title: Hand-waving Refined Algebraic Quantization

abstract:
  Some basic ideas of the Refined Algebraic Quantization scheme are outlined at
an intuitive level, using a class of simple models with a single wave equation
as quantum constraint. In addition, hints are given how the scheme is applied
to more sophisticated models, and it is tried to make transparent the general
pattern characterizing this method.


title: Dilaton gravity black holes with regular interior

abstract:
  In a one parameter family of dilaton gravity theories which allow the
coupling of the dilaton to gravity and to a U(1) gauge field to differ, we have
found the existence of everywhere regular spacetimes describing black holes
hiding expanding universes inside their horizon.


title: Absence of initial singularities in superstring cosmology

abstract:
  In a universe whose elementary constituents are point particles there does
not seem to be any obvious mechanism for avoiding the initial singularities in
physical quantities in the standard model of cosmology. In contrast in string
theory these singularities can be absent even at the level where spacetime is
treated classically. This is a consequence of the basic degrees of freedom of
strings in compact spaces, which necessitate a reinterpretation of what one
means by a very small universe. We discuss the basic degrees of freedom of a
string at the classical and quantum level, the minimum size of strings (string
uncertainty principle), the t-duality symmetry, and string thermodynamics at
high energy densities, and then describe how these considerations suggest a
resolution of the initial singularity problem. An effort has been made to keep
this writeup self-contained and accessible to non-string theorists.


title: Kinematic self-similar locally rotationally symmetric models

abstract:
  A brief summary of results on kinematic self-similarities in general
relativity is given. Attention is focussed on locally rotationally symmetric
models admitting kinematic self-similar vectors. Coordinate expressions for the
metric and the kinematic self-similar vector are provided.
  Einstein's field equations for perfect fluid models are investigated and all
the homothetic perfect fluid solutions admitting a maximal four-parameter group
of isometries are given.


title: Lie groups of conformal motions acting on null orbits

abstract:
  Space-times admitting a 3-dimensional Lie group of conformal motions $C_3$
acting on null orbits are studied. Coordinate expressions for the metric and
the conformal Killing vectors (CKV) are provided (irrespectively of the matter
content) and then all possible perfect fluid solutions are found, although none
of these verify the weak and dominant energy conditions over the whole
space-time manifold.


title:
Large Quantum mechanics in curved space and quantization of polynomial
  Hamiltonians

abstract:
  The quantization of a single particle without spin in an appropriate curved
space-time is considered. The Hamilton formalism on reduced space for a
particle in a curved space-time is constructed and the main aspects of
quantization scheme are developed. These investigations are applied to
quantization of the particle Hamiltonian in an appropriate curved space-time.
As an example the energy eigenvalues in Einstein universe are calculated. In
the last sections o the paper approximation for small values of momenta of the
results previously obtained is considered as well as quantization of polynomial
Hamiltonians of general type is discussed.


title: Improved initial data for black hole collisions

abstract:
  Numerical relativity codes now being developed will evolve initial data
representing colliding black holes at a relatively late stage in the collision.
The choice of initial data used for code development has been made on the basis
of mathematical definitiveness and usefulness for computational implementation.
By using the ``particle limit'' (the limit of an extreme ratio of masses of
colliding holes) we recently showed that the standard choice is not a good
representation of astrophysically generated initial data. Here we show that,
for the particle limit, there is a very simple alternative choice that appears
to give excellent results. That choice, ``convective'' initial data is, roughly
speaking, equivalent to the start of a time sequence of parameterized solutions
of the Hamiltonian constraint; for a particle in circular orbit, it is the
initial data of the steady state solution on any hypersurface. The
implementation of related schemes for equal mass holes is discussed.


title:
Wave Propagation in Stochastic Spacetimes: Localization, Amplification
  and Particle Creation

abstract:
  Here we study novel effects associated with electromagnetic wave propagation
in a Robertson-Walker universe and the Schwarzschild spacetime with a small
amount of metric stochasticity. We find that localization of electromagnetic
waves occurs in a Robertson-Walker universe with time-independent metric
stochasticity, while time-dependent metric stochasticity induces exponential
instability in the particle production rate. For the Schwarzschild metric,
time-independent randomness can decrease the total luminosity of Hawking
radiation due to multiple scattering of waves outside the black hole and gives
rise to event horizon fluctuations and thus fluctuations in the Hawking
temperature.


title:
Monopole and electrically charged dust thin shells in general
  relativity: Classical and quantum comparison of hollow and atomlike
  configurations

abstract:
  We give a comparative description of monopole and electrically charged
spherically symmetric dust thin shells. Herewith we consider two of the most
interesting configurations: the hollow shell and shell, surrounding a body with
opposite charge. The classification of shells in accordance with the types of
black holes and traversable wormholes is constructed. The theorems for the
parameters of turning points are proved. Also for atomlike configurations the
effects of screening (electrical case) and amplification (monopole case) of the
internal mass by shell charge are studied. Finally, one considers the quantum
aspects; herewith, exact solutions of wave equations and bound states spectra
are found.


title: On the diffeomorphism commutators of lattice quantum gravity

abstract:
  We show that the algebra of discretized spatial diffeomorphism constraints in
Hamiltonian lattice quantum gravity closes without anomalies in the limit of
small lattice spacing. The result holds for arbitrary factor-ordering and for a
variety of different discretizations of the continuum constraints, and thus
generalizes an earlier calculation by Renteln.


title: Spacetime Foam and the Cosmological Constant

abstract:
  In the saddle point approximation, the Euclidean path integral for quantum
gravity closely resembles a thermodynamic partition function, with the
cosmological constant $\Lambda$ playing the role of temperature and the
``density of topologies'' acting as an effective density of states. For
$\Lambda<0$, the density of topologies grows superexponentially, and the sum
over topologies diverges. In thermodynamics, such a divergence can signal the
existence of a maximum temperature. The same may be true in quantum gravity:
the effective cosmological constant may be driven to zero by a rapid rise in
the density of topologies.


title:
Entropy of Quantum Fields for Nonextreme Black Holes in the Extreme
  Limit

abstract:
  Nonextreme black hole in a cavity within the framework of the canonical or
grand canonical ensemble can approach the extreme limit with a finite
temperature measured on a boundary located at a finite proper distance from the
horizon. In spite of this finite temperature, it is shown that the one-loop
contribution $S_{q\text{ }}$of quantum fields to the thermodynamic entropy due
to equilibrium Hawking radiation vanishes in the limit under consideration. The
same is true for the finite temperature version of the Bertotti-Robinson
spacetime into which a classical Reissner-Nordstr\"{o}m black hole turns in the
extreme limit. The result $S_{q}=0$ is attributed to the nature of a horizon
for the Bertotti-Robinson spacetime.


title:
The thermal and two-particle stress-energy must be ill-defined on the
  2-d Misner space chronology horizon

abstract:
  We show that an analogue of the (four dimensional) image sum method can be
used to reproduce the results, due to Krasnikov, that for the model of a real
massless scalar field on the initial globally hyperbolic region IGH of
two-dimensional Misner space there exist two-particle and thermal Hadamard
states (built on the conformal vacuum) such that the (expectation value of the
renormalised) stress-energy tensor in these states vanishes on IGH. However, we
shall prove that the conclusions of a general theorem by Kay, Radzikowski and
Wald still apply for these states. That is, in any of these states, for any
point b on the Cauchy horizon and any neighbourhood N of b, there exists at
least one pair of non-null related points (x,x'), with x and x' in the
intersection of IGH with N, such that (a suitably differentiated form of) its
two-point function is singular. (We prove this by showing that the two-point
functions of these states share the same singularities as the conformal vacuum
on which they are built.) In other words, the stress-energy tensor in any of
these states is necessarily ill-defined on the Cauchy horizon.


title: A Quantum Mechanical Model of the Reissner-Nordstrom Black Hole

abstract:
  We consider a Hamiltonian quantum theory of spherically symmetric,
asymptotically flat electrovacuum spacetimes. The physical phase space of such
spacetimes is spanned by the mass and the charge parameters $M$ and $Q$ of the
Reissner-Nordstr\"{o}m black hole, together with the corresponding canonical
momenta. In this four-dimensional phase space, we perform a canonical
transformation such that the resulting configuration variables describe the
dynamical properties of Reissner-Nordstr\"{o}m black holes in a natural manner.
The classical Hamiltonian written in terms of these variables and their
conjugate momenta is replaced by the corresponding self-adjoint Hamiltonian
operator, and an eigenvalue equation for the ADM mass of the hole, from the
point of view of a distant observer at rest, is obtained. Our eigenvalue
equation implies that the ADM mass and the electric charge spectra of the hole
are discrete, and the mass spectrum is bounded below. Moreover, the spectrum of
the quantity $M^2-Q^2$ is strictly positive when an appropriate self-adjoint
extension is chosen. The WKB analysis yields the result that the large
eigenvalues of the quantity $\sqrt{M^2-Q^2}$ are of the form $\sqrt{2n}$, where
$n$ is an integer. It turns out that this result is closely related to
Bekenstein's proposal on the discrete horizon area spectrum of black holes.


title:
Imprints of the Metrically-coupled Dilaton on Density Perturbations in
  Inflationary Cosmology

abstract:
  Spectra of density perturbations produced during chaotic inflation are
calculated, taking both adiabatic and isocurvature modes into account in a
class of scalar-tensor theories of gravity in which the dilaton is metrically
coupled. Comparing the predicted spectrum of the cosmic microwave background
radiation anisotropies with the one observed by the COBE-DMR we calculate
constraints on the parameters of these theories, which turn out to be stronger
by an order-of-magnitude than those obtained from post-Newtonian experiments.


title:
Integrable Multidimensional Classical and Quantum Cosmology for
  Intersecting p-branes

abstract:
  Multidimensional cosmological model describing the evolution of one Einstein
space of non-zero curvature and n Ricci-flat internal spaces is considered. The
action contains several dilatonic scalar fields and antisymmetric forms. When
forms are chosen to be proportional of volume forms of p-brane submanifolds of
internal space manifold, the Toda-like Lagrange representation is obtained.
Wheeler-De Witt equation for the model is presented. The exact solutions in
classical and quantum cases are obtained when dimensions of p-branes and
dilatonic couplings obey some orthogonality conditions.


