depending on the
form of couplings and self-interaction potentials. An interesting feature is
that we deal with the Brans-Dicke field and the inflaton on the same ground
since both are nonminimally coupled and not distinguished {\it a priori} as in
earlier models. This fact allows to improve dynamics to get successful extended
inflationary scenarios. Double inflationary solutions are also discussed.


title: Scalar field cosmology in three-dimensions

abstract:
  We study an analytical solution to the Einstein's equations in
2+1-dimensions. The space-time is dynamical and has a line symmetry. The matter
content is a minimally coupled, massless, scalar field. Depending on the value
of certain parameters, this solution represents three distinct space-times. The
first one is flat space-time. Then, we have a big bang model with a negative
curvature scalar and a real scalar field. The last case is a big bang model
with event horizons where the curvature scalar vanishes and the scalar field
changes from real to purely imaginary.


title: Boost-rotation symmetric type D radiative metrics in Bondi coordinates

abstract:
  The asymptotic properties of the solutions to the Einstein-Maxwell equations
with boost-rotation symmetry and Petrov type D are studied. We find series
solutions to the pertinent set of equations which are suitable for a late time
descriptions in coordinates which are well adapted for the description of the
radiative properties of spacetimes (Bondi coordinates). By calculating the
total charge, Bondi and NUT mass and the Newman-Penrose constants of the
spacetimes we provide a physical interpretation of the free parameters of the
solutions. Additional relevant aspects on the asymptotics and radiative
properties of the spacetimes considered, such as the possible polarization
states of the gravitational and electromagnetic field, are discussed through
the way.


title:
Poincar\'e invariance in the ADM Hamiltonian approach to the general
  relativistic two-body problem

abstract:
  A previously found momentum-dependent regularization ambiguity in the third
post-Newtonian two point-mass Arnowitt-Deser-Misner Hamiltonian is shown to be
uniquely determined by requiring global Poincar\'e invariance. The phase-space
generators realizing the Poincar\'e algebra are explicitly constructed.


title: Singularities in General Relativity coupled to nonlinear electrodynamics

abstract:
  We study here some consequences of the nonlinearities of the electromagnetic
field acting as a source of Einstein's equations on the propagation of photons.
We restrict to the particular case of a ``regular black hole'', and show that
there exist singularities in the effective geometry. These singularities may be
hidden behind a horizon or naked, according to the value of a parameter. Some
unusual properties of this solution are also analyzed.


title:
On the Axiomatics of the 5-dimensional Projective Unified Field Theory
  of Schmutzer

abstract:
  For more than 40 years E.Schmutzer has developed a new approach to the
(5-dimensional) projective relativistic theory which he later called Projective
Unified Field Theory (PUFT). In the present paper we introduce a new axiomatics
for Schmutzer's theory. By means of this axiomatics we can give a new
geometrical interpretation of the physical concept of the PUFT.


title:
The binary black-hole dynamics at the third post-Newtonian order in the
  orbital motion

abstract:
  The orbital dynamics of the binary point-mass systems is ambiguous at the
third post-Newtonian order of approximation. The static ambiguity is known to
be related to the difference between the Brill-Lindquist solution and the
Misner-Lindquist solution of the time-symmetric conformally flat initial value
problem for binary black holes. The kinetic ambiguity is noticed to violate in
general the standard relation between the center-of-mass velocity and the total
linear momentum as demanded by global Lorentz invariance.


title: Cosmological Time in (2+1) - Gravity

abstract:
  We consider maximal globally hyperbolic flat (2+1) spacetimes with compact
space S of genus g>1. For any spacetime M of this type, the length of time that
the events have been in existence is M defines a global time, called the
cosmological time CT of M, which reveals deep intrinsic properties of
spacetime. In particular, the past/future asymptotic states of the cosmological
time recover and decouple the linear and the translational parts of the
ISO(2,1)-valued holonomy of the flat spacetime. The initial singularity can be
interpreted as an isometric action of the fundamental group of S on a suitable
real tree. The initial singularity faithfully manifests itself as a lack of
smoothness of the embedding of the CT level surfaces into the spacetime M. The
cosmological time determines a real analytic curve in the Teichmuller space of
Riemann surfaces of genus g, which connects an interior point (associated to
the linear part of the holonomy) with a point on Thurston's natural boundary
(associated to the initial singularity).


title: Fermat-holonomic congruences

abstract:
  Fermat-holonomic congruences are proposed as a weaker substitute for the too
restrictive class of Born-rigid motions. The definition is expressed as a set
of differential equations. Integrability conditions and Cauchy data are
studied.


title: Comparative Studies of Lensing Methods

abstract:
  Predictions of the standard thin lens approximation and a new iterative
approach to gravitational lensing are compared with an ``exact'' approach in
simple test cases involving one or two lenses. We show that the thin lens and
iterative approaches are remarkably accurate in predicting time delays, source
positions and image magnifications for a single monopole lens and combinations
of two monopole lenses. In the cases studied, the iterative method provided
greater accuracy than the thin lens method. We also study the accuracy of a ``2
lens, single lens plane model,'' where two monopole lenses colinear with the
observer are modeled by a mass distribution in a single lens plane lying
between them. We see that this model can lead to large inaccuracies in
physically meaningful situations.
  A previous version of this paper was published as Phys.Rev.D62, 024025,
(2000) with errors in the computation of two lens comparisons. This paper
corrects these errors and presents new conclusions which differ from the
previous version.


title: Hypothesis of path integral duality: Applications to QED

abstract:
  We use the modified propagator for quantum field based on a ``principle of
path integral duality" proposed earlier in a paper by Padmanabhan to
investigate several results in QED. This procedure modifies the Feynman
propagator by the introduction of a fundamental length scale. We use this
modified propagator for the Dirac particles to evaluate the first order
radiative corrections in QED. We find that the extra factor of the modified
propagator acts like a regulator at the Planck scales thereby removing the
divergences that otherwise appear in the conventional radiative correction
calculations of QED. We find that:(i) all the three renormalisation factors
$Z_1$, $Z_2$, and $Z_3$ pick up finite corrections and (ii) the modified
propagator breaks the gauge invariance at a very small level of
${\mathcal{O}}(10^{-45})$. The implications of this result to generation of the
primordial seed magnetic fields are discussed.


title: Kaluza-Klein Formalism of General Spacetimes

abstract:
  I describe the Kaluza-Klein approach to general relativity of 4-dimensional
spacetimes. This approach is based on the (2,2)-fibration of a generic
4-dimensional spacetime, which is viewed as a local product of a
(1+1)-dimensional base manifold and a 2-dimensional fibre space. It is shown
that the metric coefficients can be decomposed into sets of fields, which
transform as a tensor field, gauge fields, and scalar fields with respect to
the infinite dimensional group of the diffeomorphisms of the 2-dimensional
fibre space. I discuss a few applications of this formalism.


title: (2,2)-Formalism of General Relativity: An Exact Solution

abstract:
  I discuss the (2,2)-formalism of general relativity based on the
(2,2)-fibration of a generic 4-dimensional spacetime of the Lorentzian
signature. In this formalism general relativity is describable as a Yang-Mills
gauge theory defined on the (1+1)-dimensional base manifold, whose local gauge
symmetry is the group of the diffeomorphisms of the 2-dimensional fibre
manifold. After presenting the Einstein's field equations in this formalism, I
solve them for spherically symmetric case to obtain the Schwarzschild solution.
Then I discuss possible applications of this formalism.


title: Behaviour of spin-1/2 particle around a charged black hole

abstract:
  Dirac equation is separable in curved space-time and its solution was found
for both spherically and axially symmetric geometry. But most of the works were
done without considering the charge of the black hole. Here we consider the
spherically symmetric charged black hole background namely Reissner-Nordstrom
black hole. Due to presence of the charge of black-hole charge-charge
interaction will be important for the cases of incoming charged particle (e.g.
electron, proton etc.). Therefore both gravitational and electromagnetic gauge
fields should be introduced. Naturally behaviour of the particle will be
changed from that in Schwarzschild geometry. We compare both the solutions. In
the case of Reissner-Nordstrom black hole there is a possibility of
super-radiance unlike Schwarzschild case. We also check this branch of the
solution.


title:
The Scenario for the Astrophysics with Scalar Field and the Cosmological
  Constant

abstract:
  In order to give the standard scenario of the astrophysics, we study the
Einstein theory with minimally coupled scalar field and the cosmological term
by considering the scalar field as a candidate of the dark matter. We obtained
the exact solution in the cosmological scale and the approximate gravitational
potential in the galactic or solar scale. We find that the scalar field plays
the role of the dark matter in some sense in the cosmological scale but it does
not play the role of the dark matter in the galactic or solar scale within our
approximation.


title: Cosmic crystallography: the euclidean isometries

abstract:
  Exact expressions for probability densities of conjugate pair separation in
euclidean isometries are obtained, for the cosmic crystallography.These are the
theoretical counterparts of the mean histograms arising from computer
simulation of the isometries. For completeness, also the isometries with fixed
points are examined, as well as the orientation reversing isometries.


title: The geometry of the Barbour-Bertotti theories I. The reduction process

abstract:
  The dynamics of $N\geq 3$ interacting particles is investigated in the
non-relativistic context of the Barbour-Bertotti theories. The reduction
process on this constrained system yields a Lagrangian in the form of a
Riemannian line element. The involved metric, degenerate in the flat
configuration space, is the first fundamental form of the space of orbits of
translations and rotations (the Leibniz group). The Riemann tensor and the
scalar curvature are computed by a generalized Gauss formula in terms of the
vorticity tensors of generators of the rotations. The curvature scalar is
further given in terms of the principal moments of inertia of the system. Line
configurations are singular for $N\neq 3$. A comparison with similar methods in
molecular dynamics is traced.


