title: Origin of Structure in a Supersymmetric Quantum Universe

abstract:
  In this report we advance the current repertoire of quantum cosmological
models to incorporate inhomogenous field modes in a supersymmetric manner. In
particular, we introduce perturbations about a supersymmetric FRW model. A
quantum state of our model has properties typical of the no-boundary
(Hartle--Hawking) proposal. This solution may then lead to a scale--free
spectrum of density perturbations.


title: Dominant Topologies in Euclidean Quantum Gravity

abstract:
  The dominant topologies in the Euclidean path integral for quantum gravity
differ sharply according on the sign of the cosmological constant. For
$\Lambda>0$, saddle points can occur only for topologies with vanishing first
Betti number and finite fundamental group. For $\Lambda<0$, on the other hand,
the path integral is dominated by topologies with extremely complicated
fundamental groups; while the contribution of each individual manifold is
strongly suppressed, the ``density of topologies'' grows fast enough to
overwhelm this suppression. The value $\Lambda=0$ is thus a sort of boundary
between phases in the sum over topologies. I discuss some implications for the
cosmological constant problem and the Hartle-Hawking wave function.


title: Relativistic hydrodynamic accretion onto a spherical black hole

abstract:
  This paper has been withdrawn by the author. A revised and expanded version
is gr-qc/9907028 (Phys.Rev. D60 (1999) 104043).


title: Black holes and radiometry

abstract:
  Following Grischuk and Sidorov [Phys. Rev. D 42 (1990) 3413] in putting the
Bogolubov-Hawking coefficient of Schwarzschild black-holes in the squeezing
perspective, we provide a short discussion of Schwarzschild black holes as
radiometric standards


title:
Detecting a stochastic background of gravitational radiation: Signal
  processing strategies and sensitivities

abstract:
  We analyze the signal processing required for the optimal detection of a
stochastic background of gravitational radiation using laser interferometric
detectors. Starting with basic assumptions about the statistical properties of
a stochastic gravity-wave background, we derive expressions for the optimal
filter function and signal-to-noise ratio for the cross-correlation of the
outputs of two gravity-wave detectors. Sensitivity levels required for
detection are then calculated. Issues related to: (i) calculating the
signal-to-noise ratio for arbitrarily large stochastic backgrounds, (ii)
performing the data analysis in the presence of nonstationary detector noise,
(iii) combining data from multiple detector pairs to increase the sensitivity
of a stochastic background search, (iv) correlating the outputs of 4 or more
detectors, and (v) allowing for the possibility of correlated noise in the
outputs of two detectors are discussed. We briefly describe a computer
simulation which mimics the generation and detection of a simulated stochastic
gravity-wave signal in the presence of simulated detector noise. Numerous
graphs and tables of numerical data for the five major interferometers
(LIGO-WA, LIGO-LA, VIRGO, GEO-600, and TAMA-300) are also given. The treatment
given in this paper should be accessible to both theorists involved in data
analysis and experimentalists involved in detector design and data acquisition.


title: Thermodynamics of scalar fields in Kerr's geometry

abstract:
  The one-loop contributions to the entropy for a massive scalar field in a
Kerr black hole are investigated using an approximation of the metric, which,
after a conformal transformation, permits to work in a Rindler-like spacetime.
Of course, as for the Schwarzschild case, the entropy is divergent in the
proximity of the event horizon.


title: Geodesics and geodesic deviation for impulsive gravitational waves

abstract:
  The geometry of impulsive pp-waves is explored via the analysis of the
geodesic and geodesic deviation equation using the distributional form of the
metric. The geodesic equation involves formally ill-defined products of
distributions due to the nonlinearity of the equations and the presence of the
Dirac $\de$-distribution in the space time metric. Thus, strictly speaking, it
cannot be treated within Schwartz's linear theory of distributions. To cope
with this difficulty we proceed by first regularizing the
$\de$-singularity,then solving the regularized equation within classical smooth
functions and, finally, obtaining a distributional limit as solution to the
original problem. Furthermore it is shown that this limit is independent of the
regularization without requiring any additional condition, thereby confirming
earlier results in a mathematical rigorous fashion. We also treat the Jacobi
equation which, despite being linear in the deviation vector field, involves
even more delicate singular expressions, like the ``square'' of the Dirac
$\de$-distribution. Again the same regularization procedure provides us with a
perfectly well behaved smooth regularization and a regularization-independent
distributional limit. Hence it is concluded that the geometry of impulsive
pp-waves can be described consistently using distributions as long as careful
regularization procedures are used to handle the ill-defined products.


title: Causality in Topologically Nontrivial Space-Times

abstract:
  The problems causality and causality violation in topologically nontrivial
space-time models are considered. To this end the mixed boundary problem for
traversable wormhole models is formulated and the influence of the boundary
conditions on the causal properties of space-time is analyzed


title:
Spontaneous symmetry breaking of rapidly rotating stars in general
  relativity: influence of the 3D-shift vector

abstract:
  An analytical scheme and a numerical method in order to study the effects of
general relativity on the viscosity driven secular bar mode instability of
rapidly rotating stars are presented. The approach consists in perturbing an
axisymmetric and stationary configuration and studying its evolution by
constructing a series of triaxial quasi-equilibrium configurations. These are
obtained by solution of an approximate set of field equations where only the
dominant non-axisymmetric terms are taken into account. The progress with
respect to our former investigation consists in a higher relativistic order of
the non-axisymmetric terms included into the computation, namely the fully
three-dimensional treatment of the vector part of the space-time metric tensor
as opposed to the scalar part, solely, in the former case. The scheme is
applied to rotating stars built on a polytropic equation of state and compared
to our previous results. The 3D-vector part turns out to inhibit the symmetry
breaking efficiently. Nevertheless, the bar mode instability is still possible
for an astrophysically relevant mass of M_ns=1.4 M_sun when a stiff polytropic
equation of state with an adiabatic index of gamma=2.5 is employed. Triaxial
neutron stars may be efficient emitters of gravitational waves and are thus
potentially interesting sources for the forthcoming laser interferometric
gravitational wave detectors such as LIGO, VIRGO and GEO600. From a numerical
point of view, the solution of the three-dimensional minimal-distortion shift
vector equation in spherical coordinates is an important achievement of our
code.


title: Superposition of Weyl solutions: The equilibrium forces

abstract:
  Solutions to the Einstein equation that represent the superposition of static
isolated bodies with axially symmetry are presented. The equations nonlinearity
yields singular structures (strut and membranes) to equilibrate the bodies. The
force on the strut like singularities is computed for a variety of situations.
The superposition of a ring and a particle is studied in some detail


title: Rotating Topological Black Holes

abstract:
  A class of metrics solving Einstein's equations with negative cosmological
constant and representing rotating, topological black holes is presented. All
such solutions are in the Petrov type-$D$ class, and can be obtained from the
most general metric known in this class by acting with suitably chosen discrete
groups of isometries. First, by analytical continuation of the Kerr-de Sitter
metric, a solution describing uncharged, rotating black holes whose event
horizon is a Riemann surface of arbitrary genus $g > 1$, is obtained. Then a
solution representing a rotating, uncharged toroidal black hole is also
presented. The higher genus black holes appear to be quite exotic objects, they
lack global axial symmetry and have an intricate causal structure. The toroidal
blackholes appear to be simpler, they have rotational symmetry and the amount
of rotation they can have is bounded by some power of the mass.


title:
Sparling two-forms, the conformal factor and the gravitational energy
  density of the teleparallel equivalent of general relativity

abstract:
  It has been shown recently that within the framework of the teleparallel
equivalent of general relativity (TEGR) it is possible to define the energy
density of the gravitational field. The TEGR amounts to an alternative
formulation of Einstein's general relativity, not to an alternative gravity
theory. The localizability of the gravitational energy has been investigated in
a number of space-times with distinct topologies, and the outcome of these
analises agree with previously known results regarding the exact expression of
the gravitational energy, and/or with the specific properties of the space-time
manifold. In this article we establish a relationship between the expression
for the gravitational energy density of the TEGR and the Sparling two-forms,
which are known to be closely connected with the gravitational energy. We also
show that our expression of energy yields the correct value of gravitational
mass contained in the conformal factor of the metric field.


title: Gravitational collapse: A case for thermal relaxation

abstract:
  Two relativistic models for collapsing spheres at different stages of
evolution, which include pre-relaxation processes, are presented. The influence
of relaxation time on the outcome of evolution in both cases is exhibited and
established. It is shown that relaxation processes can drastically change the
final state of the collapsing system. In particular, there are cases in which
the value of the relaxation time determines the bounce or the collapse of the
sphere.


title: Sigma Model on de Sitter Space

abstract:
  We discuss spherically symmetric, static solutions to the SU(2) sigma model
on a de Sitter background. Despite of its simplicity this model reflects many
of the features exhibited by systems of non-linear matter coupled to gravity
e.g. there exists a countable set of regular solutions with finite energy; all
of the solutions show linear instability with the number of unstable modes
increasing with energy.


title: Baryogenesis motivated on String CPT Violation

abstract:
  We discuss a mechanism for generating the baryon asymetry of the Universe
that involves a putative violation of CPT symmetry arising from string
interactions.


title: Perturbative Analysis of Bianchi IX using Ashtekar Formalism

abstract:
  The goal of this paper is to provide a new analysis of the classical dynamics
of Bianchi type I, II and IX models by applying conventional Hamiltonian
methods in the language of Ashtekhar variables. We show that Bianchi type II
models can be seen as a perturbation of Bianchi I ones, and integrated. Bianchi
IX models can be seen, in turn, as a perturbation of Bianchi IIs, but here the
integration algorithm breaks down. This is an ''interesting failure'', bringing
light onto the chaotic nature of Bianchi type IX dynamics.As a by product of
our analysis we filled some gaps in the literature, such us recovering the BKL
map in this context.


