title:
Hamiltonian, Energy and Entropy in General Relativity with
  Non-Orthogonal Boundaries

abstract:
  A general recipe to define, via Noether theorem, the Hamiltonian in any
natural field theory is suggested. It is based on a Regge-Teitelboim-like
approach applied to the variation of Noether conserved quantities. The
Hamiltonian for General Relativity in presence of non-orthogonal boundaries is
analysed and the energy is defined as the on-shell value of the Hamiltonian.
The role played by boundary conditions in the formalism is outlined and the
quasilocal internal energy is defined by imposing metric Dirichlet boundary
conditions. A (conditioned) agreement with previous definitions is proved. A
correspondence with Brown-York original formulation of the first principle of
black hole thermodynamics is finally established.


title: Quantum Inequalities for the Electromagnetic Field

abstract:
  A quantum inequality for the quantized electromagnetic field is developed for
observers in static curved spacetimes. The quantum inequality derived is a
generalized expression given by a mode function expansion of the four-vector
potential, and the sampling function used to weight the energy integrals is
left arbitrary up to the constraints that it be a positive, continuous function
of unit area and that it decays at infinity. Examples of the quantum inequality
are developed for Minkowski spacetime, Rindler spacetime and the Einstein
closed universe.


title:
Critical phenomena at the threshold of black hole formation for
  collisionless matter in spherical symmetry

abstract:
  We perform a numerical study of the critical regime at the threshold of black
hole formation in the spherically symmetric, general relativistic collapse of
collisionless matter. The coupled Einstein-Vlasov equations are solved using a
particle-mesh method in which the evolution of the phase-space distribution
function is approximated by a set of particles (or, more precisely,
infinitesimally thin shells) moving along geodesics of the spacetime.
Individual particles may have non-zero angular momenta, but spherical symmetry
dictates that the total angular momentum of the matter distribution vanish. In
accord with previous work by Rein et al, our results indicate that the critical
behavior in this model is Type I; that is, the smallest black hole in each
parametrized family has a finite mass. We present evidence that the critical
solutions are characterized by unstable, static spacetimes, with non-trivial
distributions of radial momenta for the particles. As expected for Type I
solutions, we also find power-law scaling relations for the lifetimes of
near-critical configurations as a function of parameter-space distance from
criticality.


title: On boundary terms and conformal transformations in curved space-times

abstract:
  We intend to clarify the interplay between boundary terms and conformal
transformations in scalar-tensor theories of gravity. We first consider the
action for pure gravity in five dimensions and show that, on compactifing a la
Kaluza-Klein to four dimensions, one obtains the correct boundary terms in the
Jordan (or String) Frame form of the Brans-Dicke action. Further, we analyze
how the boundary terms change under the conformal transformations which lead to
the Pauli (or Einstein) frame and to the non-minimally coupled massless scalar
field. In particular, we study the behaviour of the total energy in
asymptotically flat space-times as it results from surface terms in the
Hamiltonian formalism.


title:
Accelerated sources in de Sitter spacetime and the insufficiency of
  retarded fields

abstract:
  The scalar and electromagnetic fields produced by the geodesic and uniformly
accelerated discrete charges in de Sitter spacetime are constructed by
employing the conformal relation between de Sitter and Minkowski space.
  A special attention is paid to new effects arising in spacetimes which, like
de Sitter space, have spacelike conformal infinities. Under the presence of
particle and event horizons, purely retarded fields (appropriately defined)
become necessarily singular or even cannot be constructed at the "creation
light cones" -- future light cones of the "points" at which the sources "enter"
the universe. We construct smooth (outside the sources) fields involving both
retarded and advanced effects, and analyze the fields in detail in case of (i)
scalar monopoles, (ii) electromagnetic monopoles, and (iii) electromagnetic
rigid and geodesic dipoles.


title: Parametric Oscillatory Instability in Fabry-Perot (FP) Interferometer

abstract:
  We present an approximate analysis of a nonlinear effect of parametric
oscillatory instability in FP interferometer. The basis for this effect is the
excitation of the additional (Stokes) optical mode and of the mirror's elastic
mode when the optical energy stored in the FP resonator main mode exceeds the
certain threshold. This effect is undesirable in laser gravitational wave
antennae because it may create a specific upper limit for the value of energy
stored in FP resonator. In order to avoid it the detailed analysis of the
mirror's elastic modes and FP resonator optical modes structure is necessary.


title: Energy and angular momentum flow into a black hole in a binary

abstract:
  As a black hole in a binary spirals in gradually from large separation,
energy and angular momentum flow not only to infinity but also into or out of
the hole. In addition, the hole's horizon area increases slowly during this
process. In this paper, the changes in the black hole's mass, spin, and horizon
area during inspiral are calculated for a hole in a circular binary with a
companion body of possibly comparable mass. When the binary is composed of
equal-mass black holes that have spins aligned with the orbital angular
momentum and are rapidly rotating (with spins 99.8 percent of their maximal
values), it is found that the fractional increase in the surface area of each
hole's horizon is one percent by the time the binary spirals down to a
separation b of 6M (where M is the binary's total mass), and seven percent down
to b=2M. The flow of energy and angular momentum into the black holes' horizons
changes the number of gravitational-wave cycles in the LIGO band by no more
than a tenth of a cycle by the time the binary reaches b=2M. The results
obtained in this paper are relevant for the detection and analysis of
gravitational waves from binary systems containing a black hole.


title:
Detection in coincidence of gravitational wave bursts with a network of
  interferometric detectors (I): Geometric acceptance and timing

abstract:
  Detecting gravitational wave bursts (characterised by short durations and
poorly modelled waveforms) requires to have coincidences between several
interferometric detectors in order to reject non-stationary noise events. As
the wave amplitude seen in a detector depends on its location with respect to
the source direction and as the signal to noise ratio of these bursts are
expected to be low, coincidences between antennas may not be so likely. This
paper investigates this question from a statistical point of view by using a
simple model of a network of detectors; it also estimates the timing precision
of a detection in an interferometer which is an important issue for the
reconstruction of the source location, based on time delays.


title: Ruling Out Chaos in Compact Binary Systems

abstract:
  We investigate the orbits of compact binary systems during the final inspiral
period before coalescence by integrating numerically the second-order
post-Newtonian equations of motion. We include spin-orbit and spin-spin
coupling terms, which, according to a recent study by Levin [J. Levin, Phys.
Rev. Lett. 84, 3515 (2000)], may cause the orbits to become chaotic. To examine
this claim, we study the divergence of initially nearby phase-space
trajectories and attempt to measure the Lyapunov exponent gamma. Even for
systems with maximally spinning objects and large spin-orbit misalignment
angles, we find no chaotic behavior. For all the systems we consider, we can
place a strict lower limit on the divergence time t_L=1/gamma that is many
times greater than the typical inspiral time, suggesting that chaos should not
adversely affect the detection of inspiral events by upcoming
gravitational-wave detectors.


title: 4-Dimensional optics, an alternative to relativity

abstract:
  The starting point of this work is the principle that all movement of
particles and photons in the observable Universe must follow geodesics of a
4-dimensional space where time intervals are always a measure of geodesic arc
lengths, i.e. $c^2(\mathrm{d}t)^2 = g_{\alpha \beta} \mathrm{d} x^\alpha
\mathrm{d} x^\beta$, with $c$ is the speed of light in vacuum, $t$ time,
$g_{\alpha \beta}$ and the metric tensor; $x^\alpha$ represents any of 4 space
coordinates. The last 3 coordinates $(\alpha = 1,2,3)$ are immediately
associated with the usual physical space coordinates, while the first
coordinate $(\alpha=0)$ is later found to be related to \emph{proper time}. The
work shows that this principle is applicable in several important situations
and suggests that the underlying principle can, in fact, be used universally.
Starting with special relativity it is shown that there is perfect mapping
between the geodesics on Minkowski space-time and on this alternative space.
The discussion than follows through light propagation in a refractive medium,
and some cases of gravitation, including Schwartzschild's outer metric. The
last part of the presentation is dedicated to electromagnetic interaction and
Maxwell's equations, showing that there is a particular solution where one of
the space dimensions is eliminated and the geodesics become equivalent to light
rays in geometrical optics. A very brief discussion is made of the implications
for wave-particle duality and quantization.


title:
Frequency-dependent rigidity in large-scale interferometric
  gravitational-wave detectors

abstract:
  Electromagnetic rigidity which exists in large-scale optical resonators if
pumping frequency is detuned from the eigenfrequency of resonator have
sophisticated spectral dependence which allows to obtain sensitivity better
than the Standard Quantum Limits both for the free test mass and the harmonic
oscillator.


title: Big bang of the brane universe

abstract:
  Big bang of the Friedmann-Robertson-Walker (FRW)-brane universe is studied.
In contrast to the spacelike initial singularity of the usual FRW universe, the
initial singularity of the FRW-brane universe is point-like from the viewpoint
of causality including gravitational waves propagating in the bulk. Existence
of null singularities (seam singuralities) is also shown in the flat and open
FRW-brane universe models.


title: Space-time quantum solves three experimental paradoxes

abstract:
  I show that a Planck-scale deformation of the relativistic dispersion
relation, which has been independently considered in the quantum-gravity
literature, can explain the surprising results of three classes of experiments:
(1) observations of cosmic rays above the expected GZK limit, (2) observations
of multi-TeV photons from the BL Lac object Markarian 501, (3) studies of the
longitudinal development of the air showers produced by ultra-high-energy
hadronic particles. Experiments now in preparation, such as the ones planned
for the GLAST space telescope, will provide an independent test of this
solution of the three experimental paradoxes.


title: Shell crossing in generalized Tolman-Bondi spacetimes

abstract:
  We study the occurrence of shell crossing in spherical weakly charged dust
collapse in the presence of a non-vanishing cosmological constant. We find that
shell crossing always occurs from generic time-symmetric regular initial data,
near the center of the matter configuration. For non-time-symmetric initial
data, the occurrence---or lack thereof---of shell crossing is determined by the
initial velocity profile, for a given mass and charge distribution. Physically
reasonable initial data inevitably leads to shell crossing (near the center)
before the minimum bounce radius is reached.


title:
On the interpretation of cylindrically symmetric Levi-Civita spacetime
  for 0<sigma<infinity

abstract:
  We study Levi-Civita metric for values of its sigma parameter in the range 0<
sigma<infinity. We show that the value sigma=1/2 makes the axial and angular
coordinates switch meaning. We present its geodesics and a physical source
satisfying the energy conditions for all the range of sigma. This source allows
us to obtain an energy per unit length which agrees with the behaviour of the
geodesics and the fact that the solution has no event horizon.