title: The geometry of the Barbour-Bertotti theories II. The three body problem

abstract:
  We present a geometric approach to the three-body problem in the
non-relativistic context of the Barbour-Bertotti theories. The Riemannian
metric characterizing the dynamics is analyzed in detail in terms of the
relative separations. Consequences of a conformal symmetry are exploited and
the sectional curvatures of geometrically preferred surfaces are computed. The
geodesic motions are integrated. Line configurations, which lead to curvature
singularities for $N\neq 3$, are investigated. None of the independent scalars
formed from the metric and curvature tensor diverges there.


title: Asymptotic expansions for relativistic celestial mechanics

abstract:
  The method of asymptotic expansions is used to build an approximation scheme
relevant to celestial mechanics in relativistic theories of gravitation. A
scalar theory is considered, both as a simple example and for its own sake.
This theory is summarized, then the relevant boundary problem is seen to be the
full initial-value problem. It is shown that, with any given system of
gravitating bodies, one may associate a one-parameter family of similar
systems, the parameter measuring the gravitational field-strength. After a
specific change of units, the derivation of asymptotic expansions becomes
straightforward. Two hypotheses could be made as to which time variable has to
be used in the expansion. The first one leads to an "asymptotic" post-Newtonian
approximation (PNA) with instantaneous propagation, differing from the standard
PNA in that, in the asymptotic PNA, all fields are expanded. The second
hypothese could lead to an "asymptotic" post-Minkowskian approximation (PMA)
allowing to describe propagation effects, but it is not compatible with the
Newtonian limit. It is shown that the standard PNA is not compatible with the
application of the usual method of asymptotic expansions as envisaged here.


title: Boost-rotation symmetric spacetimes - review

abstract:
  Boost-rotation symmetric spacetimes are the only locally asymptotically flat
axially symmetric electrovacuum spacetimes with a further symmetry that are
radiative. They are realized by uniformly accelerated particles of various
kinds or black holes. Their general properties are summarized. Several examples
of boost-rotation symmetric solutions of the Maxwell and Einstein equations are
studied: uniformly accelerated electric and magnetic multipoles, the
Bonnor-Swaminarayan solutions, the C-metric and the spinning C-metric.


title: On the strength of the Kerr singularity and cosmic censorship

abstract:
  It has been suggested by Israel that the Kerr singularity cannot be strong in
the sense of Tipler, for it tends to cause repulsive effects. We show here
that, contrary to that suggestion, nearly all null geodesics reaching this
singularity do in fact terminate in Tipler's strong curvature singularity.
Implications of this result are discussed in the context of an earlier cosmic
censorship theorem which constraints the occurrence of Kerr-like naked
singularities in generic collapse situations.


title: Gravitational Radiation

abstract:
  Gravity is one of the fundamental forces of Nature, and it is the dominant
force in most astronomical systems. In common with all other phenomena, gravity
must obey the principles of special relativity. In particular, gravitational
forces must not be transmitted or communicated faster than light. This means
that when the gravitational field of an object changes, the changes ripple
outwards through space and take a finite time to reach other objects. These
ripples are called gravitational radiation or gravitational waves. This article
gives a brief introduction to the physics of gravitational radiation, including
technical material suitable for non-specialist scientists.


title: Vector field mediated models of dynamical light velocity

abstract:
  A vector-tensor theory of gravity that was introduced in an earlier
publication is analyzed in detail and its consequences for early universe
cosmology are examined. The multiple light cone structure of the theory
generates different speeds of gravitational and matter wave fronts, and the
contraction of these light cones produces acausal, superluminary inflation that
can resolve the initial value problems of cosmology.


title:
Towards a Stable Numerical Evolution of Strongly Gravitating Systems in
  General Relativity: The Conformal Treatments

abstract:
  We study the stability of three-dimensional numerical evolutions of the
Einstein equations, comparing the standard ADM formulation to variations on a
family of formulations that separate out the conformal and traceless parts of
the system. We develop an implementation of the conformal-traceless (CT)
approach that has improved stability properties in evolving weak and strong
gravitational fields, and for both vacuum and spacetimes with active coupling
to matter sources. Cases studied include weak and strong gravitational wave
packets, black holes, boson stars and neutron stars. We show under what
conditions the CT approach gives better results in 3D numerical evolutions
compared to the ADM formulation. In particular, we show that our implementation
of the CT approach gives more long term stable evolutions than ADM in all the
cases studied, but is less accurate in the short term for the range of
resolutions used in our 3D simulations.


title:
A multi-domain spectral method for scalar and vectorial Poisson
  equations with non-compact sources

abstract:
  We present a spectral method for solving elliptic equations which arise in
general relativity, namely three-dimensional scalar Poisson equations, as well
as generalized vectorial Poisson equations of the type $\Delta \vec{N} +
\lambda \vec{\nabla}(\vec{\nabla}\cdot \vec{N}) = \vec{S}$ with $\lambda \not=
-1$. The source can extend in all the Euclidean space ${\bf R}^3$, provided it
decays at least as $r^{-3}$. A multi-domain approach is used, along with
spherical coordinates $(r,\theta,\phi)$. In each domain, Chebyshev polynomials
(in $r$ or $1/r$) and spherical harmonics (in $\theta$ and $\phi$) expansions
are used. If the source decays as $r^{-k}$ the error of the numerical solution
is shown to decrease at least as $N^{-2(k-2)}$, where $N$ is the number of
Chebyshev coefficients. The error is even evanescent, i.e. decreases as
$\exp(-N)$, if the source does not contain any spherical harmonics of index
$l\geq k -3$ (scalar case) or $l\geq k-5$ (vectorial case).


title: Closed Lightlike Curves in Non-linear Electrodynamics

abstract:
  We show that non-linear electrodynamics may induce a photon to follow a
closed path in spacetime. We exhibit a specific case in which such closed
lightlike curve (CLC) appears


title: Self force on particle in orbit around a black hole

abstract:
  We study the self force acting on a scalar charge in uniform circular motion
around a Schwarzschild black hole. The analysis is based on a direct
calculation of the self force via mode decomposition, and on a regularization
procedure based on Ori's mode-sum regularization prescription. We find the four
self-force at arbitrary radii and angular velocities (both geodesic and
non-geodesic), in particular near the black hole, where general-relativistic
effects are strongest, and for fast motion. We find the radial component of the
self force to be repulsive or attractive, depending on the orbit.


title: A nongravitational wormhole

abstract:
  Using the effective metric formalism for photons in a nonlinear
electromagnetic theory, we show that a certain field configuration in
Born-Infeld electromagnetism in flat spacetime can be interpreted as an
ultrastatic spherically symmetric wormhole. We also discuss some properties of
the effective metric that are valid for any field configuration.


title:
Criteria for de Sitter inflation in Einstein-Cartan cosmology and COBE
  data

abstract:
  Criteria for the existence of de Sitter inflation with dilaton fields in
four-dimensional space-times with torsion is discussed.The relation between
matter density perturbation and the spin-density perturbation is stablished
based on this criteria.From COBE data it is shown that there is a linear
relationship between the spin-torsion density and temperature of the Universe
for the case where matter density dominates the kinetic part of dilaton fields.


title: Relativistic Effects in the Motion of the Moon

abstract:
  The main general relativistic effects in the motion of the Moon are briefly
reviewed. The possibility of detection of the solar gravitomagnetic
contributions to the mean motions of the lunar node and perigee is discussed.


title: Vacuum Polarization of Massive Scalar Fields on the Black Hole Horizon

abstract:
  Vacuum polarization of massive scalar fields in a thermal state at arbitrary
temperature is studied near the horizon of a Reissner-Nordstr\"{o}m black hole.
We derived an analytic form of $<\phi^2>$ approximately in the large mass limit
near the black hole horizon. We uses the zeroth order WKB approximation and
power series expansion near the horizon for the Euclideanized mode function.
Our formula for the vacuum polarization shows regular behavior on the horizon
if the temperature of the scalar field is equal to the Hawking temperature of
the black hole. The finite part of the vacuum polarization agrees with the
result of the DeWitt-Schwinger approximation up to $O(m^{-4})$ which is the
next leading order of the expansion.


title:
Quantum Creation of Closed Universe with Both Effects of Tunneling and
  Well

abstract:
  A new ''twice loose shoe'' method in the Wheeler-DeWitt equation of the
universe wave function on the cosmic scale factor a and a scalar field $\phi$
is suggested in this letter. We analysis the both affects come from the
tunneling effect of a and the potential well effect of $\phi$, and obtain the
initial values $a_0$ and $\phi_0$ about a primary closed universe which is born
with the largest probability in the quantum manner. Our result is able to
overcome the ''large field difficulty'' of the universe quantum creation
probability with only tunneling effect. This new born universe has to suffer a
startup of inflation, and then comes into the usual slow rolling inflation. The
universe with the largest probability maybe has a ''gentle'' inflation or an
eternal chaotic inflation, this depends on a new parameter q which describes
the tunneling character.


title:
Self-similar spherically symmetric cosmological models with a perfect
  fluid and a scalar field

abstract:
  Self-similar, spherically symmetric cosmological models with a perfect fluid
and a scalar field with an exponential potential are investigated. New
variables are defined which lead to a compact state space, and dynamical
systems methods are utilised to analyse the models. Due to the existence of
monotone functions global dynamical results can be deduced. In particular, all
of the future and past attractors for these models are obtained and the global
results are discussed. The essential physical results are that initially
expanding models always evolve away from a massless scalar field model with an
initial singularity and, depending on the parameters of the models, either
recollapse to a second singularity or expand forever towards a flat power-law
inflationary model. The special cases in which there is no barotropic fluid and
in which the scalar field is massless are considered in more detail in order to
illustrate the asymptotic results. Some phase portraits are presented and the
intermediate dynamics and hence the physical properties of the models are
discussed.


