title: Threshold analyses and Lorentz violation

abstract:
  In the context of threshold investigations of Lorentz violation, we discuss
the fundamental principle of coordinate invariance, the role of an effective
dynamical framework, and the conditions of positivity and causality. Our
analysis excludes a variety of previously considered Lorentz-breaking
parameters and opens an avenue for viable dispersion-relation investigations of
Lorentz violation.


title: Post-Newtonian Theory and its Application

abstract:
  We review some recent works on the post-Newtonian theory of slowly-moving
(post-Newtonian) sources, and its application to the problems of dynamics and
gravitational radiation from compact binary systems. Our current knowledge is
3PN on the center-of-mass energy and 3.5PN on the gravitational-wave flux of
inspiralling compact binaries. We compute the innermost circular orbit (ICO) of
binary black-hole systems and find a very good agreement with the result of
numerical relativity. We argue that the gravitational dynamics of two bodies of
comparable masses in general relativity does not resemble that of a test
particle on a Schwarzschild background. This leads us to question the validity
of some ``Schwarzschild-like'' templates for binary inspiral which are
constructed from post-Newtonian resummation techniques.


title: Geometry of black hole thermodynamics

abstract:
  The Hessian of the entropy function can be thought of as a metric tensor on
the state space. In the context of thermodynamical fluctuation theory Ruppeiner
has argued that the Riemannian geometry of this metric gives insight into the
underlying statistical mechanical system; the claim is supported by numerous
examples. We study this geometry for some families of black holes. It is flat
for the BTZ and Reissner-Nordstrom black holes, while curvature singularities
occur for the Reissner-Nordstrom-anti-de Sitter and Kerr black holes.


title: Spacetime G-structures I: Topological Defects

abstract:
  The notion of G-structure is defined and various geometrical and topological
aspects of such structures are discussed. A particular chain of subgroups in
the affine group for Minkowski space is chosen and the canonical geometrical
and topological objects that are asssociated with each reduction of the bundle
of affine frames on a four-dimensional manifold are detailed. Their physical
significance is discussed in the language of topological defects in ordered
media. Particular attention is paid to how one topologically characterizes the
wave phase of the spacetime vacuum manifold.


title: Inhomogeneous cosmologies with tachyonic dust as dark matter

abstract:
  A cosmology is considered driven by a stress-energy tensor consisting of a
perfect fluid, an inhomogeneous pressure term (which we call a ``tachyonic
dust'' for reasons which will become apparent) and a cosmological constant. The
inflationary, radiation dominated and matter dominated eras are investigated in
detail. In all three eras, the tachyonic pressure decreases with increasing
radius of the universe and is thus minimal in the matter dominated era. The
gravitational effects of the dust, however, may still strongly affect the
universe at present time. In case the tachyonic pressure is positive, it
enhances the overall matter {\em density} and is a candidate for dark matter.
In the case where the tachyonic pressure is negative, the recent acceleration
of the universe can be understood without the need for a cosmological constant.
The ordinary matter, however, has positive energy density at all times. In a
later section, the extension to a variable cosmological term is investigated
and a specific model is put forward such that recent acceleration and future
re-collapse is possible.


title: Particles here and beyond the Mirror

abstract:
  This study looks at motion of particles using mathematical methods of
chronometric invariants (physical observable values in General Relativity). It
is shown that aside for mass-bearing particles and light-like particles
"zero-particles" can exist in fully degenerated space-time (zero-space). For a
regular observer zero-particles move instantly, thus transferring long-range
action. Further we show existence of two separate areas in unhomogeneous
space-time, where observable time flows into future and into past, while this
duality is not found in homogeneous space-time. These areas are referred to as
our world, where time flows into future and as the mirror Universe, where time
flows in past. The areas are separated with a space-time membrane, referred to
as zero-space, where observable time stops.


title: On the area of the symmetry orbits in $T^2$ symmetric spacetimes

abstract:
  We obtain a global existence result for the Einstein equations. We show that
in the maximal Cauchy development of vacuum $T^2$ symmetric initial data with
nonvanishing twist constant, except for the special case of flat Kasner initial
data, the area of the $T^2$ group orbits takes on all positive values. This
result shows that the areal time coordinate $R$ which covers these spacetimes
runs from zero to infinity, with the singularity occurring at R=0.


title: Gravitational Wave Confusion Noise

abstract:
  One of the greatest challenges facing gravitational wave astronomy in the low
frequency band is the confusion noise generated by the vast numbers of
unresolved galactic and extra galactic binary systems. Estimates of the binary
confusion noise suffer from several sources of astrophysical uncertainty, such
as the form of the initial mass function and the star formation rate. There is
also considerable uncertainty about what defines the confusion limit. Various
ad-hoc rules have been proposed, such as the one source per bin rule, and the
one source per three bin rule. Here information theoretic methods are used to
derive a more realistic estimate for the confusion limit. It is found that the
gravitational wave background becomes unresolvable when there is, on average,
more than one source per eight frequency bins. This raises the best estimate
for the frequency at which galactic binaries become a source of noise from 1.45
mHz to 2.54 mHz.


title: Momentum Imparted by Gravitational Waves

abstract:
  We calculate momentum imparted by colliding gravitational waves in a closed
Friedmann Robertson-Walker background and also by gravitational waves with
toroidal wavefronts using an operational procedure. The results obtained for
toroidal wavefronts are well behaved and reduce to the spherical wavefronts for
a special choice.


title: Testing the performance of a blind burst statistic

abstract:
  In this work we estimate the performance of a method for the detection of
burst events in the data produced by interferometric gravitational wave
detectors. We compute the receiver operating characteristics in the specific
case of a simulated noise having the spectral density expected for Virgo, using
test signals taken from a library of possible waveforms emitted during the
collapse of the core of Type II Supernovae.


title: Neutron Stars in a Varying Speed of Light Theory

abstract:
  We study neutron stars in a varying speed of light (VSL) theory of gravity in
which the local speed of light depends upon the value of a scalar field $\phi$.
We find that the masses and radii of the stars are strongly dependent on the
strength of the coupling between $\phi$ and the matter field and that for
certain choices of coupling parameters, the maximum neutron star mass can be
arbitrarily small. We also discuss the phenomenon of cosmological evolution of
VSL stars (analogous to the gravitational evolution in scalar-tensor theories)
and we derive a relation showing how the fractional change in the energy of a
star is related to the change in the cosmological value of the scalar field.


title: Toward Making the Constraint Hypersurface an Attractor in Free Evolution

abstract:
  There is an abundance of empirical evidence in the numerical relativity
literature that the form in which the Einstein evolution equations are written
plays a significant role in the lifetime of numerical simulations. This paper
attempts to present a consistent framework for modifying any system of
evolution equations by adding terms that push the evolution toward the
constraint hypersurface. The method is, in principle, applicable to any system
of partial differential equations which can be divided into evolution equations
and constraints, although it is only demonstrated here through an application
to the Maxwell equations.


title:
Gravitomagnetic time delay and the Lense-Thirring effect in Brans-Dicke
  theory of gravity

abstract:
  We discuss the gravitomagnetic time delay and the Lense-Thirring effect in
the context of Brans-Dicke theory of gravity. We compare the theoretical
results obtained with those predicted by general relativity. We show that
within the accuracy of experiments designed to measure these effects both
theories predict essentially the same result.


title:
Search for quantum transducers between electromagnetic and gravitational
  radiation: A measurement of an upper limit on the transducer conversion
  efficiency of yttrium barium copper oxide

abstract:
  A minimal coupling rule for the coupling of the electron spin to curved
spacetime in general relativity suggests the possibility of a coupling between
electromagnetic and gravitational radiation mediated by means of a quantum
fluid. Thus quantum transducers between these two kinds of radiation fields
might exist. We report here on the first attempt at a Hertz-type experiment, in
which a high-$\rm{T_c}$ superconductor (YBCO) was the sample material used as a
possible quantum transducer to convert EM into GR microwaves, and a second
piece of YBCO in a separate apparatus was used to back-convert GR into EM
microwaves. An upper limit on the conversion efficiency of YBCO was measured to
be $1.6\times10^{-5}$ at liquid nitrogen temperature.


title:
Quantum Interference to Measure Spacetime Curvature: A Proposed
  Experiment at the Intersection of Quantum Mechanics and General Relativity

abstract:
  An experiment in Low Earth Orbit (LEO) is proposed to measure components of
the Riemann curvature tensor using atom interferometry. We show that the
difference in the quantum phase $\Delta\phi$ of an atom that can travel along
two intersecting geodesics is given by $mR_{0i0j}/\hbar$ times the spacetime
volume contained within the geodesics. Our expression for $\Delta\phi$ also
holds for gravitational waves in the long wavelength limit.


title: Quadratic metric-affine gravity

abstract:
  We consider spacetime to be a connected real 4-manifold equipped with a
Lorentzian metric and an affine connection. The 10 independent components of
the (symmetric) metric tensor and the 64 connection coefficients are the
unknowns of our theory. We introduce an action which is quadratic in curvature
and study the resulting system of Euler-Lagrange equations. In the first part
of the paper we look for Riemannian solutions, i.e. solutions whose connection
is Levi-Civita. We find two classes of Riemannian solutions: 1) Einstein
spaces, and 2) spacetimes with metric of a pp-wave and parallel Ricci
curvature. We prove that for a generic quadratic action these are the only
Riemannian solutions. In the second part of the paper we look for
non-Riemannian solutions. We define the notion of a "Weyl pseudoinstanton"
(metric compatible spacetime whose curvature is purely Weyl) and prove that a
Weyl pseudoinstanton is a solution of our field equations. Using the
pseudoinstanton approach we construct explicitly a non-Riemannian solution
which is a wave of torsion in Minkowski space. We discuss the possibility of
using this non-Riemannian solution as a mathematical model for the graviton or
the neutrino.


title:
Transformations of coordinates and Hamiltonian formalism in deformed
  Special Relativity

abstract:
  We investigate the transformation laws of coordinates in generalizations of
special relativity with two observer-independent scales. The request of
covariance leads to simple formulas if one assumes noncanonical Poisson
brackets, corresponding to noncommuting spacetime coordinates.


