title: A new proof of Birkhoff's theorem

abstract:
  Assuming SO(3)-spherical symmetry, the 4-dimensional Einstein equation
reduces to an equation conformally related to the field equation for
2-dimensional gravity following from the Lagrangian L = R^(1/3).
  Solutions for 2-dimensional gravity always possess a local isometry because
the traceless part of its Ricci tensor identically vanishes. Combining both
facts, we get a new proof of Birkhoff's theorem; contrary to other proofs, no
coordinates must be introduced.
  The SO(m)-spherically symmetric solutions of the (m+1)-dimensional Einstein
equation can be found by considering L = R^(1/m) in two dimensions. This yields
several generalizations of Birkhoff's theorem in an arbitrary number of
dimensions, and to an arbitrary signature of the metric.


title: Answer to question Nr. 55

abstract:
  We answer to question Nr. 55 [Are there pictorial examples that distinguish
covariant and contravariant vectors ?] posed by D. Neuenschwander, Am. J. Phys.
65 (1), 11 (1997)


title: Numerical Study of Cosmological Singularities

abstract:
  The spatially homogeneous, isotropic Standard Cosmological Model appears to
describe our Universe reasonably well. However, Einstein's equations allow a
much larger class of cosmological solutions. Theorems originally due to Penrose
and Hawking predict that all such models (assuming reasonable matter
properties) will have an initial singularity. The nature of this singularity in
generic cosmologies remains a major open question in general relativity.
Spatially homogeneous but possibly anisotropic cosmologies have two types of
singularities: (1) velocity dominated---(reversing the time direction) the
universe evolves to the singularity with fixed anisotropic collapse rates ; (2)
Mixmaster---the anisotropic collapse rates change in a deterministically
chaotic way. Much less is known about spatially inhomogeneous universes.
Belinskii, Khalatnikov, and Lifshitz (BKL) claimed long ago that a generic
universe would evolve toward the singularity as a different Mixmaster universe
at each spatial point. We shall report on the results of a program to test the
BKL conjecture numerically. Results include a new algorithm to evolve
homogeneous Mixmaster models, demonstration of velocity dominance and
understanding of evolution toward velocity dominance in the plane symmetric
Gowdy universes (spatial dependence in one direction), demonstration of
velocity dominance in polarized U(1) symmetric cosmologies (spatial dependence
in two directions), and exploration of departures from velocity dominance in
generic U(1) universes.


title: Dynamical Ambiguities in Singular Gravitational Field

abstract:
  We consider particle dynamics in singular gravitational field. In 2d
spacetime the system splits into two independent gravitational systems without
singularity. Dynamical integrals of each system define $sl(2,R)$ algebra, but
the corresponding symmetry transformations are not defined globally.
Quantization leads to ambiguity. By including singularity one can get the
global $SO(2.1)$ symmetry. Quantization in this case leads to unique quantum
theory.


title: Numerical Evolution of Dynamic 3D Black Holes: Extracting Waves

abstract:
  We consider the numerical evolution of dynamic black hole initial data sets
with a full 3D, nonlinear evolution code. These data sets consist of single
black holes distorted by strong gravitational waves, and mimic the late stages
of coalescing black holes. Through comparison with results from well
established axisymmetric codes, we show that these dynamic black holes can be
accurately evolved. In particular, we show that with present computational
resources and techniques, the process of excitation and ringdown of the black
hole can be evolved, and one can now extract accurately the gravitational waves
emitted from the 3D Cartesian metric functions, even though they may be buried
in the metric at levels on the order of $10^{-3}$ and below. Waveforms for both
the $\ell=2$ and the much more difficult $\ell=4$ modes are computed and
compared with axisymmetric calculations. In addition to exploring the physics
of distorted black hole data sets, and showing the extent to which the waves
can be accurately extracted, these results also provide important testbeds for
all fully nonlinear numerical codes designed to evolve black hole spacetimes in
3D, whether they use singularity avoiding slicings, apparent horizon boundary
conditions, or other evolution methods.


title: Space of the vertices of relativistic spin networks

abstract:
  The general solutin to the constraints that define relativistic spin networks
vertices is given and their relations with 3-dimensional quantum tetrahedra is
dicussed. An alternative way to handle the constraints is also presented.


title: Issues in gravitational wave data analysis

abstract:
  Data analysis is the application of probability and statistics to draw
inference from observation. Is a signal present or absent? Is the source an
inspiraling binary system or a supernova? At what point in the sky is the
radiation incident from? In these notes I want to address how two different
statistical methodologies --- Bayesian and Frequentist --- approach the problem
of statistical inference


title:
Fast and Slow solutions in General Relativity: The Initialization
  Procedure

abstract:
  We apply recent results in the theory of PDE, specifically in problems with
two different time scales, on Einstein's equations near their Newtonian limit.
The results imply a justification to Postnewtonian approximations when
initialization procedures to different orders are made on the initial data. We
determine up to what order initialization is needed in order to detect the
contribution to the quadrupole moment due to the slow motion of a massive body
as distinct from initial data contributions to fast solutions and prove that
such initialization is compatible with the constraint equations. Using the
results mentioned the first Postnewtonian equations and their solutions in
terms of Green functions are presented in order to indicate how to proceed in
calculations with this approach.


title: Nonperturbative Instability of Black Holes in Quantum Gravity

abstract:
  The decay rate for a black hole to decay nonperturbatively via tunneling is
shown to be related to the Bekenstein-Hawking black hole entropy $S_{bh}$. This
new physical interpretation of the black hole entropy was presented first in
1988 in this paper. I quote here the relevant statement: ``It should be noticed
that the decay rate of a black hole due to nonperturbative instability is
proportional to $\exp(-S_{bh}$, where $S_{bh}$ is the Bekenstein-Hawking
entropy. This seems to indicate that the Bekenstein-Hawking entropy is the
measure of the ability of a black hole to disappear from our Universe in the
one quantum jump, with the simultaneous production of particles carrying away
its total energy.''


title: Wave Function for the Reissner-Nordstr\"om Black-Hole

abstract:
  We study the quantum behaviour of Reissner-Nordstr\"om (RN) black-holes
interacting with a complex scalar field. A Maxwell field is also present. Our
analysis is based on M. Pollock's method and is characterized by solving a
Wheeler-DeWitt equation in the proximity of an apparent horizon of the RN
space-time. Subsequently, we obtain a wave-function $\Psi_{RN}[M, Q]$
representing the RN black-hole when its charge, $\mid Q \mid$, is small in
comparison with its mass, $M$. We then compare quantum-mechanically the cases
of $(i)$ $Q = 0$ and $(ii)$ $M \geq \mid Q \mid \neq 0 $. A special emphasis is
given to the evolution of the mass-charge rate affected by Hawking radiation.


title: Internal structure of Einstein-Yang-Mills-Dilaton black holes

abstract:
  We study the interior structure of the Einstein-Yang-Mills-Dilaton black
holes as a function of the dilaton coupling constant $\gamma\in [0,1]$. For
$\gamma\neq 0$ the solutions have no internal Cauchy horizons and the field
amplitudes follow a power law behavior near the singularity. As $\gamma$
decreases, the solutions develop more and more oscillation cycles in the
interior region, whose number becomes infinite in the limit $\gamma\to 0$.


title:
Gravitational wave extraction and outer boundary conditions by
  perturbative matching

abstract:
  We present a method for extracting gravitational radiation from a
three-dimensional numerical relativity simulation and, using the extracted
data, to provide outer boundary conditions. The method treats dynamical
gravitational variables as nonspherical perturbations of Schwarzschild
geometry. We discuss a code which implements this method and present results of
tests which have been performed with a three dimensional numerical relativity
code.


title: Cosmological Vacuum in Unified Theories

abstract:
  The unification of the Einstein theory of gravity with a conformal invariant
version of the standard model for electroweak interaction without the Higgs
potential is considered. In this theory, a module of the Higgs field is
absorbed by the scale factor component of metric so that the evolution of the
Universe and the elementary particle masses have one and the same cosmological
origin and the flat space limit corresponds to the $\sigma$-model version of
the standard model. The red shift formula and Hubble law are obtained under the
assumption of homogeneous matter distribution. We show that the considered
theory leads to a very small vacuum density of the Higgs field
$\rho_\phi^{Cosmic}=10^{-34}\rho_{cr}$ in contrast with the theory with the
Higgs potential $\rho_\phi^{Higgs}=10^{54}\rho_{cr}$.


title: The Cosmological Time Function

abstract:
  Let $(M,g)$ be a time oriented Lorentzian manifold and $d$ the Lorentzian
distance on $M$. The function $\tau(q):=\sup_{p< q} d(p,q)$ is the cosmological
time function of $M$, where as usual $p< q$ means that $p$ is in the causal
past of $q$. This function is called regular iff $\tau(q) < \infty$ for all $q$
and also $\tau \to 0$ along every past inextendible causal curve. If the
cosmological time function $\tau$ of a space time $(M,g)$ is regular it has
several pleasant consequences: (1) It forces $(M,g)$ to be globally hyperbolic,
(2) every point of $(M,g)$ can be connected to the initial singularity by a
rest curve (i.e., a timelike geodesic ray that maximizes the distance to the
singularity), (3) the function $\tau$ is a time function in the usual sense, in
particular (4) $\tau$ is continuous, in fact locally Lipschitz and the second
derivatives of $\tau$ exist almost everywhere.


title: Geometric wormhole throats

abstract:
  Wormholes and black holes have traditionally been treated a quite separate
objects with relatively little overlap. The possibility of a connection arises
in that wormholes, if they exist, might have profound influence on black holes,
their event horizons, and their internal structure. After discussing some
connections, we embark on an overview of what can generally be said about
traversable wormhole throats. We discuss the violations of the energy
conditions that typically occur at and near the throat of any traversable
wormhole and emphasize the generic nature of this result. We discuss the
original Morris-Thorne wormhole and its generalization to a spherically
symmetric time-dependent wormhole, and also discuss spherically symmetric
Brans-Dicke wormholes. We also discuss the relationship with the topological
censorship theorem. Finally we turn to a rather general class of wormholes that
permit explicit analysis: generic static traversable wormholes (without any
symmetry). We define the wormhole throat in terms of a 2--dimensional
constant-time hypersurface of minimal area. (Zero trace for the extrinsic
curvature plus a ``flare--out'' condition.) This enables us to derive
generalized theorems regarding violations of the energy conditions---theorems
that do not involve geodesic averaging but nevertheless apply to situations
much more general than the spherically symmetric Morris-Thorne traversable
wormhole. [For example: the null energy condition (NEC), when suitably weighted
and integrated over the wormhole throat, must be violated.]