title:
Electrodynamics of accelerated charges or Why electron does not radiate
  in Rutherford's atom

abstract:
  It is shown, that the radiation of the charge, moving with uniform
acceleration or uniformly moving round a circle and also freely moving in a
gravitational field, contradicts the principle of equivalence. It is also
shown, that the interaction of the charges, moving with uniform acceleration or
uniformly circling, which has been calculated within the framework of classical
electrodynamics, leads to the violation of laws of conservation of energy,
impulse and angular momentum. We have offered a method in which way to conform
electrodynamics to the principle of equivalence. So in the electrodynamics,
which has been conformed in such a way, all the mentioned violations of the
laws of conservation are automatically removed and the stability of
Rutherford's atom is explained. It is shown that the changes, which we have
brought into the electrodynamics, do not contradict the results of experiments.


title:
Closed Universes With Black Holes But No Event Horizons As a Solution to
  the Black Hole Information Problem

abstract:
  We show it is possible for the information paradox in black hole evaporation
to be resolved classically. Using standard junction conditions, we attach the
general closed spherically symmetric dust metric to a spacetime satisfying all
standard energy conditions but with a single point future c-boundary. The
resulting Omega Point spacetime, which has NO event horizons, nevertheless has
black hole type trapped surfaces and hence black holes. But since there are no
event horizons, information eventually escapes from the black holes. We show
that a scalar quintessence field with an appropriate exponential potential near
the final singularity would give rise to an Omega Point final singularity.


title: Chaos around the superposition of a monopole and a thick disk

abstract:
  We extend recent investigations on the integrability of oblique orbits of
test particles under the gravitational field corresponding to the superposition
of an infinitesimally thin disk and a monopole to the more realistic case, for
astrophysical purposes, of a thick disk. Exhaustive numerical analyses were
performed and the robustness of the recent results is confirmed. We also found
that, for smooth distributions of matter, the disk thickness can attenuate the
chaotic behavior of the bounded oblique orbits. Perturbations leading to the
breakdown of the reflection symmetry about the equatorial plane, nevertheless,
may enhance significantly the chaotic behavior, in agreement with recent
studies on oblate models.


title: The Bianchi Type I minisuperspace model

abstract:
  The minisuperspace model of a Bianchi Type I universe with compact spatial
sections is investigated. The classical solutions are brought onto a form were
the difference between compact and infinite spatial sections are manifest. One
of the features of the compact case is that it has a non-trivial moduli space.
The solution space of the compact Bianchi Type I universe is 10 dimensional
whereas the Kasner solutions only have a 1 dimensional solution space. We also
include the classical solutions with dust and a cosmological constant.
Solutions to the Wheeler-DeWitt equation are obtained in light of the tunneling
boundary proposal by Vilenkin. Backreaction effects from a simple scalar field
are also investigated.


title:
An analysis of cosmological perturbations in hydrodynamical and field
  representations

abstract:
  Density fluctuations of fluids with negative pressure exhibit decreasing time
behaviour in the long wavelength limit, but are strongly unstable in the small
wavelength limit when a hydrodynamical approach is used. On the other hand, the
corresponding gravitational waves are well behaved. We verify that the
instabilities present in density fluctuations are due essentially to the
hydrodynamical representation; if we turn to a field representation that lead
to the same background behaviour, the instabilities are no more present. In the
long wavelength limit, both approachs give the same results. We show also that
this inequivalence between background and perturbative level is a feature of
negative pressure fluid. When the fluid has positive pressure, the
hydrodynamical representation leads to the same behaviour as the field
representation both at the background and perturbative levels.


title: Inertial Effects on Berry's Phase of Neutrino Oscillations

abstract:
  The Berry phase of mixed states, as neutrino oscillations, is calculated in a
accelerating and rotating reference frame. It turns out to be depending on the
vacuum mixing angle, the mass--squared difference and on the coupling between
the momentum of the neutrino and the spinorial connection. Berry's phase for
solar neutrinos and its geometrical aspects are also discussed.


title: Massive Scalar Particles in a Modified Schwarzschild Geometry

abstract:
  Massive, spinless bosons have vanishing probability of reaching the sphere
r=2M from the region r>2M when the original Schwarzschild metric is modified by
maximal acceleration corrections.


title: New approach to the evolution of neutron star oscillations

abstract:
  We present a new derivation of the perturbation equations governing the
oscillations of relativistic non-rotating neutron star models using the
ADM-formalism. This formulation has the advantage that it immediately yields
the evolution equations in a hyperbolic form, which is not the case for the
Einstein field equations in their original form. We show that the perturbation
equations can always be written in terms of spacetime variables only,
regardless of any particular gauge. We demonstrate how to obtain the
Regge-Wheeler gauge, by choosing appropriate lapse and shift. In addition, not
only the 3-metric but also the extrinsic curvature of the initial slice have to
satisfy certain conditions in order to preserve the Regge-Wheeler gauge
throughout the evolution. We discuss various forms of the equations and show
their relation to the formulation of Allen et al. New results are presented for
polytropic equations of state. An interesting phenomenon occurs in very compact
stars, where the first ring-down phase in the wave signal corresponds to the
first quasinormal mode of an equal mass black hole, rather than to one of the
proper quasinormal modes of the stellar model. A somewhat heuristic explanation
to account for this phenomenon is given. For realistic equations of state, the
numerical evolutions exhibit an instability, which does not occur for
polytropic equations of state. We show that this instability is related to the
behavior of the sound speed at the neutron drip point. As a remedy, we devise a
transformation of the radial coordinate $r$ inside the star, which removes this
instability and yields stable evolutions for any chosen numerical resolution.


title: A Spacetime Foam Approach to the Schwarzschild-de Sitter Entropy

abstract:
  The entropy for a black hole in a de Sitter space is approached within the
framework of spacetime foam. A simple model, made by $N$ wormholes in a
semiclassical approximation, is taken under examination to compute the entropy
for such a case. An extension to the extreme case when the black hole and
cosmological horizons are equal is discussed.


title: A Spacetime Foam approach to the cosmological constant and entropy

abstract:
  A simple model of spacetime foam, made by $N$ wormholes in a semiclassical
approximation, is taken under examination. The Casimir-like energy of the
quantum fluctuation of such a model and its probability of being realized are
computed. Implications on the Bekenstein-Hawking entropy and the cosmological
constant are considered.


title: Entropy bound for a rotating system from Anti de Sitter black holes

abstract:
  General geodesic equations of the motion of spinning systems around the
(3+1)-dimensional and (2+1)-dimensional rotating anti-de Sitter black holes
have been obtained. Based upon these equations, we derived the entropy bound
for a rotating system from Kerr-Anti de Sitter black holes and BTZ black holes,
respectively. Our result coincides with that of Hod's derived from Kerr black
hole, which shows that the entropy bound of the rotating system is neither
dependent on the black hole parameters, nor on spacetime dimensions. It is a
universal entropy bound.


title: Toward a Traversable Wormhole

abstract:
  In this talk I discuss pertinence of the wormholes to the problem of
circumventing the light speed barrier and present a specific class of
wormholes. The wormholes of this class are static and have arbitrarily wide
throats, which makes them traversable. The matter necessary for these
spacetimes to be solutions of the Einstein equations is shown to consist of two
components, one of which satisfies the Weak energy condition and the other is
produced by vacuum fluctuations of neutrino, electromagnetic (in dimensional
regularization), and/or massless scalar (conformally coupled) fields.


title: Acceleration-Induced Nonlocal Electrodynamics in Minkowski Spacetime

abstract:
  We discuss two nonlocal models of electrodynamics in which the nonlocality is
induced by the acceleration of the observer. Such an observer actually measures
an electromagnetic field that exhibits persistent memory effects. We compare
Mashhoon's model with a new ansatz developed here in the framework of charge &
flux electrodynamics with a constitutive law involving the Levi-Civita
connection as seen from the observer's local frame and conclude that they are
in partial agreement only for the case of constant acceleration.


title:
Dynamical content of quantum diffeomorphisms in two-dimensional quantum
  gravity

abstract:
  A model for 2D-quantum gravity from the Virasoro symmetry is studied. The
notion of space-time naturally arises as a homogeneous space associated with
the kinematical (non-dynamical) SL(2,R) symmetry in the kernel of the
Lie-algebra central extension for the critical values of the conformal anomaly.
The rest of the generators in the group, L_n (n>1, n<-1), mix space-times with
different constant curvature. Only in the classical limit all space-times can
be identified, defining a unique Minkowski space-time, and the operators L_n
(n<1, n<-1) gauged away. This process entails a restriction to SL(2,R)
subrepresentations, which creates a non-trivial two-dimensional symplectic
classical phase space. The present model thus suggests that the role of general
covariance in quantum gravity is different from that played in the classical
limit.


title:
The quantum modes of the (1+1)-dimensional oscillators in general
  relativity

abstract:
  The quantum modes of a new family of relativistic oscillators are studied by
using the supersymmetry and shape invariance in a version suitable for (1+1)
dimensional relativistic systems. In this way one obtains the Rodrigues
formulas of the normalized energy eigenfunctions of the discrete spectra and
the corresponding rising and lowering operators.
  Pacs: 04.62.+v, 03.65.Ge


title: Open cosmologies with rotation

abstract:
  We study a rotating and expanding, Godel type metric, originally considered
by Korotkii and Obukhov, showing that, in the limit of large times and nearby
distances, it reduces to the open metric of Friedmann. In the epochs when
radiation or dust matter dominate the energy density, our solutions are similar
to the isotropic ones and, in what concerns processes occurring at small times,
the rotation leads only to higher order corrections. At large times, the
solution is dominated by a decaying positive cosmological term, with negative
pressure, and necessarily describes a quasi-flat universe if the energy
conditions have to be satisfied. The absence of closed time-like curves
requires a superior limit for the global angular velocity, which appears as a
natural explanation for the observed smallness of the present rotation. The
conclusion is that the introduction of a global rotation, in addition to be
compatible with observation, can enrich the standard model of the Universe,
explaining issues like the origin of galaxies rotation and the quasi-flatness
problem.