title: Geometrisation of Statistical Mechanics

abstract:
  Classical and quantum statistical mechanics are cast here in the language of
projective geometry to provide a unified geometrical framework for statistical
physics. After reviewing the Hilbert space formulation of classical statistical
thermodynamics, we introduce projective geometry as a basis for analysing
probabilistic aspects of statistical physics. In particular, the specification
of a canonical polarity on $RP^{n}$ induces a Riemannian metric on the state
space of statistical mechanics. In the case of the canonical ensemble, we show
that equilibrium thermal states are determined by the Hamiltonian gradient flow
with respect to this metric. This flow is concisely characterised by the fact
that it induces a projective automorphism on the state manifold. The
measurement problem for thermal systems is studied by the introduction of the
concept of a random state. The general methodology is then extended to include
the quantum mechanical dynamics of equilibrium thermal states. In this case the
relevant state space is complex projective space, here regarded as a real
manifold endowed with the natural Fubini-Study metric. A distinguishing feature
of quantum thermal dynamics is the inherent multiplicity of thermal
trajectories in the state space, associated with the nonuniqueness of the
infinite temperature state. We are then led to formulate a geometric
characterisation of the standard KMS-relation often considered in the context
of $C^{*}$-algebras. The example of a quantum spin one-half particle in heat
bath is studied in detail.


title: Coalescing binaries and Doppler experiments

abstract:
  We discuss the sensitivity of the CASSINI experiments to gravitational waves
emitted by the in-spiral of compact binaries. We show that the maximum distance
reachable by the instrument is $\sim 100$ Mpc. In particular, CASSINI can
detect massive black hole binaries with chirp mass $\simgt 10^6 \Ms$ in the
Virgo Cluster with signal-to-noise ratio between 5 and 30 and possible compact
objects of mass $\simgt 30 \Ms$ orbiting the massive black hole that our
Galactic Centre is likely to harbour.


title:
Improved filters for gravitational waves from inspiralling compact
  binaries

abstract:
  The order of the post-Newtonian expansion needed, to extract in a reliable
and accurate manner the fully general relativistic gravitational wave signal
from inspiralling compact binaries, is explored. A class of approximate wave
forms, called P-approximants, is constructed based on the following two inputs:
(a) The introduction of two new energy-type and flux-type functions e(v) and
f(v), respectively, (b) the systematic use of Pade approximation for
constructing successive approximants of e(v) and f(v). The new P-approximants
are not only more effectual (larger overlaps) and more faithful (smaller
biases) than the standard Taylor approximants, but also converge faster and
monotonically. The presently available O(v/c)^5-accurate post-Newtonian results
can be used to construct P-approximate wave forms that provide overlaps with
the exact wave form larger than 96.5% implying that more than 90% of potential
events can be detected with the aid of P-approximants as opposed to a mere
10-15 % that would be detectable using standard post-Newtonian approximants.


title: Binary Black Hole Mergers in 3d Numerical Relativity

abstract:
  The standard approach to the numerical evolution of black hole data using the
ADM formulation with maximal slicing and vanishing shift is extended to
non-symmetric black hole data containing black holes with linear momentum and
spin by using a time-independent conformal rescaling based on the puncture
representation of the black holes. We give an example for a concrete three
dimensional numerical implementation. The main result of the simulations is
that this approach allows for the first time to evolve through a brief period
of the merger phase of the black hole inspiral.


title: Non-Abelian black holes: The inside story

abstract:
  Recent progress in understanding of the internal structure of non-Abelian
black holes is discussed.
  Talk given at the international Workshop on The Internal Structure of Black
Holes and Spacetime Singularities, Haifa, Israel, June 29 -- July 3, 1997.


title:
Gravitational waves from binary systems in circular orbits: Convergence
  of a dressed multipole truncation

abstract:
  The gravitational radiation originating from a compact binary system in
circular orbit is usually expressed as an infinite sum over radiative multipole
moments. In a slow-motion approximation, each multipole moment is then
expressed as a post-Newtonian expansion in powers of v/c, the ratio of the
orbital velocity to the speed of light. The bare multipole truncation of the
radiation consists in keeping only the leading-order term in the post-Newtonian
expansion of each moment, but summing over all the multipole moments. In the
case of binary systems with small mass ratios, the bare multipole series was
shown in a previous paper to converge for all values v/c < 2/e, where e is the
base of natural logarithms. In this paper, we extend the analysis to a dressed
multipole truncation of the radiation, in which the leading-order moments are
corrected with terms of relative order (v/c)^2 and (v/c)^3. We find that the
dressed multipole series converges also for all values v/c < 2/e, and that it
coincides (within 1%) with the numerically ``exact'' results for v/c < 0.2.


title: The Gowdy T3 Cosmologies revisited

abstract:
  We have examined, repeated and extended earlier numerical calculations of
Berger and Moncrief for the evolution of unpolarized Gowdy T3 cosmological
models. Our results are consistent with theirs and we support their claim that
the models exhibit AVTD behaviour, even though spatial derivatives cannot be
neglected. The behaviour of the curvature invariants and the formation of
structure through evolution both backwards and forwards in time is discussed.


title: An ADM 3+1 formulation for Smooth Lattice General Relativity

abstract:
  A new hybrid scheme for numerical relativity will be presented. The scheme
will employ a 3-dimensional spacelike lattice to record the 3-metric while
using the standard 3+1 ADM equations to evolve the lattice. Each time step will
involve three basic steps. First, the coordinate quantities such as the Riemann
and extrinsic curvatures are extracted from the lattice. Second, the 3+1 ADM
equations are used to evolve the coordinate data, and finally, the coordinate
data is used to update the scalar data on the lattice (such as the leg
lengths). The scheme will be presented only for the case of vacuum spacetime
though there is no reason why it could not be extended to non-vacuum
spacetimes. The scheme allows any choice for the lapse function and shift
vectors. An example for the Kasner $T^3$ cosmology will be presented and it
will be shown that the method has, for this simple example, zero discretisation
error.


title: Conformally Covariant Differential Operators: Symmetric Tensor Fields

abstract:
  We extend previous work on conformally covariant differential operators to
consider the case of second order operators acting on symmetric traceless
tensor fields. The corresponding flat space Green function is explicitly
constructed and shown to be in accord with the requirements of conformal
invariance.


title: Gravity from Dirac Eigenvalues

abstract:
  We study a formulation of euclidean general relativity in which the dynamical
variables are given by a sequence of real numbers $\lambda_{n}$, representing
the eigenvalues of the Dirac operator on the curved spacetime. These quantities
are diffeomorphism-invariant functions of the metric and they form an infinite
set of ``physical observables'' for general relativity. Recent work of Connes
and Chamseddine suggests that they can be taken as natural variables for an
invariant description of the dynamics of gravity. We compute the Poisson
brackets of the $\lambda_{n}$'s, and find that these can be expressed in terms
of the propagator of the linearized Einstein equations and the energy-momentum
of the eigenspinors. We show that the eigenspinors' energy-momentum is the
Jacobian matrix of the change of coordinates from the metric to the
$\lambda_{n}$'s. We study a variant of the Connes-Chamseddine spectral action
which eliminates a disturbing large cosmological term. We analyze the
corresponding equations of motion and find that these are solved if the energy
momenta of the eigenspinors scale linearly with the mass. Surprisingly, this
scaling law codes Einstein's equations. Finally we study the coupling to a
physical fermion field.


title: More about Vacuum Spacetimes with Toroidal Null Infinities

abstract:
  Recently Bernd Schmidt has given three explicit examples of spacetimes with
toroidal null infinities. In this paper all solutions with a toroidal null
infinity within Schmidt's metric ansatz (polarized Gowdy models) are
constructed. The members of the family are determined by two smooth functions
of one variable. For the unpolarized Gowdy models the same kind of analysis
carries through.


title:
Shrinking II -- The Distortion of the Area Distance-Redshift Relation in
  Inhomogeneous Isotropic Universes

abstract:
  This paper and the others in the series challenge the standard model of the
effects of gravitational lensing on observations at large distances. We show
that due to the cumulative effect of lensing, areas corresponding to an
observed solid angle can be quite different than would be estimated from the
corresponding Friedmann-Lema\^{\i}tre model, even when averaged over large
angular scales. This paper concentrates on the specific example of spherically
symmetric but spatially inhomogeneous dust universes, the
Lema\^{\i}tre-Tolman-Bondi models, and shows that radial lensing significantly
distorts the area distance-redshift and density-redshift relations in these
exact solutions compared with the standard ones for Friedmann-Lema\^{\i}tre
models. Thus inhomogeneity may introduce significant errors into distance
estimates based on the standard FL relations, even after all-sky averaging. In
addition a useful new gauge choice is presented for these models, solving the
problem of locating the past null cone exactly.


title: Observable effects from spacetime tunneling

abstract:
  Assuming that spacetime tunnels -wormholes and ringholes- naturally exist in
the universe, we investigate the conditions making them embeddible in Friedmann
space, and the possible observable effects of these tunnels, including: lensing
and frequency-shifting of emitting sources, discontinuous change of background
temperature, broadening and intensity enhancement of spectral lines, so as a
dramatic increase of the luminosity of any object at the tunnel's throat.


title: Limits of the energy-momentum tensor in general relativity

abstract:
  A limiting diagram for the Segre classification of the energy-momentum tensor
is obtained and discussed in connection with a Penrose specialization diagram
for the Segre types. A generalization of the coordinate-free approach to limits
of Paiva et al. to include non-vacuum space-times is made. Geroch's work on
limits of space-times is also extended. The same argument also justifies part
of the procedure for classification of a given spacetime using Cartan scalars.


title: Chaos in Quantum Cosmology

abstract:
  Much of the foundational work on quantum cosmology employs a simple
minisuperspace model describing a Friedmann-Robertson-Walker universe
containing a massive scalar field. We show that the classical limit of this
model exhibits deterministic chaos and explore some of the consequences for the
quantum theory. In particular, the breakdown of the WKB approximation calls
into question many of the standard results in quantum cosmology.


title: Weber-like interactions and energy conservation

abstract:
  Velocity dependent forces varying as $k(\hat{r}/r)(1 - \mu \dot{r}^2 + \gamma
r \ddot{r})$ (such as Weber force), here called Weber-like forces, are examined
from the point of view of energy conservation and it is proved that they are
conservative if and only if $\gamma=2\mu$. As a consequence, it is shown that
gravitational theories employing Weber-like forces cannot be conservative and
also yield both the precession of the perihelion of Mercury as well as the
gravitational deflection of light.