title: Global monopole in scalar tensor theory

abstract:
  The well known monopole solution of Barriola and Vilenkin (BV) resulting from
the breaking of a global SO(3) symmetry is extended in general relativity along
with a zero mass scalar field and also in Brans-Dicke(BD) theory of gravity.In
the case of BD theory, the behaviour of spacetime and other variables such as
BD scalar field and the monopole energy density have been studied
numerically.For monopole along with a zero mass scalar field, exact solutions
are obtained and depending upon the choice of arbitary parameters, the
solutions either reduce to the BV case or to a pure scalar field solution as
special cases.It is interesting to note that unlike the BV case the global
monopole in the BD theory does exert gravitational pull on a test particle
moving in its spacetime.


title: The Newtonian Limit on Asymptotically Null Foliations

abstract:
  By suitably re-scaling the conformal Einstein's equations we are able to
apply recent results in the theory of PDE, and prove that they possess slow
solutions in a future neighborhood of an initial surface reaching ${\cal I}^+$.
The structure of the equations obtained allows to split (up to any given order)
the initial data into those generating slow solutions, i.e., those driven by
the sources, and those generating fast solutions, i.e., those which represent
gravitational radiation with no relation to the sources. Thus effectively
resulting in a proposal to prescribe initial data for solutions with no extra
radiation up to the order needed for each given application.


title:
Einstein's equations in Ashtekar's variables constitute a symmetric
  hyperbolic system

abstract:
  We show that the 3+1 vacuum Einstein field equations in Ashtekar's variables
constitutes a first order symmetric hyperbolic system for arbitrary but fixed
lapse and shift fields, by suitable adding to the system terms proportional to
the constraint equations.


title: \Lambda=0 Cosmology of a Brane-like Universe

abstract:
  We examine the possibility that Friedman-Robertson-Walker evolution is
governed by an effective (rather then by the actual) energy density. A concrete
example is provided by $\Lambda=0$ Regge-Teitelboim cosmology, where critical
cosmology only requires subcritical matter density $(\Omega_{m}<1)$, and the
age of a flat matter dominated Universe gets enhanced by a factor of 9/8. Dual
to the mature dilute Universe is the embryo Universe, the evolution of both is
governed by $P_{eff}=-{1/9}\rho_{eff}$.


title: Quantum Geometry and Thermal Radiation from Black Holes

abstract:
  A quantum mechanical description of black hole states proposed recently
within non-perturbative quantum gravity is used to study the emission and
absorption spectra of quantum black holes. We assume that the probability
distribution of states of the quantum black hole is given by the ``area''
canonical ensemble, in which the horizon area is used instead of energy, and
use Fermi's golden rule to find the line intensities. For a non-rotating black
hole, we study the absorption and emission of s-waves considering a special set
of emission lines. To find the line intensities we use an analogy between a
microscopic state of the black hole and a state of the gas of atoms.


title: Quantum Geometry and Black Hole Entropy

abstract:
  A `black hole sector' of non-perturbative canonical quantum gravity is
introduced. The quantum black hole degrees of freedom are shown to be described
by a Chern-Simons field theory on the horizon. It is shown that the entropy of
a large non-rotating black hole is proportional to its horizon area. The
constant of proportionality depends upon the Immirzi parameter, which fixes the
spectrum of the area operator in loop quantum gravity; an appropriate choice of
this parameter gives the Bekenstein-Hawking formula S = A/4*l_p^2. With the
same choice of the Immirzi parameter, this result also holds for black holes
carrying electric or dilatonic charge, which are not necessarily near extremal.


title: Loop Quantum Gravity

abstract:
  The problem of finding the quantum theory of the gravitational field, and
thus understanding what is quantum spacetime, is still open. One of the most
active of the current approaches is loop quantum gravity. Loop quantum gravity
is a mathematically well-defined, non-perturbative and background independent
quantization of general relativity, with its conventional matter couplings. The
research in loop quantum gravity forms today a vast area, ranging from
mathematical foundations to physical applications. Among the most significative
results obtained are: (i) The computation of the physical spectra of
geometrical quantities such as area and volume; which yields quantitative
predictions on Planck-scale physics. (ii) A derivation of the
Bekenstein-Hawking black hole entropy formula. (iii) An intriguing physical
picture of the microstructure of quantum physical space, characterized by a
polymer-like Planck scale discreteness. This discreteness emerges naturally
from the quantum theory and provides a mathematically well-defined realization
of Wheeler's intuition of a spacetime ``foam''. Long standing open problems
within the approach (lack of a scalar product, overcompleteness of the loop
basis, implementation of reality conditions) have been fully solved. The weak
part of the approach is the treatment of the dynamics: at present there exist
several proposals, which are intensely debated. Here, I provide a general
overview of ideas, techniques, results and open problems of this candidate
theory of quantum gravity, and a guide to the relevant literature.


title: Model of the gravitational dipole

abstract:
  A model of the gravitational dipole is proposed in a close analogy to that of
the global monopole. The physical properties and the range of validity of the
model are examined as is the motion of test particles in the dipole background.
It is found that the metric of the gravitational dipole describes a curved
space-time, so one would expect it to have a more pronounced effect on the
motion of the test particles than the spinning cosmic string. It is indeed so
and in the generic case the impact of repulsive centrifugal force results in a
motion whose orbits when projected on the equatorial plane represent unfolding
spirals or hyperbolas. Only in one special case these projections are straight
lines, pretty much in a manner observed in the field of the spinning cosmic
string. Even if open, the orbits are nevertheless bounded in the angular
coordinate $\theta$.


title: Energy conditions and galaxy formation

abstract:
  This note summarizes a model-independent analysis of the age of the universe
problem that trades off precision in favour of robustness: The energy
conditions of Einstein gravity are designed to extract as much information as
possible from classical general relativity without specifying a particular
equation of state. This is particularly useful in a cosmological setting, where
the equation of state for the cosmological fluid is extremely uncertain. The
strong energy condition (SEC) provides a simple and robust bound on the
behaviour of the look-back time as a function of red-shift. Observation
suggests that the SEC may be violated sometime between the epoch of galaxy
formation and the present.


title:
A slightly less grand challenge: Colliding Black Holes using
  perturbation techniques

abstract:
  Perturbation techniques can be used as an alternative to supercomputer
calculations in calculating gravitational radiation emitted by colliding black
holes, provided the process starts with the black holes close to each other. We
give a summary of the method and of the results obtained for various initial
configurations, both axisymmetric and without symmetry: Initially static,
boosted towards each other, counter-rotating, or boosted at an angle
(pseudo-inspiral). Where applicable, we compare the perturbation results with
supercomputer calculations.


title: Some exact results on the CGHS black-hole radiation

abstract:
  Theorems on the emission of massless scalar particles by the CGHS black hole
are presented. The convergence of the mean number of particles created
spontaneously in an arbitrary state is studied and shown to be strongly
dependent on the infrared behavior of this state. A bound for this quantity is
given and its asymptotic forms close to the horizon and far from the black hole
are investigated. The physics of a wave packet is analysed in some detail in
the black-hole background. It is also shown that for some states the mean
number of created particles is not thermal close to the horizon. These states
have a long queue extending far from the black hole, or are unlocalised in
configuration space.


title: The `Ups' and `Downs' of a Spinning Black Hole

abstract:
  We report and comment upon the principal results of an investigation into the
evolution of rotating black holes emitting massless scalar radiation via the
Hawking process. It is demonstrated that a Kerr black hole evaporating by the
emission of scalar radiation will evolve towards a state with $a \approx
0.555M$. If the initial specific angular momentum is larger than this value the
hole will spin down to this value; if it is less it will spin up to this value.
The addition of higher spin fields to the picture strongly suggests the final
asymptotic state of a realistic evaporation process will be characterized by an
$a/M = 0$.


title: A Critical Look At Massive Scalar Field Collapse

abstract:
  We present the findings of an investigation of critical behavior in the
collapse of spherically symmetric distributions of massive scalar field. Two
distinct types of phase transition are observed at the verge of black hole
formation and a criterion for determining when each type of transition will
occur is given.


title: Some Cosmological Tails of Collapse

abstract:
  We summarize the results of an investigation into the late time behavior of
massless scalar fields propagating on spherically symmetric black hole
spacetimes with a non-zero cosmological constant. The compatibility of these
results with the `minimal requirement' of Brady and Poisson is commented upon.


title: Loop constraints: A habitat and their algebra

abstract:
  This work introduces a new space $\T'_*$ of `vertex-smooth' states for use in
the loop approach to quantum gravity. Such states provide a natural domain for
Euclidean Hamiltonian constraint operators of the type introduced by Thiemann
(and using certain ideas of Rovelli and Smolin). In particular, such operators
map $\T'_*$ into itself, and so are actual operators in this space. Their
commutator can be computed on $\T'_*$ and compared with the classical
hypersurface deformation algebra. Although the classical Poisson bracket of
Hamiltonian constraints yields an inverse metric times an infinitesimal
diffeomorphism generator, and despite the fact that the diffeomorphism
generator has a well-defined non-trivial action on $\T'_*$, the commutator of
quantum constraints vanishes identically for a large class of proposals.


title: On the Eccentricity Behaviour of Radiating Slowly Rotating Bodies

abstract:
  We study different models of radiating slowly rotating bodies up to the first
order in the angular velocity. It is shown that up to this order the evolution
of the eccentricity is highly model-dependent even for very compact objects.


title:
On the consistency of the constraint algebra in spin network quantum
  gravity

abstract:
  We point out several features of the quantum Hamiltonian constraints recently
introduced by Thiemann for Euclidean gravity. In particular we discuss the
issue of the constraint algebra and of the quantum realization of the object
$q^{ab}V_b$, which is classically the Poisson Bracket of two Hamiltonians.