title:
Projective Formalism and Some Methods from Algebraic Geometry in the
  Theory of Gravitation

abstract:
  The purpose of this paper is to propose the implementation of some methods
from algebraic geometry in the theory of gravitation, and more especially in
the variational formalism. It has been assumed that the metric tensor depends
on two vector fields, defined on a manifold, and also that the gravitational
Lagrangian depends on the metric tensor and its first and second differentials
(instead on the partial or covariant derivatives, as usually assumed).
  Assuming also different operators of variation and differentiation, it has
been shown that the first variation of the gravitational Lagrangian can be
represented as a third-rank polynomial in respect to the variables, defined in
terms of the variated or differentiated vector fields. Therefore, the solution
of the variational problem is found to be equivalent to finding all the
variables - elements of an algebraic variety, which satisfy the algebraic
equation.


title: Current Trends in Mathematical Cosmology

abstract:
  We present an elementary account of mathematical cosmology through a series
of important unsolved problems. We introduce the fundamental notion of `a
cosmology' and focus on the issue of singularities as a theme unifying many
current, seemingly unrelated trends of this subject. We discuss problems
associated with the definition and asymptotic structure of the notion of
cosmological solution and also problems related to the qualification of
approximations and to the ranges of validity of given cosmologies.


title: Faster-than-c signals, special relativity, and causality

abstract:
  Motivated by the recent attention on superluminal phenomena, we investigate
the compatibility between faster-than-c propagation and the fundamental
principles of relativity and causality. We first argue that special relativity
can easily accommodate -- indeed, does not exclude -- faster-than-c signalling
at the kinematical level. As far as causality is concerned, it is impossible to
make statements of general validity, without specifying at least some features
of the tachyonic propagation. We thus focus on the Scharnhorst effect
(faster-than-c photon propagation in the Casimir vacuum), which is perhaps the
most plausible candidate for a physically sound realization of these phenomena.
We demonstrate that in this case the faster-than-c aspects are ``benign'' and
constrained in such a manner as to not automatically lead to causality
violations.


title: Conventional Forces can Explain the Anomalous Acceleration of Pioneer 10

abstract:
  Anderson, et al. find the measured trajectories of Pioneer 10 and 11
spacecraft deviate from the trajectories computed from known forces acting on
them. This unmodelled acceleration (and the less well known, but similar,
unmodelled torque) can be accounted for by non-isotropic radiation of
spacecraft heat. Various forms of non-isotropic radiation were proposed by
Katz, Murphy, and Scheffer, but Anderson, et al. felt that none of these could
explain the observed effect. This paper calculates the known effects in more
detail and considers new sources of radiation, all based on spacecraft
construction. These effects are then modelled over the duration of the
experiment. The model reproduces the acceleration from its appearance at a
heliocentric distance of 5 AU to the last measurement at 71 AU to within 10
percent. However, it predicts a larger decrease in acceleration between
intervals I and III of the Pioneer 10 observations than is observed. This is a
2 sigma discrepancy from the average of the three analyses (SIGMA, CHASMP, and
Markwardt). A more complex (but more speculative) model provides a somewhat
better fit. Radiation forces can also plausibly explain the previously
unmodelled torques, including the spindown of Pioneer 10 that is directly
proportional to spacecraft bus heat, and the slow but constant spin-up of
Pioneer 11. In any case, by accounting for the bulk of the acceleration, the
proposed mechanism makes it much more likely that the entire effect can be
explained without the need for new physics.


title:
Universe Models with a Variable Cosmological "Constant" and a "Big
  Bounce"

abstract:
  We present a rich class of exact solutions which contains radiation-dominated
and matter-dominated models for the early and late universe. They include a
variable cosmological ``constant'' which is derived from a higher dimension and
manifests itself in spacetime as an energy density for the vacuum. This is in
agreement with observational data and is compatible with extensions of general
relativity to string and membrane theory. Our solutions are also typified by a
non-singular ``big bounce'' (as opposed to a singular big bang), where matter
is created as in inflationary cosmology.


title:
Decay Rates and Probability Estimates for Massive Dirac Particles in the
  Kerr-Newman Black Hole Geometry

abstract:
  The Cauchy problem is considered for the massive Dirac equation in the
non-extreme Kerr-Newman geometry, for smooth initial data with compact support
outside the event horizon and bounded angular momentum. We prove that the Dirac
wave function decays in L^\infty_loc at least at the rate t^{-5/6}. For generic
initial data, this rate of decay is sharp. We derive a formula for the
probability p that the Dirac particle escapes to infinity. For various
conditions on the initial data, we show that p=0,1 or 0<p<1. The proofs are
based on a refined analysis of the Dirac propagator constructed in
gr-qc/0005088.


title:
A new stationary cylindrically symmetric solution of the Einstein's
  equations admiting Time machine

abstract:
  In this article a new stationary cylindrically symmetric solution of the
Einstein's field equations with cosmological constant and Time machine is
given. The garavitational field is created by ideal liquid with three massless
scalar fields or by ideal liquid with electric-magnetic field and massless
scalar field.


title: Asymptotic symmetries on Killing horizons

abstract:
  We investigate asymptotic symmetries regularly defined on spherically
symmetric Killing horizons in the Einstein theory with or without the
cosmological constant. Those asymptotic symmetries are described by asymptotic
Killing vectors, along which the Lie derivatives of perturbed metrics vanish on
a Killing horizon. We derive the general form of asymptotic Killing vectors and
find that the group of the asymptotic symmetries consists of rigid O(3)
rotations of a horizon two-sphere and supertranslations along the null
direction on the horizon, which depend arbitrarily on the null coordinate as
well as the angular coordinates. By introducing the notion of asymptotic
Killing horizons, we also show that local properties of Killing horizons are
preserved under not only diffeomorphisms but also non-trivial transformations
generated by the asymptotic symmetry group. Although the asymptotic symmetry
group contains the $\mathit{Diff}(S^1)$ subgroup, which results from the
supertranslations dependent only on the null coordinate, it is shown that the
Poisson bracket algebra of the conserved charges conjugate to asymptotic
Killing vectors does not acquire non-trivial central charges. Finally, by
considering extended symmetries, we discuss that unnatural reduction of the
symmetry group is necessary in order to obtain the Virasoro algebra with
non-trivial central charges, which will not be justified when we respect the
spherical symmetry of Killing horizons.


title:
Reduced Total Energy Requirements for a Modified Alcubierre Warp Drive
  Spacetime

abstract:
  It can be shown that negative energy requirements within the Alcubierre
spacetime can be greatly reduced when one introduces a lapse function into the
Einstein tensor. Thereby reducing the negative energy requirements of the warp
drive spacetime arbitrarily as a function of A(ct,r_s). With this function new
quantum inequality restrictions are investigated in a general form. Finally a
pseudo method for controlling a warp bubble at a velocity greater than that of
light is presented.


title:
Quasi-normal modes of toroidal, cylindrical and planar black holes in
  anti-de Sitter spacetimes: scalar, electromagnetic and gravitational
  perturbations

abstract:
  We study the quasi-normal modes (QNM) of scalar, electromagnetic and
gravitational perturbations of black holes in general relativity whose horizons
have toroidal, cylindrical or planar topology in an asymptotically anti-de
Sitter (AdS) spacetime. The associated quasinormal frequencies describe the
decay in time of the corresponding test field in the vicinities of the black
hole. In terms of the AdS/CFT conjecture, the inverse of the frequency is a
measure of the dynamical timescale of approach to thermal equilibrium of the
corresponding conformal field theory.


title:
Physical aspects of naked singularity explosion - How does a naked
  singularity explode? --

abstract:
  The behaviors of quantum stress tensor for the scalar field on the classical
background of spherical dust collapse is studied. In the previous works
diverging flux of quantum radiation was predicted. We use the exact expressions
in a 2D model formulated by Barve et al. Our present results show that the back
reaction does not become important during the semiclassical phase. The
appearance of the naked singularity would not be affected by this quantum field
radiation. To predict whether the naked singularity explosion occurs or not we
need the theory of quantum gravity. We depict the generation of the diverging
flux inside the collapsing star. The quantum energy is gathered around the
center positively. This would be converted to the diverging flux along the
Cauchy horizon. The ingoing negative flux crosses the Cauchy horizon. The
intensity of it is divergent only at the central naked singularity. This
diverging negative ingoing flux is balanced with the outgoing positive
diverging flux which propagates along the Cauchy horizon. After the replacement
of the naked singularity to the practical high density region the instantaneous
diverging radiation would change to more milder one with finite duration.


title: A note on wavemap-tensor cosmologies

abstract:
  We examine theories of gravity which include finitely many coupled scalar
fields with arbitrary couplings to the curvature (wavemaps). We show that the
most general scalar-tensor $\sigma$-model action is conformally equivalent to
general relativity with a minimally coupled wavemap with a particular target
metric. Inflation on the source manifold is then shown to occur in a novel way
due to the combined effect of arbitrary curvature couplings and wavemap
self-interactions. A new interpretation of the conformal equivalence theorem
proved for such `wavemap-tensor' theories through brane-bulk dynamics is also
discussed.


title: Nonthermal radiation of rotating black holes

abstract:
  Nonthermal radiation of a Kerr black hole is considered as tunneling of
created particles through an effective Dirac gap. In the leading semiclassical
approximation this approach is applicable to bosons as well. Our semiclassical
results for photons and gravitons do not contradict those obtained previously.
For neutrinos the result of our accurate quantum mechanical calculation is
about two times larger than the previous one.


title: Singularity avoidance by collapsing shells in quantum gravity

abstract:
  We discuss a model describing exactly a thin spherically symmetric shell of
matter with zero rest mass. We derive the reduced formulation of this system in
which the variables are embeddings, their conjugate momenta, and Dirac
observables. A non-perturbative quantum theory of this model is then
constructed, leading to a unitary dynamics. As a consequence of unitarity, the
classical singularity is fully avoided in the quantum theory.


