title: Spectral Boundary Conditions in One-Loop Quantum Cosmology

abstract:
  For fermionic fields on a compact Riemannian manifold with boundary one has a
choice between local and non-local (spectral) boundary conditions. The one-loop
prefactor in the Hartle-Hawking amplitude in quantum cosmology can then be
studied using the generalized Riemann zeta-function formed from the squared
eigenvalues of the four-dimensional fermionic operators. For a massless
Majorana spin-1/2 field, the spectral conditions involve setting to zero half
of the fermionic field on the boundary, corresponding to harmonics of the
intrinsic three-dimensional Dirac operator on the boundary with positive
eigenvalues. Remarkably, a detailed calculation for the case of a flat
background bounded by a three-sphere yields the same value zeta(0)=11/360 as
was found previously by the authors using local boundary conditions. A similar
calculation for a spin-3/2 field, working only with physical degrees of freedom
(and, hence, excluding gauge and ghost modes, which contribute to the full
Becchi-Rouet-Stora-Tyutin-invariant amplitude), again gives a value
zeta(0)=-289/360 equal to that for the natural local boundary conditions.


title: Self Excitation of the Tunneling Scalar Field in False Vacuum Decay

abstract:
  A method to determine the quantum state of a scalar field after
$O(4)$-symmetric bubble nucleation has been developed recently. The method has
an advantage that it concisely gives us a clear picture of the resultant
quantum state. In particular, one may interpret the excitations as a particle
creation phenomenon just as in the case of particle creation in curved
spacetime. As an application, we investigate in detail the spectrum of quantum
excitations of the tunneling field when it undergoes false vacuum decay. We
consider a tunneling potential which is piece-wise quadratic, hence is simple
enough to allow us an analytical treatment. We find a strong dependence of the
excitation spectrum upon the shape of the potential on the true vacuum side. We
then discuss features of the excitation spectrum common to general tunneling
potentials not restricted to our simple model.


title: Geometric Interpretation of the Mixed Invariants of the Riemann Spinor

abstract:
  Mixed invariants are used to classify the Riemann spinor in the case of
Einstein-Maxwell fields and perfect fluids. In the Einstein-Maxwell case these
mixed invariants provide information as to the relative orientation of the
gravitational and electromagnetic principal null directions. Consideration of
the perfect fluid case leads to some results about the behaviour of the
Bel-Robinson tensor regarded as a quartic form on unit timelike vectors.


title: Exact quantum state for N=1 supergravity

abstract:
  For N=1 supergravity in 3+1 dimensions we determine the graded algebra of the
quantized Lorentz generators, supersymmetry generators, and diffeo-morphism and
Hamiltonian generators and find that, at least formally, it closes in the
chosen operator ordering. Following our recent conjecture and generalizing an
ansatz for Bianchi-type models we proposed earlier we find an explicit exact
quantum solution of all constraints in the metric representation.


title: Remarks on the formation of black holes in non-symmetric gravity

abstract:
  In a recent paper, we discussed the formation of black holes in non-symmetric
gravity. That paper was then criticized by Cornish and Moffat. In the present
paper, we address the arguments raised by Cornish and Moffat. In summary, we do
not see any reason to doubt the validity of our former conclusions.


title: Limits on Kaluza-Klein Models from COBE Results

abstract:
  The large-angular-scale anisotropy of the cosmic microwave background
radiation in multidimensional cosmological models (Kaluza-Klein models) is
studied. Limits on parameters of the models imposed by the experimental data
are obtained. It is shown that in principle there is a room for Kaluza-Klein
models as possible candidates for the description of the Early Universe.
However, the obtained limits are very restrictive and none of the concrete
models, analyzed in the article, satisfy them.


title: Explicit Global Coordinates for Schwarzschild and Reissner-Nordstroem

abstract:
  We construct coordinate systems that cover all of the Reissner-Nordstroem
solution with m>|q| and m=|q|, respectively. This is possible by means of
elementary analytical functions. The limit of vanishing charge q provides an
alternative to Kruskal which, to our mind, is more explicit and simpler. The
main tool for finding these global charts is the description of highly
symmetrical metrics by two-dimensional actions. Careful gauge fixing yields
global representatives of the two-dimensional theory that can be rewritten
easily as the corresponding four-dimensional line elements.


title: Dipole Perturbations of the Reissner-Nordstrom Solution: The Polar Case

abstract:
  The formalism developed by Chandrasekhar for the linear polar perturbations
of the Reissner-Nordstrom solution is generalized to include the case of dipole
(l=1) perturbations. Then, the perturbed metric coefficients and components of
the Maxwell tensor are computed.


title:
Inhomogeneous Cosmological Models with Homogeneous Inner Hypersurface
  Geometry

abstract:
  Space-times which allow a slicing into homogeneous spatial hypersurfaces
generalize the usual Bianchi models. One knows already that in these models the
Bianchi type may change with time. Here we show which of the changes really
appear. To this end we characterize the topological space whose points are the
3-dimensional oriented homogeneous Riemannian manifolds; locally isometric
manifolds are considered as same.


title: Spin-3/2 Potentials in Backgrounds with Boundary

abstract:
  This paper studies the two-spinor form of the Rarita-Schwinger potentials
subject to local boundary conditions compatible with local supersymmetry. The
massless Rarita-Schwinger field equations are studied in four-real-dimensional
Riemannian backgrounds with boundary. Gauge transformations on the potentials
are shown to be compatible with the field equations providing the background is
Ricci-flat, in agreement with previous results in the literature. However, the
preservation of boundary conditions under such gauge transformations leads to a
restriction of the gauge freedom. The recent construction by Penrose of
secondary potentials which supplement the Rarita-Schwinger potentials is then
applied. The equations for the secondary potentials, jointly with the boundary
conditions, imply that the background four-geometry is further restricted to be
totally flat. The analysis of other gauge transformations confirms that, in the
massless case, the only admissible class of Riemannian backgrounds with
boundary is totally flat.


title: Twistors in Conformally Flat Einstein Four-Manifolds

abstract:
  This paper studies the two-component spinor form of massive spin-3/2
potentials in conformally flat Einstein four-manifolds. Following earlier work
in the literature, a non-vanishing cosmological constant makes it necessary to
introduce a supercovariant derivative operator. The analysis of supergauge
transformations of primary and secondary potentials for spin 3/2 shows that the
gauge freedom for massive spin-3/2 potentials is generated by solutions of the
supertwistor equations. The supercovariant form of a partial connection on a
non-linear bundle is then obtained, and the basic equation of massive secondary
potentials is shown to be the integrability condition on super beta-surfaces of
a differential operator on a vector bundle of rank three. Moreover, in the
presence of boundaries, a simple algebraic relation among some spinor fields is
found to ensure the gauge invariance of locally supersymmetric boundary
conditions relevant for quantum cosmology and supergravity.


title: The Equivalence Principle and the Moon

abstract:
  The perturbation of the lunar motion caused by a hypothetical violation of
the equivalence principle is analytically worked out in terms of power series
\`a la Hill-Brown. The interaction with the quadrupolar tide is found to
amplify the leading order term in the synodic range oscillation by more than
62\%. Confirming a recent suggestion of Nordtvedt, we find that this
amplification has a pole singularity for an orbit beyond the lunar orbit. This
singularity is shown to correspond to the critical prograde orbit beyond which,
as found by H\'enon, Hill's periodic orbit becomes exponentially unstable. It
is suggested that ranging between prograde and retrograde orbits around outer
planets might provide future high precision orbital tests of the equivalence
principle. It is argued that, within the context of string-derived
non-Einsteinian theories, the theoretical significance of orbital tests of the
universality of free fall is to measure the basic coupling strength of some
scalar field through composition-dependent effects. Present Lunar Laser Ranging
data yield the value $\bar{\gamma} = (-1.2\pm 1.7) \times 10^{-7}$ for the
effective Eddington parameter $\bar{\gamma} \equiv \gamma -1$ measuring this
coupling strength.


title:
Generators of Internal Lorentz Transformations and of General Affine
  Coordinate Transformations in Teleparallel Theory of (2+1)-Dimensional
  Gravity --- Cases with Static Circularly Symmetric Space-Times---

abstract:
  In a teleparallel theory of (2+1)-dimensional gravity developed in a previous
paper, we examine generators of internal Lorentz transformations and of general
affine coordinate transformations for static circularly symmetric exact
solutions of gravitational field equation. The \lq \lq spin" angular momentum,
the energy-momentum and the \lq \lq extended orbital angular momentum" are
explicitly given for each solution. Also, we give a critical comment on Deser's
claim that neither momentum nor boosts are definable for finite energy
solutions of three-dimensional Einstein gravity.


title: Predictions from Quantum Cosmology

abstract:
  After reviewing the general ideas of quantum cosmology (Wheeler-DeWitt
equation, boundary conditions, interpretation of $\psi$), I discuss how these
ideas can be tested observationally. Observational predictions differ for
different choices of boundary conditions. With tunneling boundary conditions,
$\psi$ favors initial states that lead to inflation, while with Hartle-Hawking
boundary conditions it does not. This difficulty of the Hartle-Hawking wave
function becomes particularly severe if the role of `inflatons' is played by
the moduli fields of superstring theories. In models where the constants of
Nature can take more than one set of values, $\psi$ can also determine the
probability distribution for the constants. This can be done with the aid of
the `principle of mediocrity' which asserts that we are a `typical'
civilization in the ensemble of universes described by $\psi$. The resulting
distribution favors inflation with a very flat potential, thermalization and
baryogenesis at electroweak scale, a non-negligible cosmological constant, and
density fluctuations seeded either by topological defects, or by quantum
fluctuations in models like hybrid inflation (as long as these features are
consistent with the allowed values of the constants).