title: Quantum Measurements, Nonlocality and the Arrow of Time

abstract:
  A theory is developed which attempts to reconcile the measurements of
nonlocal quantum observables with special relativity and quantum mechanics. The
collapse of a wave function, which coincides with a nonlocal measurement by
some macroscopic measuring device, is associated with the triggering of an
absorber mechanism due to the interaction of the apparatus with the charges in
the rest of the universe. The standard retarded electromagnetic field plus
radiation damping is converted, for a short time during the collapse of the
wave function, to an advanced field plus radiation. The reversal of the arrow
of time during the wave function reduction permits communication in nonlocal
quantum experiments at the speed of light, resolving paradoxes associated with
measurements of correlated quantum states and special relativity. The absorber
mechanism and the advanced field solution are consistent with conventional
Friedmann-Robertson-Walker expanding universes.


title: The reliability horizon

abstract:
  The ``reliability horizon'' for semi-classical quantum gravity quantifies the
extent to which we should trust semi-classical quantum gravity, and gives a
handle on just where the ``Planck regime'' resides. The key obstruction to
pushing semi-classical quantum gravity into the Planck regime is often the
existence of large metric fluctuations, rather than a large back-reaction.


title: Deformation Quantisation of Constrained Systems

abstract:
  We study the deformation quantisation (Moyal quantisation) of general
constrained Hamiltonian systems. It is shown how second class constraints can
be turned into first class quantum constraints. This is illustrated by the O(N)
non-linear $\sigma$-model. Some new light is also shed on the Dirac bracket.
Furthermore, it is shown how classical constraints not in involution with the
classical Hamiltonian, can be turned into quantum constraints {\em in}
involution with respect to the Hamiltonian. Conditions on the existence of
anomalies are also derived, and it is shown how some kinds of anomalies can be
removed. The equations defining the set of physical states are also given. It
turns out that the deformation quantisation of pure Yang-Mills theory is
straightforward whereas gravity is anomalous. A formal solution to the
Yang-Mills quantum constraints is found. In the \small{ADM} formalism of
gravity the anomaly is very complicated and the equations picking out physical
states become infinite order functional differential equations, whereas the
Ashtekar variables remedy both of these problems -- the anomaly becoming simply
a central extension (Schwinger term) and the equations for physical states
become finite order. We finally elaborate on the underlying geometrical
structure and show the method to be compatible with BRST methods.


title: Testing Cosmic Censorship in Kerr-like Collapse Situations

abstract:
  According to the cosmic censorship hypothesis of Penrose, naked singularities
should never occur in realistic collapse situations. One of the major open
problems in this context is the existence of a naked singularity in the Kerr
solution with |a|>m; this singularity can be interpreted as the final product
of collapse of a rapidly rotating object. Assuming that certain very general
and physically reasonable conditions hold, we show here, using the global
techniques, that a realistic gravitational collapse of any rotating object,
which develops from a regular initial state, cannot lead to the formation of a
final state resembling the Kerr solution with a naked singularity. This result
supports the validity of the cosmic censorship hypothesis.


title:
Numerical study on the hydrodynamic instability of binary stars in the
  first post Newtonian approximation of general relativity

abstract:
  We present numerical results on the hydrodynamic stability of coalescing
binary stars in the first post Newtonian(1PN) approximation of general
relativity. We pay particular attention to the hydrodynamical instability of
corotating binary stars in equilibrium states assuming the stiff polytropic
equation of state with the adiabatic constant $\Gamma=3$. In previous 1PN
numerical studies on corotating binary stars in equilibrium states, it was
found that along the sequence of binary stars as a function of the orbital
separation, they have the energy and/or angular momentum minima where the
secular instability sets in, and that with increase of the 1PN correction, the
orbital separation at these minima decreases while the angular velocity there
increases. In this paper, to know the location of the innermost stable circular
orbit(ISCO), we perform numerical simulations and find where the hydrodynamical
instability along the corotating sequences of binary sets in. From the
numerical results, we found that the dynamical stability limit seems to exist
near the energy and/or angular momentum minima not only in the Newtonian, but
also in the 1PN cases. This means that the 1PN effect of general relativity
increases the angular frequency of gravitational waves at the ISCO.


title:
Hypersurface-orthogonal generators of an orthogonally transitive
  transitive $G_2I$, topological identifications, and axially and cylindrically
  symmetric spacetimes

abstract:
  A criterion given by Castejon-Amenedo and MacCallum (1990) for the existence
of (locally) hypersurface-orthogonal generators of an orthogonally-transitive
two-parameter Abelian group of motions (a $G_2I$) in spacetime is re-expressed
as a test for linear dependence with constant coefficients between the three
components of the metric in the orbits in canonical coordinates. In general, it
is shown that such a relation implies that the metric is locally diagonalizable
in canonical coordinates, or has a null Killing vector, or can locally be
written in a generalized form of the `windmill' solutions characterized by
McIntosh. If the orbits of the $G_2I$ have cylindrical or toroidal topology and
a periodic coordinate is used, these metric forms cannot in general be realized
globally as they would conflict with the topological identification. The
geometry then has additional essential parameters, which specify the
topological identification. The physical significance of these parameters is
shown by their appearance in global holonomy and by examples of exterior
solutions where they have been related to characteristics of physical sources.
These results lead to some remarks about the definition of cylindrical
symmetry.


title:
Comment on ``Consistent Sets Yield Contrary Inferences in Quantum
  Theory''

abstract:
  In a recent paper Kent has pointed out that in consistent histories quantum
theory it is possible, given initial and final states, to construct two
different consistent families of histories, in each of which there is a
proposition that can be inferred with probability one, and such that the
projectors representing these two propositions are mutually orthogonal. In this
note we stress that, according to the rules of consistent history reasoning two
such propositions are not contrary in the usual logical sense namely, that one
can infer that if one is true then the other is false, and both could be false.
No single consistent family contains both propositions, together with the
initial and final states, and hence the propositions cannot be logically
compared. Consistent histories quantum theory is logically consistent,
consistent with experiment as far as is known, consistent with the usual
quantum predictions for measurements, and applicable to the most general
physical systems. It may not be the only theory with these properties, but in
our opinion, it is the most promising among present possibilities.


title: Evolving wormhole geometries

abstract:
  We present here analytical solutions of General Relativity that describe
evolving wormholes with a non-constant redshift function. We show that the
matter that threads these wormholes is not necessarily exotic. Finally, we
investigate some issues concerning WEC violation and human traversability in
these time-dependent geometries.


title:
Physical Applications of a Generalized Clifford Calculus (Papapetrou
  equations and Metamorphic Curvature)

abstract:
  A generalized Clifford manifold is proposed in which there are coordinates
not only for the basis vector generators, but for each element of the Clifford
group, including the identity scalar. These new quantities are physically
interpreted to represent internal structure of matter (e.g. classical or
quantum spin). The generalized Dirac operator must now include differentiation
with respect to these higher order geometric coordinates. In a Riemann space,
where the magnitude and rank of geometric objects are preserved under
displacement, these new terms modify the geodesics. One possible physical
interpretation is natural coupling of the classical spin to linear motion,
providing a new derivation of the Papapetrou equations. A generalized curvature
is proposed for the Clifford manifold in which the connection does not preserve
the rank of a multivector under parallel transport, e.g. a vector may be
``rotated'' into a scalar.


title:
Rotation of Plane of Polarization of an Electromagnetic Wave Propagating
  over Cosmological Distances in "Finite Rotating Universe" Scenario

abstract:
  A systematic rotation of the plane of polarization of electromagnetic
radiation propagating over cosmological distances has been claimed to be
detected by Nodland and Ralston.Taking the finite rotating universe of Oszvath
and Sch\"ucking as a toy model for the actual universe,we calculate the
rotation of the plane of polarization of electromagnetic waves in this
universe.It turns out that the observed data are consistent with the
Oszvath-Sch\"ucking parameter $k=0.39$.


title: Cosmological solutions with nonlinear bulk viscosity

abstract:
  A recently proposed nonlinear transport equation is used to model bulk
viscous cosmologies that may be far from equilibrium, as happens during viscous
fluid inflation or during reheating. The asymptotic stability of the de Sitter
and Friedmann solutions is investigated. The former is stable for bulk
viscosity index $q<1$ and the latter for $q>1$. New solutions are obtained in
the weakly nonlinear regime for $q=1$. These solutions are singular and some of
them represent a late-time inflationary era.


title:
Can Spontaneous Supersymmetry Breaking in a Quantum Universe Induce the
  Emergence of Classical Spacetimes ?

abstract:
  We introduce the set of constraints the wave function of the Universe has to
satisfy in order to describe an Universe undergoing through the process of
spontaneous breaking of supersymmetry and discuss the way this may lead to the
emergence of classical spacetime.


title:
A relativistic formalism to compute quasi-equilibrium configurations of
  non-synchronized neutron star binaries

abstract:
  A general relativistic version of the Euler equation for perfect fluid
hydrodynamics is applied to a system of two neutron stars orbiting each other.
In the quasi-equilibrium phase of the evolution of this system, a first
integral of motion can be derived for certain velocity fields of the neutron
star fluid including the (academic) case of co-rotation with respect to the
orbital motion (synchronized binaries) and the realistic case of
counter-rotation with respect to the orbital motion. The velocity field leading
to this latter configuration can be computed by solving three-dimensional
vector and scalar Poisson equations.


title:
Canonical Quantum Statistics of Schwarzschild Black Holes and Ising
  Droplet Nucleation

abstract:
  Recently is was shown that the imaginary part of the canonical partition
function of Schwarzschild black holes with an energy spectrum E_n = \sigma
\sqrt{n} E_P, n= 1,2, ..., has properties which - naively interpreted - leads
to the expected unusual thermodynamical properties of such black holes (Hawking
temperature, Bekenstein-Hawking entropy etc). The present paper interprets the
same imaginary part in the framework of droplet nucleation theory in which the
rate of transition from a metastable state to a stable one is proportional to
the imaginary part of the canonical partition function. The conclusions
concerning the emerging thermodynamics of black holes are essentially the same
as before. The partition function for black holes with the above spectrum was
calculated exactly recently. It is the same as that of the primitive Ising
droplet model for nucleation in 1st-order phase transitions in 2 dimensions.
Thus one might learn about the quantum statistics of black holes by studying
that Ising model, the exact complex free energy of which is presented here for
negative magnetic fields, too.