title: Relativistic fluctuating hydrodynamics

abstract:
  We derive the formulae of fluctuating hydrodynamics appropiate to a
relativistically consistent divergence type theory, obtaining Landau - Lifshitz
fluctuating hydrodynamics as a limiting case.


title:
Quantum field theory with and without conical singularities: Black holes
  with cosmological constant and the multi-horizon scenario

abstract:
  Boundary conditions and the corresponding states of a quantum field theory
depend on how the horizons are taken into account. There is ambiguity as to
which method is appropriate because different ways of incorporating the
horizons lead to different results. We propose that a natural way of including
the horizons is to first consider the Kruskal extension and then define the
quantum field theory on the Euclidean section. Boundary conditions emerge
naturally as consistency conditions of the Kruskal extension. We carry out the
proposal for the explicit case of the Schwarzschild-de Sitter manifold with two
horizons. The required period $\beta$ is the interesting condition that it is
the lowest common multiple of $2\pi$ divided by the surface gravity of both
horizons. Restricting the ratio of the surface gravity of the horizons to
rational numbers yields finite $\beta$. The example also highlights some of the
difficulties of the off-shell approach with conical singularities in the
multihorizon scenario; and serves to illustrate the much richer interplay that
can occur among horizons, quantum field theory and topology when the
cosmological constant is not neglected in black hole processes.


title: Comment on ``The Gowdy $T^3$ Cosmologies Revisited''

abstract:
  A standard and reasonable definition of asymptotic velocity term dominance
(AVTD) shows that the numerical study by Hern and Stewart (gr-qc/9708038)
confirms previous results that generic Gowdy cosmologies on $T^3 \times R$ have
an AVTD singularity.


title: Torsion and the Electromagnetic Field

abstract:
  In the framework of the teleparallel equivalent of general relativity, we
study the dynamics of a gravitationally coupled electromagnetic field. It is
shown that the electromagnetic field is able not only to couple to torsion, but
also, through its energy-momentum tensor, to produce torsion. Furthermore, it
is shown that the coupling of the electromagnetic field with torsion preserves
the local gauge invariance of Maxwell's theory.


title: Textures and Newtonian Gravity

abstract:
  Newtonian theory is used to study the gravitational effects of a texture, in
particular the formation of massive structures.


title: Topology at the Planck Length

abstract:
  A basic arbitrariness in the determination of the topology of a manifold at
the Planck length is discussed. An explicit example is given of a `smooth'
change in topology from the 2-sphere to the 2-torus through a sequence of
noncommuting geometries. Applications are considered to the theory of D-branes
within the context of the proposed $M$(atrix) theory.


title: Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity

abstract:
  We study the phase space structure and the quantization of a pointlike
particle in 2+1 dimensional gravity. By adding boundary terms to the first
order Einstein Hilbert action, and removing all redundant gauge degrees of
freedom, we arrive at a reduced action for a gravitating particle in 2+1
dimensions, which is invariant under Lorentz transformations and a group of
generalized translations. The momentum space of the particle turns out to be
the group manifold SL(2). Its position coordinates have non-vanishing Poisson
brackets, resulting in a non-commutative quantum spacetime. We use the
representation theory of SL(2) to investigate its structure. We find a
discretization of time, and some semi-discrete structure of space. An
uncertainty relation forbids a fully localized particle. The quantum dynamics
is described by a discretized Klein Gordon equation.


title: Comments on the Problem of Time

abstract:
  The problem of time, considered as a problem in the usual physical context,
is reflected in relation with the paper by Kauffman and Smolin (gr-qc/9703026).
It is shown that the problem is a misposed problem in the sense that it was
raised with a lack of the recognition of mathematically known facts.


title: On an integral formula on hypersurfaces in General Relativity

abstract:
  We derive a general integral formula on an embedded hypersurface for general
relativistic space-times. Suppose the hypersurface is foliated by
two-dimensional compact ``sections'' $S_s$. Then the formula relates the rate
of change of the divergence of outgoing light rays integrated over $S_s$ under
change of section to geometric (convexity and curvature) properties of $S_s$
and the energy-momentum content of the space-time. We derive this formula using
the Sparling-Nester-Witten identity for spinor fields on the hypersurface by
appropriate choice of the spinor fields. We discuss several special cases which
have been discussed in the literature before, most notably the Bondi mass loss
formula.


title: Post-Newtonian Lagrangian planetary equations

abstract:
  We present a method to study the time variation of the orbital parameters of
a Post-Keplerian binary system undergoing a generic external perturbation. The
method is the relativistic extension of the planetary Lagrangian equations. The
theory only assumes the smallness of the external perturbation while
relativistic effects are already included in the unperturbed problem. This is
the major advantage of this novel approach over classical Lagrangian methods.


title:
Intersecting electric and magnetic p-branes: spherically symmetric
  solutions

abstract:
  We consider a D-dimensional self-gravitating spherically symmetric
configuration of a generalized electro-magnetic n-form F and a dilatonic scalar
field, admitting an interpretation in terms of intersecting p-branes. For
theories with multiple times, selection rules are obtained, which obstruct the
existence of p-branes in certain subspaces. General static solutions are
obtained under a specific restriction on the model parameters, which
corresponds to the known "intersection rules". More special families of
solutions (with equal charges for some of the F-field components) are found
with weakened restrictions on the input parameters. Black-hole solutions are
determined, and it is shown that in the extreme limit the Hawking temperature
may tend to zero, a finite value, or infinity, depending on the p-brane
intersection dimension. A kind of no-hair theorem is obtained, claiming that
black holes cannot coexist with a quasiscalar component of the F-field.


title:
A regularizing commutant duality for a kinematically covariant partial
  ordered net of observables

abstract:
  We consider a net of *-algebras, locally around any point of observation,
equipped with a natural partial order related to the isotony property. Assuming
the underlying manifold of the net to be a differentiable, this net shall be
kinematically covariant under general diffeomorphisms. However, the dynamical
relations, induced by the physical state defining the related net of (von
Neumann) observables, are in general not covariant under all diffeomorphisms,
but only under the subgroup of dynamical symmetries.
  We introduce algebraically both, IR and UV cutoffs, and assume that these are
related by a commutant duality. The latter, having strong implications on the
net, allows us to identify a 1-parameter group of the dynamical symmetries with
the group of outer modular automorphisms.
  For thermal equilibrium states, the modular dilation parameter may be used
locally to define the notions of both, time and a causal structure.


title: Quantum geometrodynamics for black holes and wormholes

abstract:
  The geometrodynamics of the spherical gravity with a selfgravitating thin
dust shell as a source is constructed. The shell Hamiltonian constraint is
derived 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, quasicontinuous.


title:
Cosmological sector for localized mass and spin in 2+1 dimensional
  topologically massive gravity

abstract:
  The cosmological sector to the full non-linear topologically massive gravity
(TMG) is obtained for localized sources of mass $m$ and spin $\sigma$ besides
the asymptotically spinning conical flat sector previously obtained. In a small
region near but outside the sources, the metric resembles the spinning conical
flat metric, but we find that the mass $m$ creates a negative deficit angle of
$3m$ as opposed to $m$. Furthermore, it is not possible to recover the results
of pure Einstein gravity in the limit $\mu \to \infty$ unlike the flat sector.


title:
Action and entropy of black holes in spacetimes with a cosmological
  constant

abstract:
  In the Euclidean path integral approach, we calculate the actions and the
entropies for the Reissner-Nordstr\"om-de Sitter solutions. When the
temperatures of black hole and cosmological horizons are equal, the entropy is
the sum of one-quarter areas of black hole and cosmological horizons; when the
inner and outer black hole horizons coincide, the entropy is only one-quarter
area of cosmological horizon; and the entropy vanishes when the two black hole
horizons and cosmological horizon coincide. We also calculate the Euler numbers
of the corresponding Euclidean manifolds, and discuss the relationship between
the entropy of instanton and the Euler number.


title: Topological dilaton black holes

abstract:
  In four-dimensional spacetime, when the two-sphere of black hole event
horizons is replaced by a two-dimensional hypersurface with zero or negative
constant curvature, the black hole is referred to as a topological black hole.
In this paper we present some exact topological black hole solutions in the
Einstein-Maxwell-dilaton theory with a Liouville-type dilaton potential.


title: Hairs on the cosmological horizon

abstract:
  We investigate the possibility of having hairs on the cosmological horizon.
The cosmological horizon shares similar properties of black hole horizons in
the aspect of having hairs on the horizons. For those theories admitting haired
black hole solutions, the nontrivial matter fields may reach and extend beyond
the cosmological horizon. For Q-stars and boson stars, the matter fields cannot
reach the cosmological horizon. The no short hair conjecture keeps valid,
despite the asymptotic behavior (de Sitter or anti-de Sitter) of black hole
solutions. We prove the no scalar hair theorem for anti-de Sitter black holes.
Using the Bekenstein's identity method, we also prove the no scalar hair
theorem for the de Sitter space and de Sitter black holes if the scalar
potential is convex.


title: High-powered Gravitational News

abstract:
  We describe the computation of the Bondi news for gravitational radiation. We
have implemented a computer code for this problem. We discuss the theory behind
it as well as the results of validation tests. Our approach uses the
compactified null cone formalism, with the computational domain extending to
future null infinity and with a worldtube as inner boundary. We calculate the
appropriate full Einstein equations in computational eth form in (a) the
interior of the computational domain and (b) on the inner boundary. At future
null infinity, we transform the computed data into standard Bondi coordinates
and so are able to express the news in terms of its standard $N_{+}$ and
$N_{\times}$ polarization components. The resulting code is stable and
second-order convergent. It runs successfully even in the highly nonlinear
case, and has been tested with the news as high as 400, which represents a
gravitational radiation power of about $10^{13}M_{\odot}/sec$.


title: Quantization of Black Holes in the Wheeler-DeWitt Approach

abstract:
  We discuss black hole quantization in the Wheeler-DeWitt approach. Our
consideration is based on a detailed investigation of the canonical formulation
of gravity with special considerations of surface terms. Since the phase space
of gravity for non-compact spacetimes or spacetimes with boundaries is
ill-defined unless one takes boundary degrees of freedom into account, we give
a Hamiltonian formulation of the Einstein-Hilbert-action as well as a
Hamiltonian formulation of the surface terms. It then is shown how application
to black hole spacetimes connects the boundary degrees of freedom with
thermodynamical properties of black hole physics. Our treatment of the surface
terms thereby naturally leads to the Nernst theorem. Moreover, it will produce
insights into correlations between the Lorentzian and the Euclidean theory.
Next we discuss quantization, which we perform in a standard manner. It is
shown how the thermodynamical properties can be rediscovered from the quantum
equations by a WKB like approximation scheme. Back reaction is treated by going
beyond the first order approximation. We end our discussion by a rigorous
investigation of the so-called BTZ solution in 2+1 dimensional gravity.