title:
Sensitivity of spherical gravitational-wave detectors to a stochastic
  background of non-relativistic scalar radiation

abstract:
  We analyze the signal-to-noise ratio for a relic background of scalar
gravitational radiation composed of massive, non-relativistic particles,
interacting with the monopole mode of two resonant spherical detectors. We find
that the possible signal is enhanced with respect to the differential mode of
the interferometric detectors. This enhancement is due to: {\rm (a)} the
absence of the signal suppression, for non-relativistic scalars, with respect
to a background of massless particles, and {\rm (b)} for flat enough spectra, a
growth of the signal with the observation time faster than for a massless
stochastic background.


title:
A One-Parameter Family of Time-Symmetric Initial Data for the Radial
  Infall of a Particle into a Schwarzschild Black Hole

abstract:
  A one-parameter family of time-symmetric initial data for the radial infall
of a particle into a Schwarzschild black hole is constructed within the
framework of black-hole perturbation theory. The parameter measures the amount
of gravitational radiation present on the initial spacelike surface. These
initial data sets are then evolved by integrating the Zerilli-Moncrief wave
equation in the presence of the particle. Numerical results for the
gravitational waveforms and their power spectra are presented; we show that the
choice of initial data strongly influences the waveforms, both in their shapes
and their frequency content. We also calculate the total energy radiated by the
particle-black-hole system, as a function of the initial separation between the
particle and the black hole, and as a function of the choice of initial data.
Our results confirm that for large initial separations, a conformally-flat
initial three-geometry minimizes the initial gravitational-wave content, so
that the total energy radiated is also minimized. For small initial
separations, however, we show that the conformally-flat solution no longer
minimizes the energy radiated.


title:
Solution generating in scalar-tensor theories with a massless scalar
  field and stiff perfect fluid as a source

abstract:
  We present a method for generating solutions in some scalar-tensor theories
with a minimally coupled massless scalar field or irrotational stiff perfect
fluid as a source. The method is based on the group of symmetries of the
dilaton-matter sector in the Einstein frame. In the case of Barker's theory the
dilaton-matter sector possesses SU(2) group of symmetries. In the case of
Brans-Dicke and the theory with "conformal coupling", the dilaton- matter
sector has $SL(2,R)$ as a group of symmetries. We describe an explicit
algorithm for generating exact scalar-tensor solutions from solutions of
Einstein-minimally-coupled-scalar-field equations by employing the nonlinear
action of the symmetry group of the dilaton-matter sector. In the general case,
when the Einstein frame dilaton-matter sector may not possess nontrivial
symmetries we also present a solution generating technique which allows us to
construct exact scalar-tensor solutions starting with the solutions of
Einstein-minimally-coupled-scalar-field equations. As an illustration of the
general techniques, examples of explicit exact solutions are constructed. In
particular, we construct inhomogeneous cosmological scalar-tensor solutions
whose curvature invariants are everywhere regular in space-time. A
generalization of the method for scalar-tensor-Maxwell gravity is outlined.


title:
Gravitational lensing in spherically symmetric static spacetimes with
  centrifugal force reversal

abstract:
  In Schwarzschild spacetime the value $r=3m$ of the radius coordinate is
characterized by three different properties: (a) there is a ``light sphere'',
(b) there is ``centrifugal force reversal'', (c) it is the upper limiting
radius for a non-transparent Schwarschild source to act as a gravitational lens
that produces infinitely many images. In this paper we prove a theorem to the
effect that these three properties are intimately related in {\em any}
spherically symmetric static spacetime. We illustrate the general results with
some examples including black-hole spacetimes and Morris-Thorne wormholes.


title: Local Prescribed Mean Curvature foliations in cosmological spacetimes

abstract:
  A theorem about local in time existence of spacelike foliations with
prescribed mean curvature in cosmological spacetimes will be proved. The time
function of the foliation is geometrically defined and fixes the diffeomorphism
invariance inherent in general foliations of spacetimes. Moreover, in contrast
to the situation of the more special constant mean curvature foliations, which
play an important role in the global analysis of spacetimes, this theorem
overcomes the existence problem arising from topological restrictions for
surfaces of constant mean curvature.


title: Quantization of static space-times

abstract:
  A 4-dimensional Lorentzian static space-time is equivalent to 3-dimensional
Euclidean gravity coupled to a massless Klein-field. By canonically quantizing
the coupling model in the framework of loop quantum gravity, we obtain a
quantum theory which actually describes quantized static space-times. The
Kinematical Hilbert space is the product of the Hilbert space of gravity with
that of imaginary scalar fields. It turns out that the Hamiltonian constraint
of the 2+1 model corresponds to a densely defined operator in the underlying
Hilbert space, and hence it is finite without renormalization. As a new point
of view, this quantized model might shed some light on a few physical problems
concerning quantum gravity.


title: Isotropic singularities in shear-free perfect fluid cosmologies

abstract:
  We investigate barotropic perfect fluid cosmologies which admit an isotropic
singularity. From the General Vorticity Result of Scott, it is known that these
cosmologies must be irrotational. In this paper we prove, using two different
methods, that if we make the additional assumption that the perfect fluid is
shear-free, then the fluid flow must be geodesic. This then implies that the
only shear-free, barotropic, perfect fluid cosmologies which admit an isotropic
singularity are the FRW models.


title:
Scalar field induced oscillations of neutron stars and gravitational
  collapse

abstract:
  We study the interaction of massless scalar fields with self-gravitating
neutron stars by means of fully dynamic numerical simulations of the
Einstein-Klein-Gordon perfect fluid system. Our investigation is restricted to
spherical symmetry and the neutron stars are approximated by relativistic
polytropes. Studying the nonlinear dynamics of isolated neutron stars is very
effectively performed within the characteristic formulation of general
relativity, in which the spacetime is foliated by a family of outgoing light
cones. We are able to compactify the entire spacetime on a computational grid
and simultaneously impose natural radiative boundary conditions and extract
accurate radiative signals. We study the transfer of energy from the scalar
field to the fluid star. We find, in particular, that depending on the
compactness of the neutron star model, the scalar wave forces the neutron star
either to oscillate in its radial modes of pulsation or to undergo
gravitational collapse to a black hole on a dynamical timescale. The radiative
signal, read off at future null infinity, shows quasi-normal oscillations
before the setting of a late time power-law tail.


title: Clasical solids dynamics as 4D statics of elastic strings

abstract:
  Variational principle for a solid in classical mechanics is formulated in
terms of a thin elastic 4D bar strain in Minkowsky events space of special
relativity. It is shown, that the sum of elastic 4-energies of weak twist and
bending under some identifications takes the form of classical non-relativistic
action for a solids dynamics. The necessary conditions on 4D bar parameters and
elastic constants, providing validity of Newton mechanics, are found.


title: Non-radial null geodesics in spherical dust collapse

abstract:
  The issue of the local visibility of the shell-focussing singularity in
marginally bound spherical dust collapse is considered from the point of view
of the existence of future-directed null geodesics with angular momentum which
emanate from the singularity. The initial data (i.e. the initial density
profile) at the onset of collapse is taken to be of class $C^3$. Simple
necessary and sufficient conditions for the existence of a naked singularity
are derived in terms of the data. It is shown that there exist future-directed
non-radial null geodesics emanating from the singularity if and only if there
exist future-directed radial null geodesics emanating from the singularity.
This result can be interpreted as indicating the robustness of previous results
on radial geodesics, with respect to the presence of angular momentum.


title: The thin string limit of Cosmic Strings coupled to gravity

abstract:
  The thin string limit of Cosmic Strings is investigated using a description
in terms of Colombeau's theory of nonlinear generalised functions. It is shown
that in this description the energy-momentum tensor has a well defined thin
string limit. Furthermore the deficit angle of the conical spacetime that one
obtains in the limit may be given in terms of the distributional
energy-momentum tensor. On the other hand it is only in the special case of
critical coupling that the energy-momentum tensor defined in the Colombeau
algebra is associated to a conventional distribution. The asymptotics of both
the matter and gravitational field are investigated in the thin string limit
and it is shown how this leads to the `conical approximation' which is valid
outside the inner core of the string.


title: Is There a 'Conservation of Information Law' for the Universe?

abstract:
  What are the implications if the total 'information' in the universe is
conserved? Black holes might be 'logic gates' recomputing the 'lost
information' from incoming 'signals' from outside their event horizons into
outgoing 'signals' representing evaporative or radiative decay 'products' of
the reconfiguration process of the black hole quantum logic 'gate'. Apparent
local imbalances in the information flow can be corrected by including the
effects of the coupling of the vacuum 'reservoir' of information as part of the
total information involved in any evolutionary process. In this way perhaps the
'vacuum' computes the future of the observable universe.


title: Higher dimensional inhomogeneous dust collapse and cosmic censorship

abstract:
  We investigate the occurrence and nature of a naked singularity in the
gravitational collapse of an inhomogeneous dust cloud described by higher
dimensional Tolman-Bondi space-times. The naked singularities are found to be
gravitationally strong in the sense of Tipler. Higher dimensions seem to favour
black holes rather than naked singularities.


title: Stable singularities of wave-fronts in general relativity

abstract:
  A wave-front in a space-time $\cal M$ is a family of null geodesics
orthogonal to a smooth spacelike two-surface in $\cal M$; it is of some
interest to know how a wave-front can fail to be a smoothly immersed surface in
$\cal M$. In this paper we see that the space of null geodesics $\cal N$ of
$\cal M$, considered as a contact manifold, provides a natural setting for an
efficient study of the stable singularities arising in the time evolution of
wave-fronts.


title: Gravitational collapse on the brane: a no-go theorem

abstract:
  We investigate how braneworld gravity affects gravitational collapse and
black hole formation by studying Oppenheimer-Snyder-like collapse on a
Randall-Sundrum type brane. Without making any assumptions about the bulk, we
prove a no-go theorem: the exterior spacetime on the brane cannot be static,
which is in stark contrast with general relativity. We also consider the role
of Kaluza-Klein energy density in collapse, using a toy model.


title: Causal monotonicity, omniscient foliations and the shape of space

abstract:
  What is the shape of space in a spacetime? One way of addressing this issue
is to consider edgeless spacelike submanifolds of the spacetime. An alternative
is to foliate the spacetime by timelike curves and consider the quotient
obtained by identifying points on the same timelike curve. In this article we
investigate each of these notions and obtain conditions such that it yields a
meaningful shape of space. We also consider the relationship between these two
notions and find conditions for the quotient space to be diffeomorphic to any
edgeless spacelike hypersurface. In particular, we find conditions in which
merely local behavior (being spacelike) combined with the correct behavior on
the homotopy level guarantees that a putative shape of space really is
precisely that.