title:
Measuring gravitational waves from binary black hole coalescences: II.
  the waves' information and its extraction, with and without templates

abstract:
  We discuss the extraction of information from detected binary black hole
(BBH) coalescence gravitational waves, focusing on the merger phase that occurs
after the gradual inspiral and before the ringdown. Our results are: (1) If
numerical relativity simulations have not produced template merger waveforms
before BBH detections by LIGO/VIRGO, one can band-pass filter the merger waves.
For BBHs smaller than about 40 solar masses detected via their inspiral waves,
the band pass filtering signal to noise ratio indicates that the merger waves
should typically be just barely visible in the noise for initial and advanced
LIGO interferometers. (2) We derive an optimized (maximum likelihood) method
for extracting a best-fit merger waveform from the noisy detector output; one
"perpendicularly projects" this output onto a function space (specified using
wavelets) that incorporates our prior knowledge of the waveforms. An extension
of the method allows one to extract the BBH's two independent waveforms from
outputs of several interferometers. (3) If numerical relativists produce codes
for generating merger templates but running the codes is too expensive to allow
an extensive survey of the merger parameter space, then a coarse survey of this
parameter space, to determine the ranges of the several key parameters and to
explore several qualitative issues which we describe, would be useful for data
analysis purposes. (4) A complete set of templates could be used to test the
nonlinear dynamics of general relativity and to measure some of the binary
parameters. We estimate the number of bits of information obtainable from the
merger waves (about 10 to 60 for LIGO/VIRGO, up to 200 for LISA), estimate the
information loss due to template numerical errors or sparseness in the template
grid, and infer approximate requirements on template accuracy and spacing.


title: The notions of time and evolution in quantum cosmology

abstract:
  We re-examine the notions of time and evolution in the light of the
mathematical properties of the solutions of the Wheeler-DeWitt equation which
are revealed by an extended adiabatic treatment. The main advantage of this
treatment is to organize the solutions in series that make explicit both the
connections with the corresponding Schr\"odinger equation as well as the
modifications introduced by the quantum character of gravity. When the universe
is macroscopic, the ordered character of the expansion leads to connections
with the Schr\"odinger equation so precise that the interpretation of the
solutions of the Wheeler-DeWitt equation is unequivocally determined. On the
contrary, when the expansion behaves quantum mechanically, i.e. in the presence
of backscattering, major difficulties concerning the interpretation persist.


title:
Constants of the Motion and the Quantum Modular Group in (2+1) -
  Dimensional Gravity

abstract:
  Constants of motion are calculated for 2+1 dimensional gravity with topology
R \times T^2 and negative cosmological constant. Certain linear combinations of
them satisfy the anti - de Sitter algebra so(2,2) in either ADM or holonomy
variables. Quantisation is straightforward in terms of the holonomy parameters,
and the modular group is generated by these conserved quantities. On inclusion
of the Hamiltonian three new global constants are derived and the quantum
algebra extends to the conformal algebra so(2,3).


title: Euclidean Supergravity in Terms of Dirac Eigenvalues

abstract:
  It has been recently shown that the eigenvalues of the Dirac operator can be
considered as dynamical variables of Euclidean gravity. The purpose of this
paper is to explore the possiblity that the eigenvalues of the Dirac operator
might play the same role in the case of supergravity. It is shown that for this
purpose some primary constraints on covariant phase space as well as secondary
constraints on the eigenspinors must be imposed. The validity of primary
constraints under covariant transport is further analyzed. It is show that in
the this case restrictions on the tanget bundle and on the spinor bundle of
spacetime arise. The form of these restrictions is determined under some
simplifying assumptions. It is also shown that manifolds with flat curvature of
tangent bundle and spinor bundle and spinor bundle satisfy these restrictons
and thus they support the Dirac eigenvalues as global observables.


title: Metric Versus Ashtekar Variables in Two Killing Field Reduced Gravity

abstract:
  The relation between the SL(2,R)/SO(2)- and the SL(2,C)-chiral model that
naturally arise within the metric respectively the Ashtekar formulation of two
Killing field reduced Einstein gravity is revealed. Both chiral models turn out
to be completely equivalent even though the transition from the coset- to the
SL(2,C)-model is accompanied by a disappearance of the non-ultralocal terms in
the Poisson brackets.


title:
Non-precessional spin-orbit effects on gravitational waves from
  inspiraling compact binaries to second post-Newtonian order

abstract:
  We derive all second post-Newtonian (2PN), non-precessional effects of spin-
orbit coupling on the gravitational wave forms emitted by an inspiraling binary
composed of spinning, compact bodies in a quasicircular orbit. Previous post-
Newtonian calculations of spin-orbit effects (at 1.5PN order) relied on a fluid
description of the spinning bodies. We simplify the calculations by introducing
into post-Newtonian theory a delta-function description of the influence of the
spins on the bodies' energy-momentum tensor. This description was recently used
by Mino, Shibata, and Tanaka (MST) in Teukolsky-formalism analyses of particles
orbiting massive black holes, and is based on prior work by Dixon. We compute
the 2PN contributions to the wave forms by combining the MST energy-momentum
tensor with the formalism of Blanchet, Damour, and Iyer for evaluating the
binary's radiative multipoles, and with the well-known 1.5PN order equations of
motion for the binary. Our results contribute at 2PN order only to the
amplitudes of the wave forms. The secular evolution of the wave forms' phase,
the quantity most accurately measurable by LIGO, is not affected by our results
until 2.5PN order, at which point other spin-orbit effects also come into play.
We plan to evaluate the entire 2.5PN spin-orbit contribution to the secular
phase evolution in a future paper, using the techniques of this paper.


title: Inflation driven by causal heat flux

abstract:
  We find a simple inflationary solution in an inhomogeneous spacetime with
heat flux. The heat flux obeys a causal transport equation, and counteracts the
inflationary decrease of energy density. At late times, the heat flux tends to
zero and the fluid approaches the equation of state $p=-\rho$.


title: The Time Evolution of Quantum Universe in The Quantum Potential Picture

abstract:
  We use the quantum potential approach to analyse the quantum cosmological
model of the universe. The quantum potential arises from exact solutions of the
full Wheeler-De Witt equation.


title: Metric fluctuations in semiclassical gravity

abstract:
  The Einstein-Langevin equation is a perturbative correction to the
semiclassical Einstein equation which takes into account the lowest order
quantum fluctuations of the matter stress-energy tensor. It predicts classical
stochastic fluctuations in the metric field which may describe some of the
remnant gravitational fluctuations after the process of environment induced
decoherence driving the quantum to classical transition of gravity.


title: Moving Black Holes in 3D

abstract:
  We model a radiating, moving black hole in terms of a worldtube-nullcone
boundary value problem. We evolve this data in the region interior to the
worldtube but exterior to a trapped surface by means of a characteristic
evolution based upon a family of ingoing null hypersurfaces. Data on the
worldtube is induced from a Schwarzschild spacetime but the worldtube is
allowed to move relative to the static Schwarzschild trajectories. When the
worldtube is stationary (static or rotating in place), a distorted black hole
inside it evolves to equilibrium with the Schwarzschild boundary. A boost of
the worldtube with respect to the Schwarzschild black hole does not affect
these results. The code also stably tracks an unlimited number of orbits when
the worldtube wobbles periodically. The work establishes that characteristic
evolution can evolve a spacetime with a distorted black hole moving on a
3-dimensional grid with the controlled accuracy and long term stability
necessary to investigate new facets of black hole physics.


title: Palatini Variational Principle for $N$-Dimensional Dilaton Gravity

abstract:
  We consider a Palatini variation on a general $N$-Dimensional second order,
torsion-free dilaton gravity action and determine the resulting equations of
motion. Consistency is checked by considering the restraint imposed due to
invariance of the matter action under simple coordinate transformations, and
the special case of N=2 is examined. We also examine a sub-class of theories
whereby a Palatini variation dynamically coincides with that of the "ordinary"
Hilbert variational principle; in particular we examine a generalized
Brans-Dicke theory and the associated role of conformal transformations.


title:
Relativistic Hydrodynamics in Close Binary Systems: Analysis of
  Neutron-Star Collapse

abstract:
  We discuss the underlying relativistic physics which causes neutron stars to
compress and collapse in close binary systems as has recently been observed in
numerical (3+1) dimensional general relativistic hydrodynamic simulations. We
show that compression is driven by velocity-dependent relativistic hydrodynamic
terms which increase the self gravity of the stars. They also produce fluid
motion with respect to the corotating frame of the binary. We present numerical
and analytic results which confirm that such terms are insignificant for
uniform translation or when the hydrodynamics is constrained to rigid
corotation.
  However, when the hydrodynamics is unconstrained, the neutron star fluid
relaxes to a compressed nonsynchronized state of almost no net intrinsic spin
with respect to a distant observer.
  We also show that tidal decompression effects are much less than the
velocity-dependent compression terms. We discuss why several recent attempts to
analyze this effect with constrained hydrodynamics or an analysis of tidal
forces do not observe compression. We argue that an independent test of this
must include unconstrained relativistic hydrodynamics to sufficiently high
order that all relevant velocity-dependent terms and their possible
cancellations are included.


title: Pure and gravitational radiation

abstract:
  The well-known treatment of asymptotically flat vacuum fields is adapted to
pure radiation fields. In this approach we find a natural normalization of the
radiation null vector. The energy balance at null infinity shows that the mass
loss results from a linear superposition of the pure and the gravitational
radiation parts. By transformation to Bondi-Sachs coordinates the Kinnersley
photon rocket is found to be the only axisymmetric Robinson-Trautman pure
radiation solution without gravitational radiation.


title:
On the role of density inhomogeneity and local anisotropy in the fate of
  spherical collapse

abstract:
  We obtain an expression for the active gravitational mass of a collapsing
fluid distribution, which brings out the role of density inhomogeneity and
local anisotropy in the fate of spherical collapse.


title: Palatini Variational Principle for an Extended Einstein-Hilbert Action

abstract:
  We consider a Palatini variation on a generalized Einstein-Hilbert action. We
find that the Hilbert constraint, that the connection equals the Christoffel
symbol, arises only as a special case of this general action, while for
particular values of the coefficients of this generalized action, the
connection is completely unconstrained. We discuss the relationship between
this situation and that usually encountered in the Palatini formulation.


title:
Anisotropic Homogeneous Cosmology in the Nonsymmetric Theory of
  Gravitation

abstract:
  Solutions to the field equations of the Nonsymmetric Gravitational Theory
with $g_[i0] = 0$ are obtained for the homogeneous, plane-symmetric,
time-dependent case, both in vacuum and in the presence of a perfect fluid.
Cosmological consequences include a dependence of the speed of light on its
polarisation, as in a birefringent crystal.