title: Quick and dirty methods for studying black-hole resonances

abstract:
  We discuss simple integration methods for the calculation of rotating black
hole scattering resonances both in the complex frequency plane (quasinormal
modes) and the complex angular momentum plane (Regge poles). Our numerical
schemes are based on variations of "phase-amplitude" methods. In particular, we
discuss the Pruefer transformation, where the original (frequency domain)
Teukolsky wave equation is replaced by a pair of first-order non-linear
equations governing the introduced phase functions. Numerical integration of
these equations, performed along the real coordinate axis, or along rotated
contours in the complex coordinate plane, provides the required S-matrix
element (the ratio of amplitudes of the outgoing and ingoing waves at
infinity). Mueller's algorithm is then employed to conduct searches in the
complex plane for the poles of this quantity (which are, by definition, the
desired resonances). We have tested this method by verifying known results for
Schwarzschild quasinormal modes and Regge poles, and provide new results for
the Kerr black hole problem. We also describe a new method for estimating the
"excitation coefficients" for quasinormal modes. The method is applied to
scalar waves moving in the Kerr geometry, and the obtained results shed light
on the long-lived quasinormal modes that exist for black holes rotating near
the extreme Kerr limit.


title: De Sitter Waves and the Zero Curvature Limit

abstract:
  We show that a particular set of global modes for the massive de Sitter
scalar field (the de Sitter waves) allows to manage the group representations
and the Fourier transform in the flat (Minkowskian) limit. This is in
opposition to the usual acceptance based on a previous result, suggesting the
appearance of negative energy in the limit process. This method also confirms
that the Euclidean vacuum, in de Sitter spacetime, has to be preferred as far
as one wishes to recover ordinary QFT in the flat limit.


title: Spacetime at the Planck Scale: The Quantum Computer View

abstract:
  We assume that space-time at the Planck scale is discrete, quantised in
Planck units and "qubitsed" (each pixel of Planck area encodes one qubit), that
is, quantum space-time can be viewed as a quantum computer. Within this model,
one finds that quantum space-time itself is entangled, and can quantum-evaluate
Boolean functions which are the laws of Physics in their discrete and
fundamental form.


title: Internal symmetry in Bianchi type-I cosmologies

abstract:
  Using the one-parameter internal symmetry group in the Bianchi type-I
spacetime for cosmological models with a perfect fluid, we show that a system
of coordinates exists in the associated internal space where two scale factors
become equal. We find the general solution for an anisotropic model containing
a perfect fluid with constant baryotropic index and investigate the asymptotic
regimes. We obtain exact solutions for a set of anisotropic fluids which
includes an anisotropic stiff fluid.


title: Fluctuations of Quantum Radiation Pressure in Dissipative Fluid

abstract:
  Using the generalized Langevin equations involving the stress tensor
approach, we study the dynamics of a perfectly reflecting mirror which is
exposed to the electromagnetic radiation pressure by a laser beam in a fluid at
finite temperature. Based on the fluctuation-dissipation theorem, the minimum
uncertainty of the mirror's position measurement from both quantum and thermal
noises effects including the photon counting error in the laser interferometer
is obtained in the small time limit as compared with the "standard quantum
limit".
  The result of the large time behavior of fluctuations of the mirror's
velocity in a dissipative environment can be applied to the laser
interferometer of the ground-based gravitational wave detector.


title: Gravitational Collapse of Self-Similar Perfect Fluid in 2+1 Gravity

abstract:
  Perfect fluid with kinematic self-similarity is studied in 2+1 dimensional
spacetimes with circular symmetry, and various exact solutions to the Einstein
field equations are given. In particular, these include all the solutions of
dust and stiff perfect fluid with self-similarity of the first kind, and all
the solutions of perfect fluid with a linear equation of state and
self-similarity of the zeroth or second kind. It is found that some of these
solutions represent gravitational collapse, and the final state of the collapse
can be either black holes or naked singularities.


title:
On the Stability of Spherically Symmetric Configurations in Newtonian
  Limit of Jordan, Brans-Dicke Theory

abstract:
  We discuss stability of spherically symmetric static solutions in Newtonian
limit of Jordan, Brans-Dicke field equations. The behavior of the stable
equilibrium solutions for the spherically symmetric configurations considered
here, it emerges that the more compact a model is, the more stable it is.
Moreover, linear stability analysis shows the existence of stable
configurations for any polytropic index.


title: On Diffeomorphism Invariance and Black Hole Entropy

abstract:
  The Noether-charge realization and the Hamiltonian realization for the
$\diff({\cal M})$ algebra in diffeomorphism invariant gravitational theories
are studied in a covariant formalism. For the Killing vector fields, the
Nother-charge realization leads to the mass formula as an entire vanishing
Noether charge for the vacuum black hole spacetimes in general relativity and
the corresponding first law of the black hole mechanics. It is analyzed in
which sense the Hamiltonian functionals form the $\diff({\cal M})$ algebra
under the Poisson bracket and shown how the Noether charges with respect to the
diffeomorphism generated by vector fields and their variations in general
relativity form this algebra. The asymptotic behaviors of vector fields
generating diffeomorphism of the manifold with boundaries are discussed. In
order to get more precise estimation for the "central extension" of the
algebra, it is analyzed in the Newman-Penrose formalism and shown that the
"central extension" for a large class of vector fields is always zero on the
Killing horizon. It is also checked whether the Virasoro algebra may be picked
up by choosing the vector fields near the horizon. The conclusion is
unfortunately negative.


title: The Copernican Principle in Compact Spacetimes

abstract:
  Copernicus realised we were not at the centre of the universe. A universe
made finite by topological identifications introduces a new Copernican
consideration: while we may not be at the geometric centre of the universe,
some galaxy could be. A finite universe also picks out a preferred frame: the
frame in which the universe is smallest. Although we are not likely to be at
the centre of the universe, we must live in the preferred frame (if we are at
rest with respect to the cosmological expansion). We show that the preferred
topological frame must also be the comoving frame in a homogeneous and
isotropic cosmological spacetime. Some implications of topologically
identifying time are also discussed.


title: Closed Trapped Surfaces in Cosmology

abstract:
  The existence of closed trapped surfaces need not imply a cosmological
singularity when the spatial hypersurfaces are compact. This is illustrated by
a variety of examples, in particular de Sitter spacetime admits many closed
trapped surfaces and obeys the null convergence condition but is non-singular
in the k=+1 frame.


title: Global constants in (2+1)--dimensional gravity

abstract:
  The extended conformal algebra (so)(2,3) of global, quantum, constants of
motion in 2+1 dimensional gravity with topology R x T^2 and negative
cosmological constant is reviewed. It is shown that the 10 global constants
form a complete set by expressing them in terms of two commuting spinors and
the Dirac gamma matrices. The spinor components are the globally constant
holonomy parameters, and their respective spinor norms are their quantum
commutators.


title: Reply to "Acausality of Massive Charged Spin 2 Fields"

abstract:
  We show that, contrary to the claim in hep-th/0304050, the propagation of a
spin-2 field in an electromagnetic background is {\em causal}.


title: Do black holes radiate?

abstract:
  The prediction that black holes radiate due to quantum effects is often
considered one of the most secure in quantum field theory in curved space-time.
Yet this prediction rests on two dubious assumptions: that ordinary physics may
be applied to vacuum fluctuations at energy scales increasing exponentially
without bound; and that quantum-gravitational effects may be neglected. Various
suggestions have been put forward to address these issues: that they might be
explained away by lessons from sonic black hole models; that the prediction is
indeed successfully reproduced by quantum gravity; that the success of the link
provided by the prediction between black holes and thermodynamics justifies the
prediction.
  This paper explains the nature of the difficulties, and reviews the proposals
that have been put forward to deal with them. None of the proposals put forward
can so far be considered to be really successful, and simple dimensional
arguments show that quantum-gravitational effects might well alter the
evaporation process outlined by Hawking. Thus a definitive theoretical
treatment will require an understanding of quantum gravity in at least some
regimes. Until then, no compelling theoretical case for or against radiation by
black holes is likely to be made.
  The possibility that non-radiating "mini" black holes exist should be taken
seriously; such holes could be part of the dark matter in the Universe.
Attempts to place observational limits on the number of "mini" black holes
(independent of the assumption that they radiate) would be most welcome.


title: United Approach to the Universe Model and the Local Gravitation Problem

abstract:
  A united approach of the large-scale structure of a closed universe and the
local spherically symmetric gravitational field is given by supposing an
appropriate boundary condition. The general feature of the model obtained are
the following. The universe is approximately homogeneous and isotropic on the
average on large scale and is expanding at present, as described by the
standard model; while locally, the small exterior region of a star started long
ago to contract, as expected by the gravitational collapse theory.


title:
A Classification of Spherically Symmetric Kinematic Self-Similar
  Perfect-Fluid Solutions. II

abstract:
  We give a classification of spherically symmetric kinematic self-similar
solutions. This classification is complementary to that given in a previous
work by the present authors [Prog. Theor. Phys. 108, 819 (2002)]. Dust
solutions of the second, zeroth and infinite kinds, perfect-fluid solutions and
vacuum solutions of the first kind are treated. The kinematic self-similarity
vector is either parallel or orthogonal to the fluid flow in the perfect-fluid
and vacuum cases, while the `tilted' case, i.e., neither parallel nor
orthogonal case, is also treated in the dust case. In the parallel case, there
are no dust solutions of the second (except when the self-similarity index
$\alpha$ is 3/2), zeroth and infinite kinds, and in the orthogonal case, there
are no dust solutions of the second and infinite kinds. Except in these cases,
the governing equations can be integrated to give exact solutions. It is found
that the dust solutions in the tilted case belong to a subclass of the Lema{\^
i}tre-Tolman-Bondi family of solutions for the marginally bound case. The flat
Friedmann-Robertson-Walker (FRW) solution is the only dust solution of the
second kind with $\alpha=3/2$ in the tilted and parallel cases and of the
zeroth kind in the orthogonal case. The flat, open and closed FRW solutions
with $p=-\mu/3$, where $p$ and $\mu$ are the pressure and energy density,
respectively, are the only perfect-fluid first-kind self-similar solutions in
the parallel case, while a new exact solution with $p=\mu$, which we call the
``singular stiff-fluid solution'', is the only such solution in the orthogonal
case. The Minkowski solution is the only vacuum first-kind self-similar
solution both in the parallel and orthogonal cases. Some important corrections
and complements to the authors' previous work are also presented.