title: Response of VIRGO detectors to pre-big-bang gravitons

abstract:
  The sensitivity achievable by a pair of VIRGO detectors to stochastic and
isotropic gravitational wave backgrounds produced in pre-big-bang models is
discussed in view of the development of a second VIRGO interferometer. We
describe a semi-analytical technique allowing to compute the signal-to-noise
ratio for (monotonic or non-monotonic) logarithmic energy spectra of relic
gravitons of arbitrary slope. We apply our results to the case of two
correlated and coaligned VIRGO detectors and we compute their achievable
sensitivities. We perform our calculations both for the usual case of minimal
string cosmological scenario and in the case of a non-minimal scenario where a
long dilaton dominated phase is present prior to the onset of the ordinary
radiation dominated phase. In this framework, we investigate possible
improvements of the achievable sensitivities by selective reduction of the
thermal contributions (pendulum and pendulum's internal modes) to the noise
power spectra of the detectors. Since a reduction of the shot noise does not
increase significantly the expected sensitivity of a VIRGO pair (in spite of
the relative spatial location of the two detectors) our findings support the
experimental efforts directed towards a substantial reduction of thermal noise.


title: Quintessence as a run-away dilaton

abstract:
  We consider a late-time cosmological model based on a recent proposal that
the infinite-bare-coupling limit of superstring/M-theory exists and has good
phenomenological properties, including a vanishing cosmological constant, and a
massless, decoupled dilaton. As it runs away to $+ \infty$, the dilaton can
play the role of the quintessence field recently advocated to drive the
late-time accelerated expansion of the Universe. If, as suggested by some
string theory examples, appreciable deviations from General Relativity persist
even today in the dark matter sector, the Universe may smoothly evolve from an
initial "focusing" stage, lasting untill radiation--matter equality, to a
"dragging" regime, which eventually gives rise to an accelerated expansion with
frozen $\Omega(\rm{dark energy})/\Omega(\rm{dark matter})$.


title: Ghost spinors, shadow electrons and the Deutsch Multiverse

abstract:
  In this article a new solution of the Einstein-Dirac's equations is
presented. There are ghost spinors, i.e. the stress-energy tensor is equal to
zero and the current of these fields is non-zero vector. Last the ghost
neutrino was found. These ghost spinors and shadow particles of Deutsch are
identified. And in result the ghost spinors have a physical interpretation and
solutions of the field equations for shadow electrons as another shadow
particles are found.


title: A Conserved Bach Current

abstract:
  The Bach tensor and a vector which generates conformal symmetries allow a
conserved four-current to be defined. The Bach four-current gives rise to a
quasilocal two-surface expression for power per luminosity distance in the
Vaidya exterior of collapsing fluid interiors. This is interpreted in terms of
entropy generation.


title:
Non-existence of New Quantum Ergosphere Effect of a Vaidya-type Black
  Hole

abstract:
  Hawking evaporation of Dirac particles and scalar fields in a Vaidya-type
black hole is investigated by the method of generalized tortoise coordinate
transformation. It is shown that Hawking radiation of Dirac particles does not
exist for $P_1, Q_2$ components but for $P_2, Q_1$ components in any
Vaidya-type black holes. Both the location and the temperature of the event
horizon change with time. The thermal radiation spectrum of Dirac particles is
the same as that of Klein-Gordon particles. We demonstrates that there is no
new quantum ergosphere effect in the thermal radiation of Dirac particles in
any spherically symmetry black holes.


title:
Spherically Symmetric solutions in Multidimensional Gravity with the
  SU(2) Gauge Group as the Extra Dimensions

abstract:
  The multidimensional gravity on the principal bundle with the SU(2) gauge
group is considered. The numerical investigation of the spherically symmetric
metrics with the center of symmetry is made. The solution of the gravitational
equations depends on the boundary conditions of the ``SU(2) gauge potential''
(off-diagonal metric components) at the symmetry center and on the type of
symmetry (symmetrical or antisymmetrical) of these potentials. In the chosen
range of the boundary conditions it is shown that there are two types of
solutions: wormhole-like and flux tube. The physical application of such kind
of solutions as quantum handles in a spacetime foam is discussed.


title: Classical Histories in Hamiltonian Systems

abstract:
  The incompatibility between the treatment of time in the classical and in the
quantum theory results in the so-called problem of time in canonical quantum
gravity. For this reason, attempts have been made to devise algorithms of
quantization which accomodate the covariance of the classical theory from the
outset. One of the most prominent of these attempts is based on the notion of
continuous histories (Isham and Linden) in the context of the consistent
histories approach to quantum theory (Griffiths, Omnes, Gell-Mann and Hartle).
By the term continuous histories it is implied that the canonical fields and
the symplectic structure of the theory depend on time as well as space. The aim
of this thesis (in the form it was submitted to the University of London,
February 2000) is to show that, even at the purely classical level, a history
approach has several advantages (compared to its equal-time counterpart) when
it comes to discussing spacetime issues. This is illustrated here by reframing
and generalizing the derivation of geometrodynamics from first principles
(Hojman, Kuchar, Teitelboim) in the language of the history phase space.


title:
Diffeomorphisms as Symplectomorphisms in History Phase Space: Bosonic
  String Model

abstract:
  The structure of the history phase space $\cal G$ of a covariant field system
and its history group (in the sense of Isham and Linden) is analyzed on an
example of a bosonic string. The history space $\cal G$ includes the time map
$\sf T$ from the spacetime manifold (the two-sheet) $\cal Y$ to a
one-dimensional time manifold $\cal T$ as one of its configuration variables. A
canonical history action is posited on $\cal G$ such that its restriction to
the configuration history space yields the familiar Polyakov action. The
standard Dirac-ADM action is shown to be identical with the canonical history
action, the only difference being that the underlying action is expressed in
two different coordinate charts on $\cal G$. The canonical history action
encompasses all individual Dirac-ADM actions corresponding to different choices
$\sf T$ of foliating $\cal Y$. The history Poisson brackets of spacetime fields
on $\cal G$ induce the ordinary Poisson brackets of spatial fields in the
instantaneous phase space ${\cal G}_{0}$ of the Dirac-ADM formalism. The
canonical history action is manifestly invariant both under spacetime
diffeomorphisms Diff$\cal Y$ and temporal diffeomorphisms Diff$\cal T$. Both of
these diffeomorphisms are explicitly represented by symplectomorphisms on the
history phase space $\cal G$. The resulting classical history phase space
formalism is offered as a starting point for projection operator quantization
and consistent histories interpretation of the bosonic string model.


title: Kaluza's theory in generalized coordinates

abstract:
  Maxwell's equations can be obtained in generalized coordinates by considering
the electromagnetic field as an external agent. The work here presented shows
how to obtain the electrodynamics for a charged particle in generalized
coordinates eliminating the concept of external force. Based on Kaluza's
formalism, the one here presented extends the 5x5 metric into a 6x6 space-time
giving enough room to include magnetic monopoles in a very natural way.


title:
Comment on `An extreme critical space-time: echoing and black-hole
  perturbations'

abstract:
  We show that the black hole perturbations of the Hayward static solution to
the massless Einstein-Klein-Gordon equations are actually gauge artifacts
resulting from the linearization of a coordinate transformation.


title:
Strength and genericity of singularities in Tolman-Bondi-de Sitter
  collapse

abstract:
  We study the curvature strength and visibility of the central singularity
arising in Tolman-Bondi-de Sitter collapse. We find that the singularity is
visible and Tipler strong along an infinite number of timelike geodesics,
independently of the initial data, and thus stable against perturbations of the
latter.


title:
Gravity and the Quantum Vacuum Inertia Hypothesis. I. Formalized
  Groundwork for Extension to Gravity

abstract:
  It has been shown [1,2] that the electromagnetic quantum vacuum makes a
contribution to the inertial mass, $m_i$, in the sense that at least part of
the inertial force of opposition to acceleration, or inertia reaction force,
springs from the electromagnetic quantum vacuum. As experienced in a Rindler
constant acceleration frame the electromagnetic quantum vacuum mainfests an
energy-momentum flux which we call the Rindler flux (RF). The RF, and its
relative, Unruh-Davies radiation, both stem from event-horizon effects in
accelerating reference frames. The force of radiation pressure produced by the
RF proves to be proportional to the acceleration of the reference frame, which
leads to the hypothesis that at least part of the inertia of an object should
be due to the interaction of its quarks and electrons with the RF. We
demonstrate that this quantum vacuum inertia hypothesis is consistent with
general relativity (GR) and that it answers a fundamental question left open
within GR, viz. is there a physical mechanism that generates the reaction force
known as weight when a specific non-geodesic motion is imposed on an object?
The quantum vacuum inertia hypothesis provides such a mechanism, since by
assuming the Einstein principle of local Lorentz-invariance (LLI), we can
immediately show that the same RF arises due to curved spacetime geometry as
for acceleration in flat spactime. Thus the previously derived expression for
the inertial mass contribution from the electromagnetic quantum vacuum field is
exactly equal to the corresponding contribution to the gravitational mass,
$m_g$. Therefore, within the electromagnetic quantum vacuum viewpoint proposed
in [1,2], the Newtonian weak equivalence principle, $m_i=m_g$, ensues in a
straightforward manner.


title: On the Space Time of a Galaxy

abstract:
  We present an exact solution of the averaged Einstein's field equations in
the presence of two real scalar fields and a component of dust with spherical
symmetry. We suggest that the space-time found provides the characteristics
required by a galactic model that could explain the supermassive central object
and the dark matter halo at once, since one of the fields constitutes a central
oscillaton surrounded by the dust and the other scalar field distributes far
from the coordinate center and can be interpreted as a halo. We show the
behavior of the rotation curves all along the background. Thus, the solution
could be a first approximation of a ``long exposition photograph'' of a galaxy.


title: Pseudoinstantons in metric-affine field theory

abstract:
  In abstract Yang-Mills theory the standard instanton construction relies on
the Hodge star having real eigenvalues which makes it inapplicable in the
Lorentzian case. We show that for the affine connection an instanton-type
construction can be carried out in the Lorentzian setting. The Lorentzian
analogue of an instanton is a spacetime whose connection is metric compatible
and Riemann curvature irreducible ("pseudoinstanton"). We suggest a
metric-affine action which is a natural generalization of the Yang-Mills action
and for which pseudoinstantons are stationary points. We show that a spacetime
with a Ricci flat Levi-Civita connection is a pseudoinstanton, so the vacuum
Einstein equation is a special case of our theory. We also find another
pseudoinstanton which is a wave of torsion in Minkowski space. Analysis of the
latter solution indicates the possibility of using it as a model for the
neutrino.