title:
Two Kerr black holes with axisymmetric spins: An improved Newtonian
  model for the head-on collision and gravitational radiation

abstract:
  We present a semi-analytical approach to the interaction of two (originally)
Kerr black holes through a head-on collision process. An expression for the
rate of emission of gravitational radiation is derived from an exact solution
to the Einstein's field equations. The total amount of gravitational radiation
emitted in the process is calculated and compared to current numerical
investigations. We find that the spin-spin interaction increases the emission
of gravitational wave energy up to 0.2% of the total rest mass. We discuss also
the possibility of spin-exchange between the holes.


title: Duality of Quasilocal Black Hole Thermodynamics

abstract:
  We consider T-duality of the quasilocal black hole thermodynamics for the
three-dimensional low energy effective string theory. Quasilocal thermodynamic
variables in the first law are explicitly calculated on a general axisymmetric
three-dimensional black hole solution and corresponding dual one. Physical
meaning of the dual invariance of the black hole entropy is considered in terms
of the Euclidean path integral formulation.


title: Realism And Empirical Evidence

abstract:
  We define realism using a slightly modified version of the EPR criterion of
reality. This version is strong enough to show that relativity is incomplete.
  We show that this definition of realism is nonetheless compatible with the
general principles of causality and canonical quantum theory as well as with
experimental evidence in the (special and general) relativistic domain.
  We show that the realistic theories we present here, compared with the
standard relativistic theories, have higher empirical content in the strong
sense defined by Popper's methodology.


title:
The imposition of Cauchy data to the Teukolsky equation I: The
  nonrotating case

abstract:
  Gravitational perturbations about a Kerr black hole in the Newman-Penrose
formalism are concisely described by the Teukolsky equation. New numerical
methods for studying the evolution of such perturbations require not only the
construction of appropriate initial data to describe the collision of two
orbiting black holes, but also to know how such new data must be imposed into
the Teukolsky equation. In this paper we show how Cauchy data can be
incorporated explicitly into the Teukolsky equation for non-rotating black
holes. The Teukolsky function $% \Psi $ and its first time derivative
$\partial_t \Psi $ can be written in terms of only the 3-geometry and the
extrinsic curvature in a gauge invariant way. Taking a Laplace transform of the
Teukolsky equation incorporates initial data as a source term. We show that for
astrophysical data the straightforward Green function method leads to divergent
integrals that can be regularized like for the case of a source generated by a
particle coming from infinity.


title:
Propagation of gravitational waves from slow motion sources in a Coulomb
  type potential

abstract:
  We consider the propagation of gravitational waves generated by slow motion
sources in Coulomb type potential due to the mass of the source. Then, the
formula for gravitational waveform including tail is obtained in a
straightforward manner by using the spherical Coulomb function. We discuss its
relation with the formula in the previous work.


title: Energy and Momentum in the Tetrad Theory of Gravitation

abstract:
  We study the energy and momentum of an isolated system in the tetrad theory
of gravitation, starting from the most general Lagrangian quadratic in torsion,
which involves four unknown parameters. When applied to the static spherically
symmetric case, the parallel vector fields take a diagonal form, and the field
equation has an exact solution. We analyze the linearized field equation in
vacuum at distances far from the isolated system without assuming any symmetry
property of the system. The linearized equation is a set of coupled equations
for a symmetric and skew-symmetric tensor fields, but it is possible to solve
it up to $O(1/r)$ for the stationary case. It is found that the general
solution contains two constants, one being the gravitational mass of the source
and the other a constant vector ${\grave B_\alpha}$. The total energy is
calculated from this solution and is found to be equal to the gravitational
mass of the source. We also calculate the spatial momentum and find that its
value coincides with the constant vector ${\grave B_\alpha}$. The linearized
field equation in vacuum, which is valid at distances far from the source, does
not give any information about whether the constant vector ${\grave B_\alpha}$
is vanishing or not. For a weakly gravitating source for which the field is
weak everywhere, we find that the constant vector ${\grave B_\alpha}$ vanishes.


title: An exterior for the G\"{o}del spacetime

abstract:
  We match the vacuum, stationary, cylindrically symmetric solution of
Einstein's field equations with $\Lambda$, in a form recently given by Santos,
as an exterior to an infinite cylinder of dust cut out of a G\"{o}del universe.
There are three cases, depending on the radius of the cylinder. Closed timelike
curves are present in the exteriors of some of the solutions. There is a
considerable similarity between the spacetimes investigated here and those of
van Stockum referring to an infinite cylinder of rotating dust matched to
vacuum, with $\Lambda=0$.


title: Homogeneous spacelike singularities inside spherical black holes

abstract:
  Recent numerical simulations have found that the Cauchy horizon inside
spherical charged black holes, when perturbed nonlinearly by a
self-gravitating, minimally-coupled, massless, spherically-symmetric scalar
field, turns into a null weak singularity which focuses monotonically to $r=0$
at late times, where the singularity becomes spacelike.
  Our main objective is to study this spacelike singularity. We study
analytically the spherically-symmetric Einstein-Maxwell-scalar equations
asymptotically near the singularity. We obtain a series-expansion solution for
the metric functions and for the scalar field near $r=0$ under the simplifying
assumption of homogeneity. Namely, we neglect spatial derivatives and keep only
temporal derivatives. We find that there indeed exists a generic spacelike
singularity solution for these equations (in the sense that the solution
depends on enough free parameters), with similar properties to those found in
the numerical simulations. This singularity is strong in the Tipler sense,
namely, every extended object would inevitably be crushed to zero volume. In
this sense this is a similar singularity to the spacelike singularity inside
uncharged spherical black holes. On the other hand, there are some important
differences between the two cases. Our model can also be extended to the more
general inhomogeneous case.
  The question of whether the same kind of singularity evolves in more
realistic models (of a spinning black hole coupled to gravitational
perturbations) is still an open question.


title:
Nonlocal Conservation Laws Derived from an Explicit Equivalence
  Principle

abstract:
  According to this principle (EEP), in order that the local physical laws
cannot change, after changes of velocity and potentials of a measuring system,
the relativistic changes of any particle and any stationary radiation (like
those used to measure it) must occur in identical proportion. Thus particles
and stationary radiations must have the same general physical properties. In
principle more exact and better defined physical laws for particles and their
gravitational (G) fields can be derived from properties of particle models made
up of radiation in stationary states after using fixed reference frames that
don't change in the same way as the objects. Effectively, the new laws derived
in this way do correspond with relativistic quantum mechanics and with all of
the G tests. The main difference with current gravity is the linearity fixed by
the EEP, i.e., the G field itself has not a real field energy to exchange with
the bodies and it is not a secondary source of field. G work liberates energy
confined in the models stationary states. The EEP also fixes a new
astrophysical context that has fundamental differences with the current ones.
This one has been presented in a separated work as a test for the EEP. The
whole theory,including the new universe context fixed by the EEP, was published
in a book.


title: Chaotic exit to inflation: the dynamics of pre-inflationary universes

abstract:
  We show that anisotropic Bianchi type-IX models, with matter and cosmological
constant have chaotic dynamics, connected to the presence of a saddle-center in
phase space. The topology of cylinders emanating from unstable periodic orbits
about the saddle-center provides an invariant characterization of chaos in the
models. The model can be thought to describe the early stages of inflation, the
way out to inflation being chaotic.


title: BH Punctures as Initial Data for General Relativity

abstract:
  We construct initial data for several black holes with arbitrary momenta and
spins by a new method that is based on a compactification of Brill-Lindquist
wormholes. When treated numerically, the method leads to a significant
simplification over the conventional approach which is based on throats and an
isometry condition.


title: Three Dimensional Distorted Black Holes: Initial Data and Evolution

abstract:
  We present a new class of 3D black hole initial data sets for numerical
relativity. These data sets go beyond the axisymmetric, ``gravity wave plus
rotating black hole'' single black hole data sets by creating a dynamic,
distorted hole with adjustable distortion parameters in 3D. These data sets
extend our existing test beds for 3D numerical relativity, representing the
late stages of binary black hole collisions resulting from on-axis collision or
3D spiralling coalescence, and should provide insight into the physics of such
systems. We describe the construction of these sets, the properties for a
number of example cases, and report on progress evolving them.


title: The Matter Plus Black Hole Problem in Axisymmetry

abstract:
  We present preliminary results in our long-term project of studying the
evolution of matter in a dynamical spacetime. To achieve this, we have
developed a new code to evolve axisymmetric initial data sets corresponding to
a black hole surrounded by matter fields. The code is based on the coupling of
two previously existing codes. The matter fields are evolved with a 2D
shock-capturing method which uses the characteristic information of the GR
hydro equations to build up a linearized Riemann solver. The spacetime is
evolved with a 2D ADM code designed to evolve a wormhole in full general
relativity. An example of the kind of problems we are currently investigating
is the on axis collision of a star with a black hole.


title: New Coordinate Systems for Axisymmetric Black Hole Collisions

abstract:
  We describe a numerical grid generating procedure to construct new classes of
orthogonal coordinate systems that are specially adapted to binary black hole
spacetimes. The new coordinates offer an alternative approach to the
conventional \v{C}ade\v{z} coordinates, in addition to providing a potentially
more stable and flexible platform to extend previous calculations of binary
black hole collisions.


title: Nonholonomic approach to rotating matter in general relativity

abstract:
  Rigidly rotating stationary matter in general relativity has been
investigated by Kramer by the Ernst coordinate method. A weakness of this
approach is that the Ernst potential does not exist for differential rotation.
We now generalize the techniques by the use of a nonholonomic and nonrigid
frame. We apply these techniques for differentially rotating perfect fluids. We
construct a complex analytic tensor, characterizing the class of matter states
in which both the interior Schwarzschild and the Kerr solution are contained.
We derive consistency relations for this class of perfect fluids. We
investigate incompressible fluids characterized by these tensors.


title: Microcanonical Quantum Statistics of Schwarzschild Black Holes

abstract:
  It is shown that a quantized Schwarzschild black hole, if described by a
square root energy spectrum with exponential multiplicity, can be treated as a
microcanonical ensemble without problem leading to the expected thermodynamical
properties.