title: Exact Path Integral Quantization of 2-D Dilaton Gravity

abstract:
  We demonstrate that in the absence of `matter' fields to all orders of
perturbation theory and for all 2D dilaton theories the quantum effective
action coincides with the classical one. This resolves the apparent
contradiction between the well established results of Dirac quantization and
perturbative (path-integral) approaches which seemed to yield non-trivial
quantum corrections. For the Jackiw--Teitelboim (JT) model, our result is even
extended to the situation when a matter field is present.


title: Gravitational vacuum polarization

abstract:
  The energy conditions of classical Einstein gravity fail once quantum effects
are introduced. These quantum violations of the energy conditions are not
subtle high-energy Planck scale effects. Rather the quantum violations of the
energy conditions already occur in semiclassical quantum gravity and are
first-order O(\hbar) effects. Quantum violations of the energy conditions are
widespread, albeit small.


title:
Cosmological Vorticity in a Gravity with Quadratic Order Curvature
  Couplings

abstract:
  We analyse the evolution of the rotational type cosmological perturbation in
a gravity with general quadratic order gravitational coupling terms. The result
is expressed independently of the generalized nature of the gravity theory, and
is simply interpreted as a conservation of the angular momentum.


title:
Quantum Analysis of the Compactification Process in the Multidimensional
  Einstein-Yang-Mills System

abstract:
  We study solutions of the Wheeler-DeWitt equation obtained when considering
homogeneous and isotropic (up to a gauge transformation) field configurations
of the Einstein-Yang-Mills system in $D=4+d$ dimensions with an $R \times S^3
\times S^d$ topology and assuming the Hartle-Hawking boundary conditions.


title: Quadrupole-quadrupole gravitational waves

abstract:
  This paper investigates the non-linear self-interaction of quadrupole
gravitational waves generated by an isolated system. The vacuum Einstein field
equations are integrated in the region exterior to the system by means of a
post-Minkowskian algorithm. Specializing in the quadrupole-quadrupole
interaction (at the quadratic non-linear order), we recover the known results
concerning the non-local modification of the ADM mass-energy of the system
accounting for the emission of quadrupole waves, and the non-local memory
effect due to the re-radiation by the stress-energy distribution of linear
waves. Then we compute all the local (instantaneous) terms which are associated
in the quadrupole-quadrupole metric with the latter non-local effects.
Expanding the metric at large distances from the system, we obtain the
corresponding radiation-field observables, including all non-local and
transient contributions. This permits notably the completion of the observable
quadrupole moment at the 5/2 post-Newtonian order.


title: Gravitational-wave tails of tails

abstract:
  The tails of gravitational waves are caused by scattering of linear waves
onto the space-time curvature generated by the total mass-energy of the source.
Quite naturally, the tails of tails are caused by curvature scattering of the
tails of waves themselves. The tails of tails are associated with the cubic
non-linear interaction between two mass monopole moments and, dominantly, the
mass quadrupole of the source. In this paper we determine the radiation field
at large distances from the source for this particular
monopole-monopole-quadrupole interaction. We find that the tails of tails
appear at the third post-Newtonian (3PN) order beyond the usual quadrupole
radiation. Motivated by the need of accurate templates to be used in the data
analysis of future detectors of gravitational waves, we compute the
contribution of tails, and of tails of tails, up to the 3.5PN order in the
energy flux generated by inspiraling compact binaries.


title: Constraints and Solutions of Quantum Gravity in Metric Representation

abstract:
  We construct the regularised Wheeler-De Witt operator demanding that the
algebra of constraints of quantum gravity is anomaly free. We find that for a
subset of all wavefunctions being integrals of scalar densities this condition
can be satisfied. We proceed to finding exact solutions of quantum gravity
being of the form of functionals of volume and average curvature of compact
three-manifold.


title:
Nonlinear wave equations for numerical relativity: towards the
  computation of gravitational wave forms of black hole binaries

abstract:
  The prime candidate of LIGO/VIRGO sources of gravitational waves is the
spiral in of black holes and neutron stars in compact binaries. While the early
stages of the evolution of compact binaries is computable from post-Newtonian
calculations, prediction of their late stages requires large scale numerical
simulation. A fully covariant and strictly hyperbolic formulation for numerical
relativity is described, and illustrated in a one-dimensional computation of a
Gowdy-wave on the three-torus. This formulation allows foliations in full
generality, in particular it poses no restriction on the lapse function.


title: Einstein-Bianchi Hyperbolic System for General Relativity

abstract:
  By employing the Bianchi identities for the Riemann tensor in conjunction
with the Einstein equations, we construct a first order symmetric hyperbolic
system for the evolution part of the Cauchy problem of general relativity. In
this system, the metric evolves at zero speed with respect to observers at rest
in a foliation of spacetime by spacelike hypersurfaces while the curvature and
connection propagate at the speed of light. The system has no unphysical
characteristics, and matter sources can be included.


title: Entropy of Constant Curvature Black Holes in General Relativity

abstract:
  We consider the thermodynamic properties of the constant curvature black hole
solution recently found by Banados. We show that it is possible to compute the
entropy and the quasilocal thermodynamics of the spacetime using the
Einstein-Hilbert action of General Relativity. The constant curvature black
hole has some unusual properties which have not been seen in other black hole
spacetimes. The entropy of the black hole is not associated with the event
horizon; rather it is associated with the region between the event horizon and
the observer. Further, surfaces of constant internal energy are not isotherms
so the first law of thermodynamics exists only in an integral form. These
properties arise from the unusual topology of the Euclidean black hole
instanton.


title:
Free evolution of nonlinear scalar field collapse in double-null
  coordinates

abstract:
  We study numerically the fully nonlinear spherically-symmetric collapse of a
self-gravitating, minimally-coupled, massless scalar field. Our numerical code
is based on double-null coordinates and on free evolution of the metric
functions and the scalar field. The numerical code is stable and second-order
accurate. We use this code to study the late-time asymptotic behavior at fixed
$r$ (outside the black hole), along the event horizon, and along future null
infinity. In all three asymptotic regions we find that, after the decay of the
quasi-normal modes, the perturbations are dominated by inverse power-law tails.
The corresponding power indices agree with the integer values predicted by
linearized theory. We also study the case of a charged black hole nonlinearly
perturbed by a (neutral) self-gravitating scalar field, and find the same type
of behavior---i.e., quasi-normal modes followed by inverse power-law tails,
with the same indices as in the uncharged case.


title: Structure of the Cauchy horizon singularity

abstract:
  We study the Cauchy horizon (CH) singularity of a spherical charged black
hole perturbed nonlinearly by a self-gravitating massless scalar field. We show
numerically that the singularity is weak both at the early and at the late
sections of the CH, where the focusing of the area coordinate $r$ is strong. In
the early section the metric perturbations vanish, and the fields behave
according to perturbation analysis. We find exact analytical expressions for
the gradients of $r$ and of the scalar field, which are valid at both sections.
We then verify these analytical results numerically.


title: Colliding Plane Waves in Einstein-Maxwell Theory

abstract:
  Recently a simple solution of the vacuum Einstein-Maxwell field equations was
given describing a plane electromagnetic shock wave sharing its wave front with
a plane gravitational impulse wave. We present here an exact solution of the
vacuum Einstein-Maxwell field equations describing the head-on collision of
such a wave with a plane gravitational impulse wave. The solution has the
Penrose-Khan solution and a solution obtained by Griffiths as separate limiting
cases.


title:
Limiting solutions of sequences of globally regular and black hole
  solutions in SU(N)-EYMD theories

abstract:
  Static spherically symmetric solutions in SU(N)-EYM and EYMD theories are
classified by the node numbers of their non-trivial gauge field functions. With
increasing node numbers, the solutions form sequences, tending to limiting
solutions. The limiting solutions are based on subalgebras of $su(N)$,
consisting of a neutral non-abelian part and a charged abelian part, belonging
to the Cartan subalgebra


title:
Static Regular and Black Hole Solutions with Axial Symmetry in EYM and
  EYMD theory

abstract:
  We discuss the recently discovered new class of globally regular and black
hole solutions in Einstein-Yang-Mills and Einstein-Yang-Mills-dilaton theory.
These asymptotically flat solutions are static and possess only axial symmetry.
The black hole solutions possess a regular event horizon.


title: Gravitational memory of boson stars

abstract:
  `Gravitational memory' refers to the possibility that, in cosmologies with a
time-varying gravitational `constant', objects such as black holes may retain a
memory of conditions at the time of their birth. We consider this phenomenon in
a different physical scenario, where the objects under consideration are boson
stars. We construct boson star solutions in scalar-tensor gravity theories, and
consider their dependence on the asymptotic value of the gravitational
strength. We then discuss several possible physical interpretations, including
the concept of pure gravitational stellar evolution.


title:
Impulsive waves in de Sitter and anti-de Sitter space-times generated by
  null particles with an arbitrary multipole structure

abstract:
  We describe a class of impulsive gravitational waves which propagate either
in a de Sitter or an anti-de Sitter background. They are conformal to impulsive
waves of Kundt's class. In a background with positive cosmological constant
they are spherical (but non-expanding) waves generated by pairs of particles
with arbitrary multipole structure propagating in opposite directions. When the
cosmological constant is negative, they are hyperboloidal waves generated by a
null particle of the same type. In this case, they are included in the
impulsive limit of a class of solutions described by Siklos that are conformal
to pp-waves.


title: Covariant path integrals and black holes

abstract:
  The thermal nature of the propagator in a collapsed black-hole spacetime is
shown to follow from the non-trivial topology of the configuration space in
tortoise coordinates by using the path integral formalism.


title: The Inertial Forces / Test Particle Motion Game

abstract:
  The somewhat fragmented body of current literature analyzing the properties
of test particle motion in static and stationary spacetimes and in general
spacetimes is pulled together and clarified using the framework of
gravitoelectromagnetism.


title: Black Holes of Constant Curvature

abstract:
  Black holes of constant curvature are constructed by identifying points in
anti-de Sitter space. In n dimensions the resulting topology is R^{n-1} * S_1,
as opposed to the usual R^2 * S_{n-2} Schwarzschild black hole.


title: Cosmological spacetimes not covered by a constant mean curvature slicing

abstract:
  We show that there exist maximal globally hyperbolic solutions of the
Einstein-dust equations which admit a constant mean curvature Cauchy surface,
but are not covered by a constant mean curvature foliation.