title:
Dual Metrics and Non-Generic Supersymmetries for a Class of Siklos
  Spacetimes

abstract:
  The presence of Killing-Yano tensors implies the existence of non-generic
supercharges in spinning point particle theories on curved backgrounds. Dual
metrics are defined through their associated non-degenerate Killing tensors of
valence two. Siklos spacetimes, which are the only non-trivial Einstein spaces
conformal to non-flat pp-waves are investigated in regards to the existence of
their corresponding Killing and Killing-Yano tensors. It is found that under
some restrictions, pp-wave metrics and Siklos spacetimes admit dual metrics and
non-generic supercharges. Possible significance of those dual spacetimes are
discussed.


title:
Family of solutions for axisymmetric electrovacuum Einstein-Maxwell
  field equations

abstract:
  We present a family of solutions for the axisymmetric Plebanski-Demianski
metric and other corresponding reduced metrics. We also present the black hole
characteristics using a new set of parameters for Kerr-Newman metric.


title: Supersymmetric quantum solution for FRW cosmological model with matter

abstract:
  Using technique of supersymmetric quantum mechanics we present new
cosmological quantum solution, in the regime for FRW cosmological model using a
barotropic perfect fluid as matter field.


title:
The State Space of Perturbative Quantum Field Theory in Curved
  Spacetimes

abstract:
  The space of continuous states of perturbative interacting quantum field
theories in globally hyperbolic curved spacetimes is determined. Following
Brunetti and Fredenhagen, we first define an abstract algebra of observables
which contains the Wick-polynomials of the free field as well as their
time-ordered products, and hence, by the well-known rules of perturbative
quantum field theory, also the observables (up to finite order) of interest for
the interacting quantum field theory. We then determine the space of continuous
states on this algebra. Our result is that this space consists precisely of
those states whose truncated n-point functions of the free field are smooth for
all n not equal to two, and whose two-point function has the singularity of a
Hadamard fundamental form. A crucial role in our analysis is played by the
positivity property of states. On the technical side, our proof involves
functional analytic methods, in particular the methods of microlocal analysis.


title: The Principle of Symmetric Criticality in General Relativity

abstract:
  We consider a version of Palais' Principle of Symmetric Criticality (PSC)
that is applicable to the Lie symmetry reduction of Lagrangian field theories.
PSC asserts that, given a group action, for any group-invariant Lagrangian the
equations obtained by restriction of Euler-Lagrange equations to
group-invariant fields are equivalent to the Euler-Lagrange equations of a
canonically defined, symmetry-reduced Lagrangian. We investigate the validity
of PSC for local gravitational theories built from a metric. It is shown that
there are two independent conditions which must be satisfied for PSC to be
valid. One of these conditions, obtained previously in the context of
transverse symmetry group actions, provides a generalization of the well-known
unimodularity condition that arises in spatially homogeneous cosmological
models. The other condition seems to be new. The conditions that determine the
validity of PSC are equivalent to pointwise conditions on the group action
alone. These results are illustrated with a variety of examples from general
relativity. It is straightforward to generalize all of our results to any
relativistic field theory.


title: On the Universality of the Entropy-Area Relation

abstract:
  We present an argument that, for a large class of possible dynamics, a
canonical quantization of gravity will satisfy the Bekenstein-Hawking
entropy-area relation. This result holds for temperatures low compared to the
Planck temperature and for boundaries with areas large compared to Planck area.
We also relate our description, in terms of a grand canonical ensemble, to
previous geometric entropy calculations using area ensembles.


title: Gauge invariant metric perturbations during reheating

abstract:
  The possible amplification of gauge invariant metric fluctuations in the
infrared sector are very important during reheating stage of inflation. In this
stage the inflaton oscillates arount the minimum of the scalar potential. The
evolution for super Hubble scales gauge invariant metric fluctuations can be
studied by means of the Bardeen parameter. For a massive scalar field with a
quadratic potential for a nonzero cosmological constant. I find that (in the
reheating regime and for super Hubble scales), the Sasaki-Mukhanov parameter
oscillates with amplitude constant such that there is no amplification of $Q$
during reheating.


title: Frequency and Wavelength of Light for Relativistically Rotating Frames

abstract:
  Non-time-orthogonal frame analysis is applied to determine the frequency and
wavelength of light as observed i) in a relativistically rotating frame when
emission is from a source fixed in the non-rotating frame, ii) in a
non-rotating frame when emission is from a source fixed in the rotating frame,
and iii) when both source and observer are fixed in the rotating frame and the
source emission direction varies with respect to the rotating frame.
Appropriate Doppler effects are demonstrated, and second order differences from
translating (time-orthogonal) frame analysis are noted.


title: Microscopic Properties of Horizons

abstract:
  We suggest that all horizons of spacetime, no matter whether they are black
hole, Rindler or de Sitter horizons, have certain microscopic properties in
common. We propose that these propertues may be used as the starting points, or
postulates, of a microscopic theory of gravity.


title: Algorithmic Complexity in Cosmology and Quantum Gravity

abstract:
  In this article we use the idea of algorithmic complexity (AC) to study
various cosmological scenarios, and as a means of quantizing the gravitational
interaction. We look at 5D and 7D cosmological models where the Universe begins
as a higher dimensional Planck size spacetime which fluctuates between
Euclidean and Lorentzian signatures. These fluctuations are governed by the AC
of the two different signatures. At some point a transition to a 4D Lorentzian
signature Universe occurs, with the extra dimensions becoming ``frozen'' or
non-dynamical. We also apply the idea of algorithmic complexity to study
composite wormholes, the entropy of blackholes, and the path integral for
quantum gravity.


title: Plane fronted parallel waves in a warm two-component plasma

abstract:
  A general system of equations is derived, using the 1+3 orthonormal tetrad
formalism, describing the influence of a plane-fronted-parallel gravitational
wave on a warm relativistic two-component plasma. We focus our attention on
phenomena that are induced by terms that are higher order in the gravitational
wave amplitude. In particular, it is shown that parametric excitations of
ion-acoustic waves takes place, due to these higher order gravitational
non-linearities. The implications of the results are discussed.


title: Quantum Gravity: a Progress Report

abstract:
  The problem of reconciling general relativity and quantum theory has
fascinated and bedeviled physicists for more than 70 years. Despite recent
progress in string theory and loop quantum gravity, a complete solution remains
out of reach. I review the status of the continuing effort to quantize gravity,
emphasizing the underlying conceptual issues and the various attempts to come
to grips with them.


title: Distributional Sources for Newman's Holomorphic Field

abstract:
  In 1973, E. T. Newman considered the holomorphic extension \tilde E(x+iy) of
the Coulomb field E(x) in R^3. By analyzing its multipole expansion, he showed
that the real and imaginary parts of \tilde E(x+iy), viewed as functions of x
for fixed y, are the electric and magnetic fields generated by a spinning ring
of charge R. This represents the electromagnetic part of the Kerr-Newman
solution to the Einstein-Maxwell equations. As already pointed out by Newman
and Janis in 1965, this interpretation is somewhat problematic since the fields
are double-valued. To make them single-valued, a branch cut must be introduced
so that R is replaced by a charged disk D having R as its boundary. In the
context of curved spacetime, D becomes a spinning disk of charge and mass
representing the singularity of the Kerr-Newman solution. Here we confirm the
above interpretation of the real and imaginary parts of \tilde E(x+iy) by
computing the charge- and current densities directly as distributions in R^3
supported in the source disk D. This shows in particular that D spins rigidly
at the critical rate, so that its rim R moves at the speed of light.
  It is a pleasure to thank Ted Newman, Andrzej Trautman and Iwo
Bialinicki-Birula for many instructive discussions, particularly in Warsaw and
during a visit to Pittsburgh.


title:
A Method for Finding Solutions of the Hermitian Theory of Relativity
  which Depend on Three Co-ordinates

abstract:
  A method is presented, which can generate solutions of the Hermitian theory
of relativity from known solutions of the general theory of relativity, when
the latter depend on three co-ordinates and are invariant under reversal of the
fourth one.


title: Topology and the Cosmic Microwave Background

abstract:
  Nature abhors an infinity. The limits of general relativity are often
signaled by infinities: infinite curvature as in the center of a black hole,
the infinite energy of the singular big bang. We might be inclined to add an
infinite universe to the list of intolerable infinities. Theories that move
beyond general relativity naturally treat space as finite. In this review we
discuss the mathematics of finite spaces and our aspirations to observe the
finite extent of the universe in the cosmic background radiation.


title: Planetary g(t) for which resistive atmospheric falling is rising

abstract:
  A Darboux-transformed surface gravitational acceleration of the constant
gravitational acceleration for a body endowed with an atmospheric layer is
shown to turn the atmospheric free fall with quadratic resistance in the
opposite motion, i.e., a free rising. Although the atmosphere of such a body
may look completely normal, it is the time dependence of its gravitational
field that produces this type of motion. The result is a consequence of
general, one-parameter-dependent Darboux transformations in mathematical
physics


title:
A Rule for the Equilibrium of Forces in the Hermitian Theory of
  Relativity

abstract:
  When the behaviour of the singularities, which are used to represent masses,
charges or currents in exact solutions to the field equations of the Hermitian
theory of relativity, is restricted by a no-jump rule, conditions are obtained,
which determine the relative positions of masses, charges and currents. Due to
these conditions the Hermitian theory of relativity appears to provide a
unified description of gravitational, colour and electromagnetic forces.


title: Branes for Relativists

abstract:
  Recently, branes in supergravity have become an indispensable tool even for
traditional relativists. The purpose of this manuscript is to provide a
pedagogical account of the brane technology so that the relativists can use
branes in their study. The type IIA supergravity theory is mainly discussed and
other cases are briefly mentioned. The repulson singularity is also explained
as an interesting application.