title: Aspects of Analyticity (Lectures held at Kazan Summer School)

abstract:
  CONTENTS:
  1 Introduction
  2 Analytic Manifolds and Analytic Continuation of
  Metrics
  3 Walker's Spacetimes and their Maximal Extension
  4 Global Structure of de Sitter and Reissner-Nordstr\"om-de Sitter Cosmos
  4.1 Special Cases
  4.2 Collapsing Dust
  5 Euclidean Metrics
  6 Physical Interpretation of Euclidean Solutions, and a remark about the
  Gravitational Action
  6.1 Thermal Interpretation
  6.2 Tunneling Interpretation
  7 The Multi-Black-Hole Solutions
  7.1 Merging Black Holes
  7.2 Continuing Beyond the Horizons
  8 Naked Singularities?
  References


title: Cauchy Problem for Gott Spacetime

abstract:
  Gott recently has constructed a spacetime modeled by two infinitely long,
parallel cosmic strings which pass and gravitationally interact with each
other. For large enough velocity, the spacetime will contain closed timelike
curves. An explicit construction of the solution for a scalar field is
presented in detail and a proof for the existence of such a solution is given
for initial data satisfying conditions on an asymptotically null partial Cauchy
surface.
  Solutions to smooth operators on the covering space are invariant under the
isometry are shown to be pull back of solutions of the associated operator on
the base space.
  Projection maps and translation operators for the covering space are
developed for the spacetime, and explicit expressions for the projection
operator and the isometry group of the covering space are given. It is shown
that the Gott spacetime defined is a quotient space of Minkowski space by the
discrete isometry subgroup of self-equivalences of the projection map.


title: Segre Types of Symmetric Two-tensors in n-Dimensional Spacetimes

abstract:
  Three propositions about Jordan matrices are proved and applied to
algebraically classify the Ricci tensor in n-dimensional Kaluza-Klein-type
spacetimes. We show that the possible Segre types are [1,1...1], [21...1],
[31\ldots 1], [z\bar{z}1...1] and degeneracies thereof. A set of canonical
forms for the Segre types is obtained in terms of semi-null bases of vectors.


title: On a Quasi-Local Energy Outside the Cosmological Horizon

abstract:
  We investigate a quasi-local energy naturally introduced by Kodama's
prescription for a spherically symmetric space-time with a positive
cosmological constant $\Lambda$. We find that this quasi-local energy is well
behaved inside a cosmological horizon. However, when there is a scalar field
with a long enough Compton wavelength, the quasi-local energy diverges in the
course of its time evolution outside the cosmological horizon. This means that
the quasi-local energy has a meaning only inside the cosmological horizon.


title: Particle Interpretations and Green Functions for a Free Scalar Field

abstract:
  The formalism of Ashtekar and Magnon \cite{AshtekarMagnon:1975} for the
definition of particles in quantum field theory in curved spacetime is further
developed. The relation between basic objects of this formalism (e.g., the
complex structure) and different Green functions is found. It allows one to
derive composition laws for Green functions. The relation of two definitions of
particles is reformulated in the formalism and the base-independent Bogoljubov
transformation is expressed using quantities which are derivable directly from
the ``in-out'' Green function.


title: Sensible Quantum Mechanics: Are Probabilities only in the Mind?

abstract:
  Quantum mechanics may be formulated as {\it Sensible Quantum Mechanics} (SQM)
so that it contains nothing probabilistic except conscious perceptions. Sets of
these perceptions can be deterministically realized with measures given by
expectation values of positive-operator-valued {\it awareness operators}.
Ratios of the measures for these sets of perceptions can be interpreted as
frequency-type probabilities for many actually existing sets. These
probabilities generally cannot be given by the ordinary quantum
``probabilities'' for a single set of alternatives. {\it Probabilism}, or
ascribing probabilities to unconscious aspects of the world, may be seen to be
an {\it aesthemamorphic myth}.


title: Aspects of Quantum Cosmology

abstract:
  Quantum mechanics may be formulated as SENSIBLE QUANTUM MECHANICS (SQM) so
that it contains nothing probabilistic, except, in a certain frequency sense,
conscious perceptions. Sets of these perceptions can be deterministically
realized with measures given by expectation values of positive-operator-valued
AWARENESS OPERATORS in a quantum state of the universe which never jumps or
collapses. Ratios of the measures for these sets of perceptions can be
interpreted as frequency-type probabilities for many actually existing sets
rather than as propensities for potentialities to be actualized, so there is
nothing indeterministic in SQM. These frequency-type probabilities generally
cannot be given by the ordinary quantum "probabilities" for a single set of
alternatives. PROBABILISM, or ascribing probabilities to unconscious aspects of
the world, may be seen to be an AESTHEMAMORPHIC MYTH. No fundamental
correlation or equivalence is postulated between different perceptions (each
being the entirety of a single conscious experience and thus not in direct
contact with any other), so SQM, a variant of Everett's "many-worlds"
framework, is a "many-perceptions" framework but not a "many-minds" framework.
Different detailed SQM theories may be tested against experienced perceptions
by the TYPICALITIES (defined herein) they predict for these perceptions. One
may adopt the CONDITIONAL AESTHEMIC PRINCIPLE: among the set of all conscious
perceptions, our perceptions are likely to be typical.


title: Heat Kernel and Loop Currents by the Generating Function Method

abstract:
  The generating function method is applied to the trace of the heat kernel and
the one-loop effective action derived from the covariant perturbation theory.
The basis of curvature invariants of second order for the heat kernel (Green
function) is built and simple rules for form factor manipulations are proposed.
The results are checked by deriving the Schwinger-DeWitt series of the heat
kernel and divergences of one-loop currents.


title: Wilsonian Black Hole Entropy in Quantum Gravity

abstract:
  Using Wilsonian procedure (renormalization group improvement) we discuss the
finite quantum corrections to black hole entropy in renormalizable theories. In
this way, the Wilsonian black hole entropy is found for GUTs (of asymptotically
free form, in particularly) and for the effective theory of conformal factor
aiming to describe quantum gravity in infrared region. The off-critical regime
(where the coupling constants are running) for effective theory of conformal
factor in quantum gravity (with or without torsion) is explicitly constructed.
The correspondent renormalization group equations for the effective couplings
are found using Schwinger-De Witt technique for the calculation of the
divergences of fourth order operator.


title: Quantum Cosmology Lectures

abstract:
  Quantum cosmology is the quantum theory of the entire universe. Although
strange at first sight, it is appropriate because (1) our world appears to be
fundamentally quantum, (2) the classical description of gravity breaks down at
singularities it would give at the beginning of the universe, and (3) our
universe has many properties that cannot be explained by a classical
description of them. A quantum state of the universe should obey certain
constraints, such as the Wheeler-DeWitt equations. One approach to interpreting
such a state is {\it Sensible Quantum Mechanics} (SQM), in which nothing is
probabilistic, except, in a certain frequency sense, conscious perceptions.
Sets of these perceptions can be deterministically realized with measures given
by expectation values of positive-operator-valued {\it awareness operators}.
These may be defined even when the quantum state itself is not normalizable,
though there still seem to be problems of divergences when one has an infinite
amount of inflation, producing infinitely large spatial volumes with presumably
infinite measures of perceptions. Ratios of the measures for sets of
perceptions (if finite) can be interpreted as frequency-type probabilities for
many actually existing sets rather than as propensities for potentialities to
be actualized, so there is nothing indeterministic in a specific SQM. One can
do a Bayesian analysis to test between different specific SQMs. One can also
make statistical predictions of what one might perceive within a specific SQM
by invoking the {\it Conditional Aesthemic Principle}: among the set of all
conscious perceptions, our perceptions are likely to be typical.


title: Many-body systems in Einstein-Maxwell-Dilaton theory

abstract:
  We study the interaction of maximally-charged dilatonic black holes at low
velocity. We compute the metric on moduli space for three extreme black holes
under a simple constraint. The Hamiltonian of the multi-black hole system of
$O(v^2)$ is also calculated for the $a=1$ and $a=1/\sqrt{3}$ cases, where $a$
is the dilaton coupling constant. The behavior of the system is discussed
qualitatively.


title: A Class of Stationary Rotating String Cosmological Models

abstract:
  We obtain a one parameter class of stationary rotating string cosmological
models of which the well-known G$\ddot o $del Universe is a particular case. By
suitably choosing the free parameter function, it is always possible to satisfy
the energy conditions. The rotation of the model hinges on the cosmological
constant which turns out to be negative.


title: String-Dust Distributions with the Kerr-NUT symmetry

abstract:
  We attempt to solve the Einstein equations for string dust and null flowing
radiation for the general axially symmetric metric, which we believe is being
done for the first time. We obtain the string-dust and radiating
generalizations of the Kerr and the NUT solutions. There also occurs an
interesting case of radiating string-dust which arises from string-dust
generalization of Vaidya's solution of a radiating star.


title: Temperatures of extremal black holes

abstract:
  The temperature of an extremal Reissner - Nordstrom black hole is not
restricted by the requirement of absence of a conical singularity. It is
demonstrated how Kruskal-like coordinates may be constructed corresponding to
any temperature whatsoever. A recently discovered stringy extremal black hole
which apparently has an infinite temperature is also shown to have its
temperature unrestricted by conical singularity arguments.


title:
Topologimeter and the problem of physical interpretation of topology
  lattice

abstract:
  The collection of all topologies on the set of three points is studied
treating the topology as quantum-like observable. It turns out to be possible
under the assumption of the asymmetry between the spaces of bra- and
ket-vectors. The analogies between the introduced topologimeter and the
Stern-Gerlach experiments are outlined.


title:
Wave Propagation in Gravitational Systems: Completeness of Quasinormal
  Modes

abstract:
  The dynamics of relativistic stars and black holes are often studied in terms
of the quasinormal modes (QNM's) of the Klein-Gordon (KG) equation with
different effective potentials $V(x)$. In this paper we present a systematic
study of the relation between the structure of the QNM's of the KG equation and
the form of $V(x)$. In particular, we determine the requirements on $V(x)$ in
order for the QNM's to form complete sets, and discuss in what sense they form
complete sets. Among other implications, this study opens up the possibility of
using QNM expansions to analyse the behavior of waves in relativistic systems,
even for systems whose QNM's do {\it not} form a complete set. For such
systems, we show that a complete set of QNM's can often be obtained by
introducing an infinitesimal change in the effective potential.