title:
The Reissner-Nordstrom Problem for Intersecting Electric and Magnetic
  p-Branes

abstract:
  A multidimensional model with (at most) one curved factor space and n
Ricci-flat internal spaces is considered, with arbitrary numbers of dilatonic
scalar fields and antisymmetric forms of both electric and magnetic types,
associated with p-branes in theories like M-theory. The problem setting covers,
in particular, homogeneous cosmologies, static, spherically symmetric and
Euclidean models. Exact solutions are obtained when the p-brane dimensions and
the dilatonic couplings obey orthogonality conditions in minisuperspace.
Conditions for black hole and wormhole existence among static models are
formulated. For black holes, a kind of no-hair theorem, leading to F-form
selection, is obtained; it is shown that even in spaces with multiple times a
black hole may only exist with its unique, one-dimensional time; infinite
Hawking temperature is explicitly shown to imply a curvature singularity at an
assumed horizon, and such cases among extreme black-hole solutions are
indicated.


title: Scalar Field Quantum Inequalities in Static Spacetimes

abstract:
  We discuss quantum inequalities for minimally coupled scalar fields in static
spacetimes. These are inequalities which place limits on the magnitude and
duration of negative energy densities. We derive a general expression for the
quantum inequality for a static observer in terms of a Euclidean two-point
function. In a short sampling time limit, the quantum inequality can be written
as the flat space form plus subdominant correction terms dependent upon the
geometric properties of the spacetime. This supports the use of flat space
quantum inequalities to constrain negative energy effects in curved spacetime.
Using the exact Euclidean two-point function method, we develop the quantum
inequalities for perfectly reflecting planar mirrors in flat spacetime. We then
look at the quantum inequalities in static de~Sitter spacetime, Rindler
spacetime and two- and four-dimensional black holes. In the case of a
four-dimensional Schwarzschild black hole, explicit forms of the inequality are
found for static observers near the horizon and at large distances. It is show
that there is a quantum averaged weak energy condition (QAWEC), which states
that the energy density averaged over the entire worldline of a static observer
is bounded below by the vacuum energy of the spacetime. In particular, for an
observer at a fixed radial distance away from a black hole, the QAWEC says that
the averaged energy density can never be less than the Boulware vacuum energy
density.


title: A note on area variables in Regge calculus

abstract:
  We consider the possibility of setting up a new version of Regge calculus in
four dimensions with areas of triangles as the basic variables rather than the
edge-lengths. The difficulties and restrictions of this approach are discussed.


title: Loop Corrections for 2D Hawking Radiation

abstract:
  We describe how the reduced phase space quantization of the CGHS model of 2d
black hole formation allows one to calculate the backreaction up to any finite
order in matter loops. We then analyze the backreaction in the Hawking
radiation up to two loops. At one-loop order the Hawking temperature does not
change, while at two-loop order the temperature increases three times with
respect to the classical value. We argue that such a behavior is consistent
with the behaviour of the operator quantization Hawking flux for times which
are not too late. For very late times the two-loop flux goes to zero which
indicates that the backreaction can stop the black hole evaporation.


title: Gravitation Gauge Group

abstract:
  Suggested theory involves a drastic revision of a role of local internal
symmetries in physical concept of curved geometry. Under the reflection of
fields and their dynamics from Minkowski to Riemannian space a standard gauge
principle of local internal symmetries is generalized. The gravitation gauge
group is proposed, which is generated by hidden local internal symmetries. The
developed mechanism enables one to infer Einstein's equation of gravitation,
but only with strong difference from Einstein's theory at the vital point of
well-defined energy-momentum tensor of gravitational field and conservation
laws. The gravitational interaction as well as general distortion of manifold
G(2.2.3) with hidden group U(1) was considered.


title: The validity of the Background Field Approximation

abstract:
  In the absence of a tractable theory of quantum gravity, quantum matter field
effects have been so far computed by treating gravity at the Background Field
Approximation. The principle aim of this paper is to investigate the validity
of this approximation which is not specific to gravity. To this end, for
reasons of simplicity and clarity, we shall compare the descriptions of thermal
processes induced by constant acceleration (i.e. the Unruh effect) in four
dynamical frameworks. In this problem, the position of the ``heavy''
accelerated system plays the role of gravity. In the first framework, the
trajectory is treated at the BFA: it is given from the outset and unaffected by
radiative processes. In the second one, recoil effects induced by these
emission processes are taken into account by describing the system's position
by WKB wave functions. In the third one, the accelerated system is described by
second quantized fields and in the fourth one, gravity is turned on. It is most
interesting to see when and why transitions amplitudes evaluated in different
frameworks but describing the same process do agree. It is indeed this
comparison that determines the validity of the BFA. It is also interesting to
notice that the abandonment of the BFA delivers new physical insights
concerning the processes. For instance, in the fourth framework, the
``recoils'' of gravity show that the acceleration horizon area acts as an
entropy in delivering heat to accelerated systems.


title: Abrupt Changes in the Multipole Moments of a Gravitating Body

abstract:
  An example is described in which an asymptotically flat static vacuum Weyl
space-time experiences a sudden change across a null hypersurface in the
multipole moments of its isolated axially symmetric source. A light-like shell
and an impulsive gravitational wave are identified, both having the null
hypersurface as history. The stress-energy in the shell is dominated (at large
distance from the source) by the jump in the monopole moment (the mass) of the
source with the jump in the dipole moment mainly responsible for the stress
being anisotropic. The gravitational wave owes its existence prrincipally to
the jump in th quadrupole moment of the source confirming what would be
expected. This serves as a model of a cataclysmic astrophysical event such as a
supernova.


title:
Gravitational Wave Spectrums from Pole-like Inflations based on
  Generalized Gravity Theories

abstract:
  We present a general and unified formulation which can handle the classical
evolution and quantum generation processes of the cosmological gravitational
wave in a broad class of generalized gravity theories. Applications are made in
several inflation models based on the scalar-tensor theory, the induced
gravity, and the low energy effective action of string theory. The
gravitational wave power spectrums based on the vacuum expectation value of the
quantized fluctuating metric during the pole-like inflation stages are derived
in analytic forms. Assuming that the gravity theory transits to Einstein one
while the relevant scales remain in the superhorizon scale, we derive the
consequent power spectrums and the directional fluctuations of the relic
radiation produced by the gravitational wave. The spectrums seeded by the
vacuum fluctuations in the pole-like inflation models based on the generalized
gravity show a distinguished common feature which differs from the scale
invariant spectrum generated in an exponential inflation in Einstein gravity
which is supported by observations.


title: On the Causal Structure of Spinning Einstein-Yang-Mills-Higgs Strings

abstract:
  It is claimed that it will be exceedingly unlikely to obtain CTC's in the
spacetime of a spinning EYMH-string. It is conjectured that the pathological
problems concerning the induced angular momentum and helical structure of time
that afflict the U(1)-gauge string, will be solved in the non-abelian YM string
model. In the pure YM case we find regular solutions, which resembles the
abelian counterpart solutions but without causality violating regions. Just as
in the spherical symmetric case, there will be probably critical behavior of
the field equations at the threshold of blackhole masses.


title:
Spin effects in gravitational radiation backreaction I. The
  Lense-Thirring approximation

abstract:
  The gravitational radiation backreaction effects are considered in the
Lense-Thirring approximation. New methods for parameterizing the orbit and for
averaging the instantaneous radiative losses are developed. To first order in
the spin S of the black hole, both in the absence and in the presence of
gravitational radiation, a complete description of the test-particle orbit is
given. This is achieved by two improvements over the existing descriptions.
First, by introducing new angle variables with a straightforward geometrical
meaning. Second, by finding a new parametrization of a generic orbit, which
assures that the integration over a radial period can be done in an especially
simple way, by applying the residue theorem. The instantaneous radiation losses
of the system are computed using the formulation of Blanchet, Damour and
Iyer(1989). All losses are given both in terms of the dynamical constants of
motion and the properly defined orbital elements $a,e,\iota$ and $\Psi_0$. The
radiative losses of the constants characterizing the Lense-Thirring motion,
when suitably converted, are in agreement with earlier results of Kidder, Will
and Wiseman(1993), Ryan(1996) and Shibata(1994). In addition, the radiative
losses of two slowly changing orbital elements $\Psi_0,\Phi_0$ are given in
order to complete the characterization of the orbit.


title: Steps towards an axiomatic pregeometry of space-time

abstract:
  We present a deductive theory of space-time which is realistic, objective,
and relational. It is realistic because it assumes the existence of physical
things endowed with concrete properties. It is objective because it can be
formulated without any reference to cognoscent subjects or sensorial fields.
Finally, it is relational because it assumes that space-time is not a thing but
a complex of relations among things. In this way, the original program of
Leibniz is consummated, in the sense that space is ultimately an order of
coexistents, and time is an order of succesives. In this context, we show that
the metric and topological properties of Minkowskian space-time are reduced to
relational properties of concrete things. We also sketch how our theory can be
extended to encompass a Riemmanian space-time.


title: Field of a Radiation Distributuion

abstract:
  General relativistic spherically symmetric matter field with a vanishing
stress energy scalar is analyzed. Procedure for generating exact solutions of
the field equations for such matter distributions is given. It is further
pointed out that all such type I spherically symmetric fields with distinct
eignvalues in the radial two space can be treated as a mixture of isotropic and
directed radiations. Various classes of exact solutions are given. Junction
conditions for such a matter field to the possible exterior solutions are also
discussed.


title: Nonspherical perturbations of critical collapse and cosmic censorship

abstract:
  Choptuik has demonstrated that naked singularities can arise in gravitational
collapse from smooth, asymptotically flat initial data, and that such data have
codimension one in spherical symmetry. Here we show, for perfect fluid matter
with equation of state $p=\rho/3$, by perturbing around spherical symmetry,
that such data have in fact codimension one in the full phase space, at least
in a neighborhood of spherically symmetric data.