title:
The Equivalence between the Connection and the Loop Representation of
  Quantum Gravity

abstract:
  The recent developments of the ``connection'' and ``loop'' representations
have given the possibility to show that the two representation are equivalent
and that it is possible to transform any result from one representation into
the other. The glue between the two representations is the loop transform. Its
use, combined with the techincs Penrose's binor calculus, gives the possibility
to establish the exact correspondence between operators and states in the
connection representation and those in the loop representation.
  The main ingredients in the prove of the equivalence are: the concept of
embedded spin network, the Penrose graphical method of SU(2) calculus, and the
existence of a generalized measure on the space of connections.


title:
The Lanczos potential for Weyl-candidate tensors exists only in four
  dimensions

abstract:
  We prove that a Lanczos potential L_abc for the Weyl candidate tensor W_abcd
does not generally exist for dimensions higher than four. The technique is
simply to assume the existence of such a potential in dimension n, and then
check the integrability conditions for the assumed system of differential
equations; if the integrability conditions yield another non-trivial
differential system for L_abc and W_abcd, then this system's integrability
conditions should be checked; and so on. When we find a non-trivial condition
involving only W_abcd and its derivatives, then clearly Weyl candidate tensors
failing to satisfy that condition cannot be written in terms of a Lanczos
potential L_abc.


title:
Chaotic exit to inflation: pre-inflationary Friedmann-Robertson-Walker
  universes

abstract:
  We show that homogeneous and isotropic cosmological models with radiation and
scalar field have, in general, two possible chaotic exits to inflation. These
models may describe the early stages of inflation. The central point of our
analysis is based on the possible existence of one or two saddle-centers points
in the phase space of the models.


title: Mass inflation inside non-Abelian black holes

abstract:
  The interior geometry of static, spherically symmetric black holes of the
Einstein-Yang-Mills-Higgs theory is analyzed. It is found that in contrast to
the Abelian case generically no inner (Cauchy) horizon is formed inside
non-Abelian black holes. Instead the solutions come close to a Cauchy horizon
but then undergo an enormous growth of the mass function, a phenomenon which
can be termed `mass inflation' in analogy to what is observed for perturbations
of the Reissner-Nordstr{\o}m solution. A significant difference between the
theories with and without a Higgs field is observed. Without a Higgs field the
YM field induces repeated cycles of massinflation -- taking the form of violent
`explosions' -- interrupted by quiescent periods and subsequent approaches to
an almost Cauchy horizon. With the Higgs field no such cycles occur. Besides
the generic solutions there are non-generic families with a Schwarzschild,
Reissner-Nordstr{\o}m and a pseudo Reissner-Nordstr{\o}m type singularity at
$r=0$.


title:
Stress-energy tensor in colliding plane wave space-times: An
  approximation procedure

abstract:
  In a recent work on the quantization of a massless scalar field in a
particular colliding plane wave space-time, we computed the vacuum expectation
value of the stress-energy tensor on the physical state which corresponds to
the Minkowski vacuum before the collision of the waves. We did such a
calculation in a region close to both the Killing-Cauchy horizon and the
folding singularities that such a space-time contains. In the present paper, we
give a suitable approximation procedure to compute this expectation value, in
the conformal coupling case, throughout the causal past of the center of the
collision. This will allow us to approximately study the evolution of such an
expectation value from the beginning of the collision until the formation of
the Killing-Cauchy horizon. We start with a null expectation value before the
arrival of the waves, which then acquires nonzero values at the beginning of
the collision and grows unbounded towards the Killing-Cauchy horizon. The value
near the horizon is compatible with our previous result, which means that such
an approximation may be applied to other colliding plane wave space-times. Even
with this approximation, the initial modes propagated into the interaction
region contain a function which cannot be calculated exactly and to ensure the
correct regularization of the stress-energy tensor with the point-splitting
technique, this function must be given up to adiabatic order four of
approximation.


title: Topology and Fragility in Cosmology

abstract:
  We introduce the notion of topological fragility and briefly discuss some
examples from the literature. An important example of this type of fragility is
the way globally anisotropic Bianchi V generalisations of the FLRW $k=-1$ model
result in a radical restriction on the allowed topology of spatial sections,
thereby excluding compact cosmological models with negatively curved
three-sections with anisotropy. An outcome of this is to exclude chaotic mixing
in such models, which may be relevant, given the many recent attempts at
employing compact FLRW $k=-1$ models to produce chaotic mixing in the cosmic
microwave background radiation, if the Universe turns out to be globally
anisotropic.


title: Radiation from a Charge Uniformly Accelerated for All Time

abstract:
  A recent paper of Singal [Gen. Rel. Grav. 27 (1995), 953-967] argues that a
uniformly accelerated particle does not radiate, in contradiction to the
consensus of the research literature over the past 30 years. This note points
out some questionable aspects of Singal's argument and shows how similar
calculations can lead to the opposite conclusion.


title: A note on the formal structure of quantum constrained systems

abstract:
  The space of the solutions of Dirac's quantum constraints cannot be
constructed factoring the quantum state space by the ``simple'' gauge
transformations generated by the constraints. However, we show here that it can
be constructed by factoring the state space by suitably defined ``complete''
gauge transformations. These are generated by the action of the quantum
constraints on individual components of the quantum state.


title: Semiclassical Quantization on Black Hole Spacetimes

abstract:
  The thermodynamical description of black holes is reviewed and critiqued. We
present an alternative, microcanonical description of black holes and discuss
the major differences. In particular the decay rates of black holes are
compared in the two different pictures.


title: Quantum Inequalities and Singular Energy Densities

abstract:
  There has been much recent work on quantum inequalities to constrain negative
energy. These are uncertainty principle-type restrictions on the magnitude and
duration of negative energy densities or fluxes. We consider several examples
of apparent failures of the quantum inequalities, which involve passage of an
observer through regions where the negative energy density becomes singular. We
argue that this type of situation requires one to formulate quantum
inequalities using sampling functions with compact support. We discuss such
inequalities, and argue that they remain valid even in the presence of singular
energy densities.


title: Quantum Theory of Geometry II: Volume operators

abstract:
  A functional calculus on the space of (generalized) connections was recently
introduced without any reference to a background metric. It is used to continue
the exploration of the quantum Riemannian geometry. Operators corresponding to
volume of three-dimensional regions are regularized rigorously. It is shown
that there are two natural regularization schemes, each of which leads to a
well-defined operator. Both operators can be completely specified by giving
their action on states labelled by graphs. The two final results are closely
related but differ from one another in that one of the operators is sensitive
to the differential structure of graphs at their vertices while the second is
sensitive only to the topological characteristics. (The second operator was
first introduced by Rovelli and Smolin and De Pietri and Rovelli using a
somewhat different framework.) The difference between the two operators can be
attributed directly to the standard quantization ambiguity. Underlying
assumptions and subtleties of regularization procedures are discussed in detail
in both cases because volume operators play an important role in the current
discussions of quantum dynamics.


title:
Analytic study of the null singularity inside spherical charged black
  holes

abstract:
  We study analytically the features of the Cauchy horizon (CH) singularity
inside a spherically-symmetric charged black hole, nonlinearly perturbed by a
self-gravitating massless scalar field. We derive exact expressions for the
divergence rate of the blue-shift factors, namely the derivatives in the
outgoing direction of the scalar field $\Phi$ and the area coordinate $r$. Both
derivatives are found to grow along the contracting CH exactly like $1/r$. Our
results are valid everywhere along the CH singularity, up to the point of full
focusing. These exact analytic expressions are verified numerically.


title: Multidimensional Gravity on the Principal Bundles

abstract:
  The multidimensional gravity on the total space of principal bundle is
considered. In this theory the gauge fields arise as nondiagonal components of
multidimensional metric. The spherically symmetric and cosmology solutions for
gravity on SU(2) principal bundle are obtained. The static spherically
symmetric solution is wormhole-like solution located between two null surfaces,
in contrast to 4D Einstein-Yang-Mills theory where corresponding solution
(black hole) located outside of event horizon. Cosmology solution (at least
locally) has the bouncing off effect for spatial dimensions. In spirit of
Einstein these solutions are vacuum solutions without matter.


title:
Transmission and reflection coefficients for a scalar field inside a
  charged black hole

abstract:
  Using the late-time expansion we calculate the leading-order coefficients
describing the evolution of a massless scalar field inside a Reissner-Nordstrom
black hole. These coefficients may be interpreted as the reflection and
transmission coefficients for scalar-field modes propagating from the event
horizon to the Cauchy horizon. Our results agree with those obtained previously
by Gursel et al by a different method.


title: Chaotic Dynamics and Two-Field Inflation

abstract:
  We demonstrate the existence of chaos in realistic models of two-field
inflation. The chaotic motion takes place after the end of inflation, when the
fields are free to oscillate and their motion is only lightly damped by the
expansion of the universe. We then investigate whether the presence of chaos
affects the predictions of two-field models, and show that chaos enhances the
production of topological defects and renders the growth rate of the universe
sensitively dependent upon the ``initial'' conditions at the beginning of the
oscillatory era.


title: Local cosmic string in generalised scalar tensor theory

abstract:
  A recent investigation shows that a local gauge string with a
phenomenological energy momentum tensor, as prescribed by Vilenkin, is
inconsistent in Brans-Dicke theory. In this work it has been shown that such a
string is consistent in a more general scalar tensor theory where $\omega$ is
function of the scalar field.A set of solutions of full nonlinear Einstein's
equations for interior region of such a string are presented.


title: Wheeler-DeWitt equation and Feynman diagrams

abstract:
  We present a systematic expansion of all constraint equations in canonical
quantum gravity up to the order of the inverse Planck mass squared. It is
demonstrated that this method generates the conventional Feynman diagrammatic
technique involving graviton loops and vertices. It also reveals explicitly the
back reaction effects of quantized matter and graviton vacuum polarization.
This provides an explicit correspondence between the frameworks of canonical
and covariant quantum gravity in the semiclassical limit.


title: Cosmological Pair Creation of Charged and Rotating Black Holes

abstract:
  In this paper, we investigate the pair creation of charged and rotating black
hole pairs in a background with a positive cosmological constant. Instantons to
describe this situation are constructed from the Kerr-Newmann deSitter
solutions to the Einstein-Maxwell equations and the actions of these instantons
are calculated in order to estimate pair creation rates and the entropy of the
created spacetimes.