title: Wave Propagation in Gravitational Systems: Late Time Behavior

abstract:
  It is well-known that the dominant late time behavior of waves propagating on
a Schwarzschild spacetime is a power-law tail; tails for other spacetimes have
also been studied. This paper presents a systematic treatment of the tail
phenomenon for a broad class of models via a Green's function formalism and
establishes the following. (i) The tail is governed by a cut of the frequency
Green's function $\tilde G(\omega)$ along the $-$~Im~$\omega$ axis,
generalizing the Schwarzschild result. (ii) The $\omega$ dependence of the cut
is determined by the asymptotic but not the local structure of space. In
particular it is independent of the presence of a horizon, and has the same
form for the case of a star as well. (iii) Depending on the spatial
asymptotics, the late time decay is not necessarily a power law in time. The
Schwarzschild case with a power-law tail is exceptional among the class of the
potentials having a logarithmic spatial dependence. (iv) Both the amplitude and
the time dependence of the tail for a broad class of models are obtained
analytically. (v) The analytical results are in perfect agreement with
numerical calculations.


title: Dynamics of Totally Constrained Systems I. Classical Theory

abstract:
  This is the first of a series of papers in which a new formulation of quantum
theory is developed for totally constrained systems, that is, canonical systems
in which the hamiltonian is written as a linear combination of constraints
$h_\alpha$ with arbitrary coefficients. The main purpose of the present paper
is to make clear that classical dynamics of a totally constrained system is
nothing but the foliation of the constraint submanifold in phase space by the
involutive system of infinitesimal canonical transformations $Y_\alpha$
generated by the constraint functions. From this point of view it is shown that
statistical dynamics for an ensemble of a totally constrained system can be
formulated in terms of a relative distribution function without gauge fixing or
reduction. There the key role is played by the fact that the canonical measure
in phase space and the vector fields $Y_\alpha$ induce natural conservative
measures on acausal submanifolds, which are submanifolds transversal to the
dynamical foliation. Further it is shown that the structure coefficients
$c^\gamma_{\alpha\beta}$ defined by $\{h_\alpha,h_\beta\}=\sum_\gamma
c^\gamma_{\alpha\beta}h_\gamma$ should weakly commute with $h_\alpha$,
$\sum_\gamma\{h_\gamma,c^\gamma_{\alpha\beta}\}\approx0$, in order that the
description in terms of the relative distribution function is consistent. The
overall picture on the classical dynamics given in this paper provides the
basic motivation for the quantum formulation developed in the subsequent
papers.


title: Dynamics of Totally Constrained Systems II. Quantum Theory

abstract:
  In this paper a new formulation of quantum dynamics of totally constrained
systems is developed, in which physical quantities representing time are
included as observables. In this formulation the hamiltonian constraints are
imposed on a relative probability amplitude functional $\Psi$ which determines
the relative probability for each state to be observed, instead of on the state
vectors as in the conventional Dirac quantization. This leads to a foliation of
the state space by linear manifolds on each of which $\Psi$ is constant, and
dynamics is described as linear mappings among acausal subspaces which are
transversal to these linear manifolds. This is a quantum analogue of the
classical statistical dynamics of totally constrained systems developed in the
previous paper. It is shown that if the von Neumann algebra $\C$ generated by
the constant of motion is of type I, $\Psi$ can be consistently normalizable on
the acausal subspaces on which a factor subalgebra of $\C$ is represented
irreducibly, and the mappings among these acausal subspaces are conformal. How
the formulation works is illustrated by simple totally constrained systems with
a single constraint such as the parametrized quantum mechanics, a relativistic
free particle in Minkowski and curved spacetimes, and a simple minisuperspace
model. It is pointed out that the inner product of the relative probability
amplitudes induced from the original Hilbert space picks up a special
decomposition of the wave functions to the positive and the negative frequency
modes.


title: Evolving Constants of Motion

abstract:
  A critical presentation of Rovelli's ``evolving constants of motion'' is
given. Previous criticisms by Kucha\v{r} concerning the role of factor ordering
and the non-existence of observables are dealt with and shown to be unfounded.
Kucha\v{r}'s criticisms that this approach does not solve the global, multiple
choice or Hilbert space problems of time are confirmed, and new insight into
why this is so is obtained.


title: Clocks and Time

abstract:
  A general definition of a clock is proposed, and the role of clocks in
establishing temporal pre-conditions in quantum mechanical questions is
critically discussed. The different status of clocks as used by theorists
external to a system and as used by participant-observers within a system is
emphasized. It is shown that the foliation of spacetime into instants of time
is necessary to correctly interpret the readings of clocks and that clocks are
thus insufficient to reconstruct time in the absence of such a foliation.


title: Testing the Equivalence Principle by Lamb shift Energies

abstract:
  The Einstein Equivalence Principle has as one of its implications that the
non-gravitational laws of physics are those of special relativity in any local
freely-falling frame. We consider possible tests of this hypothesis for systems
whose energies are due to radiative corrections, i.e. which arise purely as a
consequence of quantum field theoretic loop effects. Specifically, we evaluate
the Lamb shift transition (as given by the energy splitting between the
$2S_{1/2}$ and $2P_{1/2}$ atomic states) within the context of violations of
local position invariance and local Lorentz invariance, as described by the $T
H \epsilon\mu$ formalism. We compute the associated red shift and time dilation
parameters, and discuss how (high-precision) measurements of these quantities
could provide new information on the validity of the equivalence principle.


title: Space-time dimension, Euclidean action and signature change

abstract:
  This talk is devoted to the problem how to compute relative nucleation
probabilities of configurations with different topology and dimension in
quantum cosmology. Assuming the semiclassical approximation, the usual formula
for the nucleation probability induced by the no-boundary wave function is
$P_{NB}\approx\exp(-I)$, where $I$ is the Euclidean action, evaluated at a
solution of the Euclidean Einstein equations with effective cosmological
constant $\Lambda$. Relative probabilities of different configurations are
usually compared at equal values of $\Lambda$. When configurations with
different dimensions are admitted (the $n$-dimensional gravitational constant
being subject to a rather mild restriction), as e.g. ${\bf S}^n$ for any $n$,
this procedure leads to the prediction that the space-time dimension tends to
be as large as possible. In this contribution, I would like to propose an
alternative scheme, namely to compare the probabilities $P_{NB}\approx\exp(-I)$
at equal values of the {\it energy} $E$, instead of the {\it energy density}
$\Lambda$. As a result, the space-time dimension settles at $n=4$. Attempts to
predict the topology of the spacelike slices lead to the candidates ${\bf S}^3$
and ${\bf S}^1\times {\bf S}^2$. Since the ''process'' of nucleation (possibly
connected with decoherence) is not well known in detail, we expect that either
{\it both} configurations may be realized with roughly equal probability, or
the {\it latter} one is favoured. Finally, we comment on the analogous
situation based on the tunneling wave function.


title: Black Hole Entropy and Renormalization

abstract:
  Using a new regulator, we examine 't Hooft's approach for evaluating black
hole entropy through a statistical-mechanical counting of states for a scalar
field propagating outside the event horizon. We find that this calculation
yields precisely the one-loop renormalization of the standard
Bekenstein-Hawking formula, $S={\Cal A}/(4G)$. Thus our result provides
evidence confirming a suggestion by Susskind and Uglum regarding black hole
entropy.


title: A Model for Stars of Interacting Bosons and Fermions

abstract:
  In this paper we introduce a current-current type interaction term in the
Lagrangian density of gravity coupled to complex scalar fields, in the presence
of a degenerated Fermi gas. For low transferred momenta such a term, which
might account for the interaction among boson and fermion constituents of
compact stellar objects, is subsequently reduced to a quadratic one in the
scalar sector. This procedure enforces the use of a complex radial field
counterpart in the equations of motion. The real and the imaginary components
of the scalar field exhibit different behaviour as the interaction increases.
The results also suggest that the Bose-Fermi system undergoes a BCS-like phase
transition for a suitable choice of the coupling constant.


title: Homogeneous 2+1 Dimensional Gravity in the Ashtekar Formulation

abstract:
  The constraint hypersurfaces defining the Witten and Ashtekar formulations
for 2+1 gravity are very different. In particular the constraint hypersurface
in the Ashtekar case is not a manifold but consists of several sectors that
intersect each other in a complicated way. The issue of how to define a
consistent dynamics in such a situation is then rather non-trivial. We discuss
this point by working out the details in a simplified (finite dimensional)
homogeneous reduction of 2+1 gravity in the Ashtekar formulation.


title: Constraints on Supergravity Chaotic Inflationary Models

abstract:
  We discuss, in the context of $N=1$ hidden sector non-minimal supergravity
chaotic inflationary models, constraints on the parameters of a polynomial
superpotential resulting from existing bounds on the reheating temperature and
on the amplitude of the primordial energy density fluctuations as inferred from
COBE. We present a specific two-parameter chaotic inflationary model which
satisfies these constraints and discuss a possible scenario for adequate baryon
asymmetry generation.


title: Dirac Operator and Eigenvalues in Riemannian Geometry

abstract:
  The aim of the lectures is to introduce first-year Ph.D. students and
research workers to the theory of the Dirac operator, spinor techniques, and
their relevance for the theory of eigenvalues in Riemannian geometry. Topics:
differential operators on manifolds, index of elliptic operators, Dirac
operator, index problem for manifolds with a boundary, index of the Dirac
operator and anomalies, spectral asymmetry and Riemannian geometry, spectral or
local boundary conditions for massless spin-1/2 fields, potentials for massless
spin-3/2 fields, conformal anomalies for massless spin-1/2 fields.


title: Mass Inflation in a Rotating Charged Black Hole

abstract:
  The structure of the Cauchy horizon of a charged rotating black hole is
analyzed under the combined effect of an ingoing and outgoing flux of
gravitational waves. In particular, by means of an axisymmetric realization of
the Ori model, the growth of the mass parameter near the Cauchy horizon is
studied in the slow rotation approximation. It is shown that the mass-parameter
inflates, while the angular momentum per unit mass deflates, but initial
deviations from spherical symmetry survive.


title: Radiative Evolution of Orbits Around a Kerr Black Hole

abstract:
  We propose a simple approach for the radiative evolution of generic orbits
around a Kerr black hole. For a scalar-field, we recover the standard results
for the evolution of the energy $E$ and the azimuthal angular momentum $L_z$ .
In addition, our method provides a closed expression for the evolution of the
Carter constant $Q$.