title: Angle and Volume Studies in Quantized Space

abstract:
  The search for a quantum theory of gravity is one of the major challenges
facing theoretical physics today. While no complete theory exists, a promising
avenue of research is the loop quantum gravity approach. In this approach,
quantum states are represented by spin networks, essentially graphs with
weighted edges. Since general relativity predicts the structure of space, any
quantum theory of gravity must do so as well; thus, "spatial observables" such
as area, volume, and angle are given by the eigenvalues of Hermitian operators
on the spin network states. We present results obtained in our investigations
of the angle and volume operators, two operators which act on the vertices of
spin networks. We find that the minimum observable angle is inversely
proportional to the square root of the total spin of the vertex, a fairly slow
decrease to zero. We also present numerical results indicating that the angle
operator can reproduce the classical angle distribution. The volume operator is
significantly harder to investigate analytically; however, we present
analytical and numerical results indicating that the volume of a region scales
as the 3/2 power of its bounding surface, which corresponds to the classical
model of space.


title:
Doubly covariant action principle of singular hypersurfaces in general
  relativity and scalar-tensor theories

abstract:
  An action principle of singular hypersurfaces in general relativity and
scalar-tensor type theories of gravity in the Einstein frame is presented
without assuming any symmetry. The action principle is manifestly doubly
covariant in the sense that coordinate systems on and off a hypersurface are
disentangled and can be independently specified. It is shown that, including
variation of the metric, the position of the hypersurface and matter fields,
the variational principle gives the correct set of equations of motion: the
Einstein equation off the hypersurface, Israel's junction condition in a doubly
covariant form and equations of motion of matter fields including the scalar
fields. The position of the hypersurface measured from one side of the
hypersurface and that measured from another side can be independently variated
as required by the double covariance.


title: Can one detect a non-smooth null infinity?

abstract:
  It is shown that the precession of a gyroscope can be used to elucidate the
nature of the smoothness of the null infinity of an asymptotically flat
spacetime (describing an isolated body). A model for which the effects of
precession in the non-smooth null infinity case are of order $r^{-2}\ln r$ is
proposed. By contrast, in the smooth version the effects are of order $r^{-3}$.
This difference should provide an effective criterion to decide on the nature
of the smoothness of null infinity.


title:
Exact Solution of Photon Equation in Stationary G\"{o}del-type and
  G\"{o}del Space-Times

abstract:
  In this work the photon equation (massless Duffin-Kemmer-Petiau equation) is
written expilicitly for general type of stationary G\"{o}del space-times and is
solved exactly for G\"{o}del-type and G\"{o}del space-times. Harmonic
oscillator behaviour of the solutions is discussed and energy spectrum of
photon is obtained.


title:
Gravitational effects on entangled states and interferometer with
  entangled atoms

abstract:
  It is discussed how systems of quantum-correlated (entangled)particles or
atoms behave in external gravitational fields and what gravitational effects
may exist in such systems. An experimental setup is proposed which improves the
sensitivity of the Ramsey interferometer by the usage of quantum-correlated
atoms. Entanglement of $n$ atoms improves the sensitivity to small phase shifts
in $n^2$ times. This scheme may be used for observing gravity-induced phase
shifts in laboratory.


title:
The Origin of the Electromagnetic Interaction in Einstein's Unified
  Field Theory with Sources

abstract:
  Einstein's unified field theory is extended by the addition of matter terms
in the form of a symmetric energy tensor and of two conserved currents. From
the field equations and from the conservation identities emerges the picture of
a gravoelectrodynamics in a dynamically polarizable Riemannian continuum.
Through an approximate calculation exploiting this dynamical polarizability it
is argued that ordinary electromagnetism may be contained in the theory.


title: Quantum cosmological perfect fluid model and its classical analogue

abstract:
  The quantization of gravity coupled to a perfect fluid model leads to a
Schr\"odinger-like equation, where the matter variable plays the role of time.
The wave function can be determined, in the flat case, for an arbitrary
barotropic equation of state $p = \alpha\rho$; solutions can also be found for
the radiative non-flat case. The wave packets are constructed, from which the
expectation value for the scale factor is determined. The quantum scenarios
reveal a bouncing Universe, free from singularity. We show that such quantum
cosmological perfect fluid models admit a universal classical analogue,
represented by the addition, to the ordinary classical model, of a repulsive
stiff matter fluid. The meaning of the existence of this universal classical
analogue is discussed. The quantum cosmological perfect fluid model is, for a
flat spatial section, formally equivalent to a free particle in ordinary
quantum mechanics, for any value of $\alpha$, while the radiative non-flat case
is equivalent to the harmonic oscillator. The repulsive fluid needed to
reproduce the quantum results is the same in both cases.


title:
A Conventional Physics Explanation for the Anomalous Acceleration of
  Pioneer 10/11

abstract:
  Anderson, et al., find the measured trajectories of Pioneer 10 and 11
spacecraft deviate from the trajectories computed from known forces acting on
them. This unmodelled acceleration can be accounted for by non-isotropic
radiation of spacecraft heat. Various forms of non-isotropic radiation were
proposed by Katz, Murphy, and Scheffer, but Anderson, et al. felt that none of
these could explain the observed effect. This paper calculates the known
effects in more detail and considers new sources of radiation, all based on
spacecraft construction. These effects are then modelled over the duration of
the experiment. The model provides a reasonable fit to the acceleration from
its appearance at a heliocentric distance of 5 AU to the last measurement at 71
AU, but overpredicts by 9% the decrease in acceleration between intervals I and
III of the Pioneer 10 observations. (For comparison, the two different
measurements of the effect (SIGMA and CHASMP) themselves differ by 4% in
interval III.) In any case, by accounting for the bulk of the acceleration, the
proposed mechanism makes it much more likely that the entire effect can be
explained without the need for new physics.


title:
Equations for Complex-Valued, Twisting, Type N, Vacuum Solutions, with
  one or two Killing/homothetic vectors

abstract:
  HH-spaces, i.e., complex spacetimes, of Petrov type NxN are determined by a
trio of pde's for two functions, lambda and a, of three independent variables
(and also two gauge functions, chosen to be two of the independent variables if
one prefers). As in common integrable systems, these form a second order,
linear system for lambda; howver, here the integrability conditions, involving
a, are more complicated than is common. Therefore, with the hope of finding new
solutions, these equations are now constrained to also admit both one and two
homothetic or Killing vectors. The case with one Killing and one homothetic
vector reduces these equations to two ode's for two unknown functions of the
one remaining variable.
  In addition, we also describe in detail the explicit forms of the metric,
tetrad, connections, and curvature for twisting HH-spaces of Petrov type NxN,
modulo the determining equations. This simplifies considerably the process of
obtaining these details cleanly from earlier articles on the subject, thus
simplifying access to the research area.


title: Past and future gauge in numerical relativity

abstract:
  Numerical relativity describes a discrete initial value problem for general
relativity. A choice of gauge involves slicing space-time into space-like
hypersurfaces. This introduces past and future gauge relative to the
hypersurface of present time. Here, we propose solving the discretized Einstein
equations with a choice of gauge in the future and a dynamical gauge in the
past. The method is illustrated on a polarized Gowdy wave.


title:
Stationary Electromagnetic Fields of a Slowly Rotating Magnetized
  Neutron Star in General Relativity

abstract:
  Following the general formalism presented by Rezzolla, Ahmedov and Miller
(MNRAS, 322, 723 2001), we here derive analytic solutions of the
electromagnetic fields equations in the internal and external background
spacetime of a slowly rotating highly conducting magnetized neutron star. The
star is assumed to be isolated and in vacuum, with a dipolar magnetic field not
aligned with the axis of rotation. Our results indicate that the
electromagnetic fields of a slowly rotating neutron star are modified by
general relativistic effects arising from both the monopolar and the dipolar
parts of the gravitational field. The results presented here differ from the
ones discussed by Rezzolla, Ahmedov and Miller (MNRAS, 322, 723 2001) mainly in
that we here consider the interior magnetic field to be dipolar with the same
radial dependence as the external one. While this assumption might not be a
realistic one, it should be seen as the application of our formalism to a case
often discussed in the literature.


title: Stability of Transparent Spherically Symmetric Thin Shells and Wormholes

abstract:
  The stability of transparent spherically symmetric thin shells (and
wormholes) to linearized spherically symmetric perturbations about static
equilibrium is examined. This work generalizes and systematizes previous
studies and explores the consequences of including the cosmological constant.
The approach shows how the existence (or not) of a domain wall dominates the
landscape of possible equilibrium configurations.


title: The singularity problem in string theory

abstract:
  We review the current status of the singularity problem in string theory for
non-experts. After the problem is discussed from the point of view of
supergravity, we discuss classic examples and recent examples of singularity
resolution in string theory.


title: Density Discontinuity of a Neutron Star and Gravitational Waves

abstract:
  We calculate quasi-normal f- and g-modes of a neutron star with density
discontinuity, which may appear in a phase transition at extreme high density.
We find that discontinuity will reflect largely on the f-mode, and that the
g-mode could also be important for a less massive star.


title: Linking and causality in (2+1)-dimensional static spacetimes

abstract:
  Given a (d+1)-dimensional spacetime (M,g), one can consider the set N of all
its null geodesics. If (M,g) is globally hyperbolic then this set is naturally
a smooth (2d-1)-manifold. The sky of an event x in M is the set X of all null
geodesics through x, and is an embedded submanifold of N diffeomorphic to
S^{d-1}. Low conjectured that if d=2 then x,y are causally related in M iff X,Y
are linked in N. We prove Low's conjecture for a (large) class of static
spacetimes.


title: Consistent discretizations for classical and quantum general relativity

abstract:
  We consider discretizations of the Einstein action of general relativity such
that the resulting discrete equations of motion form a consistent constrained
system. Upon ``spin foam'' quantization of the system, consistency allows a
natural way of recovering the correct semi-classical theory. A consistent set
of approximations to the Einstein equations could also have implications for
numerical relativity and for the construction of approximate classical
observables for the theory.


title: Teleparallel orthonormal frames constraints on torsion detection?

abstract:
  Spin-polarised cylindrically symmetric solution are shown not to be
compatible with teleparallel gravity.This can be done in two distinct
manners.The first is to show that not all components of the orthonormal tetrad
(OT).It is argue however that this result maybe done by a bad choice of the
spin distribution along the cylinder.A cylindrically symmetric Riemannian
solution is obtained which represents a conical geometry of defects.


title: Comment on Ricci Collineations for spherically symmetric space-times

abstract:
  It is shown that the results of the paper by Contreras et al. [Contreras, G.,
Nunez, L. A., Percoco, U. "Ricci Collineations for Non-degenerate, Diagonal and
Spherically Symmetric Ricci Tensors" (2000) Gen. Rel. Grav. 32, 285-294]
concerning the Ricci Collineations in spherically symmetric space-times with
non-degenerate and diagonal Ricci tensor do not cover all possible cases.
Furthermore the complete algebra of Ricci Collineations of certain
Robertson-Walker metrics of vanishing spatial curvature are given.