title: Towards the mass spectrum of quantum black holes and wormholes

abstract:
  The quantum black hole model with a self-gravitating spherically symmetric
thin dust shell as a source is considered. The shell Hamiltonian constraint is
written and the corresponding Schroedinger equation is obtained. This equation
appeared to be a finite differences equation. Its solutions are required to be
analytic functions on the relevant Riemannian surface. The method of finding
discrete spectra is suggested based on the analytic properties of the
solutions. The large black hole approximation is considered and the discrete
spectra for bound states of quantum black holes and wormholes are found. They
depend on two quantum numbers and are, in fact, quasi-continuous. The quantum
black hole bound state depends not only on mass but also on additional quantum
number, and black holes with the same mass have different quantum hairs. These
hairs exhibit themselves at the Planckian distances near the black hole
horizon. For the observer who can not measure the distances smaller than the
Planckian length the black hole has the only parameter, its mass. The other,
non-measurable parameter leads to existence of the black hole entropy.


title: Gravitational Collapse and Cosmic Censorship

abstract:
  We review the status of the weak cosmic censorship conjecture, which asserts,
in essence, that all singularities of gravitational collapse are hidden within
black holes. Although little progress has been made toward a general proof (or
disproof) of this conjecture, there has been some notable recent progress in
the study of some examples and special cases related to the conjecture. These
results support the view that naked singularities cannot arise generically.


title: Ideal gas sources for the Lemaitre-Tolman-Bondi metrics

abstract:
  New exact solutions emerge by replacing the dust source of the
Lem\^aitre-Tolman-Bondi metrics with a viscous fluid satisfying the monatomic
gas equation of state. The solutions have a consistent thermodynamical
interpretation. The most general transport equation of Extended Irreversible
Thermodynamics is satisfied, with phenomenological coefficients bearing a close
resemblance to those characterizing a non relativistic Maxwell-Bolzmann gas.


title: A Closed Contour of Integration in Regge Calculus

abstract:
  The analytic structure of the Regge action on a cone in $d$ dimensions over a
boundary of arbitrary topology is determined in simplicial minisuperspace. The
minisuperspace is defined by the assignment of a single internal edge length to
all 1-simplices emanating from the cone vertex, and a single boundary edge
length to all 1-simplices lying on the boundary. The Regge action is analyzed
in the space of complex edge lengths, and it is shown that there are three
finite branch points in this complex plane. A closed contour of integration
encircling the branch points is shown to yield a convergent real wave function.
This closed contour can be deformed to a steepest descent contour for all sizes
of the bounding universe. In general, the contour yields an oscillating wave
function for universes of size greater than a critical value which depends on
the topology of the bounding universe. For values less than the critical value
the wave function exhibits exponential behaviour. It is shown that the critical
value is positive for spherical topology in arbitrary dimensions. In three
dimensions we compute the critical value for a boundary universe of arbitrary
genus, while in four and five dimensions we study examples of product manifolds
and connected sums.


title: Can a self-gravitating thin cosmic string obey the Nambu-Goto dynamics ?

abstract:
  We assume that a self-gravitating string is locally described by a thin tube
of matter represented by a ``smoothed conical metric''. If we impose a specific
constraint on the model of string then its central line obeys the Nambu-Goto
dynamics in the limit where the radius of the tube tends to zero. If no
constraint is added then the world sheet of the central line is totally
geodesic.


title:
Energy-Momentum Tensor Valued Distributions for the Schwarzschild and
  Reissner-Nordstrom Geometries

abstract:
  An approach to computing, withing the framework of distribution theory, the
distributional valued energy-momentum tensor for the Schwarzschild spacetime is
disscused. This approach avoids the problems associated with the regularization
of singularities in the curvature tensors and shares common features with the
by now standard treatment of discontinuities in General Relativity. Finally,
the Reissner-Nordstrom spacetime is also considered using the same approach.


title: Newtonian and post-Newtonian binary neutron star mergers

abstract:
  We present two of our efforts directed toward the numerical analysis of
neutron star mergers, which are the most plausible sources for gravitational
wave detectors that should begin operating in the near future. First we present
Newtonian 3D simulations including radiation reaction (2.5PN) effects. We
discuss the gravitational wave signals and luminosity from the merger
with/without radiation reaction effects. Second we present the matching problem
between post-Newtonian formulations and general relativity in numerical
treatments. We prepare a spherical, static neutron star in a post-Newtonian
matched spacetime, and find that discontinuities at the matching surface become
smoothed out during fully relativistic evolution if we use a proper slicing
condition.


title: Lorentzian dynamics in the Ashtekar gravity

abstract:
  We examine the advantages of the SO(3)-ADM (Ashtekar) formulation of general
relativity, from the point of following the dynamics of the Lorentzian
spacetime in direction of applying this into numerical relativity. We describe
our strategy how to treat new constraints and reality conditions, together with
a proposal of new variables. We show an example of passing a degenerate point
in flat spacetime numerically by posing `reality recovering' conditions on
spacetime. We also discuss some available advantages in numerical relativity.


title:
Gravitational waves from inspiralling compact binaries: Angular momentum
  flux, evolution of the orbital elements and the wave form to the second
  post-Newtonian order

abstract:
  The post-post-Newtonian (2PN) accurate mass quadrupole moment, for compact
binaries of arbitrary mass ratio, moving in general orbits is obtained by the
multi-polar post Minkowskian approach of Blanchet, Damour, and Iyer (BDI).
Using this, for binaries in general orbits, the 2PN contributions to the
gravitational waveform, and the associated far-zone energy and angular momentum
fluxes are computed. For quasi-elliptic orbits, the energy and angular momentum
fluxes are averaged over an orbital period, and employed to determine the 2PN
corrections to the rate of decay of the orbital elements.


title: Quantum Black Holes as Atoms

abstract:
  In some respects the black hole plays the same role in gravitation that the
atom played in the nascent quantum mechanics. This analogy suggests that black
hole mass $M$ might have a discrete spectrum. I review the physical arguments
for the expectation that black hole horizon area eigenvalues are uniformly
spaced, or equivalently, that the spacing between stationary black hole mass
levels behaves like 1/M. This sort of spectrum has also emerged in a variety of
formal approaches to black hole quantization by a number of workers (with some
notable exceptions). If true, this result indicates a distortion of the
semiclassical Hawking spectrum which could be observable even for macroscopic
black holes. Black hole entropy suggests that the mentioned mass levels should
be degenerate to the tune of an exponential in $M^2$, as first noted by
Mukhanov. This has implications for the statistics of the radiation. I also
discuss open questions: whether radiative decay will spread the levels beyond
recognition, whether extremal black holes can be described by this scheme, etc.
I then describe an elementary algebra for the relevant black hole observables,
an outcome of work by Mukhanov and myself, which reproduces the uniformly
spaced area spectrum.


title: On the perturbation of domain wall coupled to gravitational waves

abstract:
  The equation of motion for domain wall coupled to gravitational field is
derived. The domain wall is treated as a source of gravitational field around
the wall. The perturbed equation is also obtained with taking account of the
gravitational back reaction on the motion of the domain wall.


title:
Cylindrical Domain Walls and Gravitational Waves -- Einstein Rosen wave
  emission from momentarily static initial configuration --

abstract:
  A self-gravitating cylindrical domain wall is considered as an example of
non-spherical wall to clarify the interaction between a domain wall and
gravitational waves. We consider the time evolution from a momentarily static
initial configuration within an infinitesimal time interval using the metric
junction formalism. We found that the wall with a large initial radius radiates
large amplitude of the gravitational waves and undergoes its large back
reaction.


title: Low-Frequency Sources of Gravitational Waves: A Tutorial

abstract:
  Gravitational wave detectors in space, particularly the LISA project, can
study a rich variety of astronomical systems whose gravitational radiation is
not detectable from the ground, because it is emitted in the low-frequency
gravitational wave band (0.1 mHz to 1 Hz) that is inaccessible to ground-based
detectors. Sources include binary systems in our Galaxy and massive black holes
in distant galaxies. The radiation from many of these sources will be so strong
that it will be possible to make remarkably detailed studies of the physics of
the systems. These studies will have importance both for astrophysics (most
notably in binary evolution theory and models for active galaxies) and for
fundamental physics. In particular, it should be possible to make decisive
measurements to confirm the existence of black holes and to test, with
accuracies better than 1%, general relativity's description of them. Other
observations can have fundamental implications for cosmology and for physical
theories of the unification of forces. In order to understand these
conclusions, one must know how to estimate the gravitational radiation produced
by different sources. In the first part of this lecture I review the dynamics
of gravitational wave sources, and I derive simple formulas for estimating wave
amplitudes and the reaction effects on sources of producing this radiation.
With these formulas one can estimate, usually to much better than an order of
magnitude, the physics of most of the interesting low-frequency sources. In the
second part of the lecture I use these estimates to discuss, in the context of
the expected sensitivity of LISA, what we can learn by from observations of
binary systems, massive black holes, and the early Universe itself.


title: Introduction to the Analysis of Low-Frequency Gravitational Wave Data

abstract:
  The space-based gravitational wave detector LISA will observe in the
low-frequency gravitational-wave band (0.1 mHz up to 1 Hz). LISA will search
for a variety of expected signals, and when it detects a signal it will have to
determine a number of parameters, such as the location of the source on the sky
and the signal's polarisation. This requires pattern-matching, called matched
filtering, which uses the best available theoretical predictions about the
characteristics of waveforms. All the estimates of the sensitivity of LISA to
various sources assume that the data analysis is done in the optimum way.
Because these techniques are unfamiliar to many young physicists, I use the
first part of this lecture to give a very basic introduction to time-series
data analysis, including matched filtering. The second part of the lecture
applies these techniques to LISA, showing how estimates of LISA's sensitivity
can be made, and briefly commenting on aspects of the signal-analysis problem
that are special to LISA.


title:
The role of dilations in diffeomorphism covariant algebraic quantum
  field theory

abstract:
  The quantum analogue of general relativistic geometry should be implementable
on smooth manifolds without an a priori metric structure, the kinematical
covariance group acting by diffeomorphisms.
  Here I approach quantum gravity (QG) in the view of constructive, algebraic
quantum field theory (QFT). Comparing QG with usual QFT, the algebraic approach
clarifies analogies and peculiarities. As usual, an isotonic net of *-algebras
is taken to encode the quantum field operators. For QG, the kinematical
covariance group acts via diffeomorphisms on the open sets of the manifold, and
via algebraic isomorphisms on the algebras. In general, the algebra of
observables is covariant only under a (dynamical) subgroup of the general
diffeomorphism group.
  After an algebraic implementation of the dynamical subgroup of dilations,
small and large scale cutoffs may be introduced algebraically. So the usual a
priori conflict of cutoffs with general covariance is avoided. Even more, these
cutoffs provide a natural local cobordism for topological quantum field theory.
  A new commutant duality between the minimal and maximal algebra allows to
extract the modular structure from the net of algebras. The outer modular
isomorphisms are then again related to dilations, which (under certain
conditions) may provide a notion of time.