title: Gravitational Phase Operator and Cosmic Strings

abstract:
  A quantum equivalence principle is formulated by means of a gravitational
phase operator which is an element of the Poincare group. This is applied to
the spinning cosmic string which suggests that it may (but not necessarily)
contain gravitational torsion. A new exact solution of the Einstein-
Cartan-Sciama-Kibble equations for the gravitational field with torsion is
obtained everywhere for a cosmic string with uniform energy density, spin
density and flux. A novel effect due to the quantized gravitational field of
the cosmic string on the wave function of a particle outside the string is used
to argue that spacetime points are not meaningful in quantum gravity.


title: Electromagnetic Field in Some Anisotropic Stiff Fluid Universes

abstract:
  The electromagnetic field is studied in a family of exact solutions of the
Einstein equations whose material content is a perfect fluid with stiff
equation of state (p = $\epsilon $ ). The field equations are solved exactly
for several members of the family.


title: Cosmic Strings from N=2, D=5 Supergravity

abstract:
  Exact solutions of N=2 supergravity in five dimensions are found in the
metric with cylindrical symmetry, a particular case corresponds to the exterior
of a cosmic string.


title: Quailocal Formalism for Dilaton Gravity with Yang-Mills Fields

abstract:
  We present a quasilocal formalism, based on the one proposed by Brown and
York, for dilaton gravity with Yang-Mills fields. For solutions possessing
sufficient symmetry, we define conserved quantities such as mass, angular
momentum, and charge. We also present a micro-canonical action and use it to
arrive at a quasilocal version of the first law of thermodynamics for static
systems containing a black hole.


title: One-loop effective potential for SO(10) GUT theories in de Sitter space

abstract:
  Zeta-function regularization is applied to evaluate the one-loop effective
potential for SO(10) grand-unified theories in de Sitter cosmologies. When the
Higgs scalar field belongs to the 210-dimensional irreducible representation of
SO(10), attention is focused on the mass matrix relevant for the
SU(3)xSU(2)xU(1) symmetry-breaking direction, to agree with low-energy
phenomenology of the particle-physics standard model. The analysis is
restricted to those values of the tree-level-potential parameters for which the
absolute minima of the classical potential have been evaluated. As shown in the
recent literature, such minima turn out to be SO(6)xSO(4)- or
SU(3)xSU(2)xSU(2)xU(1)-invariant. Electroweak phenomenology is more naturally
derived, however, from the former minima. Hence the values of the parameters
leading to the alternative set of minima have been discarded. Within this
framework, flat-space limit and general form of the one-loop effective
potential are studied in detail by using analytic and numerical methods. It
turns out that, as far as the absolute-minimum direction is concerned, the
flat-space limit of the one-loop calculation about a de Sitter background does
not change the results previously obtained in the literature, where the
tree-level potential in flat space-time was studied. Moreover, when curvature
effects are no longer negligible in the one-loop potential, it is found that
the early universe remains bound to reach only the SO(6)xSO(4) absolute
minimum.


title: The Choptuik spacetime as an eigenvalue problem

abstract:
  By fine-tuning generic Cauchy data, critical phenomena have recently been
discovered in the black hole/no black hole "phase transition" of various
gravitating systems. For the spherisymmetric real scalar field system, we find
the "critical" spacetime separating the two phases by demanding discrete
scale-invariance, analyticity, and an additional reflection-type symmetry. The
resulting nonlinear hyperbolic boundary value problem, with the rescaling
factor Delta as the eigenvalue, is solved numerically by relaxation. We find
Delta = 3.4439 +/- 0.0004.


title:
Global Extensions of Spacetimes Describing Asymptotic Final States of
  Black Holes

abstract:
  We consider a globally hyperbolic, stationary spacetime containing a black
hole but no white hole. We assume, further, that the event horizon, $\tn$, of
the black hole is a Killing horizon with compact cross-sections. We prove that
if surface gravity is non-zero constant throughout the horizon one can {\it
globally} extend such a spacetime so that the image of $\cal N$ is a proper
subset of a regular bifurcate Killing horizon in the enlarged spacetime. The
necessary and sufficient conditions are given for the extendibility of matter
fields to the enlarged spacetime. These conditions are automatically satisfied
if the spacetime is static (and, hence ``$t$"-reflection symmetric) or
stationary-axisymmetric with ``$t-\phi$" reflection isometry and the matter
fields respect the reflection isometry. In addition, we prove that a necessary
and sufficient condition for the constancy of the surface gravity on a Killing
horizon is that the exterior derivative of the twist of the horizon Killing
field vanish on the horizon. As a corollary of this, we recover a result of
Carter that constancy of surface gravity holds for any black hole which is
static or stationary- axisymmetric with the ``$t-\phi$" reflection isometry. No
use of Einstein's equation is made in obtaining any of the above results. Taken
together, these results support the view that any spacetime representing the
asymptotic final state of a black hole formed by gravitational collapse may be
assumed to possess a bifurcate Killing horizon or a Killing horizon with
vanishing surface gravity.


title: On singular solutions in multidimensional gravity

abstract:
  It is proved that the Riemann tensor squared is divergent as $\tau \ra 0$ for
a wide class of cosmological metrics with non-exceptional Kasner-like behaviour
of scale factors as $\tau \ra 0$, where $\tau$ is synchronous time. Using this
result it is shown that any non-trivial generalization of the
spherically-symmetric Tangherlini solution to the case of $n$ Ricci-flat
internal spaces \cite{FIM} has a divergent Riemann tensor squared as $R \ra
R_0$, where $R_0$ is parameter of length of the solution. Multitemporal naked
singularities are also considered.


title: Quantum Measure Theory and its Interpretation

abstract:
  We propose a realistic, spacetime interpretation of quantum theory in which
reality constitutes a *single* history obeying a "law of motion" that makes
definite, but incomplete, predictions about its behavior. We associate a
"quantum measure" |S| to the set S of histories, and point out that |S|
fulfills a sum rule generalizing that of classical probability theory. We
interpret |S| as a "propensity", making this precise by stating a criterion for
|S|=0 to imply "preclusion" (meaning that the true history will not lie in S).
The criterion involves triads of correlated events, and in application to
electron-electron scattering, for example, it yields definite predictions about
the electron trajectories themselves, independently of any measuring devices
which might or might not be present. (So we can give an objective account of
measurements.) Two unfinished aspects of the interpretation involve
*conditonal* preclusion (which apparently requires a notion of coarse-graining
for its formulation) and the need to "locate spacetime regions in advance"
without the aid of a fixed background metric (which can be achieved in the
context of conditional preclusion via a construction which makes sense both in
continuum gravity and in the discrete setting of causal set theory).


title:
Time and Entropy from Semi-classical Tunneling of the Cosmological Scale
  Function

abstract:
  Two major apparently unrelated problems, that of the origin of time in the
universe associated with quantum gravity and to the entropy in de Sitter
cosmological models, are found to have their origin in a single physical
phenomenon: the semi-classical tunneling through a classically forbidden region
of the cosmological scale function. In this region there is a mixing of the
states of quantum matter and those of the semi-classical gravity which produces
a thermal mixture of the matter states and hence an "entropy"; this same mixing
effect brings about the conversion of a parametric time variable into a
physical intrinsic time.


title: A model universe with variable dimension: Expansion as decrumpling

abstract:
  We propose a model universe, in which the dimension of the space is a
continuous variable, which can take any real positive number. The dynamics
leads to a model in which the universe has no singularity. The difference
between our model and the standard Friedman-Robertson-Walker models become
effective for times much before the presently accepted age of the universe.


title:
Existence of maximal hypersurfaces in some spherically symmetric
  spacetimes

abstract:
  We prove that the maximal development of any spherically symmetric spacetime
with collisionless matter (obeying the Vlasov equation) or a massless scalar
field (obeying the massless wave equation) and possessing a constant mean
curvature $S^1 \times S^2$ Cauchy surface also contains a maximal Cauchy
surface. Combining this with previous results establishes that the spacetime
can be foliated by constant mean curvature Cauchy surfaces with the mean
curvature taking on all real values, thereby showing that these spacetimes
satisfy the closed-universe recollapse conjecture. A key element of the proof,
of interest in itself, is a bound for the volume of any Cauchy surface $\Sigma$
in any spacetime satisfying the timelike convergence condition in terms of the
volume and mean curvature of a fixed Cauchy surface $\Sigma_0$ and the maximal
distance between $\Sigma$ and $\Sigma_0$. In particular, this shows that any
globally hyperbolic spacetime having a finite lifetime and obeying the
timelike-convergence condition cannot attain an arbitrarily large spatial
volume.


title:
Two Topics concerning Black Holes: Extremality of the Energy, Fractality
  of the Horizon

abstract:
  We treat two aspects of the physics of stationary black holes. First we prove
that the proportionality, d(energy) ~ d(area) for arbitrary perturbations
(``extended first law''), follows directly from an extremality theorem drawn
from earlier work. Second we consider quantum fluctuations in the shape of the
horizon, concluding heuristically that they exhibit a fractal character, with
order lambda fluctuations occurring on all scales lambda below M^{1/3} in
natural units.


title: A No-Go Theorem in String Cosmology

abstract:
  A no-go theorem pertaining to the graceful exit problem in Pre-Big-Bang
inflation is reviewed. It is shown that dilaton self-interactions and string
fluid sources fail to facilitate branch changing necessary to avoid
singularities. A comment on the failure of the higher genus corrections to
induce graceful exit is also included.


title:
Observation of the Final Boundary Condition: Extragalactic Background
  Radiation and the Time symmetry of the Universe

abstract:
  This paper examines an observable consequence for the diffuse extragalactic
background radiation (EGBR) of the hypothesis that if closed, our universe
possesses time symmetric boundary conditions. For simplicity, attention is
focused on optical wavelengths. The universe is modeled as closed Friedmann-
Roberston-Walker. It is shown that, over a wide range of frequencies,
electromagnetic radiation can propagate largely unabsorbed from the present
epoch into the recollapsing phase, confirming and demonstrating the generality
of results of Davies and Twamley. As a consequence, time symmetric boundary
conditions imply that the optical EGBR is at least twice that due to the
galaxies on our past light cone, and possibly considerably more. It is
therefore possible to test experimentally the notion that if our universe is
closed, it may be in a certain sense time symmetric. The lower bound on the
"excess" EGBR in a time symmetric universe is consistent with present
observations. Nevertheless, better observations and modelling may soon rule it
out entirely. In addition, many physical complications arise in attempting to
reconcile a transparent future light cone with time symmetric boundary
conditions, thereby providing further arguments against the possibility that
our universe is time symmetric.