title: Higher dimensional flat embeddings of (2+1) dimensional black holes

abstract:
  We obtain the higher dimensional global flat embeddings of static, rotating,
and charged BTZ black holes. On the other hand, we also study the similar
higher dimensional flat embeddings of the (2+1) de Sitter black holes which are
the counterparts of the anti-de Sitter BTZ black holes. As a result, the
charged dS black hole is shown to be embedded in (3+2) GEMS, contrast to the
charged BTZ one having (3+3) GEMS structure.


title:
Solutions to Cosmological Problems with Energy Conservation and Varying
  c, G and Lambda

abstract:
  The flatness and cosmological constant problems are solved with varying speed
of light c, gravitational coupling strength G and cosmological parameter
Lambda, by explicitly assuming energy conservation of observed matter. The
present solution to the flatness problem is the same as the previous solution
in which energy conservation was absent.


title:
Adaptive filtering techniques for gravitational wave interferometric
  data: Removing long-term sinusoidal disturbances and oscillatory transients

abstract:
  It is known by the experience gained from the gravitational wave detector
proto-types that the interferometric output signal will be corrupted by a
significant amount of non-Gaussian noise, large part of it being essentially
composed of long-term sinusoids with slowly varying envelope (such as violin
resonances in the suspensions, or main power harmonics) and short-term ringdown
noise (which may emanate from servo control systems, electronics in a
non-linear state, etc.). Since non-Gaussian noise components make the detection
and estimation of the gravitational wave signature more difficult, a denoising
algorithm based on adaptive filtering techniques (LMS methods) is proposed to
separate and extract them from the stationary and Gaussian background noise.
The strength of the method is that it does not require any precise model on the
observed data: the signals are distinguished on the basis of their
autocorrelation time. We believe that the robustness and simplicity of this
method make it useful for data preparation and for the understanding of the
first interferometric data. We present the detailed structure of the algorithm
and its application to both simulated data and real data from the LIGO 40meter
proto-type.


title: Gravitational Energy-Momentum Density in Teleparallel Gravity

abstract:
  In the context of a gauge theory for the translation group, a conserved
energy-momentum gauge current for the gravitational field is obtained. It is a
true spacetime and gauge tensor, and transforms covariantly under global
Lorentz transformations. By rewriting the gauge gravitational field equation in
a purely spacetime form, it becomes the teleparallel equivalent of Einstein's
equation, and the gauge current reduces to the M{\o}ller's canonical
energy-momentum density of the gravitational field.


title: Numerical hydrodynamics in general relativity

abstract:
  The current status of numerical solutions for the equations of ideal general
relativistic hydrodynamics is reviewed. With respect to an earlier version of
the article the present update provides additional information on numerical
schemes and extends the discussion of astrophysical simulations in general
relativistic hydrodynamics. Different formulations of the equations are
presented, with special mention of conservative and hyperbolic formulations
well-adapted to advanced numerical methods. A large sample of available
numerical schemes is discussed, paying particular attention to solution
procedures based on schemes exploiting the characteristic structure of the
equations through linearized Riemann solvers. A comprehensive summary of
astrophysical simulations in strong gravitational fields is presented. These
include gravitational collapse, accretion onto black holes and hydrodynamical
evolutions of neutron stars. The material contained in these sections
highlights the numerical challenges of various representative simulations. It
also follows, to some extent, the chronological development of the field,
concerning advances on the formulation of the gravitational field and
hydrodynamic equations and the numerical methodology designed to solve them.


title:
A Class of Einstein-Maxwell Fields Generalizing the Equilibrium
  Solutions

abstract:
  The Einstein-Maxwell fields of rotating stationary sources are represented by
the SU(2,1) spinor potential $\Psi_A$ satisfying \[ \nabla \cdot [\Theta
^{-1}(\Psi_A\nabla \Psi_B-\Psi_B\nabla \Psi_A)]=-2\Theta ^{-2}\vec{C}\cdot
(\Psi_A\nabla \Psi_B-\Psi_B\nabla \Psi_A) \] where $\Theta =\Psi ^{\dagger
}\cdot \Psi $ is the SU(2,1) norm of $\Psi $% . The Ernst potentials are
expressed in terms of the spinor potential by $% {\cal E}=\frac{\Psi_1-\Psi
_2}{\Psi_1+\Psi_2}$, $\Phi =\frac{\Psi_3}{% \Psi_1+\Psi_2}$ . The group
invariant vector $\vec{C}=-2i\func{Im}\{\Psi ^{\dagger}\cdot \nabla \Psi \}$ is
generated exclusively by the rotation of the source, hence it is appropriate to
refer to $\vec{C}$ as the {\em swirl} of the field. Static fields have no
swirl.
  The fields with no swirl are a class generalizing the equilibrium ($| e| =m$)
class of Einstein-Maxwell fields. We obtain the integrability conditions and a
highly symmetrical set of field equations for this class, as well as exact
solutions and an open research problem.


title: New quantum aspects of a vacuum-dominated universe

abstract:
  In a new model that we proposed, nonperturbative vacuum contributions to the
effective action of a free quantized massive scalar field lead to a
cosmological solution in which the scalar curvature becomes constant after a
time $t_j$ (when the redshift $z \sim 1$) that depends on the mass of the
scalar field and its curvature coupling. This spatially-flat solution implies
an accelerating universe at the present time and gives a good one-parameter fit
to high-redshift Type Ia supernovae (SNe-Ia) data, and the present age and
energy density of the universe. Here we show that the imaginary part of the
nonperturbative curvature term that causes the cosmological acceleration,
implies a particle production rate that agrees with predictions of other
methods and extends them to non-zero mass fields. The particle production rate
is very small after the transition and is not expected to alter the nature of
the cosmological solution. We also show that the equation of state of our model
undergoes a transition at $t_j$ from an equation of state dominated by
non-relativistic pressureless matter (without a cosmological constant) to an
effective equation of state of mixed radiation and cosmological constant, and
we derive the equation of state of the vacuum. Finally, we explain why
nonperturbative vacuum effects of this ultralow-mass particle do not
significantly change standard early universe cosmology.


title: Uniform Spaces in the Pregeometric Modeling of Quantum Non-Separability

abstract:
  We introduce a pregeometry employing uniform spaces over the denumerable set
X of spacetime events. The discrete uniformity D_X over X is used to obtain a
pregeometric model of macroscopic spacetime neighborhoods. We then use a
uniformity base generated by a topological group structure over X to provide a
pregeometric model of microscopic spacetime neighborhoods. Accordingly, quantum
non-separability as it pertains to non-locality is understood pregeometrically
as a contrast between microscopic spacetime neighborhoods and macroscopic
spacetime neighborhoods. A nexus between this pregeometry and conventional
spacetime physics is implied per the metric induced by D_X. A metric over the
topological group Z2 x ... x Z2 is so generated. Implications for quantum
gravity are enumerated.


title: Unexpectedly large surface gravities for acoustic horizons?

abstract:
  Acoustic black holes are fluid dynamic analogs of general relativistic black
holes, wherein the behaviour of sound waves in a moving fluid acts as an analog
for scalar fields propagating in a gravitational background. Acoustic horizons
possess many of the properties more normally associated with the event horizons
of general relativity, up to and including Hawking radiation. They have
received much attention because it would seem to be much easier to
experimentally create an acoustic horizon than to create an event horizon. We
wish to point out some potential difficulties (and opportunities) in actually
setting up an experiment that possesses an acoustic horizon. We show that in
zero-viscosity, stationary fluid flow with generic boundary conditions, the
creation of an acoustic horizon is accompanied by a formally infinite ``surface
gravity'', and a formally infinite Hawking flux. Only by applying a suitable
non-constant external body force, and for very specific boundary conditions on
the flow, can these quantities be kept finite. This problem is ameliorated in
more realistic models of the fluid. For instance, adding viscosity always makes
the Hawking flux finite, but greatly complicates the behaviour of the acoustic
radiation --- viscosity is tantamount to explicitly breaking ``acoustic Lorentz
invariance''. Thus, this issue represents both a difficulty and an opportunity
--- acoustic horizons may be somewhat more difficult to form than naively
envisaged, but if formed, they may be much easier to detect than one would at
first suppose.


title: Conformal positive mass theorems

abstract:
  We show the following two extensions of the standard positive mass theorem
(one for either sign): Let (N,g) and (N,g') be asymptotically flat Riemannian
3-manifolds with compact interior and finite mass, such that g and g' are twice
Hoelder differentiable and related via the conformal rescaling g' = (phi^4).g,
with a twice Hoelder differentiable function phi>0. Assume further that the
corresponding Ricci scalars satisfy either R + (phi^4).R' >= 0 or R -
(phi^4).R' >= 0. Then the corresponding masses satisfy m + m' >= 0 or m - m' >=
0, respectively. Moreover, in the case of the minus signs, equality holds iff g
and g' are isometric, whereas for the plus signs equality holds iff both (N,g)
and (N,g') are flat Euclidean spaces.
  While the proof of the case with the minus signs is rather obvious, the case
with the plus signs requires a subtle extension of Witten's proof of the
standard positive mass theorem. The idea for this extension is due to
Masood-ul-Alam who, in the course of an application, proved the rigidity part m
+ m' = 0 of this theorem, for a special conformal factor. We observe that
Masood-ul-Alam's method extends to the general situation.


title: Quantum Radiation of a Uniformly Accelerated Refractive Body

abstract:
  We study quantum radiation generated by an accelerated motion of a small body
with a refractive index n which differes slightly from 1. To simplify
calculations we consider a model with a scalar massless field. We use the
perturbation expansion in a small parameter n-1 to obtain a correction to the
vacuum Hadamard function for a uniformly accelerated motion of the body. We
obtain the vacuum expectation for the energy density flux in the wave zone and
discuss its properties.