title: Multiple Photonic Shells Around a Line Singularity

abstract:
  Line singularities including cosmic strings may be screened by photonic
shells until they appear as a planar wall.


title: Anisotropic brane cosmologies with exponential potentials

abstract:
  We study Bianchi I type brane cosmologies with scalar matter self-interacting
through combinations of exponential potentials. Such models correspond in some
cases to inflationary universes. We discuss the conditions for accelerated
expansion to occur, and pay particular attention to the influence of extra
dimensions and anisotropy. Our results show that the associated effects evolve
in such a way that they become negligible in the late time limit, those related
to the anisotropy disappearing earlier. This study focuses mainly on single
field models, but we also consider a generalization yielding models with
multiple non-interacting fields and examine its features briefly. We conclude
that in the brane scenario, as happens in general relativity, an increase in
the number of fields assists inflation.


title: Microcausality and Quantum Cylindrical Gravitational Waves

abstract:
  We study several issues related to the different choices of time available
for the classical and quantum treatment of linearly polarized cylindrical
gravitational waves. We pay especial attention to the time evolution of
creation and annihilation operators and the definition of Fock spaces for the
different choices of time involved. We discuss also the issue of microcausality
and the use of field commutators to extract information about the causal
properties of quantum spacetime.


title:
On low energy quantum gravity induced effects on the propagation of
  light

abstract:
  Present models describing the interaction of quantum Maxwell and
gravitational fields predict a breakdown of Lorentz invariance and a non
standard dispersion relation in the semiclassical approximation. Comparison
with observational data however, does not support their predictions. In this
work we introduce a different set of ab initio assumptions in the canonical
approach, namely that the homogeneous Maxwell equations are valid in the
semiclassical approximation, and find that the resulting field equations are
Lorentz invariant in the semiclassical limit. We also include a
phenomenological analysis of possible effects on the propagation of light, and
their dependence on energy, in a cosmological context.


title: On the Big Bounce Singularity of a Simple 5D Cosmological Model

abstract:
  The big bounce singularity of a simple 5D cosmological model is studied.
Contrary to the standard big bang space-time singularity, this big bounce
singularity is found to be an event horizon at which the scale factor and the
mass density of the universe are finite, while the pressure undergoes a sudden
transition from negative infinity to positive infinity. By using coordinate
transformation it is also shown that before the bounce the universe contracts
deflationary, and the universe has been existed, according to the proper-time,
for an infinitely long time.


title: The Future of Tilted Bianchi Universes

abstract:
  An asymptotic stability analysis of spatially homogeneous models of Bianchi
type containing tilted perfect fluids is performed. Using the known attractors
for the non-tilted Bianchi type universes, we check whether they are stable
against perturbations with respect to tilted perfect fluids. We perform the
analysis for all Bianchi class B models and the Bianchi type VI_0 model. In
particular, we find that none of the non-tilted equilibrium points are stable
against tilted perfect fluids stiffer than radiation. We also indicate parts of
the phase space where new tilted exact solutions might be found.


title: Matter-Antimatter Asymmetry Generated by Loop Quantum Gravity

abstract:
  We show that Loop Quantum Gravity provides new mechanisms through which
observed matter-antimatter asymmetry in the Universe can naturally arise at
temperatures less than GUT scale. This is enabled through the introduction of a
new length scale ${\cal L}$, much greater than Planck length ($l_P$), to obtain
semi-classical weave states in the theory. This scale which depends on the
momentum of the particle modifies the dispersion relation for different
helicities of fermions and leads to lepton asymmetry.


title: Developments in General Relativity: Black Hole Singularity and Beyond

abstract:
  At the 20-th Texas Symposium on Relativistic Astrophysics there was a plenary
talk devoted to the recent developments in classical Relativity. In that talk
the problems of gravitational collapse, collisions of black holes, and of black
holes as celestial bodies were discussed. But probably the problems of the
internal structure of black holes are a real great challenge. In my talk I want
to outline the recent achievements in our understanding of the nature of the
singularity (and beyond!) inside a realistic rotating black hole. This
presentation also addresses the following questions: Can we see what happens
inside a black hole? Can a falling observer cross the singularity without being
crushed? An answer to these questions is probably "yes".


title:
Quasinormal modes of d-dimensional spherical black holes with a near
  extreme cosmological constant

abstract:
  We derive an expression for the quasinormal modes of scalar perturbations in
near extreme d-dimensional Schwarzschild-de Sitter and Reissner-Nordstrom-de
Sitter black holes. We show that, in the near extreme limit, the dynamics of
the scalar field is characterized by a Poschl-Teller effective potential. The
results are qualitatively independent of the spacetime dimension and field
mass.


title: Asymptotic Flatness and Bondi Energy in Higher Dimensional Gravity

abstract:
  We give a general geometric definition of asymptotic flatness at null
infinity in $d$-dimensional general relativity ($d$ even) within the framework
of conformal infinity. Our definition is arrived at via an analysis of linear
perturbations near null infinity and shown to be stable under such
perturbations. The detailed fall off properties of the perturbations, as well
as the gauge conditions that need to be imposed to make the perturbations
regular at infinity, are qualitatively different in higher dimensions; in
particular, the decay rate of a radiating solution at null infinity differs
from that of a static solution in higher dimensions. The definition of
asymptotic flatness in higher dimensions consequently also differs
qualitatively from that in $d=4$.
  We then derive an expression for the generator conjugate to an asymptotic
time translation symmetry for asymptotically flat spacetimes in $d$-dimensional
general relativity ($d$ even) within the Hamiltonian framework, making use
especially of a formalism developed by Wald and Zoupas. This generator is given
by an integral over a cross section at null infinity of a certain local
expression and is taken to be the definition of the Bondi energy in $d$
dimensions. Our definition yields a manifestly positive flux of radiated
energy.
  Our definitions and constructions fail in odd spacetime dimensions,
essentially because the regularity properties of the metric at null infinity
seem to be insufficient in that case. We also find that there is no direct
analog of the well-known infinite set of angle dependent translational
symmetries in more than 4 dimensions.


title: Immirzi Ambiguity, Boosts and Conformal Frames for Black Holes

abstract:
  We analyze changes of the Immirzi parameter in loop quantum gravity and
compare their consequences with those of Lorentz boosts and constant conformal
transformations in black hole physics. We show that the effective value deduced
for the Planck length in local measurements of vacuum black holes by an
asymptotic observer may depend on its conformal or Lorentz frame. This
introduces an apparent ambiguity in the expression of the black hole entropy
which is analogous to that produced by the Immirzi parameter. For quantities
involving a notion of energy, the similarity between the implications of the
Immirzi ambiguity and a conformal scaling disappears, but the parallelism with
boosts is maintained.


title: Lyapunov timescales and black hole binaries

abstract:
  Black holes binaries support unstable orbits at very close separations. In
the simplest case of geodesics around a Schwarzschild black hole the orbits,
though unstable, are regular. Under perturbation the unstable orbits can become
the locus of chaos. All unstable orbits, whether regular or chaotic, can be
quantified by their Lyapunov exponents. The exponents are observationally
relevant since the phase of gravitational waves can decohere in a Lyapunov
time. If the timescale for dissipation due to gravitational waves is shorter
than the Lyapunov time, chaos will be damped and essentially unobservable. We
find the timescales can be comparable. We emphasize that the Lyapunov exponents
must only be used cautiously for several reasons: they are relative and depend
on the coordinate system used, they vary from orbit to orbit, and finally they
can be deceptively diluted by transient behaviour for orbits which pass in and
out of unstable regions.


title: Quantum Noise and Fluctuations in Gravitation and Cosmology

abstract:
  We give a short update of our research program on nonequilibrium statistical
field theory applied to quantum processes in the early universe and black
holes, as well as the development of stochastic gravity theory as an extension
of semiclassical gravity and an intermediary in the 'bottom-up' approach to
quantum gravity.


title:
Scale Invariant Spectrum from Variable Speed of Light Metric in a
  Bimetric Gravity Theory

abstract:
  An approximately scale invariant spectrum generating the seeds of structure
formation is derived from a bimetric gravity theory. By requiring that the
amplitude of the CMB fluctuations from the model matches the observed value, we
determine the fundamental length scale in the model to be a factor of 10^5
times larger than the Planck length, which results in a scalar mode spectral
index: n_s\approx 0.97, and its running: \alpha_s\approx -5\times 10^{-4}. This
is accomplished in the variable speed of light (VSL) metric frame, in which the
dynamics of perturbations of the bimetric scalar field are determined by a
minimally-coupled Klein-Gordon equation, and it is assumed that modes are born
in a ground state at a scale given by the fundamental length scale appearing in
the bimetric structure. We show that while this is taking place for scales of
interest, the background (primordial) radiation energy density is strongly
suppressed as a result of the bimetric structure of the model. Nevertheless,
the enlarged lightcone of matter fields ensures that the horizon and flatness
problems are solved.


title: Quantum Gravitational Optics

abstract:
  In quantum theory, the curved spacetime of Einstein's general theory of
relativity acts as a dispersive optical medium for the propagation of light.
Gravitational rainbows and birefringence replace the classical picture of light
rays mapping out the null geodesics of curved spacetime. Even more remarkably,
{\it superluminal} propagation becomes a real possibility, raising the question
of whether it is possible to send signals into the past. In this article, we
review recent developments in the quantum theory of light propagation in
general relativity and discuss whether superluminal light is compatible with
causality.


title:
Low pumping energy mode of the "optical bars''/"optical lever"
  topologies of gravitational-wave antennae

abstract:
  The ``optical bars''/``optical lever'' topologies of gravitational-wave
antennae allow to obtain sensitivity better that the Standard Quantum Limit
while keeping the optical pumping energy in the antenna relatively low. Element
of the crucial importance in these schemes is the local meter which monitors
the local test mirror position. Using cross-correlation of this meter
back-action noise and its measurement noise it is possible to further decrease
the optical pumping energy. In this case the pumping energy minimal value will
be limited by the internal losses in the antenna only. Estimates show that for
values of parameters available for contemporary and planned gravitational-wave
antennae, sensitivity about one order of magnitude better than the Standard
Quantum Limit can be obtained using the pumping energy about one order of
magnitude smaller energy than is required in the traditional topology in order
to obtain the the Standard Quantum Limit level of sensitivity.