title: Spinors, Jets, and the Einstein Equations

abstract:
  Many important features of a field theory, {\it e.g.}, conserved currents,
symplectic structures, energy-momentum tensors, {\it etc.}, arise as tensors
locally constructed from the fields and their derivatives. Such tensors are
naturally defined as geometric objects on the jet space of solutions to the
field equations. Modern results from the calculus on jet bundles can be
combined with a powerful spinor parametrization of the jet space of Einstein
metrics to unravel basic features of the Einstein equations. These techniques
have been applied to computation of generalized symmetries and ``characteristic
cohomology'' of the Einstein equations, and lead to results such as a proof of
non-existence of ``local observables'' for vacuum spacetimes and a uniqueness
theorem for the gravitational symplectic structure.


title: From a Relativistic Point Particle to String Theory

abstract:
  Using a classical action associated to a point-particle in (1+1)-dimensions
the classical string theory is derived. In connection with this result two
aspects are clarified: First, the point particle in (1+1)-dimensions is not an
ordinary relativistic system, but rather a some kind of a relativistic top; and
second, through the quantization of such a kind of top the ordinary string
theory is not obtained, but rather a $\sigma$-model associated to a non-compact
group which may be understood as an extended string theory.


title: Non-thermal aspects of black hole radiance

abstract:
  The phenomenon of black hole thermodynamics raises several deep issues which
any proper theory of quantum gravity must confront: to what extent does the
inclusion of the back-reaction alter the thermal character of the radiation,
how can the entropy be understood from a microscopic standpoint, what is the
ultimate fate of an evaporating black hole, and is the outcome reconcilable
with unitary time evolution in quantum mechanics?
  In the first part of this thesis, we address the issue of determining what
the actual emission spectrum from a black hole is, once the gravitational field
of the emitted quanta is included in a quantum mechanical manner. To make the
problem tractable, we employ two important approximations: we quantize only the
s-wave sector of the full theory, and we consider only single particle
emission. By proceeding in the framework of a Hamiltonian path integral
description of this system, we are able to integrate out the gravitational
field, thereby obtaining an effective action depending only on the matter
degrees of freedom. This effective action can then be second quantized in terms
of new, corrected, mode solutions thus enabling the calculation of the emission
spectrum from modified Bogoliubov coefficients. The results are particularly
interesting in the case of emission from Reissner-Nordstrom black holes, since
in the extremal limit our results are dramatically different from what a naive,
and incorrect, semi-classical calculation would yield.
  The other major topic which we discuss is the dynamics of quantum fields on
background geometries which undergo quantum tunneling. An example of such a
system which has important implications for both cosmology and quantum gravity
in general, is the tunneling of a false vacuum bubble leading to the creation


title: Collapsing regions and black hole formation

abstract:
  Up to a conjecture in Riemannian geometry, we significantly strengthen a
recent theorem of Eardley by proving that a compact region in an initial data
surface that is collapsing sufficiently fast in comparison to its
surface-to-volume ratio must contain a future trapped region. In addition to
establishing this stronger result, the geometrical argument used does not
require any asymptotic or energy conditions on the initial data. It follows
that if such a region can be found in an asymptotically flat Cauchy surface of
a spacetime satisfying the null-convergence condition, the spacetime must
contain a black hole with the future trapped region therein. Further, up to
another conjecture, we prove a strengthened version of our theorem by arguing
that if a certain function (defined on the collection of compact subsets of the
initial data surface that are themselves three-dimensional manifolds with
boundary) is not strictly positive, then the initial data surface must contain
a future trapped region. As a byproduct of this work, we offer a slightly
generalized notion of a future trapped region as well as a new proof that
future trapped regions lie within the black hole region.


title: Unitary Theory of Evaporating 2D Black Holes

abstract:
  We study a manifestly unitary formulation of 2d dilaton quantum gravity based
on the reduced phase space quantization. The spacetime metric can be expanded
in a formal power series of the matter energy-momentum tensor operator. This
expansion can be used for calculating the quantum corrections to the classical
black hole metric by evaluating the expectation value of the metric operator in
an appropriate class of the physical states. When the normal ordering in the
metric operator is chosen to be with respect to Kruskal vacuum, the lowest
order semiclassical metric is exactly the one-loop effective action metric
discovered by Bose, Parker and Peleg. The corresponding semiclassical geometry
describes an evaporating black hole which ends up as a remnant. The calculation
of higher order corrections and implications for the black hole fate are
discussed.


title: Quantum Effects in Friedmann-Robertson-Walker Cosmologies

abstract:
  Electrodynamics for self-interacting scalar fields in spatially flat
Friedmann-Robertson-Walker space-times is studied. The corresponding one-loop
field equation for the expectation value of the complex scalar field in the
conformal vacuum is derived. For exponentially expanding universes, the
equations for the Bogoliubov coefficients describing the coupling of the scalar
field to gravity are solved numerically. They yield a non-local correction to
the Coleman-Weinberg effective potential which does not modify the pattern of
minima found in static de Sitter space. Such a correction contains a
dissipative term which, accounting for the decay of the classical configuration
in scalar field quanta, may be relevant for the reheating stage. The physical
meaning of the non-local term in the semiclassical field equation is
investigated by evaluating this contribution for various background field
configurations.


title:
Gravitational waves from coalescing binaries: detection strategies and
  Monte Carlo estimation of parameters

abstract:
  The paper deals with issues pertaining the detection of gravitational waves
from coalescing binaries. We introduce the application of differential geometry
to the problem of optimal detection of the `chirp signal'. We have also carried
out extensive Monte Carlo simulations to understand the errors in the
estimation of parameters of the binary system. We find that the errors are much
more than those predicted by the covariance matrix even at a high SNR of 10-15.
We also introduce the idea of using the instant of coalescence rather than the
time of arrival to determine the direction to the source.


title:
Alternative Derivation of the Correspondence Between Rindler and
  Minkowski Particles

abstract:
  We develop an alternative derivation of Unruh and Wald's seminal result that
the absorption of a Rindler particle by a detector as described by uniformly
accelerated observers corresponds to the emission of a Minkowski particle as
described by inertial observers. Actually, we present it in an inverted
version, namely, that the emission of a Minkowski particle corresponds in
general to either the emission or the absorption of a Rindler particle.


title:
Exact solutions, symmetries and quantization of two-dimensional
  higher-derivative gravity with dynamical torsion

abstract:
  We investigate two-dimensional higher derivative gravitational theories in a
Riemann-Cartan framework and obtain the most general static black hole
solutions in conformal coordinates. We also consider the hamiltonian
formulation of the theory and discuss its symmetries, showing they are
implemented by a non-linear generalizations of the 2-dimensional Poincar\'e
algebra. Finally, we discuss the quantization in the Dirac formalism.


title: Finding Apparent Horizons in Numerical Relativity

abstract:
  This paper presents a detailed discussion of the ``Newton's method''
algorithm for finding apparent horizons in 3+1 numerical relativity.
  We describe a method for computing the Jacobian matrix of the finite
differenced $H(h)$ function by symbolically differentiating the finite
difference equations, giving the Jacobian elements directly in terms of the
finite difference molecule coefficients used in computing $H(h)$. Assuming the
finite differencing scheme commutes with linearization, we show how the
Jacobian elements may be computed by first linearizing the continuum $H(h)$
equations, then finite differencing the linearized (continuum) equations.
  We find this symbolic differentiation method of computing the $H(h)$ Jacobian
to be {\em much} more efficient than the usual numerical perturbation method,
and also much easier to implement than is commonly thought.
  When solving the discrete $H(h) = 0$ equations, we find that Newton's method
generally converges very rapidly. However, if the initial guess for the horizon
position contains significant high-spatial-frequency error components, Newton's
method has a small (poor) radius of convergence. This is {\em not} an artifact
of insufficient resolution in the finite difference grid; rather, it appears to
be caused by a strong nonlinearity in the continuum $H(h)$ function for
high-spatial-frequency error components in $h$. Robust variants of Newton's
method can boost the radius of convergence by O(1) factors, but the underlying
nonlinearity remains, and appears to worsen rapidly with increasing
initial-guess-error spatial frequency.
  Using 4th~order finite differencing, we find typical accuracies for computed
horizon positions in the $10^{-5}$ range for $\Delta\theta = \frac{\pi/2}{50}$.


title: Refined Algebraic Quantization: Systems with a single constraint

abstract:
  This paper explores in some detail a recent proposal (the Rieffel
induction/refined algebraic quantization scheme) for the quantization of
constrained gauge systems. Below, the focus is on systems with a single
constraint and, in this context, on the uniqueness of the construction. While
in general the results depend heavily on the choices made for certain auxiliary
structures, an additional physical argument leads to a unique result for
typical cases. We also discuss the `superselection laws' that result from this
scheme and how their existence also depends on the choice of auxiliary
structures. Again, when these structures are chosen in a physically motivated
way, the resulting superselection laws are physically reasonable.


title: Decoherence of the Unruh Detector

abstract:
  As it is well known, the Minkowski vacuum appears thermally populated to a
quantum mechanical detector on a uniformly accelerating course. We investigate
how this thermal radiation may contribute to the classical nature of the
detector's trajectory through the criteria of decoherence. An uncertainty-type
relation is obtained for the detector involving the fluctuation in temperature,
the time of flight and the coupling to the bath.


title: Gravitational waves from coalescing compact binaries

abstract:
  This article is intended to provide a pedagogical account of issues related
to, and recent work on, gravitational waves from coalescing compact binaries
(composed of neutron stars and/or black holes). These waves are the most
promising for kilometer-size interferometric detectors such as LIGO and VIRGO.
Topics discussed include: interferometric detectors and their noise; coalescing
compact binaries and their gravitational waveforms; the technique of matched
filtering for signal detection and measurement; waveform calculations in
post-Newtonian theory and in the black-hole perturbation approach; and the
accuracy of the post-Newtonian expansion.