title:
de Broglie-Bohm Interpretation for the Wave Function of Quantum Black
  Holes

abstract:
  We study the quantum theory of the spherically symmetric black holes. The
theory yields the wave function inside the apparent horizon, where the role of
time and space coordinates is interchanged. The de Broglie-Bohm interpretation
is applied to the wave function and then the trajectory picture on the
minisuperspace is introduced in the quantum as well as the semi-classical
region. Around the horizon large quantum fluctuations on the trajectories of
metrics $U$ and $V$ appear in our model, where the metrics are functions of
time variable $T$ and are expressed as $ds^2=-{\alpha^2}/U dT^2 + U dR^2 + V
d\Omega^2$. On the trajectories, the classical relation $U=-V^{1/2}+2Gm$ holds,
and the event horizon U=0 corresponds to the classical apparent horizon on
$V=2Gm$. In order to investigate the quantum fluctuation near the horizon, we
study a null ray on the dBB trajectory and compare it with the one in the
classical black hole geometry.


title:
Time Machines with Non-compactly Generated Cauchy Horizons and ``Handy
  Singularities"

abstract:
  The use of "handy singularities" (i.e. singularities similar to those arising
in the Deutch-Politzer space) enables one to avoid (almost) all known
difficulties inherent usually to creation of time machines. A simple method is
discussed for constructing a variety of such singularities. A few 3-dimensional
examples are cited.


title: Colliding waves in metric-affine gravity

abstract:
  We generalize the formulation of the colliding gravitational waves to
metric-affine theories and present an example of such kind of exact solutions.
The plane waves are equipped with five symmetries and the resulting geometry
after the collision possesses two spacelike Killing vectors.


title: A handlebody calculus for topology change

abstract:
  We consider certain interesting processes in quantum gravity which involve a
change of spatial topology. We use Morse theory and the machinery of
handlebodies to characterise topology changes as suggested by Sorkin. Our
results support the view that that the pair production of Kaluza-Klein
monopoles and the nucleation of various higher dimensional objects are allowed
transitions with non-zero amplitude.


title: Covariant Spin Structure

abstract:
  Every Dirac spin structure on a world manifold is associated with a certain
gravitational field, and is not preserved under general covariant
transformations. We construct a composite spinor bundle such that any Dirac
spin structure is its subbundle, and this bundle admits general covariant
transformations.


title: A Wormhole at the core of an infinite cosmic string

abstract:
  We study a solution of Einstein's equations that describes a straight cosmic
string with a variable angular deficit, starting with a $2 \pi$ deficit at the
core. We show that the coordinate singularity associated to this defect can be
interpreted as a traversible wormhole lodging at the the core of the string. A
negative energy density gradually decreases the angular deficit as the distance
from the core increases, ending, at radial infinity, in a Minkowski spacetime.
The negative energy density can be confined to a small transversal section of
the string by gluing to it an exterior Gott's like solution, that freezes the
angular deficit existing at the matching border. The equation of state of the
string is such that any massive particle may stay at rest anywhere in this
spacetime. In this sense this is 2+1 spacetime solution.


title: Gravitational Capture of Cosmic Strings by a Black Hole

abstract:
  The gravitational interaction of an infinitely long cosmic string with a
Schwarzschild black hole is studied. We consider a straight string that is
initially at a great distance and moving at some initial velocity v (0 < v < c)
towards the black hole. The equations of motion of the string are solved
numerically to obtain the dependence of the capture impact parameter on the
initial velocity.


title:
On a Theory for Nonminimal Gravitational-Electromagnetic Coupling
  Consistent with Observational Data

abstract:
  The idea that the seed primordial magnetic fields can be explained by the
nonminimal coupling between gravitational and electromagnetic fields is
discussed. The predicted values of the magnetic field of the spiral galaxies
are in agreement with the observations.


title: Singularities and Classical Limit in Quantum Cosmology

abstract:
  Minisuperspace models derived from Kaluza-Klein theories and low energy
string theory are studied. They are equivalent to one and two minimally coupled
scalar fields. The general classical and quantum solutions are obtained.
Gaussian superposition of WKB solutions are constructed. Contrarily to what is
usually expected, these states are sharply peaked around the classical
trajectories only for small values of the scale factor. This behaviour is
confirmed in the framework of the causal interpretation: the Bohmian
trajectories of many quantum states are classical for small values of the scale
factor but present quantum behaviour when the scale factor becomes large. A
consequence of this fact is that these states present an initial singularity.
However, there are some particular superpositions of these wave functions which
have Bohmian trajectories without singularities. There are also singular
Bohmian trajectories with a short period of inflation which grow forever. We
could not find any non-singular trajectory which grows to the size of our
universe.


title: A Topological Formulation of the Standard Model

abstract:
  A topological theory for the interactions in Nature is presented. The theory
derives from the cyclic properties of the topological manifold Q=2T^3 + 3S^1 x
S^2 which has 23 intrinsic degrees of freedom, discrete Z_3 and Z_2 x Z_3
internal groups, an SU(5) gauge group, and an anomalous U(1) symmetry. These
properties reproduce the standard model with a stable proton, a natural place
for CP violation and doublet-triplet splitting. The equation of motion for the
unified theory is derived and leads to a Higgs field. The thermodynamic
properties of Q are discussed and yield a consistent amplitude for the cosmic
microwave background fluctuations. The manifold Q possesses internal energy
scales which are independent of the field theory defined on it, but which
constrain the predicted mass hierarchy of such theories. In particular the
electron and its neutrino are identified as ground states and their masses are
predicted. The correct masses of quarks and the CKM mixing angles can be
derived as well from these energy scales if one uses the anomalous U(1)
symmetry. Furthermore, it is shown that if the Planck scale topology of the
universe involves loops as fundamental objects, its spatial dimension is equal
to three. The existence of the prime manifold T^3=S^1 x S^1 S^1 is then
required for a dynamical universe, i.e. a universe which supports forces. Some
links with M-theory are pointed out.


title: Null Geodesic Expansion in Spherical Gravitational Collapse

abstract:
  We derive an expression for the expansion of outgoing null geodesics in
spherical dust collapse and compute the limiting value of the expansion in the
approach to singularity formation. An analogous expression is derived for the
spherical collapse of a general form of matter. We argue on the basis of these
results that the covered as well as the naked singularity solutions arising in
spherical dust collapse are stable under small changes in the equation of
state.


title:
Bar mode instability in relativistic rotating stars: a post Newtonian
  treatment

abstract:
  We construct analytic models of incompressible, rigidly rotating stars in PN
gravity and study their stability against nonaxisymmetric Jacobi-like bar
modes. PN configurations are modeled by homogeneous triaxial ellipsoids and the
metric is obtained as a solution of Einstein's equations in 3+1 ADM form. We
use an approximate subset of the equations well-suited to numerical integration
for strong field, 3D configurations in quasi--equilibrium. These equations are
exact at PN order, and admit an analytic solution for homogeneous ellipsoids.
In this paper we present this solution, as well as analytic functionals for the
conserved global quantities, M, M_0 and J. By using a variational principle we
construct sequences of axisymmetric equilibria of constant density and rest
mass, i.e. the PN generalization of Maclaurin spheroids, which are compared to
other PN and full relativistic sequences presented by previous authors. We then
consider nonaxisymmetric ellipsoidal deformations of the configurations,
holding J constant and the rotation uniform, and we locate the point at which
the bar modes will be driven secularly unstable by a dissipative agent like
viscosity. We find that the value of the eccentricity, as well as the ratios
\Omega^2/(\pi\rho_0) and T/|W|, defined invariantly, all increase at the onset
of instability as the stars become more relativistic. Since higher degrees of
rotation are required to trigger a viscosity-driven bar mode as the star's
compactness increases, the effect of GR is to weaken the instability, at least
to PN order. This behavior is opposite to that found for secular instability
via Dedekind-like modes driven unstable by gravitational radiation, supporting
the suggestion that in GR, nonaxisymmetric modes driven unstable by viscosity
and gravitational radiation may no longer coincide.


title: Emergence of Time

abstract:
  In the groupoid approach to noncommutative quantization of gravity,
gravitational field is quantized in terms of a C*-algebra A of complex valued
funcions on a groupoid G (with convolution as multiplication). In the
noncommutative quantum gravitational regime the concepts of space and time are
meaningless. We study the "emergence of time" in the transition process from
the noncommutative regime to the standard space-time geometry. Precise
conditions are specified under which modular groups of the von Neumann algebra
generated by A can be defined. These groups are interpreted as a state
depending time flow. If the above conditions are further refined one obtains a
state independent time flow. We show that quantum gravitational dynamics can be
expressed in terms of modular groups.


title: A lattice worldsheet sum for 4-d Euclidean general relativity

abstract:
  A lattice model for four dimensional Euclidean quantum general relativity is
proposed for a simplicial spacetime. It is shown how this model can be
expressed in terms of a sum over worldsheets of spin networks, and an
interpretation of these worldsheets as spacetime geometries is given, based on
the geometry defined by spin networks in canonical loop quantized GR. The
spacetime geometry has a Planck scale discreteness which arises "naturally"
from the discrete spectrum of spins of SU(2) representations (and not from the
use of a spacetime lattice).
  The lattice model of the dynamics is a formal quantization of the classical
lattice model of \cite{Rei97a}, which reproduces, in a continuum limit,
Euclidean general relativity.


title:
Distinguishing causal time from Minkowski time and a model for the black
  hole quantum eigenstates

abstract:
  A discussion is presented of the principle of black hole com- plementarity.
It is argued that this principle could be viewed as a breakdown of general
relativity, or alternatively, as the introduction of a time variable with
multiple `sheets' or `branches'
  A consequence of the theory is that the stress-energy tensor as viewed by an
outside observer is not simply the Lorentz-transform of the tensor viewed by an
ingoing observer. This can serve as a justification of a new model for the
black hole atmosphere, recently re-introduced. It is discussed how such a model
may lead to a dynamical description of the black hole quantum states.


title:
General relativity reformed to a genuine Yang-Mills gauge theory for
  gravity

abstract:
  The theory of general relativity is reformed to a genuine Yang-Mills gauge
theory of the Poincar\'e group for gravity. Several pathologies of the
conventional theory are thus removed, but not every GR vacuum satisfies the Y-M
equations. The sector of GR solutions which survive is fully classified and it
is found to include the Schwarzschild black hole. Two other solutions presented
here have no GR counterpart and they describe expanding Friedmann universes
with torsion which vanishes only asymptotically. They are discussed along with
novel theoretical possibilities, such as a well-defined energy-momentum tensor
for the gravitational field, and novel perspectives for unification and
quantization.