title:
Hypersurface homogeneous locally rotationally symmetric spacetimes
  admitting conformal symmetries

abstract:
  All hypersurface homogeneous locally rotationally symmetric spacetimes which
admit conformal symmetries are determined and the symmetry vectors are given
explicitly. It is shown that these spacetimes must be considered in two sets.
One set containing Ellis Class II and the other containing Ellis Class I, III
LRS spacetimes. The determination of the conformal algebra in the first set is
achieved by systematizing and completing results on the determination of CKVs
in 2+2 decomposable spacetimes. In the second set new methods are developed.
The results are applied to obtain the classification of the conformal algebra
of all static LRS spacetimes in terms of geometrical variables. Furthermore all
perfect fluid nontilted LRS spacetimes which admit proper conformal symmetries
are determined and the physical properties some of them are discussed.


title:
Spherically symmetric Weitzenb\"{o}ck defect solution of Einstein field
  equation

abstract:
  A new class of spacetime defect solutions of Einstein Field equations of
Edelen's direct Poincar\'{e} Gauge Field theory without biaxial symmetry is
presented. The interior solution describes a core of defects where curvature
vanishes and Cartan torsion is nonvanishing. Outside the core (in vacuum) the
solution represents a spacetime with vanishing curvature and torsion describing
a nontrivial topological defect solution of Einstein equations of gravity. Our
solution corresponds to a very weak strenght of Tachyons can be found far away
from the core defect.


title:
Energy associated with a static spherically symmetric nonsingular black
  hole

abstract:
  We evaluate the energy distributions of the Dymnikova space-time using the
Weinberg, Papapetrou, and M{\o}ller energy-momentum complexes. This result
sustain the importance of the energy-momentum complexes in the evaluation of
the energy distribution of a given space-time. To compare the energy
distributions obtained by using several definitions, these results show that
the Einstein, Tolman, and Weinberg energy complexes are the same in
Schwarzschild Cartesian coordinates, but the Papapetrou and the M{\o}ller are
not.


title: Gibbs and Quantum Discrete Spaces

abstract:
  Gibbs measure is one of the central objects of the modern probability,
mathematical statistical physics and euclidean quantum field theory. Here we
define and study its natural generalization for the case when the space, where
the random field is defined is itself random. Moreover, this randomness is not
given apriori and independently of the configuration, but rather they depend on
each other, and both are given by Gibbs procedure; We call the resulting object
a Gibbs family because it parametrizes Gibbs fields on different graphs in the
support of the distribution. We study also quantum (KMS) analog of Gibbs
families. Various applications to discrete quantum gravity are given.


title: Kappa - Poincare dispersion relations and the black hole radiation

abstract:
  Following the methods developed by Corley and Jacobson, we consider
qualitatively the issue of Hawking radiation in the case when the dispersion
relation is dictated by quantum kappa-Poincare algebra. This relation
corresponds to field equations that are non-local in time, and, depending on
the sign of the parameter kappa, to sub- or superluminal signal propagation. We
also derive the conserved inner product, that can be used to count modes, and
therefore to obtain the spectrum of black hole radiation in this case.


title: Thermodynamics of binary black holes and neutron stars

abstract:
  We consider compact binary systems, modeled in general relativity as vacuum
or perfect-fluid spacetimes with a helical Killing vector k^\alpha,
heuristically, the generator of time-translations in a corotating frame.
Systems that are stationary in this sense are not asymptotically flat, but have
asymptotic behavior corresponding to equal amounts of ingoing and outgoing
radiation. For black-hole binaries, a rigidity theorem implies that the Killing
vector lies along the horizon's generators, and from this one can deduce the
zeroth law (constant surface gravity of the horizon). Remarkably, although the
mass and angular momentum of such a system are not defined, there is an exact
first law, relating the change in the asymptotic Noether charge to the changes
in the vorticity, baryon mass, and entropy of the fluid, and in the area of
black holes.
  Binary systems with M\Omega small have an approximate asymptopia in which one
can write the first law in terms of the asymptotic mass and angular momentum.
Asymptotic flatness is precise in two classes of solutions used to model binary
systems: spacetimes satisfying the post-Newtonian equations, and solutions to a
modified set of field equations that have a spatially conformally flat metric.
(The spatial conformal flatness formalism with helical symmetry, however, is
consistent with maximal slicing only if replaces the extrinsic curvature in the
field equations by an artificially tracefree expression in terms of the shift
vector.) For these spacetimes, nearby equilibria whose stars have the same
vorticity obey the relation \delta M = \Omega \delta J, from which one can
obtain a turning point criterion that governs the stability of orbits.


title:
Dimensional Dependence of Black Hole Formation in Self-Similar Collapse
  of Scalar Field

abstract:
  We study classical and quantum self-similar collapses of a massless scalar
field in higher dimensions, and examine how the increase in the number of
dimensions affects gravitational collapse and black hole formation. Higher
dimensions seem to favor formation of black hole rather than other final
states, in that the initial data space for black hole formation enlarges as
dimension increases. On the other hand, the quantum gravity effect on the
collapse lessens as dimension increases. We also discuss the gravitational
collapse in a brane world with large but compact extra dimensions.


title: Hawking Radiation in Laboratories

abstract:
  We propose an experimental model using the Laval nozzle of a sonic analogue
of the Hawking radiation. We observe a power spectrum of the out-going wave
emitted from the vicinity a sonic horizon in place of a created particle
number. Our treatment is based on classical theory, and it will make
experiments to be easier. This experimental possibility is a great advantage of
our model.


title: Kaluza-Klein anisotropy in the CMB

abstract:
  We show that 5-dimensional Kaluza-Klein graviton stresses can slow the decay
of shear anisotropy on the brane to observable levels, and we use cosmic
microwave background anisotropies to place limits on the initial anisotropy
induced by these stresses. An initial shear to Hubble distortion of only \sim
10^{-3}\Omega_0h_0^2 at the 5D Planck time would allow the observed large-angle
CMB signal to be a relic mainly of KK tidal effects.


title: Renormalization Group Approach to Causal Viscous Cosmological Models

abstract:
  The renormalization group method is applied to the study of homogeneous and
flat Friedmann-Robertson-Walker type Universes, filled with a causal bulk
viscous cosmological fluid. The starting point of the study is the
consideration of the scaling properties of the gravitational field equations,
of the causal evolution equation of the bulk viscous pressure and of the
equations of state. The requirement of scale invariance imposes strong
constraints on the temporal evolution of the bulk viscosity coefficient,
temperature and relaxation time, thus leading to the possibility of obtaining
the bulk viscosity coefficient-energy density dependence. For a cosmological
model with bulk viscosity coefficient proportional to the Hubble parameter, we
perform the analysis of the renormalization group flow around the scale
invariant fixed point, therefore obtaining the long time behavior of the scale
factor.


title: Retarded radiation from colliding black holes in the close limit

abstract:
  We use null hypersurface techniques in a new approach to calculate the
retarded waveform from a binary black hole merger in the close approximation.
The process of removing ingoing radiation from the system leads to two notable
features in the shape of the close approximation waveform for a head-on
collision of black holes: (i) an initial quasinormal ringup and (ii) weak
sensitivity to the parameter controlling the collision velocity. Feature (ii)
is unexpected and has the potential importance of enabling the design of an
efficient template for extracting the gravitational wave signal from the noise.


title: Corotating and irrotational binary black holes in quasi-circular orbits

abstract:
  A complete formalism for constructing initial data representing black-hole
binaries in quasi-equilibrium is developed. Radiation reaction prohibits, in
general, true equilibrium binary configurations. However, when the timescale
for orbital decay is much longer than the orbital period, a binary can be
considered to be in quasi-equilibrium. If each black hole is assumed to be in
quasi-equilibrium, then a complete set of boundary conditions for all initial
data variables can be developed. These boundary conditions are applied on the
apparent horizon of each black hole, and in fact force a specified surface to
be an apparent horizon. A global assumption of quasi-equilibrium is also used
to fix some of the freely specifiable pieces of the initial data and to
uniquely fix the asymptotic boundary conditions. This formalism should allow
for the construction of completely general quasi-equilibrium black hole binary
initial data.


title: Comment on the transition amplitude for toy universe models

abstract:
  The parametrized system called ``ideal clock'' is turned into an ordinary
gauge system and quantized by means of a path integral in which canonical
gauges are admissible. Then the possibility of applying the results to obtain
the transition amplitude for empty minisuperspaces, and the restrictions
arising from the topology of the constraint surface, are studied by matching
the models with the ideal clock. A generalization to minisuperspaces with true
degrees of freedom is also discussed.


title:
Global phase time and path integral for the Kantowski--Sachs anisotropic
  univers

abstract:
  The action functional of the anisotropic Kantowski--Sachs cosmological model
is turned into that of an ordinary gauge system. Then a global phase time is
identified for the model by imposing canonical gauge conditions, and the
quantum transition amplitude is obtained by means of the usual path integral
procedure of Fadeev and Popov.


title: Gauge invariance of parametrized systems and path integral quantization

abstract:
  Gauge invariance of systems whose Hamilton-Jacobi equation is separable is
improved by adding surface terms to the action fuctional. The general form of
these terms is given for some complete solutions of the Hamilton-Jacobi
equation. The procedure is applied to the relativistic particle and toy
universes, which are quantized by imposing canonical gauge conditions in the
path integral; in the case of empty models, we first quantize the parametrized
system called ``ideal clock'', and then we examine the possibility of obtaining
the amplitude for the minisuperspaces by matching them with the ideal clock.
The relation existing between the geometrical properties of the constraint
surface and the variables identifying the quantum states in the path integral
is discussed.


title: Quantization of minisuperspaces as ordinary gauge systems

abstract:
  Simple cosmological models are used to show that gravitation can be quantized
as an ordinary gauge system if the Hamilton-Jacobi equation for the model under
consideration is separable. In this situation, a canonical transformation can
be performed such that in terms of the new variables the model has a linear and
homogeneous constraint, and therefore canonical gauges are admissible in the
path integral. This has the additional practical advantage that gauge
conditions that do not generate Gribov copies are then easy to choose.