title:
A Causal Order for Spacetimes with $C^0$ Lorentzian Metrics: Proof of
  Compactness of the Space of Causal Curves

abstract:
  We recast the tools of ``global causal analysis'' in accord with an approach
to the subject animated by two distinctive features: a thoroughgoing reliance
on order-theoretic concepts, and a utilization of the Vietoris topology for the
space of closed subsets of a compact set. We are led to work with a new causal
relation which we call $K^+$, and in terms of it we formulate extended
definitions of concepts like causal curve and global hyperbolicity. In
particular we prove that, in a spacetime $\M$ which is free of causal cycles,
one may define a causal curve simply as a compact connected subset of $\M$
which is linearly ordered by $K^+$. Our definitions all make sense for
arbitrary $C^0$ metrics (and even for certain metrics which fail to be
invertible in places). Using this feature, we prove for a general $C^0$ metric,
the familiar theorem that the space of causal curves between any two compact
subsets of a globally hyperbolic spacetime is compact. We feel that our
approach, in addition to yielding a more general theorem, simplifies and
clarifies the reasoning involved. Our results have application in a recent
positive energy theorem, and may also prove useful in the study of topology
change. We have tried to make our treatment self-contained by including proofs
of all the facts we use which are not widely available in reference works on
topology and differential geometry.


title: Quantum Cosmology and the Structure of Inflationary Universe

abstract:
  In this review I consider several different issues related to inflation. I
will begin with the wave function of the Universe. This issue is pretty old,
but recently there were some new insights based on the theory of the
self-reproducing inflationary universe. Then we will discuss stationarity of
inflationary universe and the possibility to make predictions in the context of
quantum cosmology using stochastic approach to inflation. Returning to more
pragmatic aspects of inflationary theory, we will discuss inflationary models
with $\Omega < 1$. Finally, we will describe several aspects of the theory of
reheating of the Universe based on the effect of parametric resonance.


title:
Classical and Quantum Gravity in 1+1 Dimensions, Part I: A Unifying
  Approach

abstract:
  We provide a concise approach to generalized dilaton theories with and
without torsion and coupling to Yang-Mills fields. Transformations on the space
of fields are used to trivialize the field equations locally. In this way their
solution becomes accessible within a few lines of calculation only. In this
first of a series of papers we set the stage for a thorough global
investigation of classical and quantum aspects of more or less all available 2D
gravity-Yang-Mills models.


title: Differential Structure of Space-Time and Physical Fields

abstract:
  A physical interpretation of axioms of the differential structure of
space-time is presented. Consequences of such interpretation for cosmic
string's space-time with a scalar field are studied. It is shown that the
assumption of smoothness of the scalar field leads either to modification of
cosmic string's space-time global properties or to quantization of the deficit
of angle: $\Delta =2\pi (1-1/n)$, $n=1,2,\dots$.


title: Closure of Constraints for Plane Gravity Waves

abstract:
  The metric for gravitational plane waves has very high symmetry (two
spacelike commuting Killing vectors). For this high symmetry, a simple
renormalization of the lapse function is found which allows the constraint
algebra for canonical quantum gravity to close; also, the vector constraint has
the correct form to generate spatial diffeomorphisms. A measure is constructed
which respects the reality conditions, but does not yet respect the invariances
of the theory.


title: Quantum Mechanics at the Planck Scale

abstract:
  Usual quantum mechanics requires a fixed, background, spacetime geometry and
its associated causal structure. A generalization of the usual theory may
therefore be needed at the Planck scale for quantum theories of gravity in
which spacetime geometry is a quantum variable. The elements of generalized
quantum theory are briefly reviewed and illustrated by generalizations of usual
quantum theory that incorporate spacetime alternatives, gauge degrees of
freedom, and histories that move forward and backward in time. A generalized
quantum framework for cosmological spacetime geometry is sketched. This theory
is in fully four-dimensional form and free from the need for a fixed causal
structure. Usual quantum mechanics is recovered as an approximation to this
more general framework that is appropriate in those situations where spacetime
geometry behaves classically.
  (Talk given at the Workshop on Physics at the Planck Scale, Puri, India,
December12-21, 1994. This talk is a precis of the author's 1992 Les Houches
Lectures: Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime,
gr-qc/9304006).


title: Scalar Field Cosmologies with Viscous Fluid

abstract:
  We investigate cosmological models with a free scalar field and a viscous
fluid. We find exact solutions for a linear and nonlinear viscosity pressure.
Both yield singular and bouncing solutions. In the first regime, a de Sitter
stage is asymptotically stable, while in the second case we find power-law
evolutions for vanishing cosmological constant.


title: Estimation of parameters of gravitational waves from coalescing binaries

abstract:
  In this paper we deal with the measurement of the parameters of the
gravitational wave signal emitted by a coalescing binary signal.
  We present the results of Monte Carlo simulations carried out for the case of
the initial LIGO, incorporating the first post-Newtonian corrections into the
waveform. Using the parameters so determined, we estimate the direction to the
source. We stress the use of the time-of-coalescence rather than the
time-of-arrival of the signal to determine the direction of the source. We show
that this can considerably reduce the errors in the determination of the
direction of the source.


title: Colliding black holes with linearized gravity

abstract:
  We give a brief summary of results and ongoing research in the application of
linearized theory to the study of black hole collisions in the limit in which
the holes start close to each other. This approximation can be a valuable tool
for comparison and code-checking of full numerical relativity computations. The
approximation works quite well for the head-on case and this is motivation to
pursue its use in other more interesting contexts. We summarize current efforts
towards establishing the domain of validity of the approximation and its use in
generation and evolution of initial data for more interesting physical cases.


title: Hawking Radiation and Unitary evolution

abstract:
  We find a family of exact solutions to the semi-classical equations
(including back-reaction) of two-dimensional dilaton gravity, describing
infalling null matter that becomes outgoing and returns to infinity without
forming a black hole. When a black hole almost forms, the radiation reaching
infinity in advance of the original outgoing null matter has the properties of
Hawking radiation. The radiation reaching infinity after the null matter
consists of a brief burst of negative energy that preserves unitarity and
transfers information faster than the theoretical bound for positive energy.


title: On the Canonical Reduction of Spherically Symmetric Gravity

abstract:
  In a thorough paper Kuchar has examined the canonical reduction of the most
general action functional describing the geometrodynamics of the maximally
extended Schwarzschild geometry. This reduction yields the true degrees of
freedom for (vacuum) spherically symmetric general relativity. The essential
technical ingredient in Kuchar's analysis is a canonical transformation to a
certain chart on the gravitational phase space which features the Schwarzschild
mass parameter $M_{S}$, expressed in terms of what are essentially
Arnowitt-Deser-Misner variables, as a canonical coordinate. In this paper we
discuss the geometric interpretation of Kuchar's canonical transformation in
terms of the theory of quasilocal energy-momentum in general relativity given
by Brown and York. We find Kuchar's transformation to be a ``sphere-dependent
boost to the rest frame," where the ``rest frame'' is defined by vanishing
quasilocal momentum. Furthermore, our formalism is general enough to cover the
case of (vacuum) two-dimensional dilaton gravity. Therefore, besides reviewing
Kucha\v{r}'s original work for Schwarzschild black holes from the framework of
hyperbolic geometry, we present new results concerning the canonical reduction
of Witten-black-hole geometrodynamics.


title: How natural is a small but nonzero cosmological constant?

abstract:
  Based on our previous attempt, we propose a better way to understand a small
but nonzero cosmological constant, as indicated by a number of recent
observational studies. We re-examine the assumptions of our model of two scalar
fields, trying to explain the basic mechanism resulting in a series of
mini-inflations occuring nearly periodically with respect to $\ln t$ with $t$
the cosmic time. We also discuss how likely the solution of this type would be,
depending on the choice of the parameters.


title: The Geometry of Complex Space-Times with Torsion

abstract:
  The necessary and sufficient condition for the existence of $\alpha$-surfaces
in complex space-time manifolds with nonvanishing torsion is derived. For these
manifolds, Lie brackets of vector fields and spinor Ricci identities contain
explicitly the effects of torsion. This leads to an integrability condition for
$\alpha$-surfaces which does not involve just the self-dual Weyl spinor, as in
complex general relativity, but also the torsion spinor, in a nonlinear way,
and its covariant derivative. A similar result also holds for four-dimensional,
smooth real manifolds with a positive-definite metric. Interestingly, a
particular solution of the integrability condition is given by conformally
right-flat and right-torsion-free space-times.


title: How is a Closed String Loop like a Black Hole?

abstract:
  We demonstrate that under plausible assumptions the entropy and temperature
associated with the small oscillations on a circular loop of radius $R$ and a
black hole of mass $M=R/2G$ are identical.


title: The Effect of Boundaries in One-Loop Quantum Cosmology

abstract:
  The problem of boundary conditions in a supersymmetric theory of quantum
cosmology is studied, with application to the one-loop prefactor in the quantum
amplitude. Our background cosmological model is flat Euclidean space bounded by
a three-sphere, and our calculations are based on the generalized Riemann
zeta-function. One possible set of supersymmetric local boundary conditions
involves field strengths for spins 1, 3/2 and 2, the undifferentiated spin-1/2
field, and a mixture of Dirichlet and Neumann conditions for spin 0. In this
case the results we can obtain are: zeta(0)=7/45 for a complex scalar field,
zeta(0)=11/360 for spin 1/2, zeta(0)= -77/180 (magnetic) and 13/180 (electric)
for spin 1, and zeta(0)=112/45 for pure gravity when the linearized magnetic
curvature is vanishing on $S^3$. The zeta(0) values for gauge fields have been
obtained by working only with physical degrees of freedom. An alternative set
of boundary conditions can be motivated by studying transformation properties
under local supersymmetry; these involve Dirichlet conditions for the spin-2
and spin-1 fields, a mixture of Dirichlet and Neumann conditions for spin-0,
and local boundary conditions for the spin-1/2 field and the spin-3/2
potential. For the latter one finds: zeta(0)=-289/360. The full zeta(0) does
not vanish in extended supergravity theories, indicating that supersymmetry is
one-loop divergent in the presence of boundaries.


title: Field Theory as Free Fall

abstract:
  It is shown that the classical field equations pertaining to gravity coupled
to other bosonic fields are equivalent to a single geodesic equation,
describing the free fall of a point particle in superspace. Some implications
for quantum gravity are discussed.