title:
Numerical Evolution of Black Holes with a Hyperbolic Formulation of
  General Relativity

abstract:
  We describe a numerical code that solves Einstein's equations for a
Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation
introduced by Choquet-Bruhat and York. This is the first time this formulation
has been used to evolve a numerical spacetime containing a black hole. We
excise the hole from the computational grid in order to avoid the central
singularity. We describe in detail a causal differencing method that should
allow one to stably evolve a hyperbolic system of equations in three spatial
dimensions with an arbitrary shift vector, to second-order accuracy in both
space and time. We demonstrate the success of this method in the spherically
symmetric case.


title: Gauge dependence in the theory of non-linear spacetime perturbations

abstract:
  Diffeomorphism freedom induces a gauge dependence in the theory of spacetime
perturbations. We derive a compact formula for gauge transformations of
perturbations of arbitrary order. To this end, we develop the theory of Taylor
expansions for one-parameter families (not necessarily groups) of
diffeomorphisms. First, we introduce the notion of knight diffeomorphism, that
generalises the usual concept of flow, and prove a Taylor's formula for the
action of a knight on a general tensor field. Then, we show that any
one-parameter family of diffeomorphisms can be approximated by a family of
suitable knights. Since in perturbation theory the gauge freedom is given by a
one-parameter family of diffeomorphisms, the expansion of knights is used to
derive our transformation formula. The problem of gauge dependence is a purely
kinematical one, therefore our treatment is valid not only in general
relativity, but in any spacetime theory.


title: On the gravity renormalization off shell

abstract:
  Using as an example the Einstein gravity with the cosmological constant, we
discuss the calculation of renormalization group functions off shell. We found,
that gauge dependent terms should be absorbed by the nonlinear renormalization
of metric. Nevertheless, some terms can be included in the renormalization of
Newton's constant. This ambiguity in the renormalization prescription is
discussed.


title: Signatures of Quantum Gravity in the Large-Scale Universe

abstract:
  The quantum gravity processes that have taken place in the very early
Universe are probably responsible for the observed large-scale cosmological
perturbations. The comparison of the theory with the detected microwave
background anisotropies favors the conclusion that the very early Universe was
not driven by a scalar field with whichever scalar field potential. At the same
time, the observations allow us to conclude that there is a good probability of
a direct detection of the higher frequency relic gravitational waves with the
help of the advanced laser interferometers.


title:
Generation of scalar-tensor gravity effects in equilibrium state boson
  stars

abstract:
  Boson stars in zero-, one-, and two-node equilibrium states are modeled
numerically within the framework of Scalar-Tensor Gravity. The complex scalar
field is taken to be both massive and self-interacting. Configurations are
formed in the case of a linear gravitational scalar coupling (the Brans-Dicke
case) and a quadratic coupling which has been used previously in a cosmological
context. The coupling parameters and asymptotic value for the gravitational
scalar field are chosen so that the known observational constraints on
Scalar-Tensor Gravity are satisfied. It is found that the constraints are so
restrictive that the field equations of General Relativity and Scalar-Tensor
gravity yield virtually identical solutions. We then use catastrophe theory to
determine the dynamically stable configurations. It is found that the maximum
mass allowed for a stable state in Scalar-Tensor gravity in the present
cosmological era is essentially unchanged from that of General Relativity. We
also construct boson star configurations appropriate to earlier cosmological
eras and find that the maximum mass for stable states is smaller than that
predicted by General Relativity, and the more so for earlier eras. However, our
results also show that if the cosmological era is early enough then only states
with positive binding energy can be constructed.


title: An Extension of Multiple Cosmic String Solution

abstract:
  We extend the work done for cosmic strings on the perturbative calculation of
vacuum polarization of a massless field in the space-time of multiple cosmic
strings and show that for a more general class of locally flat metrics the one
loop calculation do not introduce any new divergences to the VEV of the energy
of a scalar particle or a spinor particle. We explicitly perform the
calculation for the configuration where we have one cosmic string in the
presence of a dipole made out of cosmic strings both for the scalar and the
spinor cases.


title: Gravity on Fuzzy Space-Time

abstract:
  A review is made of recent efforts to add a gravitational field to
noncommutative models of space-time. Special emphasis is placed on the case
which could be considered as the noncommutative analog of a parallelizable
space-time. It is argued that, at least in this case, there is a rigid relation
between the noncommutative structure of the space-time on the one hand and the
nature of the gravitational field which remains as a `shadow' in the
commutative limit on the other.


title: Quasi-toroidal oscillations in rotating relativistic stars

abstract:
  Quasi-toroidal oscillations in slowly rotating stars are examined in the
framework of general relativity. The oscillation frequency to first order of
the rotation rate is not a single value even for uniform rotation unlike the
Newtonian case. All the oscillation frequencies of the r-modes are purely
neutral and form a continuous spectrum limited to a certain range. The allowed
frequencies are determined by the resonance condition between the perturbation
and background mean flow. The resonant frequency varies with the radius
according to general relativistic dragging effect.


title: Massive string modes and non-singular pre-big-bang cosmology

abstract:
  Perturbative $\alpha '$ corrections to the low energy string effective action
have been recently found to have a potentially regularizing effect on the
singularity of the lowest order pre-big-bang solutions. Whether they actually
regularize it, however, cannot be determined working at any finite order in a
perturbative expansion in powers of the string constant $\alpha '$, because of
scheme dependence ambiguities. Physically, these corrections are dominated by
the integration over the first few massive string states. Very massive string
modes, instead, can have a regularizing effect which is non-perturbative in
$\alpha '$ and which basically comes from the fact that in a gravitational
field with Hubble constant $H$ they are produced with an effective Hawking
temperature $T=H/(2\pi)$, and an infinite production rate would occur if this
temperature exceeded the Hagedorn temperature. We discuss technical and
conceptual difficulties of this non-perturbative regularization mechanism.


title: Bohmian Time Versus Probabilistic Time

abstract:
  One of the basic peoblems of quantum cosmology is the problem of time.
Various solutions have been proposed for this problem. One approach is to use
the Bohmian time. Another Approach is to use the probabilistic time which was
recently introduced by Castagnino. We consider both of these definitions as
generalizations of a semi-classical time and compare them for a mini-super
space.


title: Integrable Multidimensional Cosmology for Intersecting $p$-Branes

abstract:
  A multidimensional field model describing the behaviour of (at most) one
Einstein space of non-zero curvature and n Ricci-flat internal spaces is
considered. The action contains several dilatonic scalar fields and
antisymmetric forms. The problem setting covers various problems with field
dependence on a single space-time coordinate, in particular, isotropic and
anisotropic homogeneous cosmologies. When the forms are chosen to be
proportional to volume forms of p-brane factor spaces, a Toda-like Lagrange
representation arises. Exact solutions are obtained when the p-brane dimensions
and the dilatonic couplings obey some orthogonality conditions. General
features and some special cases of cosmological solutions are discussed. It is
shown, in particular, that all hyperbolic models with a 3-dimensional external
space possess an asymptotic with the external scale factor a(t) is proportional
to |t| (the cosmic time), while all internal scale factors and all scalar
fields tend to finite limits. For D=11 a family of models with one 5-brane and
three 2-branes is described.


title:
Coalescing binary systems of compact objects: Dynamics of angular
  momenta

abstract:
  The end state of a coalescing binary of compact objects depends strongly on
the final total mass M and angular momentum J. Since gravitational radiation
emission causes a slow evolution of the binary system through quasi-circular
orbits down to the innermost stable one, in this paper we examine the
corresponding behavior of the ratio J/M^2 which must be less than 1(G/c) or
about 0.7(G/c) for the formation of a black hole or a neutron star
respectively. The results show cases for which, at the end of the inspiral
phase, the conditions for black hole or neutron star formation are not
satisfied. The inclusion of spin effects leads us to a study of precession
equations valid also for the calculation of gravitational waveforms.


title: Singularities, initial and boundary problems for the Tolman-Bondi model

abstract:
  Boundary problem for Tolman-Bondi model is formulated. One-to-one
correspondence between singularities hypersurfaces and initial conditions of
the Tolman-Bondi model is constructed.


title: Timelike Infinity and Asymptotic Symmetry

abstract:
  By extending Ashtekar and Romano's definition of spacelike infinity to the
timelike direction, a new definition of asymptotic flatness at timelike
infinity for an isolated system with a source is proposed. The treatment
provides unit spacelike 3-hyperboloid timelike infinity and avoids the
introduction of the troublesome differentiability conditions which were
necessary in the previous works on asymptotically flat spacetimes at timelike
infinity. Asymptotic flatness is characterized by the fall-off rate of the
energy-momentum tensor at timelike infinity, which makes it easier to
understand physically what spacetimes are investigated. The notion of the order
of the asymptotic flatness is naturally introduced from the rate. The
definition gives a systematized picture of hierarchy in the asymptotic
structure, which was not clear in the previous works. It is found that if the
energy-momentum tensor falls off at a rate faster than $\sim t^{-2}$, the
spacetime is asymptotically flat and asymptotically stationary in the sense
that the Lie derivative of the metric with respect to $\ppp_t$ falls off at the
rate $\sim t^{-2}$. It also admits an asymptotic symmetry group similar to the
Poincar\'e group. If the energy-momentum tensor falls off at a rate faster than
$\sim t^{-3}$, the four-momentum of a spacetime may be defined. On the other
hand, angular momentum is defined only for spacetimes in which the
energy-momentum tensor falls off at a rate faster than $\sim t^{-4}$.