title:
Plane Light-Like Shells and Impulsive Gravitational Waves in
  Scalar-Tensor Theories of Gravity

abstract:
  We study gravitational plane impulsive waves and electromagnetic shock waves
in a scalar-tensor theory of gravity of the Brans-Dicke type. In vacuum, we
present an exact solution of Brans-Dicke's field equations and give an example
in which a plane impulsive gravitational wave and a null shell of matter
coexist on the same hypersurface. In the homogenous case, we characterize them
by their surface energy density and wave amplitude and discuss the inhomogenous
case. We also give an exact solution of the Brans-Dicke's field equations in
the electrovacuum case which admits a true curvature singularity and use it to
built an example where a plane impulsive gravitational wave and an
electromagnetic shock wave have the same null hypersurface as history of their
wave fronts and propagate independently and decoupled from a null shell of
matter. This last solution is shown to correspond to the space-time describing
the interaction region resulting from the collision of two electromagnetic
shock waves leading to the formation of two gravitational impulsive waves. The
properties of this solution are discussed and compared to those of the
Bell-Szekeres solution of general relativity.


title: The Structure of Singularity in Gravitational Collapse

abstract:
  We will describe here the structure of singularity forming in gravitational
collapse of spherically symmetric inhomogeneous dust. Such a collapse is
described by the Tolman-Bondi-Lema{\^i}tre metric. The main new result here
relates, in a general way, the formation of black holes and naked
shell-focusing singularities resulting as the final fate of such a collapse to
the generic form of regular initial data. Such a data is characterized in terms
of the density and velocity profiles of the matter, specified on an initial
time slice from which the collapse commences. We show that given any generic
density profile at the initial time slice, there exists a corresponding
velocity profile which gives rise to a strong curvature naked singularity. This
establishes that strong naked singularities arise for a generic density
profile. We also establish here that similar results hold for black hole
formation as well. Keeping the model to be spherically symmetric we also
consider more general form of matter fields, i.e. equation of state $p =
k\rho$. We will analyse here the nature of non-central singularity forming due
to collapse of spherically symmetric perfect fluid subject to weak energy
condition.


title:
The Causal Interpretation of Dust and Radiation Fluids Non-Singular
  Quantum Cosmologies

abstract:
  We apply the causal interpretation of quantum mechanics to homogeneous and
isotropic quantum cosmology where the sources of the gravitational field are
either dust or radiation perfect fluids. We find non-singular quantum
trajectories which tends to the classical one when the scale factor becomes
much larger then the Planck length. In this situation, the quantum potential
becomes negligible. There are no horizons. As radiation is a good approximation
for the matter content of the early universe, this result suggests that the
universe can be eternal due to quantum effects.


title: Gravitational excitons from extra dimensions

abstract:
  We study inhomogeneous multidimensional cosmological models with a higher
dimensional space-time manifold under dimensional reduction and show that small
inhomogeneous excitations of the scale factors of the internal spaces near
minima of effective potentials should be observable as massive scalar particles
(gravitational excitons) in the external space-time.


title: Stable compactification and gravitational excitons from extra dimensions

abstract:
  We study inhomogeneous multidimensional cosmological models with a higher
dimensional space-time manifold under dimensional reduction. Stability due to
different types of effective potentials is analyzed for specific configurations
of internal spaces. Necessary restrictions on the parameters of the models are
found and masses of gravitational excitons (small inhomogeneous excitations of
the scale factors of the internal spaces near minima of effective potentials)
are calculated.


title:
Gravitational Wave Emission and Mass Extraction from a Perturbed
  Schwarzschild Black Hole (continue)

abstract:
  A relativistic model for the emission of gravitational waves from an
initially unperturbed Schwarzschild black hole, or spherical collapsing
configuration, is completely integrated. The model consists basically of
gravitational perturbations of the Robinson-Trautman type on the Schwarzschild
spacetime. In our scheme of perturbation, gravitational waves may extract mass
from the collapsing configuration. Robinson-Trautmann perturbations also
include another mode of emission of mass, which we denote shell emission mode:
in the equatorial plane of the configuration, a timelike $(1+2)$ shell of
matter may be present, whose stress-energy tensor is modelled by neutrinos and
strings emitted radially on the shell; no gravitational waves are present in
this mode. The invariant characterization of gravitational wave perturbations
and of the gravitational wave zone is made through the analysis of the
structure of the curvature tensor and the use of the Peeling Theorem.


title: Energy-Momentum Tensor and Particle Creation in the de Sitter Universe

abstract:
  For a quantum field in a curved background the choice of the vacuum state is
crucial. We exhibit a vacuum state in which the expectation values of the
energy and pressure allow an intuitive interpretation. We apply this general
result to the de Sitter universe.


title: Unified first law of black-hole dynamics and relativistic thermodynamics

abstract:
  A unified first law of black-hole dynamics and relativistic thermodynamics is
derived in spherically symmetric general relativity. This equation expresses
the gradient of the active gravitational energy E according to the Einstein
equation, divided into energy-supply and work terms. Projecting the equation
along the flow of thermodynamic matter and along the trapping horizon of a
blackhole yield, respectively, first laws of relativistic thermodynamics and
black-hole dynamics. In the black-hole case, this first law has the same form
as the first law of black-hole statics, with static perturbations replaced by
the derivative along the horizon. There is the expected term involving the area
and surface gravity, where the dynamic surface gravity is defined as in the
static case but using the Kodama vector and trapping horizon. This surface
gravity vanishes for degenerate trapping horizons and satisfies certain
expected inequalities involving the area and energy. In the thermodynamic case,
the quasi-local first law has the same form, apart from a relativistic factor,
as the classical first law of thermodynamics, involving heat supply and
hydrodynamic work, but with E replacing the internal energy. Expanding E in the
Newtonian limit shows that it incorporates the Newtonian mass, kinetic energy,
gravitational potential energy and thermal energy. There is also a weak type of
unified zeroth law: a Gibbs-like definition of thermal equilibrium requires
constancy of an effective temperature, generalising the Tolman condition and
the particular case of Hawking radiation, while gravithermal equilibrium
further requires constancy of surface gravity. Finally, it is suggested that
the energy operator of spherically symmetric quantum gravity is determined by
the Kodama vector, which encodes a dynamic time related to E.


title: Can we obtain Conserved Currents in Supersymmetric Quantum Cosmology?

abstract:
  In this paper we report whether conserved currents can be sensibly defined in
supersymmetric minisuperspaces. Our analysis deals with a k=1 FRW model.
Supermatter in the form of scalar supermultiplets is included. We show that
conserved currents cannot be adequately established except for some very simple
scenarios.


title: Constrained Euler-Poincare Supergravity in Five Dimensions

abstract:
  The N=2 supergravity action in D=5 is generalized by the inclusion of
dimensionally continued Euler-Poincare form. The spacetime torsion implied by
the Einsteinean supergravity is imposed by a Lagrangian constraint and
resulting variational equations are solved for the Lagrange multipliers. The
corresponding terms in the Einstein and Rarita-Schwinger field equations are
determined. These indicate new types of interactions that could be included in
the action to achieve local supersymmetry.


title: Cold black holes in scalar-tensor theories

abstract:
  We study the possible existence of black holes in scalar-tensor theories of
gravity in four dimensions. Their existence is verified for anomalous versions
of these theories, with a negative kinetic term in the Lagrangian. The Hawking
temperature T_H of these holes is zero, while the horizon area is (in most
cases) infinite. It is shown that an infinite value of T_H can occur only at a
curvature singularity rather than a horizon. As a special case, the Brans-Dicke
theory is studied in more detail, and two kinds of infinite-area black holes
are revealed, with finite and infinite proper time needed for an infalling
particle to reach the horizon.


title: Dynamical System Analysis for Inflation with Dissipation

abstract:
  We examine the solutions of the equations of motion for an expanding
Universe, taking into account the radiation of the inflaton field energy. We
then analyze the question of the generality of inflationary solutions in this
more general setting of a dissipative system. We find a surprisingly rich
behavior for the solutions of the dynamical system of equations in the presence
of dissipational effects. We also determine that a value of dissipation as
small as $\sim 10^{-7} H$ can lead to a smooth exit from inflation to
radiation.


title: Binary-Induced Gravitational Collapse: A Trivial Example

abstract:
  We present a simple model illustrating how a highly relativistic, compact
object which is stable in isolation can be driven dynamically unstable by the
tidal field of a binary companion. Our compact object consists of a
test-particle in a relativistic orbit about a black hole; the binary companion
is a distant point mass. Our example is presented in light of mounting
theoretical opposition to the possibility that sufficiently massive, binary
neutron stars inspiraling from large distance can collapse to form black holes
prior to merger. Our strong-field model suggests that first order
post-Newtonian treatments of binaries, and stability analyses of binary
equilibria based on orbit-averaged, mean gravitational fields, may not be
adequate to rule out this possibility.


title:
Diffeomorphism Invariance of Geometric Descriptions of Palatini and
  Ashtekar Gravity

abstract:
  In this paper, we explicitly prove the presymplectic forms of the Palatini
and Ashtekar gravity to be zero along gauge orbits of the Lorentz and
diffeomorphism groups, which ensures the diffeomorphism invariance of these
theories.


title: Evolving the Bowen-York initial data for spinning black holes

abstract:
  The Bowen-York initial value data typically used in numerical relativity to
represent spinning black hole are not those of a constant-time slice of the
Kerr spacetime. If Bowen-York initial data are used for each black hole in a
collision, the emitted radiation will be partially due to the ``relaxation'' of
the individual holes to Kerr form. We compute this radiation by treating the
geometry for a single hole as a perturbation of a Schwarzschild black hole, and
by using second order perturbation theory. We discuss the extent to which
Bowen-York data can be expected accurately to represent Kerr holes.


title:
Mass correction and gravitational energy radiation in black hole
  perturbation theory

abstract:
  Using second order black hole perturbation theory, we show that the
difference between the ADM mass and the final black hole mass, computed to the
lowest significant order, is equal, to the same order, to the total
gravitational radiation energy, obtained applying the Landau and Lifschitz
(pseudotensor) equation to the first order perturbation. This result may be
considered as a consistency check for the theory.