title:
Non-minimally coupled complex scalar field in classical and quantum
  cosmology

abstract:
  We investigate the cosmological model with complex scalar self-interacting
inflaton field non-minimally coupled to gravity. The different geometries of
the Euclidean classically forbidden regions are represented. The instanton
solutions of the corresponding Euclidean equations of motion are found by
numerical calculations. These solutions give a rather non-trivial examples of
real tunnelling geometries. Possible interpretation of obtained results and
their connection with inflationary cosmology is discussed.


title: Dynamics of Dimensions in Factor Space Cosmology

abstract:
  We consider multidimensional cosmological models with a generalized
space-time manifold M = R x M_1 ...x M_n, composed from a finite number of
factor spaces M_i, i=1,..n. While usually each factor space M_i is considered
to be some Riemannian space of integer dimension d_i, here it is, more
generally, a fractal space, the dimension of which is a smooth function d_i(t)
of time. Hence, besides the scale factor exponents ln a_i and their
derivatives, we consider also the dimensions d_i of the factor spaces as
classical dynamical variables. The classical equation of motions and the
corresponding Wheeler-de Witt equation are set up generally, and the
qualitative behaviour of the system is discussed for some specific model with 2
factor spaces.


title: Quantization and Regularization in Perturbative Quantum Cosmology

abstract:
  Reduction to physical degrees of freedom before quantization leads to
predictions for one-loop amplitudes in quantum cosmology in the presence of
boundaries which disagree with the results obtained from Faddeev-Popov theory
and boundary-counterterms technique. However, the mode-by-mode analysis of
eigenvalue equations for gauge modes and ghost fields remains a very difficult
problem. Hence the equivalence or inequivalence of various quantization and
regularization techniques cannot be easily proved.


title: Quantization of Nonstandard Hamiltonian Systems

abstract:
  The quantization of classical theories that admit more than one Hamiltonian
description is considered. This is done from a geometrical viewpoint, both at
the quantization level (geometric quantization) and at the level of the
dynamics of the quantum theory. A spin-1/2 system is taken as an example in
which all the steps can be completed. It is shown that the geometry of the
quantum theory imposes restrictions on the physically allowed nonstandard
quantum theories.


title: On the Quantum Stability of the Time Machine

abstract:
  In a number of papers it has been claimed that the time machine are quantum
unstable, which manifests itself in the divergence of the vacuum expectation
value of the stress-energy tensor $\langle{\bf T}\rangle$ near the Cauchy
horizon. The expression for $\langle{\bf T}\rangle$ was found in these papers
on the basis of some specific approach \cite{Fro,KimT}.\par We show that this
approach is untenable in that the above expression firstly is not derived from
some more fundamental and undeniable premises, as it is claimed, but rather
postulated and secondly contains undefined terms, so that one can neither use
nor check it. As a counterexample we cite a few cases of (two-dimensional)
spacetimes containing time machines with $\langle{\bf T}\rangle$ bounded near
the Cauchy horizon.


title:
Classical and quantum geometrodynamics of 2d vacuum dilatonic black
  holes

abstract:
  We perform a canonical analysis of the system of 2d vacuum dilatonic black
holes. Our basic variables are closely tied to the spacetime geometry and we do
not make the field redefinitions which have been made by other authors. We
present a careful discssion of asymptotics in this canonical formalism.
Canonical transformations are made to variables which (on shell) have a clear
spacetime significance. We are able to deduce the location of the horizon on
the spatial slice (on shell) from the vanishing of a combination of canonical
data. The constraints dramatically simplify in terms of the new canonical
variables and quantization is easy. The physical interpretation of the variable
conjugate to the ADM mass is clarified. This work closely parallels that done
by Kucha{\v r} for the vacuum Schwarzschild black holes and is a starting point
for a similar analysis, now in progress, for the case of a massless scalar
field conformally coupled to a 2d dilatonic black hole.


title: A Euclidean Bianchi Model Based On $S^3/D_8^*$

abstract:
  We explain how the round four-sphere can be sliced along homogeneous
3~-~manifolds of topology $S^3/D_8^*$. This defines a Euclidean Bianchi type IX
model for Einstein's equations with cosmological constant. The geometric
properties of this model are investigated.


title:
A renormalization group improved non-local gravitational effective
  Lagrangian

abstract:
  Renormalization group techniques are used in order to obtain the improved
non-local gravitational effective action corresponding to any asymptotically
free GUT, up to invariants which are quadratic on the curvature. The
corresponding non-local gravitational equations are written down, both for the
case of asymptotically free GUTs and also for quantum R$^2$-gravity. The
implications of the results when obtaining the flux of vacuum radiation through
the future null infinity are briefly discussed.


title: Nuts have no hair

abstract:
  We show that the Riemannian Kerr solutions are the only Riemannian,
Ricci-flat and asymptotically flat ${\rm C}^{2}$-metrics $g_{\mu\nu}$ on a
4-dimensional complete manifold ${\cal M}$ of topology ${\rm R}^{2} \times {\rm
S}^{2}$ which have (at least) a 1-parameter group of periodic isometries with
only isolated fixed points ("nuts") and with orbits of bounded length at
infinity.


title: Precis of General Relativity

abstract:
  Omitting the motivations and historical connections, and also the detailed
calculations, I state succinctly the principles that determine the relativistic
idealization of a GPS system. These determine the results that Ashby presents
in his tutorial.


title: Boosting the Kerr-geometry into an arbitrary direction

abstract:
  We generalize previous work \cite{BaNa3} on the ultrarelativistic limit of
the Kerr-geometry by lifting the restriction on boosting along the axis of
symmetry.


title: Lattice Quantum Gravity from Stochastic 3-Geometries

abstract:
  I propose the Langevin equation for 3-geometries in the Ashtekar's formalism
to describe 4D Euclidean quantum gravity, in the sense that the corresponding
Fokker-Planck hamiltonian recovers the hamiltonian in 4D quantum gravity
exactly. The stochastic time corresponds to the Euclidean time in the gauge,
N=1 and $N^i=0$. In this approach, the time evolution in 4D quantum gravity is
understood as a stochastic process where the quantum fluctuation of ` ` triad
\rq\rq is characterized by the curvature at the one unit time step before. The
lattice regularization of 4D quantum gravity is presented in this context.


title: Fermions in Gravitation Theory

abstract:
  In gravitation theory, a fermion field must be regarded only in a pair with a
certain tetrad gravitational field. These pairs can be represented by sections
of the composite spinor bundle $S\to\Si\to X^4$ where values of gravitational
fields play the role of parameter coordinates, besides the familiar world
coordinates.


title: Averaging, renormalization group and criticality in cosmology

abstract:
  Several problems in physics, in particular the averaging problem in gravity,
can be described in a formalism derived from the real-space Renormalization
Group (RG) methods. It is shown that the RG flow is provided by the
Ricci-Hamilton equations which are thereby provided with a {\it physical}
interpretation. The connection between a manifold deformation according to
these equations and Thurston's conjecture is exhibited. The significance of
criticality which naturally appears in this framework is briefly discussed.
This article summarizes also recent work with M. Carfora. Moreover, a report on
some work in progress is given and some open issues in the averaging problem
pointed out.


title: `Faster than light' photons and rotating black holes

abstract:
  The effective action for QED in curved spacetime includes equivalence
principle violating interactions between the electromagnetic field and the
spacetime curvature. These interactions admit the possibility of superluminal
yet causal photon propagation in gravitational fields. In this paper, we extend
our analysis of photon propagation in gravitational backgrounds to the Kerr
spacetime describing a rotating black hole. The results support two general
theorems -- a polarisation sum rule and a `horizon theorem'. The implications
for the stationary limit surface bounding the ergosphere are also discussed.


title: Irrotational dust with Div H=0

abstract:
  For irrotational dust the shear tensor is consistently diagonalizable with
its covariant time derivative: $\sigma_{ab}=0=\dot{\sigma}_{ab},\; a\neq b$, if
and only if the divergence of the magnetic part of the Weyl tensor vanishes:
$div~H = 0$. We show here that in that case, the consistency of the Ricci
constraints requires that the magnetic part of the Weyl tensor itself vanishes:
$H_{ab}=0$.


title: Some Problems of Topology Change Description in the Theory of Space-Time

abstract:
  The problem of topology change description in gravitation theory is analized
in detailes. It is pointed out that in standard four-dimensional theories the
topology of space may be considered as a particular case of boundary conditions
(or constraints). Therefore, the possible changes of space topology in
(3+1)-dimensions do not admit dynamical description nor in classical nor in
quantum theories and the statements about dynamical supressing of topology
change have no sence. In the framework of multidimensional theories the space
(and space-time) may be considered as the embedded manifolds. It give the real
posibilities for the dynamical description of the topology of space or
space-time.


title: Quantum Field Theory on Certain Non-Globally Hyperbolic Spacetimes

abstract:
  We study real linear scalar field theory on two simple non-globally
hyperbolic spacetimes containing closed timelike curves within the framework
proposed by Kay for algebraic quantum field theory on non-globally hyperbolic
spacetimes. In this context, a spacetime (M,g) is said to be `F-quantum
compatible' with a field theory if it admits a *-algebra of local observables
for that theory which satisfies a locality condition known as `F-locality'.
Kay's proposal is that, in formulating algebraic quantum field theory on
$(M,g)$, F-locality should be imposed as a necessary condition on the *-algebra
of observables. The spacetimes studied are the 2- and 4-dimensional spacelike
cylinders (Minkowski space quotiented by a timelike translation). Kay has shown
that the 4-dimensional spacelike cylinder is F-quantum compatible with massless
fields. We prove that it is also F-quantum compatible with massive fields and
prove the F-quantum compatibility of the 2-dimensional spacelike cylinder with
both massive and massless fields. In each case, F-quantum compatibility is
proved by constructing a suitable F-local algebra.


title:
Evolutionary Laws, Initial Conditions, and Gauge Fixing in Constrained
  Systems

abstract:
  We describe in detail how to eliminate nonphysical degrees of freedom in the
Lagrangian and Hamiltonian formulations of a constrained system. Two important
and distinct steps in our method are the fixing of ambiguities in the dynamics
and the determination of inequivalent initial data. The Lagrangian discussion
is novel, and a proof is given that the final number of degrees of freedom in
the two formulations agrees. We give applications to reparameterization
invariant theories, where we prove that one of the constraints must be
explicitly time dependent. We illustrate our procedure with the examples of
trajectories in spacetime and with spatially homogeneous cosmological models.
Finally, we comment briefly on Dirac's extended Hamiltonian technique.