title:
Generalized 2d-dilaton models, the true black hole and quantum
  integrability

abstract:
  All 1+1 dimensional dipheomorphism-invariant models can be viewed in a
unified manner. This includes also general dilaton theories and especially
spherically symmetric gravity (SSG) and Witten's dilatonic black hole (DBH). A
common feature --- also in the presence of matter fields of any type --- is the
appearance of an absolutely conserved quantity C which is determined by the
influx of matter. Only for a subclass of generalized dilaton theories the
singularity structure vanishes together with C. Such `physical' theories
include, of course, SSG and DBH. It seems to have been overlooked until
recently that the (classical) 'black hole' singularity of the DBH deviates from
SSG in a physically nontrivial manner. At the quantum level for all generalized
dilaton theories --- in the absence of matter --- the local quantum effects are
shown to disappear. This enables us to compute e.g. the second loop order
correction to the Polyakov term. For non-minimal scalar coupling we also
believe to have settled the controversial issue of Hawking radiation to
infinity with a somewhat puzzling result for the case of SSG.


title:
Bounding the mass of the graviton using gravitional-wave observations of
  inspiralling compact binaries

abstract:
  If gravitation is propagated by a massive field, then the velocity of
gravitational waves (gravitons) will depend upon their frequency and the
effective Newtonian potential will have a Yukawa form. In the case of
inspiralling compact binaries, gravitational waves emitted at low frequency
early in the inspiral will travel slightly slower than those emitted at high
frequency later, modifying the phase evolution of the observed inspiral
gravitational waveform, similar to that caused by post-Newtonian corrections to
quadrupole phasing. Matched filtering of the waveforms can bound such
frequency-dependent variations in propagation speed, and thereby bound the
graviton mass. The bound depends on the mass of the source and on noise
characteristics of the detector, but is independent of the distance to the
source, except for weak cosmological redshift effects. For observations of
stellar-mass compact inspiral using ground-based interferometers of the
LIGO/VIRGO type, the bound on the graviton Compton wavelength is of the order
of $6 \times 10^{12}$ km, about double that from solar-system tests of Yukawa
modifications of Newtonian gravity. For observations of super-massive black
hole binary inspiral at cosmological distances using the proposed laser
interferometer space antenna (LISA), the bound can be as large as $6 \times
10^{16}$ km. This is three orders of magnitude weaker than model-dependent
bounds from galactic cluster dynamics.


title: On the Hamiltonian Formulation of Class B Bianchi Cosmological Models

abstract:
  The application of the divergence theorem in a non-coordinated basis is shown
to lead to a corrected variational principle for Class B Bianchi cosmological
models. This variational principle is used to construct a Hamiltonian
formulation for diagonal and symmetric vacuum Class B models. [Note: This is an
unpublished paper from 1984 that might be useful to anyone interested in Class
B Bianchi models.]


title: Gravitational collapse to toroidal, cylindrical and planar black holes

abstract:
  Gravitational collapse of non-spherical symmetric matter leads inevitably to
non-static external spacetimes. It is shown here that gravitational collapse of
matter with toroidal topology in a toroidal anti-de Sitter background proceeds
to form a toroidal black hole. According to the analytical model presented, the
collapsing matter absorbs energy in the form of radiation (be it scalar,
neutrinos, electromagnetic, or gravitational) from the exterior spacetime. Upon
decompactification of one or two coordinates of the torus one gets collapsing
solutions of cylindrical or planar matter onto black strings or black
membranes, respectively. The results have implications on the hoop conjecture.


title: Phases of massive scalar field collapse

abstract:
  We study critical behavior in the collapse of massive spherically symmetric
scalar fields. We observe two distinct types of phase transition at the
threshold of black hole formation. Type II phase transitions occur when the
radial extent $(\lambda)$ of the initial pulse is less than the Compton
wavelength ($\mu^{-1}$) of the scalar field. The critical solution is that
found by Choptuik in the collapse of massless scalar fields. Type I phase
transitions, where the black hole formation turns on at finite mass, occur when
$\lambda \mu \gg 1$. The critical solutions are unstable soliton stars with
masses $\alt 0.6 \mu^{-1}$. Our results in combination with those obtained for
the collapse of a Yang-Mills field~{[M.~W. Choptuik, T. Chmaj, and P. Bizon,
Phys. Rev. Lett. 77, 424 (1996)]} suggest that unstable, confined solutions to
the Einstein-matter equations may be relevant to the critical point of other
matter models.


title: Stable Topologies of Event Horizon

abstract:
  In our previous work, it was shown that the topology of an event horizon (EH)
is determined by the past endpoints of the EH. A torus EH (the collision of two
EH) is caused by the two-dimensional (one-dimensional) set of the endpoints. In
the present article, we examine the stability of the topology of the EH. We see
that a simple case of a single spherical EH is unstable. Furthermore, in
general, an EH with handles (a torus, a double torus, ...) is structurally
stable in the sense of catastrophe theory.


title: First order hyperbolic formalism for Numerical Relativity

abstract:
  The causal structure of Einstein's evolution equations is considered. We show
that in general they can be written as a first order system of balance laws for
any choice of slicing or shift. We also show how certain terms in the evolution
equations, that can lead to numerical inaccuracies, can be eliminated by using
the Hamiltonian constraint. Furthermore, we show that the entire system is
hyperbolic when the time coordinate is chosen in an invariant algebraic way,
and for any fixed choice of the shift. This is achieved by using the momentum
constraints in such as way that no additional space or time derivatives of the
equations need to be computed. The slicings that allow hyperbolicity in this
formulation belong to a large class, including harmonic, maximal, and many
others that have been commonly used in numerical relativity. We provide details
of some of the advanced numerical methods that this formulation of the
equations allows, and we also discuss certain advantages that a hyperbolic
formulation provides when treating boundary conditions.


title: Can a Unruh Detector Feel a Cosmic String?

abstract:
  Unruh's detector calculation is used to study the effect of the defect angle
$\beta$ in a space-time with a cosmic string for both the excitation and
deexcitation cases. It is found that a rotating detector results in a non-zero
effect for both finite (small) and infinite (large) time.


title:
Refined Algebraic Quantization and Quantum Field Theory in Curved
  Space-Time

abstract:
  Application of the so-called refined algebraic quantization scheme for
constrained systems to the relativistic particle provides an inner product that
defines a unique Fock representation for a scalar field in curved space-time.
The construction can be made rigorous for a general globally hyperbolic
space-time, but the quasifree state so obtained turns out to be unphysical in
general. We exhibit a closely related pair of Fock representations that is also
defined generically and conforms to the notion of in- and outgoing states in
those situations where particle creation by the external field is expected.


title:
A KMS-like state of Hadamard type on Robertson-Walker spacetimes and its
  time evolution

abstract:
  In this work we define a new state on the Weyl algebra of the free massive
scalar Klein-Gordon field on a Robertson-Walker spacetime and prove that it is
a Hadamard state. The state is supposed to approximate a thermal equilibrium
state on a Robertson-Walker spacetime and we call it an adiabatic KMS state.
This opens the possibility to do quantum statistical mechanics on
Robertson-Walker spacetimes in the algebraic framework and the analysis of the
free Bose gas on Robertson-Walker spacetimes. The state reduces to an adiabatic
vacuum state if the temperature is zero and it reduces to the usual KMS state
if the scaling factor in the metric of the Robertson-Walker spacetime is
constant.
  In the second part of our work we discuss the time evolution of adiabatic KMS
states. The time evolution is described in terms of semigroups. We prove the
existence of a propagator on the classical phase space. This defines a time
evolution on the one-particle Hilbert space. We use this time evolution to
analyze the evolution of the two-point function of the KMS state. The inverse
temperature change is proportional to the scale factor in the metric of the
Robertson-Walker spacetime, as one expects for a relativistic Bose gas.


title: Classical Oscilators in General Relativity

abstract:
  It is shown that in general relativity some static metrics are able to
simulate oscillatory motions. Their form depends on two arbitrary real
parameters which determine the specific oscillation modes. The conclusion is
that these metrics can be used for new geometric models of closed or even open
bags.
  Pacs: 04.02.-q and 04.02.Jb


title:
Unconstrained Hamiltonian formulation of General Relativity with
  thermo-elastic sources

abstract:
  A new formulation of the Hamiltonian dynamics of the gravitational field
interacting with(non-dissipative) thermo-elastic matter is discussed. It is
based on a gauge condition which allows us to encode the six degrees of freedom
of the ``gravity + matter''-system (two gravitational and four
thermo-mechanical ones), together with their conjugate momenta, in the
Riemannian metric q_{ij} and its conjugate ADM momentum P^{ij}. These variables
are not subject to constraints. We prove that the Hamiltonian of this system is
equal to the total matter entropy. It generates uniquely the dynamics once
expressed as a function of the canonical variables. Any function U obtained in
this way must fulfil a system of three, first order, partial differential
equations of the Hamilton-Jacobi type in the variables (q_{ij},P^{ij}). These
equations are universal and do not depend upon the properties of the material:
its equation of state enters only as a boundary condition. The well posedness
of this problem is proved. Finally, we prove that for vanishing matter density,
the value of U goes to infinity almost everywhere and remains bounded only on
the vacuum constraints. Therefore the constrained, vacuum Hamiltonian (zero on
constraints and infinity elsewhere) can be obtained as the limit of a ``deep
potential well'' corresponding to non-vanishing matter. This unconstrained
description of Hamiltonian General Relativity can be useful in numerical
calculations as well as in the canonical approach to Quantum Gravity.


title: Black-hole interiors and strong cosmic censorship

abstract:
  Strong cosmic censorship holds that given suitable initial data on a
spacelike hypersurface, the laws of general relativity should determine,
completely and uniquely, the future evolution of the spacetime. Here it is
argued that while strong cosmic censorship is enforced for all black holes
residing in asymptotically flat spacetime, it is violated (within the classical
formulation of general relativity) for some black holes residing in non
asymptotically flat spacetime. It is suggested that the semi-classical
formulation of general relativity might enforce strong cosmic censorship.


title: Matters of Gravity, the newsletter of the APS TG on gravitation

abstract:
  Contents:
  *News:
  April 1997 Joint APS/AAPT Meeting, by Beverly Berger
  The physics survey and committee on gravitational physics, by Jim Hartle
  *Research Briefs:
  Instability of rotating stars to axial perturbations, by Sharon Morsink
  LIGO project status, by Stan Whitcomb
  The Search for Frame-Dragging, by Clifford Will
  *Conference Reports:
  Conference of the Southern African Relativity Society, by Nigel Bishop
  II Warszaw workshop on canonical and quantum gravity, by Carlo Rovelli
  Alpbach summer school on fundamental physics in space, by Peter Bender
  MG8, an experimentalists' summary, by Riley Newman and Peter Saulson
  Amaldi Conference on Gravitational Waves, by M. Alessandra Papa
  Santa Fe workshop on simplicial quantum gravity, by Lee Smolin
  VII Canadian Conference on General Relativity, by David Hobill


title:
Pathologies of hyperbolic gauges in general relativity and other field
  theories

abstract:
  We present a mathematical characterization of hyperbolic gauge pathologies in
general relativity and electrodynamics. We show how non-linear gauge terms can
produce a blow-up along characteristics and how this can be identified
numerically by performing convergence analysis. Finally, we show some numerical
examples and discuss the profound implications this may have for the field of
numerical relativity.