title: Phenomenology of effective gravity

abstract:
  The cosmological constant is not an absolute constant. The gravitating part
of the vacuum energy is adjusted to the energy density of matter and to other
types of the perturbations of the vacuum. We discuss how the vacuum energy
responds (i) to the curvature of space in the Einstein closed Universe; (ii) to
the expansion rate in the de Sitter Universe; and (iii) to the rotation in the
Goedel Universe. In all these steady state Universes, the gravitating vacuum
energy is zero in the absence of the perturbation, and is proportional to the
energy density of perturbation. This is in a full agreement with the
thermodynamic Gibbs-Duhem relation applicable to any quantum vacuum. It
demonstrates that (i) the cosmological constant is not huge, since according to
the Gibbs-Duhem relation the contribution of zero point fluctuations to the
vacuum energy is cancelled by the trans-Planckian degrees of freedom; (ii) the
cosmological constant is non-zero, since the perturbations of the vacuum state
induce the non-zero vacuum energy; and (iii) the gravitating vacuum energy is
on the order of the energy density of matter and/or of other perturbations. We
also consider the vacuum response to the non-steady-state perturbations. In
this case the Einstein equations are modified to include the non-covariant
corrections, which are responsible for the relaxation of the cosmological
constant. The connection to the quintessence is demonstrated. The problem of
the energy-momentum tensor for the gravitational field is discussed in terms of
effective gravity. The difference between the momentum and pseudo-momentum of
gravitational waves in general relativity is similar to that for sound waves in
hydrodynamics.


title:
Dynamical control of the constraints growth in free evolutions of
  Einstein's equations

abstract:
  I present a new, simple method to dynamically control the growth of the
discretized constraints during a free evolution of Einstein's equations. During
an evolution, any given family of formulations is adjusted off the constraints
surface in a way such that, for any chosen numerical method and arbitrary but
fixed resolution, the constraints growth can be minimized with respect to the
freedom allowed by the formulation. In particular, provided there is enough
freedom, the discretized constraints can be maintained close to its initial
truncation value for all times, or decay from it.
  No a priori knowledge of the solution is needed, and the method can be
applied to any formulation of Einstein's equations without affecting
hyperbolicity. This method is independent of the numerical algorithm and
accounts for constraint violating modes introduced both by continuum
instabilities of the formulation and by the numerical method.


title: Spin Waves as Metric in a Kinetic Space-Time

abstract:
  1) A wave equation is derived from the kinetic equations governing media with
rotational as well as translational degrees of freedom. In this wave the
fluctuating quantity is a vector, the bulk spin. The transmission is similar to
compressive waves but propagation is possible even in the limit of
incompressibility, where such disturbances could become dominant. 2) In this
context a kinetic theory of space-time is introduced, in which hypothetical
constituents of the space-time manifold possess such a rotational degree of
freedom (spin). Physical fields (i.e. electromagnetic or gravitational) in such
a theory are represented as moments of a statistical distribution of these
constituents. The spin wave equation from 1) is treated as a candidate for
governing light and metric. Such a theory duplicates to first order Maxwell's
equations of electromagnetism, Schrodinger's equation for the electron, and the
Lorentz transformations of special relativity. Slight deviations from the
classical approach are predicted and should be experimentally verifiable.


title:
Global structure of the Zipoy-Voorhees-Weyl spacetime and the delta=2
  Tomimatsu-Sato spacetime

abstract:
  We investigate the structure of the ZVW (Zipoy-Voorhees-Weyl) spacetime,
which is a Weyl solution described by the Zipoy-Voorhees metric, and the
delta=2 Tomimatsu-Sato spacetime. We show that the singularity of the ZVW
spacetime, which is represented by a segment rho=0, -sigma<z<sigma in the Weyl
coordinates, is geometrically point-like for delta<0, string-like for 0<delta<1
and ring-like for delta>1. These singularities are always naked and have
positive Komar masses for delta>0. Thus, they provide a non-trivial example of
naked singularities with positive mass. We further show that the ZVW spacetime
has a degenerate Killing horizon with a ring singularity at the equatorial
plane for delta=2,3 and delta>=4. We also show that the delta=2 Tomimatsu-Sato
spacetime has a degenerate horizon with two components, in contrast to the
general belief that the Tomimatsu-Sato solutions with even delta do not have
horizons.


title: An inverse approach to Einstein's equations for non-conducting fluids

abstract:
  We show that a flow (timelike congruence) in any type $B_{1}$ warped product
spacetime is uniquely and algorithmically determined by the condition of zero
flux. (Though restricted, these spaces include many cases of interest.) The
flow is written out explicitly for canonical representations of the spacetimes.
With the flow determined, we explore an inverse approach to Einstein's
equations where a phenomenological fluid interpretation of a spacetime follows
directly from the metric irrespective of the choice of coordinates. This
approach is pursued for fluids with anisotropic pressure and shear viscosity.
In certain degenerate cases this interpretation is shown to be generically not
unique. The framework developed allows the study of exact solutions in any
frame without transformations. We provide a number of examples, in various
coordinates, including spacetimes with and without unique interpretations. The
results and algorithmic procedure developed are implemented as a computer
algebra program called GRSource.


title:
Anti-self-dual Riemannian metrics without Killing vectors, can they be
  realized on K3?

abstract:
  Explicit Riemannian metrics with Euclidean signature and anti-self dual
curvature that do not admit any Killing vectors are presented. The metric and
the Riemann curvature scalars are homogenous functions of degree zero in a
single real potential and its derivatives. The solution for the potential is a
sum of exponential functions which suggests that for the choice of a suitable
domain of coordinates and parameters it can be the metric on a compact
manifold. Then, by the theorem of Hitchin, it could be a class of metrics on
$K3$, or on surfaces whose universal covering is $K3$.


title: Density perturbations in a brane-world universe with dark radiation

abstract:
  We investigate the effects on cosmological density perturbations of dark
radiation in a Randall-Sundrum 2 type brane-world. Dark radiation in the
background is limited by observational constraints to be a small fraction of
the radiation energy density, but it has an interesting qualitative effect in
the radiation era. On large scales, it serves to slightly suppress the
radiation density perturbations at late times, while boosting the perturbations
in dark radiation. In a kinetic (stiff) era, the suppression is much stronger,
and drives the density perturbations to zero.


title: On a general class of brane-world black holes

abstract:
  We use the general solution to the trace of the 4-dimensional Einstein
equations for static, spherically symmetric configurations as a basis for
finding a general class of black hole (BH) metrics, containing one arbitrary
function $g_{tt} = A(r)$ which vanishes at some $r = r_h > 0$, the horizon
radius. Under certain reasonable restrictions, BH metrics are found with or
without matter and, depending on the boundary conditions, can be asymptotically
flat or have any other prescribed large $r$ behaviour. It is shown that this
procedure generically leads to families of solutions unifying non-extremal
globally regular BHs with a Kerr-like global structure, extremal BHs and
symmetric wormholes. Horizons in space-times with zero scalar curvature are
shown to be either simple or double. The same is generically true for horizons
inside a matter distribution, but in special cases there can be horizons of any
order. A few simple examples are discussed. A natural application of the above
results is the brane world concept, in which the trace of the 4D gravity
equations is the only unambiguous equation for the 4D metric, and its solutions
can be continued into the 5D bulk according to the embedding theorems.


title: Electromagnetic Waves in a Rotating Frame of Reference

abstract:
  We discuss the electromagnetic measurements of rotating observers and study
the propagation of electromagnetic waves in a uniformly rotating frame of
reference. The phenomenon of helicity-rotation coupling is elucidated and some
of the observational consequences of the coupling of the spin of a particle
with the rotation of a gravitational source are briefly examined.


title:
Global structure of Choptuik's critical solution in scalar field
  collapse

abstract:
  At the threshold of black hole formation in the gravitational collapse of a
scalar field a naked singularity is formed through a universal critical
solution that is discretely self-similar. We study the global spacetime
structure of this solution. It is spherically symmetric, discretely
self-similar, regular at the center to the past of the singularity, and regular
at the past lightcone of the singularity. At the future lightcone of the
singularity, which is also a Cauchy horizon, the curvature is finite and
continuous but not differentiable. To the future of the Cauchy horizon the
solution is not unique, but depends on a free function (the null data coming
out of the naked singularity). There is a unique continuation with a regular
center (which is self-similar). All other self-similar continuations have a
central timelike singularity with negative mass.


title: Tensorial Perturbations in an Accelerating Universe

abstract:
  We study tensorial perturbations (gravitational waves) in a universe with
particle production (OSC). The background of gravitational waves produces a
perturbation in the redshift observed from distant sources. The modes for the
perturbation in the redshift (induced redshift) are calculated in a universe
with particle production.


title: A study of higher dimensional inhomogeneous cosmological model

abstract:
  In this paper we present a class of exact inhomogeneous solutions to
Einstein's equations for higher dimensional Szekeres metric with perfect fluid
and a cosmological constant. We also show particular solutions depending on the
choices of various parameters involved and for dust case. Finally, we examine
the asymptotic behaviour of some of these solutions.


title: r-modes in Relativistic Superfluid Stars

abstract:
  We discuss the modal properties of the $r$-modes of relativistic superfluid
neutron stars, taking account of the entrainment effects between superfluids.
In this paper, the neutron stars are assumed to be filled with neutron and
proton superfluids and the strength of the entrainment effects between the
superfluids are represented by a single parameter $\eta$. We find that the
basic properties of the $r$-modes in a relativistic superfluid star are very
similar to those found for a Newtonian superfluid star. The $r$-modes of a
relativistic superfluid star are split into two families, ordinary fluid-like
$r$-modes ($r^o$-mode) and superfluid-like $r$-modes ($r^s$-mode). The two
superfluids counter-move for the $r^s$-modes, while they co-move for the
$r^o$-modes. For the $r^o$-modes, the quantity $\kappa\equiv\sigma/\Omega+m$ is
almost independent of the entrainment parameter $\eta$, where $m$ and $\sigma$
are the azimuthal wave number and the oscillation frequency observed by an
inertial observer at spatial infinity, respectively. For the $r^s$-modes, on
the other hand, $\kappa$ almost linearly increases with increasing $\eta$. It
is also found that the radiation driven instability due to the $r^s$-modes is
much weaker than that of the $r^o$-modes because the matter current associated
with the axial parity perturbations almost completely vanishes.