title: Gauge fixation and global phase time for minisuperspaces

abstract:
  Homogeneous and isotropic cosmological models whose Hamilton-Jacobi equation
is separable are deparametrized by turning their action functional into that of
an ordinary gauge system. Canonical gauge conditions imposed on the gauge
system are used to define a global phase time in terms of the canonical
coordinates and momenta of the minisuperspaces. The procedure clearly shows how
the geometry of the constraint surface restricts the choice of time; the
consequences that this has on the path integral quantization are discussed.


title: Instability of Extremal Relativistic Charged Spheres

abstract:
  With the question, ``Can relativistic charged spheres form extremal black
holes?" in mind, we investigate the properties of such spheres from a classical
point of view. The investigation is carried out numerically by integrating the
Oppenheimer-Volkov equation for relativistic charged fluid spheres and finding
interior Reissner-Nordstr\"om solutions for these objects. We consider both
constant density and adiabatic equations of state, as well as several possible
charge distributions, and examine stability by both a normal mode and an energy
analysis. In all cases, the stability limit for these spheres lies between the
extremal ($Q = M$) limit and the black hole limit ($R = R_+$). That is, we find
that charged spheres undergo gravitational collapse before they reach $Q = M$,
suggesting that extremal Reissner-Nordtr\"om black holes produced by collapse
are ruled out. A general proof of this statement would support a strong form of
the cosmic censorship hypothesis, excluding not only stable naked
singularities, but stable extremal black holes. The numerical results also
indicate that although the interior mass-energy $m(R)$ obeys the usual $m/R <
4/9$ stability limit for the Schwarzschild interior solution, the gravitational
mass $M$ does not. Indeed, the stability limit approaches $R_+$ as $Q \to M$.
In the Appendix we also argue that Hawking radiation will not lead to an
extremal Reissner-Nordstr\"om black hole. All our results are consistent with
the third law of black hole dynamics, as currently understood.


title:
Computational Cosmology: from the Early Universe to the Large Scale
  Structure

abstract:
  In order to account for the observable Universe, any comprehensive theory or
model of cosmology must draw from many disciplines of physics, including gauge
theories of strong and weak interactions, the hydrodynamics and microphysics of
baryonic matter, electromagnetic fields, and spacetime curvature, for example.
Although it is difficult to incorporate all these physical elements into a
single complete model of our Universe, advances in computing methods and
technologies have contributed significantly towards our understanding of
cosmological models, the Universe, and astrophysical processes within them. A
sample of numerical calculations (and numerical methods) applied to specific
issues in cosmology are reviewed in this article: from the Big Bang singularity
dynamics to the fundamental interactions of gravitational waves; from the
quark-hadron phase transition to the large scale structure of the Universe. The
emphasis, although not exclusively, is on those calculations designed to test
different models of cosmology against the observed Universe.


title: Enhancon and Resolution of Singularity

abstract:
  We review the enhancon mechanism proposed by Johnson, Peet and Polchinski. If
we consider the D6-brane wrapped on K3, then there appear a naked singularity
called ``repulson'' in the supergravity solution. But this singularity is
resolved by a shell structure called ``enhancon''. In the interior of the
enhancon, the abelian gauge symmetry is enhanced to a nonabelian one, and
ordinary supergravity is no more reliable. We also review the interpretation of
enhancon as fuzzy sphere. This paper is the contribution to the proceedings of
"Frontier of Cosmology and Gravitation", April 25-27 2001, YITP.


title: A Primer to Slow Light

abstract:
  Laboratory-based optical analogs of astronomical objects such as black holes
rely on the creation of light with an extremely low or even vanishing group
velocity (slow light). These brief notes represent a pedagogical attempt
towards elucidating this extraordinary form of light. This paper is a
contribution to the book Artificial Black Holes edited by Mario Novello, Matt
Visser and Grigori Volovik. The paper is intended as a primer, an introduction
to the subject for non-experts, not as a detailed literature review.


title: On the two-body problem in general relativity

abstract:
  We consider the two-body problem in post-Newtonian approximations of general
relativity. We report the recent results concerning the equations of motion,
and the associated Lagrangian formulation, of compact binary systems, at the
third post-Newtonian order (1/c^6 beyond the Newtonian acceleration). These
equations are necessary when constructing the theoretical templates for
searching and analyzing the gravitational-wave signals from inspiralling
compact binaries in VIRGO-type experiments.


title:
The massive scalar field in a closed Friedmann universe model - new
  rigorous results

abstract:
  For the minimally coupled scalar field in Einstein's theory of gravitation we
look for the space of solutions within the class of closed Friedmann universe
models. We prove that D = 1 or D > 1, where D is the (fractal) dimension of the
set of solutions which can be integrated up to t to infinity. (D > 0 was
conjectured by PAGE (1984)). We discuss concepts like ``the probability of the
appearance of a sufficiently long inflationary phase" and argue that it is
primarily a probability measure q in the space V of solutions (and not in the
space of initial conditions) which has to be applied. q is naturally defined
for Bianchi-type I cosmological models because V is a compact cube. The
problems with the closed Friedmann model (which led to controversial claims in
the literature) will be shown to originate from the fact that V has a
complicated non-compact non-Hausdorff Geroch topology: no natural definition of
q can be given. We conclude: the present state of our universe can be explained
by models of the type discussed, but thereby the anthropic principle cannot be
fully circumvented.


title: Chaos and Preheating

abstract:
  We show evidence for a relationship between chaos and parametric resonance
both in a classical system and in the semiclassical process of particle
creation. We apply our considerations in a toy model for preheating after
inflation.


title:
The metric in the superspace of Riemannian metrics and its relation to
  gravity

abstract:
  The space of all Riemannian metrics is infinite-dimensional. Nevertheless a
great deal of usual Riemannian geometry can be carried over. The superspace of
all Riemannian metrics shall be endowed with a class of Riemannian metrics;
their curvature and invariance properties are discussed. Just one of this class
has the property to bring the lagrangian of General Relativity into the form of
a classical particle's motion. The signature of the superspace metric depends
in a non-trivial manner on the signature of the original metric, we derive the
corresponding formula. Our approach is a local one: the essence is a metric in
the space of all symmetric rank-two tensors, and then the space becomes a
warped product of the real line with an Einstein space.


title:
Critical collapse in 2+1 dimensional AdS spacetime: quasi-CSS solutions
  and linear perturbations

abstract:
  We construct a one-parameter family of exact time-dependent solutions to 2+1
gravity with a negative cosmological constant and a massless minimally coupled
scalar field as source. These solutions present a continuously self-similar
(CSS) behaviour near the central singularity, as observed in critical collapse,
and an asymptotically AdS behaviour at spatial infinity. We consider the linear
perturbation analysis in this background, and discuss the crucial question of
boundary conditions. These are tested in the special case where the scalar
field decouples and the linear perturbations describe exactly the small-mass
static BTZ black hole. In the case of genuine scalar perturbations, we find a
growing mode with a behavior characteristic of supercritical collapse, the
spacelike singularity and apparent horizon appearing simultaneously and
evolving towards the AdS boundary. Our boundary conditions lead to the value of
the critical exponent $\gamma = 0.4$.


title:
The noise in gravitational-wave detectors and other classical-force
  measurements is not influenced by test-mass quantization

abstract:
  It is shown that photon shot noise and radiation-pressure back-action noise
are the sole forms of quantum noise in interferometric gravitational wave
detectors that operate near or below the standard quantum limit, if one filters
the interferometer output appropriately. No additional noise arises from the
test masses' initial quantum state or from reduction of the test-mass state due
to measurement of the interferometer output or from the uncertainty principle
associated with the test-mass state. Two features of interferometers are
central to these conclusions: (i) The interferometer output (the photon number
flux N(t) entering the final photodetector) commutes with itself at different
times in the Heisenberg Picture, [N(t), N(t')] = 0, and thus can be regarded as
classical. (ii) This number flux is linear in the test-mass initial position
and momentum operators x_o and p_o, and those operators influence the measured
photon flux N(t) in manners that can easily be removed by filtering -- e.g., in
most interferometers, by discarding data near the test masses' 1 Hz swinging
freqency. The test-mass operators x_o and p_o contained in the unfiltered
output N(t) make a nonzero contribution to the commutator [N(t), N(t')]. That
contribution is cancelled by a nonzero commutation of the photon shot noise and
radiation-pressure noise, which also are contained in N(t). This cancellation
of commutators is responsible for the fact that it is possible to derive an
interferometer's standard quantum limit from test-mass considerations, and
independently from photon-noise considerations. These conclusions are true for
a far wider class of measurements than just gravitational-wave interferometers.
To elucidate them, this paper presents a series of idealized thought
experiments that are free from the complexities of real measuring systems.


title: New exact solutions for power-law inflation Friedmann models

abstract:
  We consider the spatially flat Friedmann model. For a(t) = t^p, especially,
if p is larger or equal to 1, this is called power-law inflation. For the
Lagrangian L = R^m with p = - (m - 1)(2m - 1)/(m - 2), power-law inflation is
an exact solution, as it is for Einstein gravity with a minimally coupled
scalar field Phi in an exponential potential V(Phi) = exp(mu Phi) and also for
the higher-dimensional Einstein equation with a special Kaluza-Klein ansatz.
The synchronized coordinates are not adapted to allow a closed-form solution,
so we use another gauge. Finally, special solutions for the closed and open
Friedmann model are found.


title: The Newtonian limit of fourth and higher order gravity

abstract:
  We consider the Newtonian limit of the theory based on the Lagrangian L = R +
\sum a_k R \Box^k R. The gravitational potential of a point mass turns out to
be a combination of Newtonian and Yukawa terms. For sixth-order gravity the
coefficients are calculated explicitly. For the general case one gets as a
result: The the potential is always unbounded near the origin.


title: Comment on 'Stability of the semiclassical Einstein equation'

abstract:
  Some mathematical errors of the paper commented upon [W.-M. Suen, Phys. Rev.
D 40, (1989) 315] are corrected.


title: On space-times which cannot be distinguished by curvature invariants

abstract:
  We present an example that non-isometric space-times with non-vanishing
curvature scalar cannot be distinguished by curvature invariants.


title: On the Space of 3-dimensional Homogeneous Riemannian Manifolds

abstract:
  We answer the following question: Let l, m, n be arbitrary real numbers. Does
there exist a 3-dimensional homogeneous Riemannian manifold whose eigenvalues
of the Ricci tensor are just l, m and n ?