title:
Darboux class of cosmological fluids with time-dependent adiabatic
  indices

abstract:
  A one-parameter family of time dependent adiabatic indices is introduced for
any given type of cosmological fluid of constant adiabatic index by a
mathematical method belonging to the class of Darboux transformations. The
procedure works for zero cosmological constant at the price of introducing a
new constant parameter related to the time dependence of the adiabatic index.
These fluids can be the real cosmological fluids that are encountered at
cosmological scales and they could be used as a simple and efficient
explanation for the recent experimental findings regarding the present day
accelerating universe. In addition, new types of cosmological scale factors,
corresponding to these fluids, are presented


title: Naked singularities in higher dimensional inhomogeneous dust collapse

abstract:
  We investigate the occurrence and nature of a naked singularity in the
gravitational collapse of an inhomogeneous dust cloud described by a non
self-similar higher dimensional Tolman spacetime. The necessary condition for
the formation of a naked singularity or a black hole is obtained. The naked
singularities are found to be gravitationally strong in the sense of Tipler and
provide another example that violates the cosmic censorship conjecture.


title: The Newtonian Correspondence

abstract:
  It is shown that the field equations of general relativity in the Einstein
tensor form and the unimodular theory of gravity do not fulfill the
correspondence principle commitment completely. The consistent formalisms are
briefly discussed.


title: Triad representation of the Chern-Simons state in quantum gravity

abstract:
  We investigate a triad representation of the Chern-Simons state of quantum
gravity with a non-vanishing cosmological constant. It is shown that the
Chern-Simons state, which is a well-known exact wavefunctional within the
Ashtekar theory, can be transformed to the real triad representation by means
of a suitably generalized Fourier transformation, yielding a complex integral
representation for the corresponding state in the triad variables. It is found
that topologically inequivalent choices for the complex integration contour
give rise to linearly independent wavefunctionals in the triad representation,
which all arise from the one Chern-Simons state in the Ashtekar variables. For
a suitable choice of the normalization factor, these states turn out to be
gauge-invariant under arbitrary, even topologically non-trivial
gauge-transformations. Explicit analytical expressions for the wavefunctionals
in the triad representation can be obtained in several interesting asymptotic
parameter regimes, and the associated semiclassical 4-geometries are discussed.
In restriction to Bianchi-type homogeneous 3-metrics, we compare our results
with earlier discussions of homogeneous cosmological models. Moreover, we
define an inner product on the Hilbert space of quantum gravity, and choose a
natural gauge-condition fixing the time-gauge. With respect to this particular
inner product, the Chern-Simons state of quantum gravity turns out to be a
non-normalizable wavefunctional.


title:
Homogeneous magnetic fields in fully anisotropic string cosmological
  backgrounds

abstract:
  We present new solutions of the string cosmological effective action in the
presence of a homogeneous Maxwell field with pure magnetic component. Exact
solutions are derived in the case of space-independent dilaton and vanishing
torsion background. In our examples the four dimensional metric is either of
Bianchi-type III and VI$_{-1}$ or Kantowski-Sachs.


title:
Existence, uniqueness and other properties of the BCT (minimal strain
  lapse and shift) gauge

abstract:
  Brady, Creighton and Thorne have proposed a choice of the lapse and shift for
numerical evolutions in general relativity that extremizes a measure of the
rate of change of the three-metric (BCT gauge). We investigate existence and
uniqueness of this gauge, and comment on its use in numerical time evolutions.


title: Dynamic Cosmic Strings II: Numerical evolution of excited Cosmic Strings

abstract:
  An implicit, fully characteristic, numerical scheme for solving the field
equations of a cosmic string coupled to gravity is described. The inclusion of
null infinity as part of the numerical grid allows us to apply suitable
boundary conditions on the metric and matter fields to suppress unphysical
divergent solutions. The code is tested by comparing the results with exact
solutions, checking that static cosmic string initial data remain constant when
evolved and undertaking a time dependent convergence analysis of the code. It
is shown that the code is accurate, stable and exhibits clear second order
convergence. The code is used to analyse the interaction between a
Weber--Wheeler pulse of gravitational radiation with the string. The
interaction causes the string to oscillate at frequencies inversely
proportional to the masses of the scalar and vector fields of the string. After
the pulse has largely radiated away the string continues to ring but the
oscillations slowly decay and eventually the variables return to their static
values.


title: Gauge Symmetry and Gravito-Electromagnetism

abstract:
  A tensor description of perturbative Einsteinian gravity about an arbitrary
background spacetime is developed. By analogy with the covariant laws of
electromagnetism in spacetime, gravito-electromagnetic potentials and fields
are defined to emulate electromagnetic gauge transformations under
substitutions belonging to the gauge symmetry group of perturbative
gravitation. These definitions have the advantage that on a flat background,
with the aid of a covariantly constant timelike vector field, a subset of the
linearised gravitational field equations can be written in a form that is fully
analogous to Maxwell's equations (without awkward factors of 4 and extraneous
tensor fields). It is shown how the remaining equations in the perturbed
gravitational system restrict the time dependence of solutions to these
equations and thereby prohibit the existence of propagating vector fields. The
induced gravito-electromagnetic Lorentz force on a test particle is evaluated
in terms of these fields together with the torque on a small gyroscope. It is
concluded that the analogy of perturbative gravity to Maxwell's description of
electromagnetism can be valuable for (quasi-)stationary gravitational phenomena
but that the analogy has its limitations.


title: Mode solutions of the Klein-Gordon equation in warped spacetimes

abstract:
  In order to reduce the Klein-Gordon equation (with minimal coupling), we
introduce a generalization of the so-called "mode solutions" that are
well-known in the special case of a Robertson-Walker universe. After separation
of the variables, we end up with a partial differential equation in lower
dimension. A reduced version of the Gordon current arises and is conserved.
When the first factor-manifold is Lorentzian, distinct modes appear as mutually
orthogonal in the sense of the sesquilinear form obtained from the customary
Gordon current. Moreover, a sesquilinear form is defined on the space of
solutions to the reduced equation. Extension of this picture to curvature
coupling is possible when the second factor-manifold has a constant scalar
curvature.


title: Evidence for a continuum limit in causal set dynamics

abstract:
  We find evidence for a continuum limit of a particular causal set dynamics
which depends on only a single ``coupling constant'' $p$ and is easy to
simulate on a computer. The model in question is a stochastic process that can
also be interpreted as 1-dimensional directed percolation, or in terms of
random graphs.


title: Monopoles and the Emergence of Black Hole Entropy

abstract:
  One of the remarkable features of black holes is that they possess a
thermodynamic description, even though they do not appear to be statistical
systems. We use self-gravitating magnetic monopole solutions as tools for
understanding the emergence of this description as one goes from an ordinary
spacetime to one containing a black hole. We describe how causally distinct
regions emerge as a monopole solution develops a horizon. We define an entropy
that is naturally associated with these regions and that has a clear connection
with the Hawking-Bekenstein entropy in the critical black hole limit.


title:
Gravitational Waves from the Dynamical Bar Instability in a Rapidly
  Rotating Star

abstract:
  A rapidly rotating, axisymmetric star can be dynamically unstable to an m=2
"bar" mode that transforms the star from a disk shape to an elongated bar. The
fate of such a bar-shaped star is uncertain. Some previous numerical studies
indicate that the bar is short lived, lasting for only a few bar-rotation
periods, while other studies suggest that the bar is relatively long lived.
This paper contains the results of a numerical simulation of a rapidly rotating
gamma=5/3 fluid star. The simulation shows that the bar shape is long lived:
once the bar is established, the star retains this shape for more than 10
bar-rotation periods, through the end of the simulation. The results are
consistent with the conjecture that a star will retain its bar shape
indefinitely on a dynamical time scale, as long as its rotation rate exceeds
the threshold for secular bar instability. The results are described in terms
of a low density neutron star, but can be scaled to represent, for example, a
burned-out stellar core that is prevented from complete collapse by centrifugal
forces. Estimates for the gravitational-wave signal indicate that a dynamically
unstable neutron star in our galaxy can be detected easily by the first
generation of ground based gravitational-wave detectors. The signal for an
unstable neutron star in the Virgo cluster might be seen by the planned
advanced detectors. The Newtonian/quadrupole approximation is used throughout
this work.


title: Evidence for a null entropy of extremal black holes

abstract:
  We present some arguments in support of a {\it zero} entropy for {\it
extremal} black holes. These rely on a combination of both quantum,
thermodynamic, and statistical physics arguments. This result may shed some
light on the nature of these extreme objects. In addition, we show that within
a {\it quantum} framework the capture of a particle by an initially extremal
black hole always results with a final nonextremal black hole.


title: The nonlinear evolution of de Sitter space instabilities

abstract:
  We investigate the quantum evolution of large black holes that nucleate
spontaneously in de Sitter space. By numerical computation in the s-wave and
one-loop approximations, we verify claims that such black holes can initially
"anti-evaporate" instead of shrink. We show, however, that this is a transitory
effect. It is followed by an evaporating phase, which we are able to trace
until the black holes are small enough to be treated as Schwarzschild. Under
generic perturbations, the nucleated geometry is shown to decay into a ring of
de Sitter regions connected by evaporating black holes. This confirms that de
Sitter space is globally unstable and fragments into disconnected daughter
universes.


title: The quantization of gravity - an introduction

abstract:
  This is an introduction to quantum gravity, aimed at a fairly general
audience and concentrating on what have historically two main approaches to
quantum gravity: the covariant and canonical programs (string theory is not
covered). The quantization of gravity is discussed by analogy with the
quantization of the electromagnetic field. The conceptual and technical
problems of both approaches are discussed, and the paper concludes with a
discussion of evidence for quantum gravity from the rest of physics.
  The paper assumes some familiarity with non-relativistic quantum mechanics,
special relativity, and the Lagrangian and Hamiltonian formulations of
classical mechanics; some experience with classical field theory, quantum
electrodynamics and the gauge principle in electromagnetism might be helpful
but is not required. No knowledge of general relativity or of quantum field
theory in general is assumed.