title: Mathematical structure of loop quantum cosmology

abstract:
  Applications of Riemannian quantum geometry to cosmology have had notable
successes. In particular, the fundamental discreteness underlying quantum
geometry has led to a natural resolution of the big bang singularity. However,
the precise mathematical structure underlying loop quantum cosmology and the
sense in which it implements the full quantization program in a symmetry
reduced model has not been made explicit. The purpose of this paper is to
address these issues, thereby providing a firmer mathematical and conceptual
foundation to the subject.


title:
Gravitational Collapse of Perfect Fluid in Self-Similar Higher
  Dimensional Space-Times

abstract:
  We investigate the occurrence and nature of naked singularities in the
gravitational collapse of an adiabatic perfect fluid in self-similar higher
dimensional space-times. It is shown that strong curvature naked singularities
could occur if the weak energy condition holds. Its implication for cosmic
censorship conjecture is discussed. Known results of analogous studies in four
dimensions can be recovered.


title: High Speed Dynamics of Collapsing Cylindrical Dust Fluid

abstract:
  We construct approximate solutions that will describe the last stage of
cylindrically symmetric gravitational collapse of dust fluid. Just before the
spacetime singularity formation, the speed of the dust fluid might be almost
equal to the speed of light by gravitational acceleration. Therefore the
analytic solution describing the dynamics of cylindrical null dust might be the
crudest approximate solution of the last stage of the gravitational collapse.
In this paper, we regard this null dust solution as a background and perform
`high-speed approximation' to know the gravitational collapse of ordinary
timelike dust fluid; the `deviation of the timelike
  4-velocity vector field from null' is treated as a perturbation. In contrast
with the null dust approximation, our approximation scheme can describe the
generation of gravitational waves in the course of the cylindrically symmetric
dust collapse.


title:
A New Approach to Quantising Space-Time: II. Quantising on a Category of
  Sets

abstract:
  In a recent paper by the author, a new approach was suggested for quantising
space-time, or space. This involved developing a procedure for quantising a
system whose configuration space--or history-theory analogue--is the set of
objects in a (small) category $\Q$. In the present paper, we show how this
theory can be applied to the special case when $\Q$ is a category of sets. This
includes the physically important examples where $\Q$ is a category of causal
sets, or topological spaces.


title: Troubles with quantum anistropic cosmological models: Loss of unitarity

abstract:
  The anisotropic Bianchi I cosmological model coupled with perfect fluid is
quantized in the minisuperspace. The perfect fluid is described by using the
Schutz formalism which allows to attribute dynamical degrees of freedom to
matter. A Schr\"odinger-type equation is obtained where the matter variables
play the role of time. However, the signature of the kinetic term is
hyperbolic. This Schr\"odinger-like equation is solved and a wave packet is
constructed. The norm of the resulting wave function comes out to be time
dependent, indicating the loss of unitarity in this model. The loss of
unitarity is due to the fact that the effective Hamiltonian is hermitian but
not self-adjoint. The expectation value and the bohmian trajectories are
evaluated leading to different cosmological scenarios, what is a consequence of
the absence of a unitary quantum structure. The consistency of this quantum
model is discussed as well as the generality of the absence of unitarity in
anisotropic quantum models.


title:
The Magueijo-Smolin Group in Doubly-Special Relativity is Linear in Five
  Dimensions

abstract:
  Magueijo and Smolin have introduced a modification of the Lorentz group for
the momentum-space transformations in Doubly-Special Relativity. As presented
the group is non-linear, but we show that it is a group of fraction-linear
transformations in 4 dimensional real projective space. We pass to the
associated 5 dimensional linear space and identify the subgroup as a conjugate
of the ordinary Lorentz group, giving the conjugating matrix. Taking the dual
of the 5-space, we identify a subgroup as the Lorentz transformations about a
point different to the origin.


title:
Time-symmetric initial data for binary black holes in numerical
  relativity

abstract:
  We look for physically realistic initial data in numerical relativity which
are in agreement with post-Newtonian approximations. We propose a particular
solution of the time-symmetric constraint equation, appropriate to two
momentarily static black holes, in the form of a conformal decomposition of the
spatial metric. This solution is isometric to the post-Newtonian metric up to
the 2PN order. It represents a non-linear deformation of the solution of Brill
and Lindquist, i.e. an asymptotically flat region is connected to two
asymptotically flat (in a certain weak sense) sheets, that are the images of
the two singularities through appropriate inversion transformations. The total
ADM mass M as well as the individual masses m_1 and m_2 (when they exist) are
computed by surface integrals performed at infinity. Using second order
perturbation theory on the Brill-Lindquist background, we prove that the
binary's interacting mass-energy M-m_1-m_2 is well-defined at the 2PN order and
in agreement with the known post-Newtonian result.


title: Energy distribution in the dyadosphere of a charged black hole

abstract:
  The event horizon of a charged black hole is, according to
Ruffini\cite{Ruffini} and Preparata \emph{et al.}\cite{PreparataEtAl},
surrounded by a special region called the \emph{dyadosphere} where the
electromagnetic field exceeds the Euler-Heisenberg critical value for
electron-positron pair production. We obtain the energy distribution in the
dyadosphere region for a Reissner-Nordstr\"{o}m black hole. We find that the
energy-momentum prescriptions of Einstein, Landau-Lifshitz, Papapetrou, and
Weinberg give the same and acceptable energy distribution.


title: Quantum physics in inertial and gravitational fields

abstract:
  Covariant generalizations of well-known wave equations predict the existence
of inertial-gravitational effects for a variety of quantum systems that range
from Bose-Einstein condensates to particles in accelerators. Additional effects
arise in models that incorporate Born reciprocity principle and the notion of a
maximal acceleration. Some specific examples are discussed in detail.


title: Interaction of a brane with a moving bulk black hole

abstract:
  We study the interaction of an n-dimensional topological defect (n-brane)
described by the Nambu-Goto action with a higher-dimensional Schwarzschild
black hole moving in the bulk spacetime. We derive the general form of the
perturbation equations for an n-brane in the weak field approximation and solve
them analytically in the most interesting cases. We specially analyze
applications to brane world models. We calculate the induced geometry on the
brane generated by a moving black hole. From the point of view of a brane
observer, this geometry can be obtained by solving (n+1)-dimensional Einstein's
equations with a non-vanishing right hand side. We calculate the effective
stress-energy tensor corresponding to this `shadow-matter'. We explicitly show
that there exist regions on the brane where a brane observer sees an apparent
violation of energy conditions. We also study the deflection of light
propagating in the region of influence of this `shadow matter'.


title:
Gravitomagnetic Moments and Dynamics of Dirac's (spin 1/2) fermions in
  flat space-time Maxwellian Gravity

abstract:
  The gravitational effects in the relativistic quantum mechanics are
investigated in a relativistically derived version of Heaviside's speculative
Gravity (in flat space-time) named here as Maxwellian Gravity. The standard
Dirac's approach to the intrinsic spin in the fields of Maxwellian Gravity
yields the gravitomagnetic moment of a Dirac (spin 1/2) particle exactly equals
to its intrinsic spin. Violation of The Equivalence Principle (both at
classical and quantum mechanical level) in the relativistic domain has also
been reported in this work.


title: Towards the Final Fate of an Unstable Black String

abstract:
  Black strings, one class of higher dimensional analogues of black holes, were
shown to be unstable to long wavelength perturbations by Gregory and Laflamme
in 1992, via a linear analysis. We revisit the problem through numerical
solution of the full equations of motion, and focus on trying to determine the
end-state of a perturbed, unstable black string. Our preliminary results show
that such a spacetime tends towards a solution resembling a sequence of
spherical black holes connected by thin black strings, at least at intermediate
times. However, our code fails then, primarily due to large gradients that
develop in metric functions, as the coordinate system we use is not well
adapted to the nature of the unfolding solution. We are thus unable to
determine how close the solution we see is to the final end-state, though we do
observe rich dynamical behavior of the system in the intermediate stages.


title:
Progress in relativistic gravitational theory using the inverse
  scattering method

abstract:
  The increasing interest in compact astrophysical objects (neutron stars,
binaries, galactic black holes) has stimulated the search for rigorous methods,
which allow a systematic general relativistic description of such objects. This
paper is meant to demonstrate the use of the inverse scattering method, which
allows, in particular cases, the treatment of rotating body problems. The idea
is to replace the investigation of the matter region of a rotating body by the
formulation of boundary values along the surface of the body. In this way we
construct solutions describing rotating black holes and disks of dust
("galaxies"). Physical properties of the solutions and consequences of the
approach are discussed. Among other things, the balance problem for two black
holes can be tackled.


title: LaPlace, Weimar, Schiller and the birth of black hole theory

abstract:
  From the original papers an interesting and surprising connection is
established between LaPlace and his early discovery that black holes may occur
in nature, and a poem by Schiller.


title: From areas to lengths in quantum Regge calculus

abstract:
  Quantum area tensor Regge calculus is considered, some properties are
discussed. The path integral quantisation is defined for the usual length-based
Regge calculus considered as a particular case (a kind of a state) of the area
tensor Regge calculus. Under natural physical assumptions the quantisation of
interest is practically unique up to an additional one-parametric local factor
of the type of a power of $\det\|g_{\lambda\mu}\|$ in the measure. In
particular, this factor can be adjusted so that in the continuum limit we would
have any of the measures usually discussed in the continuum quantum gravity,
namely, Misner, DeWitt or Leutwyler measure. It is the latter two cases when
the discrete measure turns out to be well-defined at small lengths and lead to
finite expectation values of the lengths.


title: Brane-world cosmological perturbations: a covariant approach

abstract:
  The standard cosmological model, based on general relativity with an
inflationary era, is very effective in accounting for a broad range of observed
features of the universe. However, the ongoing puzzles about the nature of dark
matter and dark energy, together with the problem of a fundamental theoretical
framework for inflation, indicate that cosmology may be probing the limits of
validity of general relativity. The early universe provides a testing ground
for theories of gravity, since gravitational dynamics can lead to
characteristic imprints on the CMB and other cosmological observations.
Precision cosmology is in principle a means to constrain and possibly falsify
candidate quantum gravity theories like M theory. Generalized Randall-Sundrum
brane-worlds provide a phenomenological means to test aspects of M theory. I
outline the 1+3-covariant approach to cosmological perturbations in these
brane-worlds, and its application to CMB anisotropies.