title: Equations of Motion of Spinning Relativistic Particle in External Fields

abstract:
  We consider the motion of a spinning relativistic particle in external
electromagnetic and gravitational fields, to first order in the external field,
but to an arbitrary order in spin. The correct account for the spin influence
on the particle trajectory is obtained with the noncovariant description of
spin. Concrete calculations are performed up to second order in spin included.
A simple derivation is presented for the gravitational spin-orbit and spin-spin
interactions of a relativistic particle. We discuss the gravimagnetic moment
(GM), a specific spin effect in general relativity. It is demonstrated that for
the Kerr black hole the gravimagnetic ratio, i.e., the coefficient at the GM,
equals to unity (as well as for the charged Kerr hole the gyromagnetic ratio
equals to two). The equations of motion obtained for relativistic spinning
particle in external gravitational field differ essentially from the Papapetrou
equations.


title: Dissipative fluids out of hydrostatic equilibrium

abstract:
  In the context of the M\"{u}ller-Israel-Stewart second order phenomenological
theory for dissipative fluids, we analyze the effects of thermal conduction and
viscosity in a relativistic fluid, just after its departure from hydrostatic
equilibrium, on a time scale of the order of relaxation times. Stability and
causality conditions are contrasted with conditions for which the ''effective
inertial mass'' vanishes.


title: The Heat-Kernel in a Schwarzschild Geometry and the Casimir Energy

abstract:
  We obtain an hybrid expression for the heat-kernel, and from that the density
of the free energy, for a minimally coupled scalar field in a Schwarzschild
geometry at finite temperature. This gives us the zero-point energy density as
a function of the distance from the massive object generating the gravitational
field. The contribution to the zero-point energy due to the curvature is
extracted too, in this way arriving at a renormalised expression for the energy
density (the Casimir energy density). We use this to find an expression for
other physical quantities: internal energy, pressure and entropy. It turns out
that the disturbance of the surrounding vacuum generates entropy. For $\beta$
small the entropy is positive for $r>2M$. We also find that the internal energy
can be negative outside the horizon pointing to the existence of bound states.
The total energy inside the horizon turns out to be finite but complex, the
imaginary part being interpreted as responsible for particle creation.


title: Relativistic Studies of Close Neutron Star Binaries

abstract:
  We discuss (3+1) dimensional general relativistic hydrodynamic simulations of
close neutron star binary systems. The relativistic field equations are solved
at each time slice with a spatial 3-metric chosen to be conformally flat.
Against this solution the hydrodynamic variables and gravitational radiation
are allowed to respond. We have studied four physical processes which occur as
the stars approach merger. These include: 1) the relaxation to a hydrodynamic
state of almost no spin; 2) relativistically driven compression, heating, and
neutrino emission; 3) collapse to two black holes; and 4) orbit inspiral
occurring at a lower frequency than previously expected. We give a brief
account of the physical origin of these effects and an explanation of why they
do not appear in models based upon, 1PN hydrodynamics, a weak field multipole
expansion, a tidal analysis, or a rigidly corotating velocity field. The
implication of these results for gravity wave detectors is also discussed.


title: Phenomenology of the Gowdy Universe on $T^3 \times R$

abstract:
  Numerical studies of the plane symmetric, vacuum Gowdy universe on $T^3
\times R$ yield strong support for the conjectured asymptotically velocity term
dominated (AVTD) behavior of its evolution toward the singularity except,
perhaps, at isolated spatial points. A generic solution is characterized by
spiky features and apparent ``discontinuities'' in the wave amplitudes. It is
shown that the nonlinear terms in the wave equations drive the system
generically to the ``small velocity'' AVTD regime and that the spiky features
are caused by the absence of these terms at isolated spatial points.


title: Incorporation of Spacetime Symmetries in Einstein's Field Equations

abstract:
  In the search for exact solutions to Einstein's field equations the main
simplification tool is the introduction of spacetime symmetries. Motivated by
this fact we develop a method to write the field equations for general matter
in a form that fully incorporates the character of the symmetry. The method is
being expressed in a covariant formalism using the framework of a double
congruence. The basic notion on which it is based is that of the geometrisation
of a general symmetry. As a special application of our general method we
consider the case of a spacelike conformal Killing vector field on the
spacetime manifold regarding special types of matter fields. New perspectives
in General Relativity are discussed.


title:
The hypothesis of path integral duality II: corrections to quantum field
  theoretic results

abstract:
  In the path integral expression for a Feynman propagator of a spinless
particle of mass $m$, the path integral amplitude for a path of proper length
${\cal R}(x,x'| g_{\mu\nu})$ connecting events $x$ and $x'$ in a spacetime
described by the metric tensor $g_{\mu\nu}$ is $\exp-[m {\cal R}(x,x'|
g_{\mu\nu})]$. In a recent paper, assuming the path integral amplitude to be
invariant under the duality transformation ${\cal R} \to (L_P^2/{\cal R})$,
Padmanabhan has evaluated the modified Feynman propagator in an arbitrary
curved spacetime. He finds that the essential feature of this `principle of
path integral duality' is that the Euclidean proper distance $(\Delta x)^2$
between two infinitesimally separated spacetime events is replaced by $[(\Delta
x)^2 + 4L_P^2 ]$. In other words, under the duality principle the spacetime
behaves as though it has a `zero-point length' $L_P$, a feature that is
expected to arise in a quantum theory of gravity. In the Schwinger's proper
time description of the Feynman propagator, the weightage factor for a path
with a proper time $s$ is $\exp-(m^2s)$. Invoking Padmanabhan's `principle of
path integral duality' corresponds to modifying the weightage factor
$\exp-(m^2s)$ to $\exp-[m^2s + (L_P^2/s)]$. In this paper, we use this modified
weightage factor in Schwinger's proper time formalism to evaluate the quantum
gravitational corrections to some of the standard quantum field theoretic
results in flat and curved spacetimes. We find that the extra factor
$\exp-(L_P^2/s)$ acts as a regulator at the Planck scale thereby `removing' the
divergences that otherwise appear in the theory. Finally, we discuss the wider
implications of our analysis.


title:
Wigner Functions in Curved Spacetimes and Deformation Quantisation of
  Constrained Systems

abstract:
  We first generalise the standard Wigner function to Dirac fermions in curved
spacetimes. Secondly, we turn to the Moyal quantisation of systems with
constraints. Gravity is used as an example.


title: Quantum Correction to the Entropy of the (2+1)-Dimensional Black Hole

abstract:
  The thermodynamic properties of the (2+1)-dimensional non-rotating black hole
of Ba\~nados, Teitelboim and Zanelli are discussed. The first quantum
correction to the Bekenstein-Hawking entropy is evaluated within the on-shell
Euclidean formalism, making use of the related Chern-Simons representation of
the 3-dimensional gravity. Horizon and ultraviolet divergences in the quantum
correction are dealt with a renormalization of the Newton constant. It is
argued that the quantum correction due to the gravitational field shrinks the
effective radius of a hole and becomes more and more important as soon as the
evaporation process goes on, while the area law is not violated.


title: 3+1 formulation of non-ideal hydrodynamics

abstract:
  The equations governing dissipative relativistic hydrodynamics are formulated
within the 3+1 approach for arbitrary spacetimes. Dissipation is accounted for
by applying the theory of extended causal thermodynamics (Israel-Stewart
theory). This description eliminates the causality violating infinite signal
speeds present in the conventional Navier-Stokes equation. As an example we
treat the astrophysically relevant case of stationary and axisymmetric
spacetimes, including the Kerr metric. The equations take a simpler form
whenever the inertia due to the dissipative contributions can be neglected.


title:
On the interpretation of relativistic spin networks and the balanced
  state sum

abstract: We discuss the interpretation of the state sum of Barrett and Crane.


title:
From Schwarzschild to Kerr: Generating spinning Einstein-maxwell fields
  from static fields

abstract:
  The Kerr solution is generated from the Schwarzschild solution by a simple
combination of real global coordinate transformations and of invariance
transformations acting on the space of stationary solutions of the
Einstein-Maxwell equations. The same transformation can be used to generate a
spinning field configuration from any static axisymmetric configuration. We
illustrate this by generating from the continuous family of Voorhees--Zipoy
vacuum solutions a family of solutions endowed with mass, angular momentum,
dipole magnetic moment and quadrupole electric moment.


title: Oscillating shells: A model for a variable cosmic object

abstract:
  A model for a possible variable cosmic object is presented. The model
consists of a massive shell surrounding a compact object. The gravitational and
self-gravitational forces tend to collapse the shell, but the internal
tangential stresses oppose the collapse. The combined action of the two types
of forces is studied and several cases are presented. In particular, we
investigate the spherically symmetric case in which the shell oscillates
radially around a central compact object.


title: Stuffed Black Holes

abstract:
  Initial data corresponding to spacetimes containing black holes are
considered in the time symmetric case. The solutions are obtained by matching
across the apparent horizon different, conformally flat, spatial metrics. The
exterior metric is the vacuum solution obtained by the well known conformal
imaging method. The interior metric for every black hole is regular everywhere
and corresponds to a positive energy density. The resulting matched solutions
cover then the whole initial (Cauchy) hypersurface, without any singularity,
and can be useful for numerical applications. The simpler cases of one black
hole (Schwarzschild data) or two identical black holes (Misner data) are
explicitly solved. A procedure for extending this construction to the multiple
black hole case is also given, and it is shown to work for all time symmetric
vacuum solutions obtained by the conformal imaging method. The numerical
evolution of one such 'stuffed' black hole is compared with that of a pure
vacuum or 'plain' black hole in the spherically symmetric case.


title: Structure of the black hole's Cauchy horizon singularity

abstract:
  We study the Cauchy horizon (CH) singularity of a spherical charged black
hole perturbed nonlinearly by a self-gravitating massless scalar field. We show
numerically that the singularity is weak both at the early and at the late
sections of the CH, where the focusing of the area coordinate $r$ is strong. In
the early section the metric is almost Reissner-Nordstr\"{o}m, and the fields
behave according to perturbation analysis. We find exact analytical expressions
for the gradients of $r$ and of the scalar field, which are valid at both
sections. We then verify these analytical results numerically.