title: Fluctuations of Energy Density and Validity of Semiclassical Gravity

abstract:
  From calculations of the variance of fluctuations and of the mean of the
energy density of a massless scalar field in the Minkowski vacuum as a function
of an intrinsic scale defined by the world function between two nearby points
(as used in point separation regularization) we show that, contrary to prior
claims, the ratio of variance to mean-squared being of the order unity does not
imply a failure of semiclassical gravity. It is more a consequence of the
quantum nature of the state of matter field than any inadequacy of the theory
of spacetime with quantum matter as source.


title: Generalized slow-roll inflation

abstract:
  The slow-roll approximation to inflation is ultimately justified by the
presence of inflationary attractors for the orbits of the solutions of the
dynamical equations in phase space. There are many indications that the
inflaton field couples nonminimally to the spacetime curvature: the existence
of attractor points for inflation with nonminimal coupling is demonstrated,
subject to a condition on the inflaton potential and the value of the coupling
constant.


title: Hadamard Regularization

abstract:
  Motivated by the problem of the dynamics of point-particles in high
post-Newtonian (e.g. 3PN) approximations of general relativity, we consider a
certain class of functions which are smooth except at some isolated points
around which they admit a power-like singular expansion. We review the concepts
of (i) Hadamard ``partie finie'' of such functions at the location of singular
points, (ii) the partie finie of their divergent integral. We present and
investigate different expressions, useful in applications, for the latter
partie finie. To each singular function, we associate a partie-finie (Pf)
pseudo-function. The multiplication of pseudo-functions is defined by the
ordinary (pointwise) product. We construct a delta-pseudo-function on the class
of singular functions, which reduces to the usual notion of Dirac distribution
when applied on smooth functions with compact support. We introduce and analyse
a new derivative operator acting on pseudo-functions, and generalizing, in this
context, the Schwartz distributional derivative. This operator is uniquely
defined up to an arbitrary numerical constant. Time derivatives and partial
derivatives with respect to the singular points are also investigated. In the
course of the paper, all the formulas needed in the application to the physical
problem are derived.


title:
On the equations of motion of point-particle binaries at the third
  post-Newtonian order

abstract:
  We investigate the dynamics of two point-like particles through the third
post-Newtonian (3PN) approximation of general relativity. The infinite
self-field of each point-mass is regularized by means of Hadamard's concept of
``partie finie''. Distributional forms associated with the regularization are
used systematically in the computation. We determine the stress-energy tensor
of point-like particles compatible with the previous regularization. The
Einstein field equations in harmonic coordinates are iterated to the 3PN order.
The 3PN equations of motion are Lorentz-invariant and admit a conserved energy
(neglecting the 2.5PN radiation reaction). They depend on an undetermined
coefficient, in agreement with an earlier result of Jaranowski and Schaefer.
This suggests an incompleteness of the formalism (in this stage of development)
at the 3PN order. In this paper we present the equations of motion in the
center-of-mass frame and in the case of circular orbits.


title: Is our vacuum stable?

abstract:
  The stability of our vacuum is analyzed and several aspects concerning this
question are reviewed. 1) In the standard Glashow-Weinberg-Salam (GWS) model we
review the instability towards the formation of a bubble of lower energy
density and how the rate of such bubble formation process compares with the age
of the Universe for the known values of the GWS model. 2) We also review the
recent work by one of us (E.I.G) concerning the vacuum instability question in
the context of a model that solves the cosmological constant problem. It turns
out that in such model the same physics that solves the cosmological constant
problem makes the vacuum stable. 3) We review our recent work concerning the
instability of elementary particle embedded in our vacuum, towards the
formation of an infinite Universe. Such process is not catastrophic. It leads
to a "bifurcation type" instability in which our Universe is not eaten by a
bubble (instead a baby universe is born). This universe does not replace our
Universe rather it disconnects from it (via a wormhole) after formation.


title:
Scale Invariance, Inflation and the Present Vacuum Energy of the
  Universe

abstract:
  The possibility of mass in the context of scale-invariant, generally
covariant theories, is discussed. Scale invariance is considered in the context
of a gravitational theory where the action, in the first order formalism, is of
the form $S = \int L_{1} \Phi d^4x$ + $\int L_{2}\sqrt{-g}d^4x$ where $\Phi$ is
a density built out of degrees of freedom independent of the metric. For global
scale invariance, a "dilaton" $\phi$ has to be introduced, with non-trivial
potentials $V(\phi)$ = $f_{1}e^{\alpha\phi}$ in $L_1$ and $U(\phi)$ =
$f_{2}e^{2\alpha\phi}$ in $L_2$. This leads to non-trivial mass generation and
a potential for $\phi$ which is interesting for inflation. The model after ssb
can be connected to the induced gravity model of Zee, which is a successful
model of inflation. Models of the present universe and a natural transition
from inflation to a slowly accelerated universe at late times are discussed.


title: Post-Newtonian Gravitational Radiation

abstract:
  1 Introduction 2 Multipole Decomposition 3 Source Multipole Moments 4
Post-Minkowskian Approximation 5 Radiative Multipole Moments 6 Post-Newtonian
Approximation 7 Point-Particles 8 Conclusion


title: Gauge symmetries in Ashtekar's formulation of general relativity

abstract:
  It might seem that a choice of a time coordinate in Hamiltonian formulations
of general relativity breaks the full four-dimensional diffeomorphism
covariance of the theory. This is not the case. We construct explicitly the
complete set of gauge generators for Ashtekar's formulation of canonical
gravity. The requirement of projectability of the Legendre map from
configuration-velocity space to phase space renders the symmetry group a gauge
transformation group on configuration-velocity variables. Yet there is a sense
in which the full four-dimensional diffeomorphism group survives. Symmetry
generators serve as Hamiltonians on members of equivalence classes of solutions
of Einstein's equations and are thus intimately related to the so-called
"problem of time" in an eventual quantum theory of gravity.


title: Transformations of units and world's geometry

abstract:
  The issue of the transformations of units is treated, mainly, in a
geometrical context. It is shown that Weyl-integrable geometry is a consistent
framework for the formulation of the gravitational laws since the basic law on
which this geometry rests is invariant under point-dependent transformations of
units. Riemann geometry does not fulfill this requirement. Spacetime
singularities are then shown to be a consequence of a wrong choice of the
geometrical formulation of the laws of gravitation. This result is discussed,
in particular, for the Schwrazschild black hole and for
Friedmann-Robertson-Walker cosmology. Arguments are given that point at
Weyl-integrable geometry as a geometry implicitly containing the quantum
effects of matter. The notion of geometrical relativity is presented. This
notion may represent a natural extension of general relativity to include
invariance under the group of units transformations.


title: Lorenz Gauge in Quantum Cosmology

abstract:
  In a path-integral approach to quantum cosmology, the Lorenz gauge-averaging
term is studied for Euclidean Maxwell theory on a portion of flat four-space
bounded by two concentric three-spheres, but with arbitrary values of the gauge
parameter. The resulting set of eigenvalue equations for normal and
longitudinal modes of the electromagnetic potential cannot be decoupled, and is
here studied with a Green-function method. This means that an equivalent
equation for longitudinal modes is obtained which has integro-differential
nature, after inverting a differential operator in the original coupled system.
A complete calculational scheme is therefore obtained for the one-loop
semiclassical evaluation of the wave function of the universe in the presence
of gauge fields. This might also lead to a better understanding of how gauge
independence is actually achieved on manifolds with boundary, whose
consideration cannot be avoided in a quantum theory of the universe.


title:
Selected solutions of Einstein's field equations: their role in general
  relativity and astrophysics

abstract:
  Contents: 1) Introduction and a few excursions [A word on the role of
explicit solutions in other parts of physics and astrophysics. Einstein's field
equations. "Just so" notes on the simplest solutions: The Minkowski, de Sitter
and anti-de Sitter spacetimes. On the interpretation and characterization of
metrics. The choice of solutions. The outline] 2) The Schwarzschild solution
[Spherically symmetric spacetimes. The Schwarzschild metric and its role in the
solar system. Schwarzschild metric outside a collapsing star. The
Schwarzschild-Kruskal spacetime. The Schwarzschild metric as a case against
Lorentz-covariant approaches. The Schwarzschild metric and astrophysics] 3) The
Reissner- Nordstrom solution [Reissner-Nordstrom black holes and the question
of cosmic censorship. On extreme black holes, d-dimensional black holes, string
theory and "all that"] 4) The Kerr metric [Basic features. The physics and
astrophysics around rotating black holes. Astrophysical evidence for a Kerr
metric] 5) Black hole uniqueness and multi-black hole solutions 6) Stationary
axisymmetric fields and relativistic disks [Static Weyl metrics. Relativistic
disks as sources of the Kerr metric and other stationary spacetimes. Uniformly
rotating disks] 7) Taub-NUT space [A new way to the NUT metric. Taub-NUT
pathologies and applications] 8) Plane waves and their collisions
[Plane-fronted waves. New developments and applications. Colliding plane waves]
9) Cylindrical waves [Cylindrical waves and the asymptotic structure of
3-dimensional general relativity. Cylindrical waves and quantum gravity.
Cylindrical waves: a miscellany] 10) On the Robinson-Trautman solutions 11) The
boost-rotation symmetric radiative spacetimes 12) The cosmological models
[Spatially homogeneous cosmologies. Inhomogeneous models] 13) Concluding
remarks


title: Born-Infeld Cosmologies

abstract:
  We present a model for an inhomogeneous and anisotropic early universe filled
with a nonlinear electromagnetic field of Born-Infeld (BI) type. The effects of
the BI field are compared with the linear case (Maxwell). Since the curvature
invaria nts are well behaved then we conjecture that our model does not present
an initial big bang singularity. The existence of the BI field modifies the
curvature invariants at t=0 as well as sets bounds on the amplitude of the
conformal metric function


title: Uniqueness properties of the Kerr metric

abstract:
  We obtain a geometrical condition on vacuum, stationary, asymptotically flat
spacetimes which is necessary and sufficient for the spacetime to be locally
isometric to Kerr. Namely, we prove a theorem stating that an asymptotically
flat, stationary, vacuum spacetime such that the so-called Killing form is an
eigenvector of the self-dual Weyl tensor must be locally isometric to Kerr.
Asymptotic flatness is a fundamental hypothesis of the theorem, as we
demonstrate by writing down the family of metrics obtained when this
requirement is dropped. This result indicates why the Kerr metric plays such an
important role in general relativity. It may also be of interest in order to
extend the uniqueness theorems of black holes to the non-connected and to the
non-analytic case.