title:
Near-field Analysis of Superluminally Propagating Electromagnetic and
  Gravitational Fields

abstract:
  A near-field analysis based on Maxwells equations is presented which
indicates that the fields generated by both an electric and a magnetic dipole
or quadrapole, and also the gravitational waves generated by a quadrapole mass
source propagate superluminally in the nearfield of the source and reduce to
the speed of light as the waves propagate into the farfield. Both the phase
speed and the group speed are shown to be superluminal in the nearfield of
these systems. Although the information speed is shown to differ from group
speed in the nearfield of these systems, provided the noise of the signal is
small and the modulation method is known, the information can be extracted in a
time period much smaller than the wave propagation time, thereby making the
information speed only slightly less than the superluminal group speed. It is
shown that relativity theory indicates that these superluminal signals can be
reflected off of a moving frame causing the information to arrive before the
signal was transmitted (i.e. backward in time). It is unknown if these signals
can be used to change the past.


title: A perturbative solution for gravitational waves in quadratic gravity

abstract:
  We find a gravitational wave solution to the linearized version of quadratic
gravity by adding successive perturbations to the Einstein's linearized field
equations. We show that only the Ricci squared quadratic invariant contributes
to give a different solution of those found in Einstein's general relativity.
The perturbative solution is written as a power series in the $\beta$
parameter, the coefficient of the Ricci squared term in the quadratic
gravitational action. We also show that, for monochromatic waves of a given
angular frequency $\omega$, the perturbative solution can be summed out to give
an exact solution to linearized version of quadratic gravity, for
$0<\omega<c/\mid\beta\mid^{1/2}$.
  This result may lead to implications to the predictions for gravitational
wave backgrounds of cosmological origin.


title: Approach to the extremal limit of the Schwarzschild-de Sitter black hole

abstract:
  The quasinormal-mode spectrum of the Schwarzschild-de Sitter black hole is
studied in the limit of near-equal black-hole and cosmological radii. It is
found that the mode_frequencies_ agree with the P"oschl-Teller approximation to
one more order than previously realized, even though the effective_potential_
does not. Whether the spectrum approaches the limiting one uniformly in the
mode index is seen to depend on the chosen units (to the order investigated). A
perturbation framework is set up, in which these issues can be studied to
higher order in future.


title: Accelerating Universe in a Big Bounce Model

abstract:
  Recent observations of Type Ia supernovae provide evidence for the
acceleration of our universe, which leads to the possibility that the universe
is entering an inflationary epoch. We simulate it under a ``big bounce'' model,
which contains a time variable cosmological ``constant'' that is derived from a
higher dimension and manifests itself in 4D spacetime as dark energy. By
properly choosing the two arbitrary functions contained in the model, we obtain
a simple exact solution in which the evolution of the universe is divided into
several stages. Before the big bounce, the universe contracts from a $\Lambda
$-dominated vacuum, and after the bounce, the universe expands. In the early
time after the bounce, the expansion of the universe is decelerating. In the
late time after the bounce, dark energy (i.e., the variable cosmological
``constant'') overtakes dark matter and baryons, and the expansion enters an
accelerating stage. When time tends to infinity, the contribution of dark
energy tends to two third of the total energy density of the universe,
qualitatively in agreement with observations.


title:
First law of black hole mechanics in Einstein-Maxwell and
  Einstein-Yang-Mills theories

abstract:
  The first law of black hole mechanics is derived from the Einstein-Maxwell
(EM) Lagrangian by comparing two infinitesimally nearby stationary black holes.
With similar arguments, the first law of black hole mechanics in
Einstein-Yang-Mills (EYM) theory is also derived.


title: A Note on Matter Superenergy Tensors

abstract:
  We consider Bel-Robinson-like higher derivative conserved two-index tensors
$H_\mn$ in simple matter models, following a recently suggested Maxwell field
version. In flat space, we show that they are essentially equivalent to the
true stress-tensors. In curved Ricci-flat backgrounds it is possible to
redefine $H_\mn$ so as to overcome non-commutativity of covariant derivatives,
and maintain conservation, but they become model- and dimension- dependent, and
generally lose their simple "BR" form.


title:
Bayesian model comparison applied to the Explorer-Nautilus 2001
  coincidence data

abstract:
  Bayesian reasoning is applied to the data by the ROG Collaboration, in which
gravitational wave (g.w.) signals are searched for in a coincidence experiment
between Explorer and Nautilus. The use of Bayesian reasoning allows, under well
defined hypotheses, even tiny pieces of evidence in favor of each model to be
extracted from the data. The combination of the data of several experiments can
therefore be performed in an optimal and efficient way. Some models for
Galactic sources are considered and, within each model, the experimental result
is summarized with the likelihood rescaled to the insensitivity limit value
(``${\cal R}$ function''). The model comparison result is given in in terms of
Bayes factors, which quantify how the ratio of beliefs about two alternative
models are modified by the experimental observation


title: Slowly rotating, compact fluid sources embedded in Kerr empty space-time

abstract:
  Spherically symmetric static fluid sources are endowed with rotation and
embedded in Kerr empty space-time up to an including quadratic terms in an
angular velocity parameter using Darmois junction conditions. Einstein's
equation's for the system are developed in terms of linear ordinary
differential equations. The boundary of the rotating source is expressed
explicitly in terms of sinusoidal functions of the polar angle which differ
somewhat according to whether an equation of state exists between internal
density and supporting pressure.


title: The surface-symmetric Einstein-Vlasov system with cosmological constant

abstract:
  The results on local existence and continuation criteria obtained by G. Rein
in [4] are extended to the case with a non-zero cosmological constant. It is
also shown that for the spherically symmetric case and a positive cosmological
constant there is a large class of initial data with global existence and
inflationary asymptotics in the future as in the case of plane or hyperbolic
symmetry treated in [7]. Furthermore we analyze the behaviour of the
energy-momentum tensor at late times.


title:
Old and new results for superenergy tensors from dimensionally dependent
  tensor identities

abstract:
  It is known that some results for spinors, and in particular for superenergy
spinors, are much less transparent and require a lot more effort to establish,
when considered from the tensor viewpoint. In this paper we demonstrate how the
use of dimensionally dependent tensor identities enables us to derive a number
of 4-dimensional identities by straightforward tensor methods in a signature
independent manner. In particular, we consider the quadratic identity for the
Bel-Robinson tensor ${\cal T}_{abcx}{\cal T}^{abcy} = \delta_x^y {\cal
T}_{abcd}{\cal T}^{abcd}/4$ and also the new conservation laws for the
Chevreton tensor, both of which have been obtained by spinor means; both of
these results are rederived by {\it tensor} means for 4-dimensional spaces of
any signature, using dimensionally dependent identities, and also we are able
to conclude that there are no {\it direct} higher dimensional analogues. In
addition we demonstrate a simple way to show non-existense of such identities
via counter examples; in particular we show that there is no non-trivial Bel
tensor analogue of this simple Bel-Robinson tensor quadratic identity. On the
other hand, as a sample of the power of generalising dimensionally dependent
tensor identities from four to higher dimensions, we show that the symmetry
structure, trace-free and divergence-free nature of the four dimensional
Bel-Robinson tensor does have an analogue for a class of tensors in higher
dimensions.


title: Measurements of the optical mirror coating properties

abstract:
  The results of measurement of optical mirror coating are presented. These
results indicate that Standard Quantum Limit of sensitivity can be reached in
the second stage of LIGO project if it is limited by thermoelastic noise in the
coating only.


title: A nonlinear quantum model of the Friedmann universe

abstract:
  A discussion is given of the quantisation of a physical system with finite
degrees of freedom subject to a Hamiltonian constraint by treating time as a
constrained classical variable interacting with an unconstrained quantum state.
This leads to a quantisation scheme that yields a Schrodinger-type equation
which is in general nonlinear in evolution. Nevertheless it is compatible with
a probabilistic interpretation of quantum mechanics and in particular the
construction of a Hilbert space with a Euclidean norm is possible. The new
scheme is applied to the quantisation of a Friedmann Universe with a massive
scalar field whose dynamical behaviour is investigated numerically.


title: Is there an information-loss problem for black holes?

abstract:
  Black holes emit thermal radiation (Hawking effect). If after black-hole
evaporation nothing else were left, an arbitrary initial state would evolve
into a thermal state (`information-loss problem'). Here it is argued that the
whole evolution is unitary and that the thermal nature of Hawking radiation
emerges solely through decoherence -- the irreversible interaction with further
degrees of freedom. For this purpose a detailed comparison with an analogous
case in cosmology (entropy of primordial fluctuations) is presented. Some
remarks on the possible origin of black-hole entropy due to interaction with
other degrees of freedom are added. This might concern the interaction with
quasi-normal modes or with background fields in string theory.


title: Vacuum energy and Universe in special relativity

abstract:
  The problem of cosmological constant and vacuum energy is usually thought of
as the subject of general relativity. However, the vacuum energy is important
for the Universe even in the absence of gravity, i.e. in the case when the
Newton constant G is exactly zero, G=0. We discuss the response of the vacuum
energy to the perturbations of the quantum vacuum in special relativity, and
find that as in general relativity the vacuum energy density is on the order of
the energy density of matter. In general relativity, the dependence of the
vacuum energy on the equation of state of matter does not contain G, and thus
is valid in the limit when G tends to zero. However, the result obtained for
the vacuum energy in the world without gravity, i.e. when G=0 exactly, is
different.


title: Advance of Mercury Perihelion Explained by Cogravity - Version II

abstract:
  The theory of General Relativity explaines the advance of Mercury perihelion
using space curvature and the Schwartzschild metric. We demonstrate that this
phenomena can also be interpreted due to the cogravitational field produced by
the apparent motion of the Sun around Mercury giving exactly the same estimate
as derived from the Schwartzschild metric in general relativity theory. This is
a surprising and new result because the estimate from both theoretical
approaches match exactly the measured value. The discussion and implications of
this result is out of the scope of the present work.