title: Long-ranged forces and energy non-conservation in (1+1)-dimensions

abstract:
  We consider whether local and causal non-conservation of energy may occur in
generally covariant theories with long-ranged fields (analogs of Newton's
gravity) whose source is energy--momentum. We find that such a possibility
exists in (1+1) dimensions.


title: Time, Gauge, and the Superposition Principle in Quantum Gravity

abstract:
  The quantization of time-reparametrization invariant systems such as general
relativity is plagued by an ambiguity relating to the role of time in the
theory. If one parametrizes observables by the (unobservable) time, and then
relies on the existence of an approximate "clock" degree of freedom to give
physical meaning to the observables, one finds multiple quantum states that
yield the same predictions yet interfere with each other.


title: Averaging in Cosmology

abstract:
  In this paper we discuss the effect of local inhomogeneities on the global
expansion of nearly FLRW universes, in a perturbative setting. We derive a
generic linearized averaging operation for metric perturbations from basic
assumptions, and we explicify the issue of gauge invariance. We derive a gauge
invariant expression for the back-reaction of density inhomogeneities on the
global expansion of perturbed FLRW spacetimes, in terms of observable
quantities, and we calculate the effect quantitatively. Since we do not adopt a
comoving gauge, our result incorporates the back-reaction on the metric due to
scalar velocity and vorticity perturbations. The results are compared with the
results by other authors in this field.


title: Excitation of a Kaluza-Klein mode by parametric resonance

abstract:
  In this paper we investigate a parametric resonance phenomenon of a
Kaluza-Klein mode in a $D$-dimensional generalized Kaluza-Klein theory. As the
origin of the parametric resonance we consider a small oscillation of a scale
of the compactification around a today's value of it. To make our arguments
definite and for simplicity we consider two classes of models of the
compactification: those by $S_{d}$ ($d=D-4$) and those by $S_{d_{1}}\times
S_{d_{2}}$ ($d_1\ge d_2$, $d_{1}+d_{2}=D-4$). For these models we show that
parametric resonance can occur for the Kaluza-Klein mode. After that, we give
formulas of a creation rate and a number of created quanta of the Kaluza-Klein
mode due to the parametric resonance, taking into account the first and the
second resonance band. By using the formulas we calculate those quantities for
each model of the compactification. Finally we give conditions for the
parametric resonance to be efficient and discuss cosmological implications.


title: Dynamical Spacetime and the Curvature of Projective State Space

abstract:
  If universal quantum interaction is really connected with the coset structure
of deformations of quantum states then the curvature of projective Hilbert
state space should be observable. I discuss some approach to the measurement of
curvature-dependent values.


title: Gravity, Equivalence Principle and Clocks

abstract:
  String theory suggests the existence of gravitational-strength scalar fields
(``dilaton'' and ``moduli'') whose couplings to matter violate the equivalence
principle. This provides a new motivation for high-precision clock experiments,
as well as a generic theoretical framework for analyzing their significance.


title: Gravitation and Experiment

abstract:
  The confrontation between Einstein's gravitation theory and experimental
results, notably binary pulsar data, is summarized and its significance
discussed. Experiment and theory agree at the 10^{-3} level. All the basic
structures of Einstein's theory (coupling of gravity to matter; propagation and
self-interaction of the gravitational field, including in strong-field
conditions) have been verified. However, some recent theoretical findings
(cosmological relaxation toward zero scalar couplings) suggest that the present
agreement between Einstein's theory and experiment might be naturally
compatible with the existence of a long-range scalar contribution to gravity
(such as the dilaton, or a moduli field of string theory). This provides a new
theoretical paradigm, and new motivations for improving the experimental tests
of gravity. Ultra-high precision tests of the Equivalence Principle appear as
the most sensitive way to look for possible long-range deviations from General
Relativity: they might open a low-energy window on string-scale physics.


title: Smarr's Formula for Black Holes in String Theory

abstract:
  We investigate thermodynamical properties of four and five dimensional black
hole solutions of toroidally compactified string theory. We derive an analog of
Smarr's formula and verify it directly using the metric.


title:
Constraints on the Geometries of Black Holes in Classical and
  Semiclassical Gravity

abstract:
  Constraints on the geometries of static spherically symmetric black holes are
obtained by requiring that the spacetime curvature be analytic at the event
horizon. Further constraints are obtained by requiring that the semiclassical
trace equation be satisfied in the case that only conformally invariant fields
are present. It is found that there exists a range of sizes for which zero
temperature black holes do not exist. The range depends on the number and types
of quantized fields present.


title: Riemann-Cartan Space-times of G\"odel Type

abstract:
  A class of Riemann-Cartan G\"odel-type space-times are examined in the light
of the equivalence problem techniques. The conditions for local space-time
homogeneity are derived, generalizing previous works on Riemannian G\"odel-type
space-times. The equivalence of Riemann-Cartan G\"odel-type space-times of this
class is studied. It is shown that they admit a five-dimensional group of
affine-isometries and are characterized by three essential parameters $\ell,
m^2, \omega$: identical triads ($\ell, m^2, \omega$) correspond to locally
equivalent manifolds. The algebraic types of the irreducible parts of the
curvature and torsion tensors are also presented.


title: The Speed of Light as a Dilaton Field

abstract:
  Through dimensional analysis, eliminating the physical time, we identify the
speed of light as a dilaton field. This leads to a restmass zero, spin zero
gauge field which we call the speedon field. The complete Lagrangian for
gravitational, electromagnetic and speedon field interactions with a charged
scalar field, representing matter, is given. We then find solutions for the
gravitational-electromagnetic-speedon field equations. This then gives an
expression for the speed of light.


title:
Quantum mechanical instabilities of Cauchy horizons in two dimensions -
  a modified form of the blueshift instability mechanism

abstract:
  There are several examples known of two dimensional spacetimes which are
linearly stable when perturbed by test scalar classical fields, but which are
unstable when perturbed by test scalar quantum fields. We elucidate the
mechanism behind such instabilities by considering minimally coupled, massless,
scalar, test quantum fields on general two dimensional spacetimes with Cauchy
horizons which are classically stable. We identify a geometric feature of such
spacetimes which is a necessary condition for obtaining a quantum mechanical
divergence of the renormalized expected stress tensor on the Cauchy horizon for
regular initial states. This feature is the divergence of the affine parameter
length of a one parameter family of null geodesics which lie parallel to the
Cauchy horizon, where the affine parameter normalization is determined by
parallel transport along a fixed, transverse null geodesic which intersects the
Cauchy horizon. (By contrast, the geometric feature of such spacetimes which
underlies classical blueshift instabilities is the divergence of a holonomy
operator). We show that the instability can be understood as a ``delayed
blueshift'' instability, which arises from the infinite blueshifting of an
energy flux which is created locally and quantum mechanically. The instability
mechanism applies both to chronology horizons in spacetimes with closed
timelike curves, and to the inner horizon in black hole spacetimes like two
dimensional Reissner-Nordstrom-de Sitter.


title: The Origin of Structures in Generalized Gravity

abstract:
  In a class of generalized gravity theories with general couplings between the
scalar field and the scalar curvature in the Lagrangian, we can describe the
quantum generation and the classical evolution of both the scalar and tensor
structures in a simple and unified manner. An accelerated expansion phase based
on the generalized gravity in the early universe drives microscopic quantum
fluctuations inside a causal domain to expand into macroscopic ripples in the
spacetime metric on scales larger than the local horizon. Following their
generation from quantum fluctuations, the ripples in the metric spend a long
period outside the causal domain. During this phase their evolution is
characterized by their conserved amplitudes. The evolution of these
fluctuations may lead to the observed large scale structures of the universe
and anisotropies in the cosmic microwave background radiation.


title: Exponential potentials and cosmological scaling solutions

abstract:
  We present a phase-plane analysis of cosmologies containing a barotropic
fluid with equation of state $p_\gamma = (\gamma-1) \rho_\gamma$, plus a scalar
field $\phi$ with an exponential potential $V \propto \exp(-\lambda \kappa
\phi)$ where $\kappa^2 = 8\pi G$. In addition to the well-known inflationary
solutions for $\lambda^2 < 2$, there exist scaling solutions when $\lambda^2 >
3\gamma$ in which the scalar field energy density tracks that of the barotropic
fluid (which for example might be radiation or dust). We show that the scaling
solutions are the unique late-time attractors whenever they exist. The
fluid-dominated solutions, where $V(\phi)/\rho_\gamma \to 0$ at late times, are
always unstable (except for the cosmological constant case $\gamma = 0$). The
relative energy density of the fluid and scalar field depends on the steepness
of the exponential potential, which is constrained by nucleosynthesis to
$\lambda^2 > 20$. We show that standard inflation models are unable to solve
this `relic density' problem.


title: Building blocks for topology change in 3D

abstract:
  We investigate topology change in 3D. Using Morse theory and handle
decomposition we find the set of elementary cobordisms for 3-manifolds. These
are: (i) \O <-> S^2; (ii) \Sigma_g <-> \Sigma_{g+1}; (iii) \Sigma_{g_1} \sqcup
\Sigma_{g_2} <-> \Sigma_{g_1+g_2} and they have appealing physical
interpretations, e.g. Big Bang/Big Crunch, wormhole creation/annihilation and
Einstein-Rosen bridge creation/annihilation, respectively. This decomposition
into building blocks can be used in the path integral approach to quantum
gravity in the sum over topologies.


title: Topology Change and Causal Continuity

abstract:
  The result that, for a scalar quantum field propagating on a ``trousers''
topology in 1+1 dimensions, the crotch singularity is a source for an infinite
burst of energy has been used to argue against the occurrence of topology
change in quantum gravity. We draw attention to a conjecture due to Sorkin that
it may be the particular type of topology change involved in the trousers
transition that is problematic and that other topology changes may not cause
the same difficulties. The conjecture links the singular behaviour to the
existence of ``causal discontinuities'' in the spacetime and relies on a
classification of topology changes using Morse theory. We investigate various
topology changing transitions, including the pair production of black holes and
of topological geons, in the light of these ideas.