title: The Cauchy Horizon In Black Hole-de Sitter Spacetimes

abstract:
  The last seven years has produced a growing body of evidence which concludes
that the Cauchy horizon in black hole-de Sitter spacetimes is classically
stable when the surface gravity at the cosmological event horizon is greater
than that at the Cauchy horizon. That stability persists for a finite, but
non-zero, region of the black hole's parameter space, $(M,Q,J,\Lambda)$,
suggests that black holes immersed in de Sitter space are counter-examples to
the strong cosmic censorship hypothesis.
  In this review we chronicle that body of evidence and describe the first
steps of a program of numerical work aimed at better understanding the interior
of black hole-de Sitter spacetimes. The review ends with a speculative account
of the role that future work will take.


title: General Relativistic Models of Binary Neutron Stars in Quasiequilibrium

abstract:
  We perform fully relativistic calculations of binary neutron stars in
corotating, circular orbit. While Newtonian gravity allows for a strict
equilibrium, a relativistic binary system emits gravitational radiation,
causing the system to lose energy and slowly spiral inwards. However, since
inspiral occurs on a time scale much longer than the orbital period, we can
treat the binary to be in quasiequilibrium. In this approximation, we integrate
a subset of the Einstein equations coupled to the relativistic equation of
hydrostatic equilibrium to solve the initial value problem for binaries of
arbitrary separation. We adopt a polytropic equation of state to determine the
structure and maximum mass of neutron stars in close binaries for polytropic
indices n=1, 1.5 and 2. We construct sequences of constant rest-mass and locate
turning points along energy equilibrium curves to identify the onset of orbital
instability. In particular, we locate the innermost stable circular orbit
(ISCO) and its angular velocity. We construct the first contact binary systems
in full general relativity. These arise whenever the equation of state is
sufficiently soft >= 1.5. A radial stability analysis reveals no tendency for
neutron stars in close binaries to collapse to black holes prior to merger.


title: Evolution of gravitational waves through the cosmological QCD transition

abstract:
  The spectrum of gravitational waves that have been produced in inflation is
modified during cosmological transitions. Large drops in the number of
relativistic particles, like during the QCD transition or at $e^+e^-$
annihilation, lead to steps in the spectrum of gravitational waves. We
calculate the transfer function for the differential energy density of
gravitational waves for a first-order and for a crossover QCD transition.


title: Relativistic spin networks and quantum gravity

abstract:
  Relativistic spin networks are defined by considering the spin covering of
the group SO(4), SU(2) times SU(2). Relativistic quantum spins are related to
the geometry of the 2-dimensional faces of a 4-simplex. This extends the idea
of Ponzano and Regge that SU(2) spins are related to the geometry of the edges
of a 3-simplex.
  This leads us to suggest that there may be a 4-dimensional state sum model
for quantum gravity based on relativistic spin networks which parallels the
construction of 3-dimensional quantum gravity from ordinary spin networks.


title: Global monopoles in dilaton gravity

abstract:
  We analyse the gravitational field of a global monopole within the context of
low energy string gravity, allowing for an arbitrary coupling of the monopole
fields to the dilaton. Both massive and massless dilatons are considered. We
find that, for a massless dilaton, the spacetime is generically singular,
whereas when the dilaton is massive, the monopole generically induces a long
range dilaton cloud. We compare and contrast these results with the literature.


title:
Theory of thin shells in general relativity: Equivalence of direct and
  Wheeler-DeWitt quantizations

abstract:
  We justify the way of the direct quantization which means immediate
quantization of a conservation law. It is shown that this approach is
equivalent to introducing the super Hamiltonian on a minisuperspace in spirit
of the Wheeler-DeWitt's approach. Then we will have: (i) all values are
observable and have an obvious physical meaning and well-defined application
domain; (ii) wave function is well-defined without time slicing and often can
be exactly obtained; (iii) we can take off major mathematical troubles, and
therefore, more complicate models can be considered exactly without the
perturbation theory.


title: Multipole moments in Kaluza-Klein theories

abstract:
  This paper contains discussion of the problem of motion of extended i.e. non
point test bodies in multidimensional space. Extended bodies are described in
terms of so called multipole moments. Using approximated form of equations of
motion for extended bodies deviation from geodesic motion is derived. Results
are applied to special form of space-time.


title:
Gravitational waves from inspiraling compact binaries: The
  quadrupole-moment term

abstract:
  A rotating star's oblateness creates a deformation in the gravitational field
outside the star, which is measured by the quadrupole-moment tensor. We
consider the effect of the quadrupole moment on the orbital motion and rate of
inspiral of a compact binary system, composed of neutron stars and/or black
holes. We find that in the case of circular orbits, the quadrupole-monopole
interaction affects the relation between orbital radius and angular velocity,
and also the rate of inspiral, by a quantity of order (v/c)^4, where v is the
orbital velocity and c the speed of light.


title: Quadrupole moments of rotating neutron stars

abstract:
  Numerical models of rotating neutron stars are constructed for four equations
of state using the computer code RNS written by Stergioulas. For five selected
values of the star's gravitational mass (in the interval between 1.0 and 1.8
solar masses) and for each equation of state, the star's angular momentum is
varied from J=0 to the Keplerian limit J=J_{max}. For each neutron-star
configuration we compute Q, the quadrupole moment of the mass distribution. We
show that for given values of M and J, |Q| increases with the stiffness of the
equation of state. For fixed mass and equation of state, the dependence on J is
well reproduced with a simple quadratic fit, Q \simeq - aJ^2/M c^2, where c is
the speed of light, and a is a parameter of order unity depending on the mass
and the equation of state.


title: Thompson Scattering in an Expanding Universe

abstract:
  The Thompson cross section for scattering of electromagnetic waves by a free
electron in an expanding universe is derived here. The equations of motion of
the electron are obtained using the Einstein-Infeld-Hoffmann (EIH) surface
integral method. These integrals are evaluated approximately by perturbing off
an Einstein-deSitter cosmological field. It is found that the Thompson cross
section varies with time as the inverse square of the cosmic scale factor R(t).


title:
Cosmological perturbation with two scalar fields in reheating after
  inflation

abstract:
  We investigate the cosmological perturbation of two-scalar field model during
the reheating phase after inflation. Using the exact solution of the
perturbation in long-wavelength limit, which is expressed in terms of the
background quantities, we analyze the behavior of the metric perturbation. The
oscillating inflaton field gives rise to the parametric resonance of the
massless scalar field and this leads to the amplification of the iso-curvature
mode of the metric perturbations.


title:
Fractals and Symbolic Dynamics as Invariant Descriptors of Chaos in
  General Relativity

abstract:
  The study of dynamics in general relativity has been hampered by a lack of
coordinate independent measures of chaos. Here I review a variety of invariant
measures for quantifying chaotic dynamics in relativity that exploit the
coordinate independence of fractal dimensions and symbolic entropies.


title: The mixmaster universe is unambiguously chaotic

abstract:
  The Mixmaster or Bianchi IX cosmological model has become one of the
archetypal settings for studying gravitational dynamics. The past decade has
seen a vigourous debate about whether or not the Mixmaster's dynamics is
chaotic. In this talk we review our recent work in uncovering a chaotic
invariant set of orbits in the Mixmaster phase space, and how we used this
discovery to prove the dynamics is chaotic.


title: Adaptive Finite Elements and Colliding Black Holes

abstract:
  According to the theory of general relativity, the relative acceleration of
masses generates gravitational radiation. Although gravitational radiation has
not yet been detected, it is believed that extremely violent cosmic events,
such as the collision of black holes, should generate gravity waves of
sufficient amplitude to detect on earth. The massive Laser Interferometer
Gravitational-wave Observatory, or LIGO, is now being constructed to detect
gravity waves. Consequently there is great interest in the computer simulation
of black hole collisions and similar events, based on the numerical solution of
the Einstein field equations. In this note we introduce the scientific,
mathematical, and computational problems and discuss the development of a
computer code to solve the initial data problem for colliding black holes, a
nonlinear elliptic boundary value problem posed in an unbounded three
dimensional domain which is a key step in solving the full field equations. The
code is based on finite elements, adaptive meshes, and a multigrid solution
process. Here we will particularly emphasize the mathematical and algorithmic
issues arising in the generation of adaptive tetrahedral meshes.


title: Topological Black Holes -- Outside Looking In

abstract:
  I describe the general mathematical construction and physical picture of
topological black holes, which are black holes whose event horizons are
surfaces of non-trivial topology. The construction is carried out in an
arbitrary number of dimensions, and includes all known special cases which have
appeared before in the literature. I describe the basic features of massive
charged topological black holes in $(3+1)$ dimensions, from both an exterior
and interior point of view. To investigate their interiors, it is necessary to
understand the radiative falloff behaviour of a given massless field at late
times in the background of a topological black hole. I describe the results of
a numerical investigation of such behaviour for a conformally coupled scalar
field. Significant differences emerge between spherical and higher genus
topologies.


title: State after quantum tunneling with gravity

abstract:
  The Wheeler-DeWitt equation is investigated and used to examine a state after
a quantum tunneling with gravity. To make arguments definite we treat a
discretized version of the Wheeler-DeWitt equation and adopt the WKB method. We
expand an Euclidean wave function around an instanton, by using a deviation
equation of a vector field tangent to a congruence of instantons. The instanton
around which we expand the wave function corresponds to a so-called most
probable escape path (MPEP). It is shown that, when the wave function is
analytically continued, the corresponding state of physical perturbations is
equivalent to the vacuum state determined by positive-frequency mode functions
which satisfy appropriate boundary conditions. Thus a quantum field theory is
effective to investigate a state after a quantum tunneling with gravity. The
effective Lagrangian describing the field theory is obtained by simply reducing
the original Lagrangian to a subspace spanned by the physical perturbations.
The result of this paper does not depend on the operator ordering and can be
applied to all physical perturbations, including gravitational perturbations,
around a general MPEP.