title: A Comment on "Brans-Dicke Cosmology with a scalar field potential"

abstract:
  We show that a recent letter claiming to present exact cosmological solutions
in Brans-Dicke theory actually uses a flawed set of equations as the starting
point for their analysis. The results presented in the letter are therefore not
valid.


title: Gravitation without the equivalence principle

abstract:
  In the general relativistic description of gravitation, geometry replaces the
concept of force. This is possible because of the universal character of free
fall, and would break down in its absence. On the other hand, the teleparallel
version of general relativity is a gauge theory for the translation group and,
as such, describes the gravitational interaction by a force similar to the
Lorentz force of electromagnetism, a non-universal interaction. Relying on this
analogy it is shown that, although the geometric description of general
relativity necessarily requires the existence of the equivalence principle, the
teleparallel gauge approach remains a consistent theory for gravitation in its
absence.


title:
All-sky upper limit for gravitational radiation from spinning neutron
  stars

abstract:
  We present results of the all-sky search for gravitational-wave signals from
spinning neutron stars in the data of the EXPLORER resonant bar detector. Our
data analysis technique was based on the maximum likelihood detection method.
We briefly describe the theoretical methods that we used in our search. The
main result of our analysis is an upper limit of ${\bf 2\times10^{-23}}$ for
the dimensionless amplitude of the continuous gravitational-wave signals coming
from any direction in the sky and in the narrow frequency band from 921.00 Hz
to 921.76 Hz.


title:
Limiting noises in gravitational wave detectors: guidance from their
  statistical properties

abstract:
  It is expected that interferometric gravitational wave detectors such as LIGO
\cite{Barish99} will be eventually limited by fundamental noise sources like
shot noise and Brownian motion, as well as by seismic noise. In the
commissioning process, other technical noise sources (electronics noise,
alignment fluctuations) limit the sensitivity and are eliminated one by one. We
propose here a way to correlate the noise in the output of the gravitational
wave detector with other detector and environmental signals not through their
linear transfer functions (often unknown), but through their statistical
properties. This could prove useful for identifying the frequency bands
dominated by different noise sources in the final configuration, and also to
help the commissioning process.


title: Numerical simulation of Quasi-Normal Modes in time-dependent background

abstract:
  We study the massless scalar wave propagation in the time-dependent
Schwarzschild black hole background. We find that the Kruskal coordinate is an
appropriate framework to investigate the time-dependent spacetime. A
time-dependent scattering potential is derived by considering dynamical black
hole with parameters changing with time. It is shown that in the quasinormal
ringing both the decay time-scale and oscillation are modified in the
time-dependent background.


title: Spherically symmetric space-time with the regular de Sitter center

abstract:
  The requirements are formulated which lead to the existence of the class of
globally regular solutions to the minimally coupled GR equations which are
asymptotically de Sitter at the center. The brief review of the resulting
geometry is presented. The source term, invariant under radial boots, is
classified as spherically symmetric vacuum with variable density and pressure,
associated with an r-dependent cosmological term, whose asymptotic in the
origin, dictated by the weak energy condition, is the Einstein cosmological
term. For this class of metrics the ADM mass is related to both de Sitter
vacuum trapped in the origin and to breaking of space-time symmetry. In the
case of the flat asymptotic, space-time symmetry changes smoothly from the de
Sitter group at the center to the Lorentz group at infinity. Dependently on
mass, de Sitter-Schwarzschild geometry describes a vacuum nonsingular black
hole, or G-lump - a vacuum selfgravitating particlelike structure without
horizons. In the case of de Sitter asymptotic at infinity, geometry is
asymptotically de Sitter at both origin and infinity and describes, dependently
on parameters and choice of coordinates, a vacuum nonsingular cosmological
black hole, selfgravitating particlelike structure at the de Sitter background
and regular cosmological models with smoothly evolving vacuum energy density.


title:
Power filters for gravitational wave bursts: network operation for
  source position estimation

abstract:
  A method is presented to generalize the power detectors for short bursts of
gravitational waves that have been developed for single interferometers so that
they can optimally process data from a network of interferometers. The
performances of this method for the estimation of the position of the source
are studied using numerical simulations.


title: Generating Cosmological Solutions from Known Solutions

abstract:
  We consider three methods by which one can generate new cosmological models.
Two of these are based on the Lorentzian structure of spacetime. In a
Lorentzian manifold there can exist horizons that separate regions of spacetime
that can be interpreted as cosmological models from others that have the
character of ``black holes.'' A number of well known solutions of this type can
be used to generate both known cosmological models and others that do not seem
to have been recognized. Another method based on the Lorentzian character of
spacetime is to simply interchange some space variable with time and try to
restructure the metric to make a viable cosmology.
  A more broad-ranging method is the use of modern solution-generating
techniques to construct new models. This method has been widely used to
generate black hole solutions, but seems not to have been so widely used in
cosmology. We will discuss examples of all three methods.


title: Solution of the Helmholtz equation for spin-2 fields

abstract:
  The Helmholtz equation for symmetric, traceless, second-rank tensor fields in
three-dimensional flat space is solved in spherical and cylindrical coordinates
by separation of variables making use of the corresponding spin-weighted
harmonics. It is shown that any symmetric, traceless, divergenceless
second-rank tensor field that satisfies the Helmholtz equation can be expressed
in terms of two scalar potentials that satisfy the Helmholtz equation. Two such
expressions are given, which are adapted to the spherical or cylindrical
coordinates. The application to the linearized Einstein theory is discussed.


title: Critical Collapse of the Massless Scalar Field in Axisymmetry

abstract:
  We present results from a numerical study of critical gravitational collapse
of axisymmetric distributions of massless scalar field energy. We find
threshold behavior that can be described by the spherically symmetric critical
solution with axisymmetric perturbations. However, we see indications of a
growing, non-spherical mode about the spherically symmetric critical solution.
The effect of this instability is that the small asymmetry present in what
would otherwise be a spherically symmetric self-similar solution grows. This
growth continues until a bifurcation occurs and two distinct regions form on
the axis, each resembling the spherically symmetric self-similar solution. The
existence of a non-spherical unstable mode is in conflict with previous
perturbative results, and we therefore discuss whether such a mode exists in
the continuum limit, or whether we are instead seeing a marginally stable mode
that is rendered unstable by numerical approximation.


title:
On the quasi-linearity of the Einstein- "Gauss-Bonnet" gravity field
  equations

abstract:
  We review some properties of the Einstein-"Gauss-Bonnet" equations for
gravity--also called the Einstein-Lanczos equations in five and six dimensions,
and the Lovelock equations in higher dimensions. We illustrate, by means of
simple Kaluza-Klein and brane cosmological models, some consequences of the
quasi-linearity of these equations on the Cauchy problem (a point first studied
by Yvonne Choquet-Bruhat), as well as on "junction conditions".


title:
Shear-free and homology conditions for self-gravitating dissipative
  fluids

abstract:
  The shear free condition is studied for dissipative relativistic
self-gravitating fluids in the quasi-static approximation. It is shown that, in
the Newtonian limit, such condition implies the linear homology law for the
velocity of a fluid element, only if homology conditions are further imposed on
the temperature and the emission rate. It is also shown that the shear-free
plus the homogeneous expansion rate conditions are equivalent (in the Newtonian
limit) to the homology conditions. Deviations from homology and their
prospective applications to some astrophysical scenarios are discussed, and a
model is worked out.


title: Primordial gravitational waves in inflationary braneworld

abstract:
  We study primordial gravitational waves from inflation in Randall-Sundrum
braneworld model. The effect of small change of the Hubble parameter during
inflation is investigated using a toy model given by connecting two de Sitter
branes. We analyze the power spectrum of final zero-mode gravitons, which is
generated from the vacuum fluctuations of both initial Kaluza-Klein modes and
zero-mode. The amplitude of fluctuations is confirmed to agree with the
four-dimensional one at low energies, whereas it is enhanced due to the
normalization factor of zero-mode at high energies. We show that the
five-dimensional spectrum can be well approximated by applying a simple mapping
to the four-dimensional fluctuation amplitude.


title: Time Delay in Black Hole Gravitational Lensing as a Distance Estimator

abstract:
  We calculate the time delay between different relativistic images formed by
black hole gravitational lensing in the strong field limit. For spherically
symmetric black holes, it turns out that the time delay between the first two
images is proportional to the minimum impact angle. Their ratio gives a very
interesting and precise measure of the distance of the black hole. Moreover,
using also the separation between the images and their luminosity ratio, it is
possible to extract the mass of the black hole. The time delay for the black
hole at the center of our Galaxy is just few minutes, but for supermassive
black holes with M=10^8 - 10^9 solar masses in the neighbourhood of the Local
Group the time delay amounts to few days, thus being measurable with a good
accuracy.


title:
Dynamical study of the singularities of gravity in the presence of
  non-minimally coupled scalar fields

abstract:
  We investigate the dynamics of Einstein equations in the vicinity of the two
recently described types of singularity of anisotropic and homogeneous
cosmological models described by the action $$ S=\int d^4x \sqrt{-g}{F(\phi)R -
\partial_a\phi\partial^a\phi -2V(\phi)}, $$ with general $F(\phi)$ and
$V(\phi)$. The dynamical nature of each singularity is elucidated, and we show
that both are, in general, dynamically unavoidable, reinforcing the unstable
character of previous isotropic and homogeneous cosmological results obtained
for the conformal coupling case.


title:
A note on dualities in Einstein's gravity in the presence of a
  non-minimally coupled scalar field

abstract:
  We show that the action of Einstein's gravity with a scalar field coupled in
a generic way to spacetime curvature is invariant under a particular set of
conformal transformations. These transformations relate dual theories for which
the effective couplings of the theory are scaled uniformly. In the simplest
case, this class of dualities reduce to the S-duality of low-energy effective
action of string theory.


title:
Unambiguous angular momentum of radiative spacetimes and asymptotic
  structure in terms of the center of mass system

abstract:
  We present a definition of angular momentum for radiative spacetimes which
does not suffer from any ambiguity of supertranslations. We succeed in
providing an appropriate notion of {\it intrinsic} angular momentum; and at the
same time a definition of center of mass frame at future null infinity.
  We use the center of mass frame to present the asymptotic structure equations
for vacuum spacetimes.