title:
A possible explanation of the clash for black hole entropy in the
  extremal limit

abstract:
  It is shown that the classical entropy of the extremal black hole depends on
two different limits procedures. If we first take the extremal limit and then
the boundary limit, the entropy is zero; if we do it the other way round, we
get the Bekenstein-Hawking entropy. By means of the brick wall model, the
quantum entropy of scalar field in the extremal black hole background has been
calculated for the above two different limits procedures. A possible
explanation which considers the quantum effect for the clash of black hole
entropy in the extremal limit is given.


title:
Post-Newtonian Expansion of Gravitational Waves from a Particle in
  Circular Orbits around a Rotating Black Hole :Effects of Black Hole
  Absorption

abstract:
  When a particle moves around a Kerr black hole, it radiates gravitational
waves.Some of these waves are absorbed by the black hole. We calculate such
absorption of gravitational waves induced by a particle of mass mu in a
circular orbit on an equatorial plane around a Kerr black hole of mass M. We
assume that the velocity of the particle v is much smaller than the speed of
light c and calculate the energy absorption rate analytically. We adopt an
analytic technique for the Teukolsky equation developed by Mano, Suzuki and
Takasugi. We obtain the energy absorption rate to O((v/c)^8) compared to the
lowest order. We find that the black hole absorption occurs at O((v/c)^5)
beyond the Newtonian-quadrapole luminosity at infinity in the case when the
black hole is rotating, which is O((v/c)^3) lower than the non-rotating case.
Using the energy absorption rate, we investigate its effects on the orbital
evolution of coalescing compact binaries.


title: Complete Classification of 1+1 Gravity Solutions

abstract:
  A classification of the maximally extended solutions for 1+1 gravity models
(comprising e.g. generalized dilaton gravity as well as models with non-trivial
torsion) is presented. No restrictions are placed on the topology of the
arising solutions, and indeed it is found that for generic models solutions on
non-compact surfaces of arbitrary genus with an arbitrary non-zero number of
holes can be obtained. The moduli space of classical solutions (solutions of
the field equations with fixed topology modulo gauge transformations) is
parametrized explicitly.


title:
A Self-Consistent Vacuum for Misner Space and the Chronology Protection
  Conjecture

abstract:
  In this paper we find a self-consistent vacuum for Misner space. For this
"adapted" Rindler vacuum the renormalized stress-energy tensor is zero
throughout the Misner space. A point-like particle detector traveling on a
timelike geodesic in a Misner space with this vacuum detects nothing. Misner
space with this vacuum thus creates no problems for time travel in and of
itself but a time traveler may pose a danger to himself and to the spacetime.


title: Three Quantum Aspects of Gravity

abstract:
  It is argued that (a) In the quantum realm test-particle masses have
non-trivial observability which induces a non-geometric element in gravity, (b)
Any theory of quantum gravity, on fundamental grounds, must contain an element
of non-locality that makes position measurements non-commutative, and (c) The
classical notion of free fall does not readily generalize to the quantum
regime.


title: Black Hole Data via a Kerr-Schild Approach

abstract:
  We present a new approach for setting initial Cauchy data for multiple black
hole spacetimes. The method is based upon adopting an initially Kerr-Schild
form of the metric. In the case of non-spinning holes, the constraint equations
take a simple hierarchical form which is amenable to direct numerical
integration. The feasibility of this approach is demonstrated by solving
analytically the problem of initial data in a perturbed Schwarzschild geometry.


title: Minimal Off-Shell Version of N = 1 Chiral Supergravity

abstract:
  We construct the minimal off-shell formulation of N = 1 chiral supergravity
(SUGRA) introducing a complex antisymmetric tensor field $B_{\mu \nu}$ and a
complex axial-vector field $A_{\mu}$ as auxiliary fields. The resulting algebra
of the right- and left-handed supersymmetry (SUSY) transformations closes off
shell and generates chiral gauge transforamtions and vector gauge
transformations in addition to the transformations which appear in the case
without auxiliary fields.


title:
Boosted three-dimensional black-hole evolutions with singularity
  excision

abstract:
  Binary black hole interactions provide potentially the strongest source of
gravitational radiation for detectors currently under development. We present
some results from the Binary Black Hole Grand Challenge Alliance three-
dimensional Cauchy evolution module. These constitute essential steps towards
modeling such interactions and predicting gravitational radiation waveforms. We
report on single black hole evolutions and the first successful demonstration
of a black hole moving freely through a three-dimensional computational grid
via a Cauchy evolution: a hole moving ~6M at 0.1c during a total evolution of
duration ~60M.


title: Angular momentum at the black hole threshold

abstract:
  Near the black hole threshold in phase space, the black hole mass as a
function of the initial data shows the "critical scaling" M \simeq C
(p-p_*)^\gamma, where p labels a family of initial data, p_* is the value of p
at the threshold, and the critical exponent \gamma is universal for a given
matter model. The black hole charge Q obeys a similar law. To complete the
picture, we include angular momentum as a perturbation. For the black hole
angular momentum \vec L we find the oscillating behavior \vec L \simeq Re[
(\vec A + i \vec B) (p-p_*)^{\mu+i\omega} ]. The assumptions of the calculation
hold for p = \rho / 3 perfect fluid matter, and we calculate \mu \simeq 0.799
and \omega \simeq 0.231.


title: Mass and Weak Field Limit of Boson Stars in Brans Dicke Gravity

abstract:
  We study boson stars in Brans Dicke gravity and use them to illustrate some
of the properties of three different mass definitions: the Schwarzschild mass,
the Keplerian mass and the Tensor mass. We analyse the weak field limit of the
solutions and show that only the Tensor mass leads to a physically reasonable
definition of the binding energy. We examine numerically strong field
$\omega=-1$ solutions and show how, in this extreme case, the three mass values
and the conserved particle number behave as a function of the central boson
field amplitude. The numerical studies imply that for $\omega=-1$, solutions
with extremal Tensor mass also have extremal particle number. This is a
property that a physically reasonable definition of the mass of a boson star
must have, and we prove analytically that this is true for all values of
$\omega$. The analysis supports the conjecture that the Tensor mass uniquely
describes the total energy of an asymptotically flat solution in BD gravity.


title:
Cosmological particle production and generalized thermodynamic
  equilibrium

abstract:
  With the help of a conformal, timelike Killing-vector we define generalized
equilibrium states for cosmological fluids with particle production. For
massless particles the generalized equilibrium conditions require the
production rate to vanish and the well known ``global'' equilibrium of standard
relativistic thermodynamics is recovered as a limiting case. The equivalence
between the creation rate for particles with nonzero mass and an effective
viscous fluid pressure follows as a consequence of the generalized equilibrium
properties. The implications of this equivalence for the cosmological dynamics
are discussed, including the possibility of a power-law inflationary behaviour.
For a simple gas a microscopic derivation for such kind of equilibrium is given
on the basis of relativistic kinetic theory.


title:
Gravitational collapse with non-vanishing tangential stresses II: a
  laboratory for cosmic censorship experiments

abstract:
  The general exact solution describing the dynamics of anisotropic elastic
spheres supported only by tangential stresses is reduced to a quadrature using
Ori's mass-area coordinates. This leads to the explicit construction of the
root equation governing the nature of the central singularity. Using this
equation, we formulate and motivate on physical grounds a conjecture on the
nature of this singularity. The conjecture covers a large sector of the space
of initial data; roughly speaking, it asserts that addition of a tangential
stress cannot undress a covered dust singularity. The root equation also allows
us to analyze the case of self-similar spacetimes and to get some insight on
the role of stresses in deciding the nature of the singularities in this case.


title: A distinguished set of modes in an accelerated frame of reference

abstract:
  We construct a distinguished set of positive and negative energy modes of the
Klein-Gordon equation for any Born frame of reference in Minkowski's
space-time. Unlike the case of a galilean frame of reference it is unclear
whether this set of modes may be an appropriate basis to define the vacuum of a
quantized scalar field in an accelerated cavity.


title: Varying G and Other Constants

abstract:
  We review recent progress in the study of varying constants and attempts to
explain the observed values of the fundamental physical constants. We describe
the variation of $G$ in Newtonian and relativistic scalar-tensor gravity
theories. We highlight the behaviour of the isotropic Friedmann solutions and
consider some striking features of primordial black hole formation and
evaporation if $G$ varies. We discuss attempts to explain the values of the
constants and show how we can incorporate the simultaneou s variations of
several 'constants' exactly by using higher-dimensional unified theories.
Finally, we describe some new observational limits on possible space or time
variations of the fine structure constant.


title: Relativistic cosmological hydrodynamics

abstract:
  We investigate the relativistic cosmological hydrodynamic perturbations. We
present the general large scale solutions of the perturbation variables valid
for the general sign of three space curvature, the cosmological constant, and
generally evolving background equation of state. The large scale evolution is
characterized by a conserved gauge invariant quantity which is the same as a
perturbed potential (or three-space curvature) in the comoving gauge.


title: Cosmological structures in generalized gravity

abstract:
  In a class of generalized gravity theories with general couplings between the
scalar field and the scalar curvature in the Lagrangian, we describe the
quantum generation and the classical evolution processes of both the scalar and
tensor structures in a simple and unified manner.


title: Backscattering: an overlooked effect of General Relativity?

abstract:
  The total flux of outgoing radiation in a strong gravitational field
decreases due to backscattering if the sources are close to an apparent
horizon. It can cause detectable changes in the shape of signals.
Backscattering could well be of relevance to astrophysics and would constitute
a new test of the validity of general relativity. An explicit bound for this
effect is derived for scalar fields.


title: Towards gravitational-wave asteroseismology

abstract:
  We present new results for pulsating neutron stars. We have calculated the
eigenfrequencies of the modes that one would expect to be the most important
gravitational-wave sources: the fundamental fluid f-mode, the first pressure
p-mode and the first gravitational-wave w-mode, for twelve realistic equations
of state. From this numerical data we have inferred a set of ``empirical
relations'' between the mode-frequencies and the parameters of the star (the
radius R and the mass M). Some of these relation prove to be surprisingly
robust, and we show how they can be used to extract the details of the star
(radius, mass, eos) from observed modes with errors no larger than a few
percent.


title: The Dirac equation in Cartesian gauge

abstract:
  It is shown that in the case of the spherically symmetric static backgrounds
there is a gauge in which the Dirac equation is manifestly covariant under
rotations. This allows us to separate the spherical variables like in the flat
space-time, obtaining a pair of radial equations and a specific form of the
radial scalar product.