title: Adaptive Identification of VIRGO-like Noise Spectrum

abstract:
  The aim of this work is to show how it is possible to build an on line
whitening filter in an adaptive way. We have modeled the VIRGO noise spectrum
as an autoregressive stochastic process, after a pre-filtering of the
theoretical curve which flattens the low frequency part of the spectrum. We
have tested some very popular adaptive algorithms, based on the gradient
methods and on the least squares methods with a lattice structure filter.


title: Renormalization Group Approach to Einstein Equation in Cosmology

abstract:
  The renormalization group method has been adapted to the analysis of the
long-time behavior of non-linear partial differential equation and has
demonstrated its power in the study of critical phenomena of gravitational
collapse. In the present work we apply the renormalization group to the
Einstein equation in cosmology and carry out detailed analysis of
renormalization group flow in the vicinity of the scale invariant fixed point
in the spherically symmetric and inhomogeneous dust filled universe model.


title: Hamiltonian Thermodynamics of Black Holes in Generic 2-D Dilaton Gravity

abstract:
  We consider the Hamiltonian mechanics and thermodynamics of an eternal black
hole in a box of fixed radius and temperature in generic 2-D dilaton gravity.
Imposing boundary conditions analoguous to those used by Louko and Whiting for
spherically symmetric gravity, we find that the reduced Hamiltonian generically
takes the form: $$ H(M,\phi_+) = \sigma_0 E(M,\phi_+) -{N_0\over 2\pi} S(M) $$
where $E(M,\phi_+)$ is the quasilocal energy of a black hole of mass $M$ inside
a static box (surface of fixed dilaton field $\phi_+$) and $S(M)$ is the
associated classical thermodynamical entropy. $\sigma_0$ and $N_0$ determine
time evolution along the world line of the box and boosts at the bifurcation
point, respectively. An ansatz for the quantum partition function is obtained
by fixing $\sigma_0$ and $N_0$ and then tracing the operator $e^{-\beta H}$
over mass eigenstates. We analyze this partition function in some detail both
generically and for the class of dilaton gravity theories that is obtained by
dimensional reduction of Einstein gravity in n+2 dimensions with $S^n$
spherical symmetry.


title: Stochastic gravitational background from inflationary phase transitions

abstract:
  We consider true vacuum bubbles generated in a first order phase transition
occurring during the slow rolling era of a two field inflation: it is known
that gravitational waves are produced by the collision of such bubbles. We find
that the epoch of the phase transition strongly affects the characteristic peak
frequency of the gravitational waves, causing an observationally interesting
redshift in addition to the post-inflationary expansion. In particular it is
found that a phase transition occurring typically 10$\div$20 $e-$foldings
before the reheating at $kT\simeq 10^{15}$ GeV may be detected by the next Ligo
gravity waves interferometers. Moreover, for recently proposed models capable
of generating the observed large scale voids as remnants of the primordial
bubbles (for which the characteristic wave lengths are several tens of Mpc), it
is found that the level of anisotropy of the cosmic microwave background
provides a deep insight upon the physical parameters of the effective
Lagrangian.


title: Cross Section of a Resonant-Mass Detector for Scalar Gravitational Waves

abstract:
  Gravitationally coupled scalar fields, originally introduced by Jordan, Brans
and Dicke to account for a non constant gravitational coupling, are a
prediction of many non-Einsteinian theories of gravity not excluding
perturbative formulations of String Theory. In this paper, we compute the cross
sections for scattering and absorption of scalar and tensor gravitational waves
by a resonant-mass detector in the framework of the Jordan-Brans-Dicke theory.
The results are then specialized to the case of a detector of spherical shape
and shown to reproduce those obtained in General Relativity in a certain limit.
Eventually we discuss the potential detectability of scalar waves emitted in a
spherically symmetric gravitational collapse.


title: Cauchy Horizon Endpoints and Differentiability

abstract:
  Cauchy horizons are shown to be differentiable at endpoints where only a
single null generator leaves the horizon. A Cauchy horizon fails to have any
null generator endpoints on a given open subset iff it is differentiable on the
open subset and also iff the horizon is (at least) of class C^1 on the open
subset. Given the null convergence condition, a compact horizon which is of
class C^2 almost everywhere has no endpoints and is (at least) of class C^1 at
all points.


title: `Operational' Energy Conditions

abstract:
  I show that a quantized Klein-Gordon field in Minkowski space obeys an
`operational' weak energy condition: the energy of an isolated device
constructed to measure or trap the energy in a region, plus the energy it
measures or traps, cannot be negative. There are good reasons for thinking that
similar results hold locally for linear quantum fields in curved space-times. A
thought experiment to measure energy density is analyzed in some detail, and
the operational positivity is clearly manifested.
  If operational energy conditions do hold for quantum fields, then the
negative energy densities predicted by theory have a will-o'-the-wisp
character: any local attempt to verify a total negative energy density will be
self-defeating on account of quantum measurement difficulties. Similarly,
attempts to drive exotic effects (wormholes, violations of the second law,
etc.) by such densities may be defeated by quantum measurement problems. As an
example, I show that certain attempts to violate the Cosmic Censorship
principle by negative energy densities are defeated.
  These quantum measurement limitations are investigated in some detail, and
are shown to indicate that space-time cannot be adequately modeled classically
in negative energy density regimes.


title:
Comment on "Accelerated Detectors and Temperature in (Anti) de Sitter
  Spaces"

abstract:
  It is shown how the results of Deser and Levin on the response of accelerated
detectors in anti-de Sitter space can be understood from the same general
perspective as other thermality results in spacetimes with bifurcate Killing
horizons.


title:
The Back Reaction of Gravitational Perturbations and Applications in
  Cosmology

abstract:
  We study the back reaction of cosmological perturbations on the evolution of
the universe. The object usually employed to describe the back reaction of
perturbations is called the effective energy-momentum tensor (EEMT) of
cosmological perturbations. In this formulation, the problem of the gauge
dependence of the EEMT must be tackled. We advance beyond traditional results
that involve only high frequency perturbations in vacuo, and formulate the back
reaction problem in a gauge invariant manner for completely generic
perturbations. We give a quick proof that the EEMT for high-frequency
perturbations is gauge invariant which greatly simplifies the pioneering
approach by Isaacson. As applications we analyze the back reaction of
gravitational waves and scalar metric fluctuations in
Friedmann-Robertson-Walker background spacetimes. We investigate in particular
back reaction effects during inflation in the Chaotic scenario. Fluctuations
with a wavelength much bigger than the Hubble radius during inflation
contribute a negative energy density, and in that case back reaction
counteracts any pre-existing cosmological constant. Finally, we set up the
equations of motion for the back reaction on the geometry and on the matter,
and show how they are perfectly consistent with the Bianchi identities and the
continuity equations.


title: Classical and Quantum Anisotropic Wormholes in Pure General Relativity

abstract:
  In the homogeneous and isotropic Friedmann-Robertson-Walker minisuperspace
model, it is known that there are no Euclidean wormhole solutions in the pure
gravity system. Here it is demonstrated explicitly that in Taub cosmology,
which is one of the simplest anisotropic cosmology models, wormhole solutions
do exist in pure general relativity in both classical and quantum contexts.


title: Skeletonizations of Phase Space Paths

abstract:
  Construction of skeletonized path integrals for a particle moving on a curved
spatial manifold is considered. As shown by DeWitt, Kuchar and others, while
the skeletonized configuration space action can be written unambiguously as a
sum of Hamilton principal functions, different choices of the measure will lead
to different Schrodinger equations. On the other hand, the Liouville measure
provides a unique measure for a skeletonized phase space path integral, but
there is a corresponding ambiguity in the skeletonization of a path through
phase space. A family of skeletonization rules described by Kuchar and referred
to here as geodesic interpolation is discussed, and shown to behave poorly
under the involution process, wherein intermediate points are removed by
extremization of the skeletonized action. A new skeletonization rule, tangent
interpolation, is defined and shown to possess the desired involution
properties.


title: Spin Foam Models

abstract:
  While the use of spin networks has greatly improved our understanding of the
kinematical aspects of quantum gravity, the dynamical aspects remain obscure.
To address this problem, we define the concept of a `spin foam' going from one
spin network to another. Just as a spin network is a graph with edges labeled
by representations and vertices labeled by intertwining operators, a spin foam
is a 2-dimensional complex with faces labeled by representations and edges
labeled by intertwining operators. Spin foams arise naturally as
higher-dimensional analogs of Feynman diagrams in quantum gravity and other
gauge theories in the continuum, as well as in lattice gauge theory. When
formulated as a `spin foam model', such a theory consists of a rule for
computing amplitudes from spin foam vertices, faces, and edges. The product of
these amplitudes gives the amplitude for the spin foam, and the transition
amplitude between spin networks is given as a sum over spin foams. After
reviewing how spin networks describe `quantum 3-geometries', we describe how
spin foams describe `quantum 4-geometries'. We conclude by presenting a spin
foam model of 4-dimensional Euclidean quantum gravity, closely related to the
state sum model of Barrett and Crane, but not assuming the presence of an
underlying spacetime manifold.


title: Normal frames and the validity of the equivalence principle

abstract:
  We investigate the validity of the equivalence principle along paths in
gravitational theories based on derivations of the tensor algebra over a
differentiable manifold. We prove the existence of local bases, called normal,
in which the components of the derivations vanish along arbitrary paths. All
such bases are explicitly described. The holonomicity of the normal bases is
considered. The results obtained are applied to the important case of linear
connections and their relationship with the equivalence principle is described.
In particular, any gravitational theory based on tensor derivations which obeys
the equivalence principle along all paths, must be based on a linear
connection.


title: Background Geometry in Gauge Gravitation Theory

abstract:
  Dirac fermion fields are responsible for spontaneous symmetry breaking in
gauge gravitation theory because the spin structure associated with a tetrad
field is not preserved under general covariant transformations. Two solutions
of this problem can be suggested. (i) There exists the universal spin structure
$S\to X$ such that any spin structure $S^h\to X$ associated with a tetrad field
$h$ is a subbundle of the bundle $S\to X$. In this model, gravitational fields
correspond to different tetrad (or metric) fields. (ii) A background tetrad
field $h$ and the associated spin structure $S^h$ are fixed, while
gravitational fields are identified with additional tensor fields $q^\la{}_\m$
describing deviations $\wt h^\la_a=q^\la{}_\m h^\m_a$ of $h$. One can think of
$\wt h$ as being effective tetrad fields. We show that there exist gauge
transformations which keep the background tetrad field $h$ and act on the
effective fields by the general covariant transformation law. We come to
Logunov's Relativistic Theory of Gravity generalized to dynamic connections and
fermion fields.