title:
Stability properties and asymptotics for N non-minimally coupled scalar
  fields cosmology

abstract:
  We consider here the dynamics of some homogeneous and isotropic cosmological
models with $N$ interacting classical scalar fields non-minimally coupled to
the spacetime curvature, as an attempt to generalize some recent results
obtained for one and two scalar fields. We show that a Lyapunov function can be
constructed under certain conditions for a large class of models, suggesting
that chaotic behavior is ruled out for them. Typical solutions tend generically
to the empty de Sitter (or Minkowski) fixed points, and the previous asymptotic
results obtained for the one field model remain valid. In particular, we
confirm that, for large times and a vanishing cosmological constant, even in
the presence of the extra scalar fields, the universe tends to an infinite
diluted matter dominated era.


title:
Dynamics in Non-Globally-Hyperbolic Static Spacetimes II: General
  Analysis of Prescriptions for Dynamics

abstract:
  It was previously shown by one of us that in any static,
non-globally-hyperbolic, spacetime it is always possible to define a sensible
dynamics for a Klein-Gordon scalar field. The prescription proposed for doing
so involved viewing the spatial derivative part, $A$, of the wave operator as
an operator on a certain $L^2$ Hilbert space $\mathcal H$ and then defining a
positive, self-adjoint operator on $\mathcal H$ by taking the Friedrichs
extension (or other positive extension) of $A$. However, this analysis left
open the possibility that there could be other inequivalent prescriptions of a
completely different nature that might also yield satisfactory definitions of
the dynamics of a scalar field. We show here that this is not the case.
Specifically, we show that if the dynamics agrees locally with the dynamics
defined by the wave equation, if it admits a suitable conserved energy, and if
it satisfies certain other specified conditions, then it must correspond to the
dynamics defined by choosing some positive, self-adjoint extension of $A$ on
$\mathcal H$. Thus, subject to our requirements, the previously given
prescription is the only possible way of defining the dynamics of a scalar
field in a static, non-globally-hyperbolic, spacetime. In a subsequent paper,
this result will be applied to the analysis of scalar, electromagnetic, and
gravitational perturbations of anti-de Sitter spacetime. By doing so, we will
determine all possible choices of boundary conditions at infinity in anti-de
Sitter spacetime that give rise to sensible dynamics.


title: Reformulation and Interpretation of SMS Braneworld

abstract:
  We reformulate the Shiromizu, Maeda and Sasaki (SMS) braneworlds within the
framework of the five-dimensional Einstein equations. In many applications of
the braneworld Einstein field equations, the Weyl term is attributed to the
bulk, thus splitting the non-Einsteinian terms into `bulk' and `brane' terms.
Here by employing standard geometrical identities, we show that such a split is
non-unique, since these terms get mixed up in different formulations. An
important consequence of this non-uniqueness is that even though the full
brane-bulk systems in all such formulations are completely equivalent,
important differences can arise were one to truncate different formulations by
throwing away the associated `bulk' terms. This is particularly likely to be
the case in more general anisotropic/inhomogeneous settings with non-AdS bulks,
in which the usual truncation of the SMS (which throws away the Weyl term)
would not coincide with the full system. We emphasize that rather than
providing support for any truncation, these differences show clearly the
dangers of using any truncated equations and provide a strong argument in
favour of studying the full brane-bulk system. The different formulations we
provide also permit different ways of approaching the full brane-bulk system
which may greatly facilitate its study. An example of this is the second-order
nature of the formulations given here as opposed to the SMS's formulation which
is third-order.


title: Critical collapse of a massive vector field

abstract:
  We perform numerical simulations of the critical gravitational collapse of a
massive vector field. The result is that there are two critical solutions. One
is equivalent to the Choptuik critical solution for a massless scalar field.
The other is periodic.


title: A Simple Deformation of Special Relativity

abstract:
  A deformation of special relativity based on a dispersion relation with an
energy independent speed of light and a symmetry between positive and negative
energy states is proposed. The deformed Lorentz transformations, generators and
algebra are derived and some consequences are discussed.


title:
Note on Matter Collineations in Kantowski-Sachs, Bianchi Types I and III
  Spacetimes

abstract:
  We show that the classification of Kantowski-Sachs, Bianchi Types I and III
spacetimes admitting Matter Collineations (MCs) presented in a recent paper by
Camci et al. [Camci, U., and Sharif, M. {Matter Collineations in
Kantowski-Sachs, Bianchi Types I and III Spacetimes}, 2003 Gen. Relativ. Grav.
vol. 35, 97-109] is incomplete. Furthermore for these spacetimes and when the
Einstein tensor is non-degenerate, we give the complete Lie Algebra of MCs and
the algebraic constraints on the spatial components of the Einstein tensor.


title: Self-similar Bianchi type VIII and IX models

abstract:
  It is shown that in transitively self-similar spatially homogeneous tilted
perfect fluid models the symmetry vector is not normal to the surfaces of
spatial homogeneity. A direct consequence of this result is that there are no
self-similar Bianchi VIII and IX tilted perfect fluid models. Furthermore the
most general Bianchi VIII and IX spacetime which admit a four dimensional group
of homotheties is given.


title: Thermal Fluctuations and Black Hole Entropy

abstract:
  In this paper, we consider the effect of thermal fluctuations on the entropy
of both neutral and charged black holes. We emphasize the distinction between
fixed and fluctuating charge systems; using a canonical ensemble to describe
the former and a grand canonical ensemble to study the latter. Our novel
approach is based on the philosophy that the black hole quantum spectrum is an
essential component in any such calculation. For definiteness, we employ a
uniformly spaced area spectrum, which has been advocated by Bekenstein and
others in the literature. The generic results are applied to some specific
models; in particular, various limiting cases of an (arbitrary-dimensional)
AdS-Reissner-Nordstrom black hole. We find that the leading-order quantum
correction to the entropy can consistently be expressed as the logarithm of the
classical quantity. For a small AdS curvature parameter and zero net charge, it
is shown that, independent of the dimension, the logarithmic prefactor is +1/2
when the charge is fixed but +1 when the charge is fluctuating.We also
demonstrate that, in the grand canonical framework, the fluctuations in the
charge are large, $\Delta Q\sim\Delta A\sim S_{BH}^{1/2}$, even when $<Q> =0$.
A further implication of this framework is that an asymptotically flat,
non-extremal black hole can never achieve a state of thermal equilibrium.


title: Selected topics in Planck-scale physics

abstract:
  We review a few topics in Planck-scale physics, with emphasis on possible
manifestations in relatively low energy. The selected topics include quantum
fluctuations of spacetime, their cumulative effects, uncertainties in
energy-momentum measurements, and low energy quantum-gravity phenomenology. The
focus is on quantum-gravity-induced uncertainties in some observable
quantities. We consider four possible ways to probe Planck-scale physics
experimentally: 1. looking for energy-dependent spreads in the arrival time of
photons of the same energy from GRBs; 2. examining spacetime
fluctuation-induced phase incoherence of light from extragalactic sources; 3.
detecting spacetime foam with laser-based interferometry techniques; 4.
understanding the threshold anomalies in high energy cosmic ray and gamma ray
events. Some other experiments are briefly discussed. We show how some physics
behind black holes, simple clocks, simple computers, and the holographic
principle is related to Planck-scale physics. We also discuss a formulation of
the Dirac equation as a difference equation on a discrete Planck-scale
spacetime lattice, and a possible interplay between Planck-scale and
Hubble-scale physics encoded in the cosmological constant (dark energy).


title: Relativistic chaos is coordinate invariant

abstract:
  The noninvariance of Lyapunov exponents in general relativity has led to the
conclusion that chaos depends on the choice of the space-time coordinates.
Strikingly, we uncover the transformation laws of Lyapunov exponents under
general space-time transformations and we find that chaos, as characterized by
positive Lyapunov exponents, is coordinate invariant. As a result, the previous
conclusion regarding the noninvariance of chaos in cosmology, a major claim
about chaos in general relativity, necessarily involves the violation of
hypotheses required for a proper definition of the Lyapunov exponents.


title: Clifford Tetrads, Null Zig Zags, and Quantum Gravity

abstract:
  Quantum Gravity has been so elusive because we have tried to approach it by
two paths which can never meet: standard quantum field theory and general
relativity. The gateway is covariance under the complexified Clifford algebra
of our space-time manifold M, and its spinor representations, which Sachs
dubbed the Einstein group, E. On the microscopic scale, quantum gravity appears
as the statistical mechanics of the null zig-zag rays of spinor fields in
imaginary time T. Our unified field/particle action L_g also contains new
couplings of gravitomagnetic fields to strong fields and weak potentials. These
predict new physical phenomena: Axial jets of nuclear decay products emitted
with left helicity along the axis of a massive, spinning body.


title:
The Generalized Uncertainty Principle, entropy bounds and black hole
  (non-)evaporation in a thermal bath

abstract:
  We apply the Generalized Uncertainty Principle (GUP) to the problem of
maximum entropy and evaporation/absorption of energy of black holes near the
Planck scale. We find within this general approach corrections to the maximum
entropy, and indications for quenching of the evaporation because not only the
evaporation term goes to a finite limit, but also because absorption of quanta
seems to help the balance for black holes in a thermal bath. Then, residual
masses around the Planck scale may be the final outcome of primordial black
hole evaporation.


title: Toward standard testbeds for numerical relativity

abstract:
  In recent years, many different numerical evolution schemes for Einstein's
equations have been proposed to address stability and accuracy problems that
have plagued the numerical relativity community for decades. Some of these
approaches have been tested on different spacetimes, and conclusions have been
drawn based on these tests. However, differences in results originate from many
sources, including not only formulations of the equations, but also gauges,
boundary conditions, numerical methods, and so on. We propose to build up a
suite of standardized testbeds for comparing approaches to the numerical
evolution of Einstein's equations that are designed to both probe their
strengths and weaknesses and to separate out different effects, and their
causes, seen in the results. We discuss general design principles of suitable
testbeds, and we present an initial round of simple tests with periodic
boundary conditions. This is a pivotal first step toward building a suite of
testbeds to serve the numerical relativists and researchers from related fields
who wish to assess the capabilities of numerical relativity codes. We present
some examples of how these tests can be quite effective in revealing various
limitations of different approaches, and illustrating their differences. The
tests are presently limited to vacuum spacetimes, can be run on modest
computational resources, and can be used with many different approaches used in
the relativity community.