title: A comment on a paper by Carot et al

abstract:
  In a recent paper Carot et al. considered carefully the definition of
cylindrical symmetry as a specialisation of the case of axial symmetry. One of
their propositions states that if there is a second Killing vector, which
together with the one generating the axial symmetry, forms the basis of a
two-dimensional Lie algebra, then the two Killing vectors must commute, thus
generating an Abelian group. In this comment a similar result, valid under
considerably weaker assumptions, is recalled: any two-dimensional Lie
transformation group which contains a one-dimensional subgroup whose orbits are
circles, must be Abelian. The method used to prove this result is extended to
apply to three-dimensional Lie transformation groups. It is shown that the
existence of a one-dimensional subgroup with closed orbits restricts the
Bianchi type of the associated Lie algebra to be I (Abelian), II, III, VII_0,
VIII or IX. The relationship between the present approach and that of the
original paper is discussed.


title: Quantum creation of an Inhomogeneous universe

abstract:
  In this paper we study a class of inhomogeneous cosmological models which is
a modified version of what is usually called the Lema\^itre-Tolman model. We
assume that we have a space with 2-dimensional locally homogeneous spacelike
surfaces. In addition we assume they are compact. Classically we investigate
both homogeneous and inhomogeneous spacetimes which this model describe. For
instance one is a quotient of the AdS$_4$ space which resembles the BTZ black
hole in AdS$_3$.
  Due to the complexity of the model we indicate a simpler model which can be
quantized easily. This model still has the feature that it is in general
inhomogeneous. How this model could describe a spontaneous creation of a
universe through a tunneling event is emphasized.


title:
Brane versus shell cosmologies in Einstein and Einstein-Gauss-Bonnet
  theories

abstract:
  We first illustrate on a simple example how, in existing brane cosmological
models, the connection of a 'bulk' region to its mirror image creates matter on
the 'brane'. Next, we present a cosmological model with no $Z_2$ symmetry which
is a spherical symmetric 'shell' separating two metrically different
5-dimensional anti-de Sitter regions. We find that our model becomes
Friedmannian at late times, like present brane models, but that its early time
behaviour is very different: the scale factor grows from a non-zero value at
the big bang singularity. We then show how the Israel matching conditions
across the membrane (that is either a brane or a shell) have to be modified if
more general equations than Einstein's, including a Gauss-Bonnet correction,
hold in the bulk, as is likely to be the case in a low energy limit of string
theory. We find that the membrane can then no longer be treated in the thin
wall approximation. However its microphysics may, in some instances, be simply
hidden in a renormalization of Einstein's constant, in which cases Einstein and
Gauss-Bonnet membranes are identical.


title: The renormalized stress tensor in Kerr space-time: general results

abstract:
  We derive constraints on the form of the renormalized stress tensor for
states on Kerr space-time based on general physical principles: symmetry, the
conservation equations, the trace anomaly and regularity on (sections of) the
event horizon. This is then applied to the physical vacua of interest. We
introduce the concept of past and future Boulware vacua and discuss the
non-existence of a state empty at both scri- and scri+. By calculating the
stress tensor for the Unruh vacuum at the event horizon and at infinity, we are
able to check our earlier conditions. We also discuss the difficulties of
defining a state equivalent to the Hartle-Hawking vacuum and comment on the
properties of two candidates for this state.


title: BTZ black hole from (3+1) gravity

abstract:
  We propose an approach for constructing spatial slices of (3+1) spacetimes
with cosmological constant but without a matter content, which yields (2+1)
vacuum with $\Lambda$ solutions. The reduction mechanism from (3+1) to (2+1)
gravity is supported on a criterion in which the Weyl tensor components are
required to vanish together with a dimensional reduction via an appropriate
foliation. By using an adequate reduction mechanism from the
Pleba\'nski-Carter[A] solution in (3+1) gravity, the (2+1) BTZ solution can be
obtained.


title: Lax Tensors, Killing Tensors and Geometric Duality

abstract:
  The solution of the Lax tensor equations in the case
$L_{\alpha\beta\gamma}=-L_{\beta\alpha\gamma}$ was analyzed. The Lax tensors on
the dual metrics were investigated. We classified all two dimensional metrics
having the symmetric Lax tensor $L_{\alpha\beta\gamma}$. The Lax tensors of the
flat space, Rindler system and its dual were found.


title: Negative mode problem in false vacuum decay with gravity

abstract:
  There is a single negative mode in the spectrum of small perturbations about
the tunneling solutions describing a metastable vacuum decay in flat spacetime.
This mode is needed for consistent description of decay processes. When gravity
is included the situation is more complicated. An approach based on elimination
of scalar field perturbations shows no negative mode, whereas the recent
approach based on elimination of gravitational perturbations indicates presence
of a negative mode. In this contribution we analyse and compare the present
approaches to the negative mode problem in false vacuum decay with gravity.


title:
Discrete spacetime: classical causality,prediction, retrodiction and the
  mathematical arrow of time

abstract:
  A mathematical definition of classical causality over discrete spacetime
dynamics is formulated. The approach is background free and permits a
definition of causality in a precise way whenever the spacetime dynamics
permits. It gives a natural meaning to the concepts of cosmic time, spacelike
hypersurfaces and timelike or lightlike flows without assuming the notion of a
background metric. The concepts of causal propagators and the speed of
causality are discussed. In this approach the concepts of spacetime and
dynamics are linked in an essential and inseparable whole, with no meaning to
either on its own.


title: Boson Condensation in an Einstein Universe

abstract:
  In this paper we investigate the Bose-Einstein condensation of massive spin-1
particles in an Einstein universe. The system is considered under relativistic
conditions taking into consideration the possibility of particle-antiparticle
pair production. An exact expression for the charge density is obtained, then
certain approximations are employed in order to obtain the solutions in closed
form. A discussion of the approximations employed in this and other work is
given. The effects of finite-size and spin-curvature coupling are emphasized.


title: Generating conjecture and Einstein-Maxwell field of plane symmetry

abstract:
  For the plane symmetry we have found the electro-vacuum exact solutions of
the Einstein-Maxwell equations and we have shown that one of them is equivalent
to the McVittie solution of a charged infinite thin plane. The analytical
extension has been accomplished and the Penrose conformal diagram has been
obtained as well.


title: Spin half in classical general relativity

abstract:
  It is shown that models of elementary particles in classical general
relativity (geons) will naturally have the transformation properties of a
spinor if the spacetime manifold is not time orientable. From a purely
pragmatic interpretation of quantum theory this explains why spinor fields are
needed to represent particles. The models are based entirely on classical
general relativity and are motivated by the suggestion that the lack of a
time-orientation could be the origin of quantum phenomena.


title: A Note on Brane Inflation

abstract:
  We demonstrate that there exists an inflationary solution on the positive
tension brane in the Randall-Sundrum scenario. Inflation is driven by a
slow-rolling scalar field on the brane and is achieved within the perturbative
limit of the radion field. We find that inflation on the positive tension brane
results in a slight increase in the separation between the two branes. However,
we show that the slow-roll inflation is not possible on the negative tension
brane.


title: Exact radiative spacetimes: some recent developments

abstract:
  Five classes of radiative solutions of Einstein's field equations are
discussed in the light of some new developments. These are plane waves and
their collisions, cylindrical waves, Robinson-Trautman and type N spacetimes,
boost-rotation symmetric spacetimes and generalized Gowdy-type cosmological
models


title:
Towards the classification of static vacuum spacetimes with negative
  cosmological constant

abstract:
  We present a systematic study of static solutions of the vacuum Einstein
equations with negative cosmological constant which asymptotically approach the
generalized Kottler (``Schwarzschild--anti-de Sitter'') solution, within
(mainly) a conformal framework. We show connectedness of conformal infinity for
appropriately regular such space-times. We give an explicit expression for the
Hamiltonian mass of the (not necessarily static) metrics within the class
considered; in the static case we show that they have a finite and well defined
Hawking mass. We prove inequalities relating the mass and the horizon area of
the (static) metrics considered to those of appropriate reference generalized
Kottler metrics. Those inequalities yield an inequality which is opposite to
the conjectured generalized Penrose inequality. They can thus be used to prove
a uniqueness theorem for the generalized Kottler black holes if the generalized
Penrose inequality can be established.


title: Distributional Modes for Scalar Field Quantization

abstract:
  We propose a mode-sum formalism for the quantization of the scalar field
based on distributional modes, which are naturally associated with a slight
modification of the standard plane-wave modes. We show that this formalism
leads to the standard Rindler temperature result, and that these modes can be
canonically defined on any Cauchy surface.


title:
Infinite hierarchies of exact solutions of the Einstein and
  Einstein-Maxwell equations for interacting waves and inhomogeneous
  cosmologies

abstract:
  For space-times with two spacelike isometries, we present infinite
hierarchies of exact solutions of the Einstein and Einstein--Maxwell equations
as represented by their Ernst potentials. This hierarchy contains three
arbitrary rational functions of an auxiliary complex parameter. They are
constructed using the so called `monodromy transform' approach and our new
method for the solution of the linear singular integral equation form of the
reduced Einstein equations. The solutions presented, which describe
inhomogeneous cosmological models or gravitational and electromagnetic waves
and their interactions, include a number of important known solutions as
particular cases.


title: Wormholes in Simplicial Minisuperspace

abstract:
  Using simplicial minisuperspace techniques we obtain a wormhole
configuration, capable of modelling both a throat between two equal Euclidean
and Lorentzian universes. Computing the wavefunction associated to such
configuration we conclude that for Planck-size Euclidean wormholes there is a
prediction of a finite non-vanishing radius of their throat, even in the
absence of matter. The wavefunction associated to their Lorentzian counterparts
predicts the growth of the wormhole's throat as the two Lorentzian universes
expand.