title: A new class of (3+1) quantum geometric models

abstract:
  A new family of analytically solvable quantum geometric models is proposed.
The structure of the energy spectra as well as the form of the corresponding
eigenfunctions are presented pointing out their main specific properties.


title: Quantum Pasts and the Utility of History

abstract:
  From data in the present we can predict the future and retrodict the past.
These predictions and retrodictions are for histories -- most simply time
sequences of events. Quantum mechanics gives probabilities for individual
histories in a decoherent set of alternative histories. This paper discusses
several issues connected with the distinction between prediction and
retrodiction in quantum cosmology: the difference between classical and quantum
retrodiction, the permanence of the past, why we predict the future but
remember the past, the nature and utility of reconstructing the past(s), and
information theoretic measures of the utility of history. (Talk presented at
the Nobel Symposium: Modern Studies of Basic Quantum Concepts and Phenomena,
Gimo, Sweden, June 13-17, 1997)


title: On the Action Principle in Affine Flat Spaces with Torsion

abstract:
  To comply with the equivalence principle in Einstein-Cartan-like theories of
gravity we propose a modification of the action principle in affine flat spaces
with torsion.


title: Singularities Inside Hairy Black Holes

abstract:
  We show that the Strong Cosmic Censorship is supported by the behavior of
generic solutions on the class of static spherically symmetric black holes in
gravitating gauge models and their stringy generalizations.


title: Spinless Matter in Transposed-Equi-Affine Theory of Gravity

abstract:
  We derive and discus the equations of motion for spinless matter:
relativistic spinless scalar fields, particles and fluids in the recently
proposed by A. Saa model of gravity with covariantly constant volume with
respect to the transposed connection in Einstein-Cartan spaces.
  A new interpretation of this theory as a theory with variable Plank
"constant" is suggested.
  We show that the consistency of the semiclassical limit of the wave equation
and classical motion dictates a new definite universal interaction of torsion
with massive fields.


title: Cosmological waveguides for gravitational waves

abstract:
  We study the linearized equations describing the propagation of gravitational
waves through dust. In the leading order of the WKB approximation, dust behaves
as a non-dispersive, non-dissipative medium. Taking advantage of these
features, we explore the possibility that a gravitational wave from a distant
source gets trapped by the gravitational field of a long filament of galaxies
of the kind seen in the large scale structure of the Universe. Such a
waveguiding effect may lead to a huge magnification of the radiation from
distant sources, thus lowering the sensitivity required for a successful
detection of gravitational waves by detectors like VIRGO, LIGO and LISA.


title: Anisotropic String Cosmology at Large Curvatures

abstract:
  We study the effect of the antisymmetric tensor field $B_{\mu\nu}$ on the
large curvature phase of string cosmology. It is well-known that a
non-vanishing value of $H=dB$ leads to an anisotropic expansion of the spatial
dimensions. Correspondingly, in the string phase of the model, including
$\alpha '$ corrections, we find anisotropic fixed points of the evolution,
which act as regularizing attractors of the lowest order solutions. The
attraction basin can also include isotropic initial conditions for the scale
factors. We present explicit examples at order $\alpha '$ for different values
of the number of spatial dimensions and for different ans\"{a}tze for $H$.


title: Horizon/Matter Systems near the Extreme State

abstract:
  It is shown that in the extreme limit with a zero surface gravity but nonzero
local temperature the limiting metric of a generic static black hole is
determined by a metric induced on a horizon and one function of two
coordinates, stress-energy tensor of a source picking up its values from a
horizon. The limiting procedure is extended to rotating black holes. If the
extreme limit is due to merging a black hole horizon and cosmological one both
horizons are always in thermal equilibrium in this limit. This is proved for a
generic case of static or axially-symmetrical rotating spacetimes.


title: Chaos and Rotating Black Holes with Halos

abstract:
  The occurrence of chaos for test particles moving around a slowly rotating
black hole with a dipolar halo is studied using Poincar\'e sections. We find a
novel effect, particles with angular momentum opposite to the black hole
rotation have larger chaotic regions in phase space than particles initially
moving in the same direction.


title: Towards Noncommutative Quantization of Gravity

abstract:
  We propose a mathematical structure, based on a noncommutative geometry,
which combines essential aspects of general relativity and quantum mechanics,
and leads to correct "limiting cases" of both these theories. We quantize a
groupoid constructed on space-time rather than space-time itself. Both space
and time emerge in the transition process to the commutative case. Our approach
clearly suggests that quantum gravitational observables should be looked for
among correlations of distant phenomena rather than among local effects. A toy
model is computed (based on a finite group) which predicts the value of
"cosmological constants" (in the quantum sector) which vanish when going to the
standard space-time physics.


title: Acoustic black holes: horizons, ergospheres, and Hawking radiation

abstract:
  It is a deceptively simple question to ask how acoustic disturbances
propagate in a non-homogeneous flowing fluid. This question can be answered by
invoking the language of Lorentzian differential geometry: If the fluid is
barotropic and inviscid, and the flow is irrotational (though possibly time
dependent), then the equation of motion for the velocity potential describing a
sound wave is identical to that for a minimally coupled massless scalar field
propagating in a (3+1)-dimensional Lorentzian geometry. The acoustic metric
governing the propagation of sound depends algebraically on the density, flow
velocity, and local speed of sound. This rather simple physical system is the
basis underlying a deep and fruitful analogy between the black holes of
Einstein gravity and supersonic fluid flows. Many results and definitions can
be carried over directly from one system to another. For example, I will show
how to define the ergosphere, trapped regions, acoustic apparent horizon, and
acoustic event horizon for a supersonic fluid flow, and will exhibit the close
relationship between the acoustic metric for the fluid flow surrounding a point
sink and the Painleve-Gullstrand form of the Schwarzschild metric for a black
hole. This analysis can be used either to provide a concrete non-relativistic
model for black hole physics, up to and including Hawking radiation, or to
provide a framework for attacking acoustics problems with the full power of
Lorentzian differential geometry.


title:
Remarks on the Reduced Phase Space of (2+1)-Dimensional Gravity on a
  Torus in the Ashtekar Formulation

abstract:
  We examine the reduced phase space of the Barbero-Varadarajan solutions of
the Ashtekar formulation of (2+1)-dimensional general relativity on a torus. We
show that it is a finite-dimensional space due to existence of an infinite
dimensional residual gauge invariance which reduces the infinite-dimensional
space of solutions to a finite-dimensional space of gauge-inequivalent
solutions. This is in agreement with general arguments which imply that the
number of physical degrees of freedom for (2+1)-dimensional Ashtekar gravity on
a torus is finite.


title: Deformation Quantisation of Gravity

abstract:
  We study the deformation (Moyal) quantisation of gravity in both the ADM and
the Ashtekar approach. It is shown, that both can be treated, but lead to
anomalies. The anomaly in the case of Ashtekar variables, however, is merely a
central extension of the constraint algebra, which can be ``lifted''.
  Finally we write down the equations defining physical states and comment on
their physical content. This is done by defining a loop representation. We find
a solution in terms of a Chern-Simons state, whose Wigner function then becomes
related to BF-theory. This state exist even in the absence of a cosmological
constant but only if certain extra conditions are imposed. Another solution is
found where the Wigner function is a Gaussian in the momenta.
  Some comments on ``quantum gravity'' in lower dimensions are also made.


title: Geodesics or autoparallels from a variational principle?

abstract:
  Recently it has been argued that autoparallels should be the correct
description of free particle motion in spaces with torsion, and that such
trajectories can be derived from variational principles if these are suitably
adapted. The purpose of this letter is to call attention to the problems that
such attempts raise, namely the requirement of a more elaborate structure in
order to formulate the variational principle and the lack of a Hamiltonian
description for the autoparallel motion. Here is also raised the problem of how
to generalize this proposed new principle to quantum mechanics and to field
theory. Since all applications known of such a principle are equally well
described in terms of geodesics in non-holonomic frames we conclude that there
is no reason to modify the conventional variational principle that leads to
geodesics.


title: The Large Numbers Hypothesis and Quantum Mechanics

abstract:
  In this paper, the suggested similarity between micro and macro-cosmos is
extended to quantum behavior, postulating that quantum mechanics, like general
relativity and classical electrodynamics, is invariant under discrete scale
transformations. This hypothesis leads to a large scale quantization of angular
momenta. Using the scale factor $\Lambda \sim 10^{38}$, the corresponding
quantum of action, obtained by scaling the Planck constant, is close to the
Kerr limit for the spin of the universe -- when this is considered as a huge
rotating black-hole -- and to the spin of Godel's universe, solution of
Einstein equations of gravitation. Besides, we suggest the existence of
another, intermediate, scale invariance, with scale factor $\lambda \sim
10^{19}$. With this factor we obtain, from Fermi's scale, the values for the
gravitational radius and for the collapse proper-time of a typical black-hole,
besides the Kerr limit value for its spin. It is shown that the mass-spin
relations implied by the two referred scale transformations are in accordance
with Muradian's Regge-like relations for galaxy clusters and stars. Impressive
results are derived when we use a $\lambda$-scaled quantum approach to
calculate the mean radii of planetary orbits in solar system. Finally, a
possible explanation for the observed quantization of galactic redshifts is
suggested, based on the large scale quantization conjecture.


title: Classical and Quantum Physical Geometry

abstract:
  The task of quantizing gravity is compared with Einstein's relativization of
gravity. The philosophical and physical foundations of general relativity are
briefly reviewed. The Ehlers-Pirani-Schild scheme of operationally determining
the geometry of space-time, using freely falling classical particle
trajectories, is done using operations in an infinitesimal neighborhood around
each point. The study of the free fall of a quantum wave suggests a quantum
principle of equivalence. The principle of general covariance is clarified. The
sign change of a Fermion field when rotated by $2\pi$ radians is used to argue
for a quantum mechanical modification of space-time, which leads naturally to
supersymmetry. A novel effect in quantum gravity due to the author is used to
extend Einstein's hole argument to quantum gravity. This suggests a quantum
principle of general covariance, according to which the fundamental laws of
physics should be covariant under `quantum diffeomorphisms'. This heuristic
principle implies that space-time points have no invariant meaning in quantum
gravity.