title: Non-Abelian Black Holes in Brans-Dicke Theory

abstract:
  We find a black hole solution with non-Abelian field in Brans-Dicke theory.
It is an extension of non-Abelian black hole in general relativity. We discuss
two non-Abelian fields: "SU(2)" Yang-Mills field with a mass (Proca field) and
the SU(2)$\times$SU(2) Skyrme field. In both cases, as in general relativity,
there are two branches of solutions, i.e., two black hole solutions with the
same horizon radius. Masses of both black holes are always smaller than those
in general relativity. A cusp structure in the mass-horizon radius
($M_{g}$-$r_{h}$) diagram, which is a typical symptom of stability change in
catastrophe theory, does not appear in the Brans-Dicke frame but is found in
the Einstein conformal frame. This suggests that catastrophe theory may be
simply applied for a stability analysis as it is if we use the variables in the
Einstein frame. We also discuss the effects of the Brans-Dicke scalar field on
black hole structure.


title: On the Stability of Real Scalar Boson Stars

abstract:
  We discuss spherically symmetric static solutions of the
Einstein-Klein-Gordon equations for a real scalar field with a mass and a
quartic self-interaction term. As for the massless case the solutions have a
naked singularity at the origin. However, linear stability analysis shows that
these solutions as well as the massless ones are dynamically unstable.


title: Topology change from Kaluza-Klein dimensions

abstract:
  In this letter we show that in a Kaluza-Klein framework we can have arbitrary
topology change between the macroscopic (i.e. noncompactified) spacelike
3-hypersurfaces. This is achieved by using the compactified dimensions as a
catalyser for topology change. In the case of odd-dimensional spacetimes (such
as the 11-dimensional M-theory) this is always possible. In the
even-dimensional case, a sufficient condition is the existence of a closed,
odd-dimensional manifold as a factor (such as S^1, S^3) in the Kaluza-Klein
sector. Since one of the most common manifolds used for compactification is the
torus T^k = S^1 \times ... \times S^1, in this case we can again induce an
arbitrary topology change on the 3-hypersurfaces.


title:
On the Constant that Fixes the Area Spectrum in Canonical Quantum
  Gravity

abstract:
  The formula for the area eigenvalues that was obtained by many authors within
the approach known as loop quantum gravity states that each edge of a spin
network contributes an area proportional to sqrt{j(j+1)} times Planck length
squared to any surface it transversely intersects. However, some confusion
exists in the literature as to a value of the proportionality coefficient. The
purpose of this rather technical note is to fix this coefficient. We present a
calculation which shows that in a sector of quantum theory based on the
connection A=Gamma-gamma*K, where Gamma is the spin connection compatible with
the triad field, K is the extrinsic curvature and gamma is Immirzi parameter,
the value of the multiplicative factor is 8*pi*gamma. In other words, each edge
of a spin network contributes an area 8*pi*gamma*l_p^2*sqrt{j(j+1)} to any
surface it transversely intersects.


title: From inflation to a zero cosmological constant phase without fine tuning

abstract:
  We show that it is possible to obtain inflation and also solve the
cosmological constant problem. The theory is invariant under changes of the
Lagrangian density $L$ to $L+const$. Then the constant part of a scalar field
potential $V$ cannot be responsible for inflation. However, we show that
inflation can be driven by a condensate of a four index field strength. A
constraint appears which correlates this condensate to $V$. After a conformal
transformation, the equations are the standard GR equations with an effective
scalar field potential $V_{eff}$ which has generally an absolute minimum
$V_{eff}=0$ independently of $V$ and without fine tuning. We also show that,
after inflation, the usual reheating phase scenario (from oscillations around
the absolute minimum) is possible.


title: Deviation of geodesics in FLRW spacetime geometries

abstract:
  The geodesic deviation equation (`GDE') provides an elegant tool to
investigate the timelike, null and spacelike structure of spacetime geometries.
Here we employ the GDE to review these structures within the
Friedmann--Lema\^{\i}tre--Robertson--Walker (`FLRW') models, where we assume
the sources to be given by a non-interacting mixture of incoherent matter and
radiation, and we also take a non-zero cosmological constant into account. For
each causal case we present examples of solutions to the GDE and we discuss the
interpretation of the related first integrals. The de Sitter spacetime geometry
is treated separately.


title: On the Entropy and the Density Matrix of Cosmological Perturbations

abstract:
  We look at the transition to the semiclassical behaviour and the decoherence
process for the inhomogeneous perturbations in the inflationary universe. Two
different decoherence mechanisms appear: one dynamical, accompanied with a
negligible, if at all, entropy gain, and the other, effectively irreversible
dephasing, due to a rapid variation in time of the off-diagonal density matrix
elements in the post-inflationary epoch. We thus settle the discrepancies in
the entropy content of perturbations evaluated by different authors.


title:
The origin of the area law of the entropy of a quantum field in a black
  hole

abstract:
  It is shown that that the area law for the entropy of a quantum field in the
Schwarzschild black hole is due to the quantum statistics. The entropies for
one particle, a Boltzmann gas, a quantum mechanical gas obeying Bose-Einstein
or Fermi-Dirac statistics, and a quantum field in the Schwarzschild black hole
are calculated using the microcanonical ensemble approach and the brick wall
method. The area law holds only when the effect of quantum statistics is
dominated.


title: The Cavendish Experiment in General Relativity

abstract:
  Solutions of Einstein's equations are discussed in which the ``gravitational
force" is balanced by an electrical force, and which can serve as models for
the Cavendish experiment.


title: Geometric Bounds in Spherically Symmetric General Relativity

abstract:
  We exploit an arbitrary extrinsic time foliation of spacetime to solve the
constraints in spherically symmetric general relativity. Among such foliations
there is a one parameter family, linear and homogeneous in the extrinsic
curvature, which permit the momentum constraint to be solved exactly. This
family includes, as special cases, the extrinsic time gauges that have been
exploited in the past. These foliations have the property that the extrinsic
curvature is spacelike with respect to the the spherically symmetric superspace
metric. What is remarkable is that the linearity can be relaxed at no essential
extra cost which permits us to isolate a large non - pathological dense subset
of all extrinsic time foliations. We identify properties of solutions which are
independent of the particular foliation within this subset. When the geometry
is regular, we can place spatially invariant numerical bounds on the values of
both the spatial and the temporal gradients of the scalar areal radius, $R$.
These bounds are entirely independent of the particular gauge and of the
magnitude of the sources. When singularities occur, we demonstrate that the
geometry behaves in a universal way in the neighborhood of the singularity.


title:
Necessary Conditions for Apparent Horizons and Singularities in
  Spherically Symmetric Initial Data

abstract:
  We establish necessary conditions for the appearance of both apparent
horizons and singularities in the initial data of spherically symmetric general
relativity when spacetime is foliated extrinsically. When the dominant energy
condition is satisfied these conditions assume a particularly simple form. Let
$\rho_{Max}$ be the maximum value of the energy density and $\ell$ the radial
measure of its support. If $\rho_{Max}\ell^2$ is bounded from above by some
numerical constant, the initial data cannot possess an apparent horizon. This
constant does not depend sensitively on the gauge. An analogous inequality is
obtained for singularities with some larger constant. The derivation exploits
Poincar\'e type inequalities to bound integrals over certain spatial scalars. A
novel approach to the construction of analogous necessary conditions for
general initial data is suggested.


title:
Sufficient Conditions for Apparent Horizons in Spherically Symmetric
  Initial Data

abstract:
  We establish sufficient conditions for the appearance of apparent horizons in
spherically symmetric initial data when spacetime is foliated extrinsically.
Let $M$ and $P$ be respectively the total material energy and the total
material current contained in some ball of radius $\ell$. Suppose that the
dominant energy condition is satisfied. We show that if $M- P \ge \ell$ then
the region must possess a future apparent horizon for some non -trivial closed
subset of such gauges. The same inequality holds on a larger subset of gauges
but with a larger constant of proportionality which depends weakly on the
gauge. This work extends substantially both our joint work on moment of time
symmetry initial data as well as the work of Bizon, Malec and \'O Murchadha on
a maximal slice.


title:
Spaces with torsion from embedding and the special role of autoparallel
  trajectories

abstract:
  As a contribution to the ongoing discussion of trajectories of spinless
particles in spaces with torsion we show that the geometry of such spaces can
be induced by embedding their curves in a euclidean space without torsion.
Technically speaking, we define the tangent (velocity) space of the embedded
space imposing non-holonomic constraints upon the tangent space of the
embedding space. Parallel transport in the embedded space is determined as an
induced parallel transport on the surface of constraints. Gauss' principle of
least constraint is used to show that autoparallels realize a constrained
motion that has a minimal deviation from the free, unconstrained motion, this
being a mathematical expression of the principle of inertia.


title: Darboux coordinates for (first order) tetrad gravity

abstract:
  The Hamiltonian form of the Hilbert action in the first order tetrad
formalism is examined. We perform a non-linear field redefinition of the
canonical variables isolating the part of the spin connection which is
canonically conjugate to the tetrad. The geometrical meaning of the constraints
written in these new variables is examined.


abstract:
  Gravitational field of a stationary circular cosmic string loop has been
studied in the context of full nonlinear Einstein's theory of gravity. It has
been assumed that the radial and tangential stresses of the loop are equal to
the energy density of the string loop. An exact solution for the system has
been presented which has a singularity at a finite distance from the axis,but
is regular for any other distances from the axis of the loop.


title: Classification of multidimensional inflationary models

abstract:
  We define under which circumstances two multi-warped product spacetimes can
be considered equivalent and then we classify the spaces of constant curvature
in the Euclidean and Lorentzian signature. For dimension D=2, we get
essentially twelve representations, for D=3 exactly eighteen. More general, for
every even D, 5D+2 cases exist, whereas for every odd D, 5D+3 cases exist. For
every D, exactly one half of them has the Euclidean signature. Our definition
is well suited for the discussion of multidimensional cosmological models, and
our results give a simple algorithm to decide whether a given metric represents
the inflationary de Sitter spacetime (in unusual coordinates) or not.