title: Numerical Relativity and Inhomogeneous Cosmologies

abstract:
  In this work numerical methods for solving Einstein's equations are developed
and applied to the study of inhomogeneous cosmological models.
  A two-dimensional computer code is described which implements two advanced
numerical methods: LeVeque's multi-dimensional high-resolution integration
scheme which allows accurate evolution of solutions containing discontinuities
or steep gradients, and an adaptive mesh refinement (AMR) algorithm which
enables the local resolution of a simulation to vary dynamically in response to
the behaviour of the evolved solution.
  A family of hyperbolic formulations of the Einstein equations is derived by
generalization of an evolution system proposed by Frittelli and Reula, and
numerical solutions produced using these formulations are compared to solutions
produced using alternative reductions of the evolutions equations. Properties
of the harmonic time slicing condition are also investigated, and analytic and
numerical results concerning the formation of coordinate singularities are
presented.
  Numerical simulations are performed of planar cosmologies, described using
Gowdy's reduction of the Einstein equations, and U(1)-symmetric cosmologies,
described using Moncrief's reduction of the Einstein equations, with the
spacetimes in both cases being vacuum. Numerical studies follow up on the work
of Berger, Moncrief and co-workers, with attention being focused on the
small-scale features that develop in the models and the behaviour of linear and
nonlinear gravitational waves.


title:
The Consistent Newtonian Limit of Einstein's Gravity with a Cosmological
  Constant

abstract:
  We derive the `exact' Newtonian limit of general relativity with a positive
cosmological constant $\Lambda$. We point out that in contrast to the case with
$\Lambda = 0 $, the presence of a positive $\Lambda$ in Einsteins's equations
enforces, via the condition $| \Phi | \ll 1$, on the potential $\Phi$, a range
${\cal R}_{max}(\Lambda) \gg r \gg {\cal R}_{min} (\Lambda)$, within which the
Newtonian limit is valid. It also leads to the existence of a maximum mass,
${\cal M}_{max}(\Lambda)$. As a consequence we cannot put the boundary
condition for the solution of the Poisson equation at infinity. A boundary
condition suitably chosen now at a finite range will then get reflected in the
solution of $\Phi$ provided the mass distribution is not spherically symmetric.


title: An extreme critical space-time: echoing and black-hole perturbations

abstract:
  A homothetic, static, spherically symmetric solution to the massless
Einstein- Klein-Gordon equations is described. There is a curvature singularity
which is central, null, bifurcate and marginally trapped. The space-time is
therefore extreme in the sense of lying at the threshold between black holes
and naked singularities, just avoiding both. A linear perturbation analysis
reveals two types of dominant mode. One breaks the continuous self-similarity
by periodic terms reminiscent of discrete self-similarity, with echoing period
within a few percent of the value observed numerically in near-critical
gravitational collapse. The other dominant mode explicitly produces a black
hole, white hole, eternally naked singularity or regular dispersal, the latter
indicating that the background is critical. The black hole is not static but
has constant area, the corresponding mass being linear in the perturbation
amplitudes, explicitly determining a unit critical exponent. It is argued that
a central null singularity may be a feature of critical gravitational collapse.


title: Another exact inflationary solution

abstract:
  A new closed-form inflationary solution is given for a hyperbolic interaction
potential. The method used to arrive at this solution is outlined as it appears
possible to generate additional sets of equations which satisfy the model. In
addition a new form of decaying cosmological constant is presented.


title:
Generalized Laws of Black Hole Thermodynamics and Quantum Conservation
  Laws on Hawking Radiation Process

abstract:
  Four classical laws of black hole thermodynamics are extended from exterior
(event) horizon to interior (Cauchy) horizon. Especially, the first law of
classical thermodynamics for Kerr-Newman black hole (KNBH) is generalized to
those in quantum form. Then five quantum conservation laws on the KNBH
evaporation effect are derived in virtue of thermodynamical equilibrium
conditions. As a by-product, Bekenstein-Hawking's relation $ S=A/4 $ is exactly
recovered.


title: Geometric Cone Surfaces and (2+1)- Gravity coupled to Particles

abstract:
  We introduce the (2+1)-spacetimes with compact space of genus g and with r
gravitating particles which arise by ``Minkowskian suspensions of flat or
hyperbolic cone surfaces'', by ``distinguished deformations'' of hyperbolic
suspensions and by ``patchworking'' of suspensions. Similarly to the
matter-free case, these spacetimes have nice properties with respect to the
canonical Cosmological Time Function. When the values of the masses are
sufficiently large and the cone points are suitably spaced, the distinguished
deformations of hyperbolic suspensions determine a relevant open subset of the
full parameter space; this open subset is homeomorphic to the product of an
Euclidean space of dimension 6g-6+2r with an open subset of the Teichm\"uller
Space of Riemann surfaces of genus g with r punctures. By patchworking of
suspensions one can produce examples of spacetimes which are not distinguished
deformations of any hyperbolic suspensions, although they have the same masses;
in fact, we will guess that they belong to different connected components of
the parameter space.


title: Gravitational energy as Noether charge

abstract:
  A definition of gravitational energy is proposed for any theory described by
a diffeomorphism-invariant Lagrangian. The mathematical structure is a Noether-
current construction of Wald involving the boundary term in the action, but
here it is argued that the physical interpretation of current conservation is
conservation of energy. This leads to a quasi-local energy defined for compact
spatial surfaces. The energy also depends on a vector generating a flow of
time. Angular momentum may be similarly defined, depending on a choice of axial
vector. For Einstein gravity: for the usual vector generating asymptotic time
translations, the energy is the Bondi energy; for a stationary Killing vector,
the energy is the Komar energy; in spherical symmetry, for the Kodama vector,
the energy is the Misner-Sharp energy. In general, the lack of a preferred time
indicates the lack of a preferred energy, reminiscent of the energy-time
duality of quantum theory.


title: Hypergravity and Categorical Feynmanology

abstract:
  We propose a new line of attack to create a finite quantum theory which
includes general relativity and (perhaps) the standard model in its low energy
limit. The theory would emerge from the categorical approach. A structure is
observed on the category of unitary representations of the lorentz group which
we call hypergravity. This, combined with a study of the relationship between
Feynman diagrams and words in tensor categories, leads to the proposal.


title:
Fuchsian analysis of singularities in Gowdy spacetimes beyond
  analyticity

abstract:
  Fuchsian equations provide a way of constructing large classes of spacetimes
whose singularities can be described in detail. In some of the applications of
this technique only the analytic case could be handled up to now. This paper
develops a method of removing the undesirable hypothesis of analyticity. This
is applied to the specific case of the Gowdy spacetimes in order to show that
analogues of the results known in the analytic case hold in the smooth case. As
far as possible the likely strengths and weaknesses of the method as applied to
more general problems are displayed.


title:
Feynman Diagrams of Generalized Matrix Models and the Associated
  Manifolds in Dimension 4

abstract:
  The problem of constructing a quantum theory of gravity has been tackled with
very different strategies, most of which relying on the interplay between ideas
from physics and from advanced mathematics. On the mathematical side, a central
role is played by combinatorial topology, often used to recover the space-time
manifold from the other structures involved. An extremely attractive
possibility is that of encoding all possible space-times as specific Feynman
diagrams of a suitable field theory. In this work we analyze how exactly one
can associate combinatorial 4-manifolds to the Feynman diagrams of certain
tensor theories.


title: Variational dynamics in open spacetimes

abstract:
  We study the effect of non-vanishing surface terms at spatial infinity on the
dynamics of a scalar field in an open FLRW spacetime. Starting from the
path-integral formulation of quantum field theory we argue that classical
physics is described by field configurations which extremize the action
functional in the space of field configurations for which the variation of the
action is well defined. Since these field configurations are not required to
vanish outside a bounded domain, there is generally a non-vanishing
contribution of a surface term to the variation of the action. We then
investigate whether this surface term has an effect on the dynamics of the
action-extremizing field configurations. This question appears to be
surprisingly nontrivial in the case of the open FLRW geometry, since surface
terms tend to grow as fast as volume terms in the infinite volume limit. We
find that surface terms can be important for the dynamics of the field at a
classical and at a quantum level, when there are supercurvature perturbations.


title:
On the Mass Neutrino Phase calculations along the geodesic line and the
  null line

abstract:
  On the mass neutrino phase calculations along both the particle geodesic line
and the photon null line, there exists a double counting error--factor of 2
when comparing the geodesic phase with the null phase. For the mass neutrino
propagation in the flat spacetime, we study the neutrino interference phase
calculation in the Minkowski diagram and find that the double counting effect
originates from despising the velocity difference between two mass neutrinos.
Moreover, we compare the phase calculations among the same energy description,
the same momentum description and same velocity description by means of the
Minkowski diagram, and obtain the practical equivalence of these three
descriptions. Further, in the curved spacetime, we also prove the existence of
the double counting of the geodesic phase to the null phase.


title:
The general treatment of high/low energy particle interference phase in
  a gravitational field

abstract:
  The interference phase of the high energy mass neutrinos and the low energy
thermal neutrons in a gravitational field are studied. For the mass neutrinos,
we obtain that the phase calculated along the null is equivalent to the half
phase along the geodesic in the high energy limit, which means that the correct
relative phase of the mass neutrinos is either the null phase or the half
geodesic phase.
  Further we point out the importance of the energy condition in calculating
the mass neutrino interference phase. Moreover, we apply the covariant phase to
the calculation of the thermal neutron interference phase, and obtain the
consistent result with that exploited in COW experiment.


title: Links between gravity and dynamics of quantum liquids

abstract:
  We consider the Landau-Khalatnikov two-fluid hydrodynamics of superfluid
liquid as an effective theory, which provides a self-consistent analog of
Einstein equations for gravity and matter.