title: Geometric Bremsstrahlung in the Early Universe

abstract:
  We discuss photon emission from particles decelerlated by the cosmic
expansion. This can be interpretated as a kind of bremsstrahlung induced by the
Universe geometry. In the high momentum limit its transition probability does
not depend on detailed behavior of the expansion.


title:
Cosmological Implications of a Possible Class of Particles Able to
  Travel Faster than Light (abridged version)

abstract:
  Superluminal particles are not excluded by particle physics. The apparent
Lorentz invariance of the laws of physics does not imply that space-time is
indeed minkowskian. Matter made of solutions of Lorentz-invariant equations
would feel a relativistic space-time even if the actual space-time had a quite
different geometry (f.i. a galilean space-time). If Lorentz invariance is only
a property of equations describing a sector of matter at a given scale, an
absolute frame (the "vacuum rest frame") may exist without contradicting the
minkowskian structure felt by ordinary particles. Then c , the speed of light,
will not necessarily be the only critical speed in vacuum and superluminal
sectors of matter may equally exist feeling space-times with critical speeds
larger than c . We present a discussion of possible cosmological implications
of such a scenario, assuming that the superluminal sectors couple weakly to
ordinary matter. The universality of the equivalence between inertial and
gravitational mass will be lost. The Big Bang scenario will undergo important
modifications, and the evolution of the Universe may be strongly influenced by
superluminal particles.


title: Extreme Cosmic String

abstract:
  This paper deals with the geometry of supermassive cosmic strings. We have
used an approach that enforces the spacetime of cosmic strings to also satisfy
the conservation laws of a cylindric gravitational topological defect, that is
a spacetime kink. In the simplest case of kink number unity, the entire energy
range of supermassive strings becomes then quantized so that only cylindrical
defects with linear energy density $G\mu=1/4$ (critical string) and $G\mu=1/2$
(extreme string) are allowed to occur in this range. It has been seen that the
internal spherical coordinate $\theta$ of the string metric embedded in an
Euclidean three-space also evolves on imaginary values, leading to the creation
of a covering shell of broken phase that protects the core with trapped energy,
even for $G\mu=1/2$. Then the conical singularity becomes a removable horizaon
singularity. We re-express the extreme string metric in the Finkelstein-
McCollum standard form and remove the geodesic incompleteness by using the
Kruskal technique. The z=const. sections of the resulting metric are the same
as the hemispherical section of the metric of a De Sitter kink. Some physical
consequences from these results, including the possibility that the extreme
string drives inflation and thermal effects in its core, are also discussed.


title: Non-Local Properties in Euclidean Quantum Gravity

abstract:
  In the one-loop approximation for Euclidean quantum gravity, the boundary
conditions which are completely invariant under gauge transformations of metric
perturbations involve both normal and tangential derivatives of the metric
perturbations $h_{00}$ and $h_{0i}$, while the $h_{ij}$ perturbations and the
whole ghost one-form are set to zero at the boundary. The corresponding
one-loop divergency for pure gravity has been recently evaluated by means of
analytic techniques. It now remains to compute the contribution of all
perturbative modes of gauge fields and gravitation to the one-loop effective
action for problems with boundaries. The functional determinant has a non-local
nature, independently of boundary conditions. Moreover, the analysis of
one-loop divergences for supergravity with non-local boundary conditions has
not yet been completed and is still under active investigation.


title: Entropy of eternal black holes

abstract:
  The entropy of a quantum-statistical system which is classically approximated
by a general stationary eternal black hole is studied by means of a
microcanonical functional integral. This approach opens the possibility of
including explicitly the internal degrees of freedom of a physical black hole
in path integral descriptions of its thermodynamical properties. If the
functional integral is interpreted as the density of states of the system, the
corresponding entropy equals ${cal S} = A_H/4 - A_H/4 =0$ in the semiclassical
approximation, where $A_H$ is the area of the black hole horizon. The
functional integral reflects the properties of a pure state.


title: The Relaxation Effect in Dissipative Relativistic Fluid Theories

abstract:
  The dynamics of the fluid fields in a large class of causal dissipative fluid
theories is studied. It is shown that the physical fluid states in these
theories must relax (on a time scale that is characteristic of the microscopic
particle interactions) to ones that are essentially indistinguishable from the
simple relativistic Navier-Stokes descriptions of these states. Thus, for
example, in the relaxed form of a physical fluid state the stress energy tensor
is in effect indistinguishable from a perfect fluid stress tensor plus small
dissipative corrections proportional to the shear of the fluid velocity, the
gradient of the temperature, etc.


title:
Applying black hole perturbation theory to numerically generated
  spacetimes

abstract:
  Nonspherical perturbation theory has been necessary to understand the meaning
of radiation in spacetimes generated through fully nonlinear numerical
relativity. Recently, perturbation techniques have been found to be successful
for the time evolution of initial data found by nonlinear methods. Anticipating
that such an approach will prove useful in a variety of problems, we give here
both the practical steps, and a discussion of the underlying theory, for taking
numerically generated data on an initial hypersurface as initial value data and
extracting data that can be considered to be nonspherical perturbations.


title:
Vacuum Energy in Ultralocal metrics for TT tensors with Gaussian Wave
  Functionals

abstract:
  We calculate, in a class of Gauge invariant functionals, by variational
methods, the difference of vacuum energy between two different backgrounds:
Schwarzschild and Flat Space. We perform this evaluation in an Hamiltonian
formulation of Quantum Gravity by standard ''$3+1$'' decomposition. After the
decomposition the scalar curvature is expanded to second order with respect to
the Schwarzschild metric. We evaluate this energy difference in momentum space,
in the lowest possible state (regardless of any negative mode). We find a
singular behaviour in the UV-limit, due to the presence of the horizon when
$r=2m.$ When $r>2m$ this singular behaviour disappears, which is in agreement
with various other models presented in the literature.


title: Linear Form of Canonical Gravity

abstract:
  Recent work in the literature has shown that general relativity can be
formulated in terms of a jet bundle which, in local coordinates, has five
entries: local coordinates on Lorentzian space-time, tetrads, connection
one-forms, multivelocities corresponding to the tetrads and multivelocities
corresponding to the connection one-forms. The derivatives of the Lagrangian
with respect to the latter class of multivelocities give rise to a set of
multimomenta which naturally occur in the constraint equations. Interestingly,
all the constraint equations of general relativity are linear in terms of this
class of multimomenta. This construction has been then extended to complex
general relativity, where Lorentzian space-time is replaced by a
four-complex-dimensional complex-Riemannian manifold. One then finds a
holomorphic theory where the familiar constraint equations are replaced by a
set of equations linear in the holomorphic multimomenta, providing such
multimomenta vanish on a family of two-complex-dimensional surfaces. In quantum
gravity, the problem arises to quantize a real or a holomorphic theory on the
extended space where the multimomenta can be defined.


title: Quantization of the Schwarzschild Black Hole

abstract:
  We quantize by the Dirac - Wheeler-DeWitt method the canonical formulation of
the Schwarzschild black hole developed in a previous paper. We investigate the
properties of the operators that generate rigid symmetries of the Hamiltonian,
establish the form of the invariant measure under the rigid transformations,
and determine the gauge fixed Hilbert space of states. We also prove that the
reduced quantization method leads to the same Hilbert space for a suitable
gauge fixing.


title: Two-dimensional dilaton black holes

abstract:
  The two-dimensional CGHS model provides an interesting toy-model for the
study of black hole evaporation. For this model, a quantum effective action,
which incorporates Hawking radiation and backreaction, can be explicitly
constructed. In this paper, we study a generalization of this effective action.
In our extended model, it is possible to remove certain curvature singularities
arising for the original theory. We also find that the flux of Hawking
radiation is identical to that encountered in other two-dimensional models.


title:
The Bekenstein Bound, Topological Quantum Field Theory and Pluralistic
  Quantum Field Theory

abstract:
  An approach to quantum gravity and cosmology is proposed based on a synthesis
of four elements: 1) the Bekenstein bound and the related holographic
hypothesis of 't Hooft and Susskind, 2) topological quantum field theory, 3) a
new approach to the interpretational issues of quantum cosmology and 4) the
loop representation formulation of non-perturbative quantum gravity. A set of
postulates are described, which define a (\it pluralistic quantum cosmological
theory.) These incorporates a statistical and relational approach to the
interpretation problem, following proposals of Crane and Rovelli, in which
there is a Hilbert space associated to each timelike boundary, dividing the
universe into two parts. A quantum state of the universe is an assignment of a
statistical state into each of these Hilbert spaces, subject to certain
conditions of consistency which come from an analysis of the measurement
problem. A proposal for a concrete realization of these postulates is
described, which is based on certain results in the loop representation and
topological quantum field theory, and in particular on the fact that spin
networks and punctured surfaces appear in both contexts. The
Capovilla-Dell-Jacobson solution of the constraints of quantum gravity are
expressed quantum mechanically in the language of Chern-Simons theory, in a way
that leads also to the satisfaction of the Bekenstein bound.


title:
Gravitational Ionization: Periodic Orbits of Binary Systems Perturbed by
  Gravitational Radiation

abstract:
  The long term perturbation of a Newtonian binary system by an incident
gravitational wave is discussed in connection with the issue of gravitational
ionization. The periodic orbits of the planar tidal equation are investigated
and the conditions for their existence are presented. The possibility of
ionization of a Keplerian orbit via gravitational radiation is discussed.


title: How generic are null spacetime singularities?

abstract:
  The spacetime singularities inside realistic black holes are sometimes
thought to be spacelike and strong, since there is a generic class of solutions
(BKL) to Einsteins equations with these properties. We show that null, weak
singularities are also generic, in the following sense: there is a class of
vacuum solutions containing null, weak singularities, depending on 8 arbitrary
(up to some inequalities) analytic initial functions of 3 spatial coordinates.
Since 8 arbitrary functions are needed (in the gauge used here) to span the
generic solution, this class can be regarded as generic.


title: Classically Integrable Cosmological Models with a Scalar Field

abstract:
  New classes of classically integrable models in the cosmological theories
with a scalar field are obtained by using freedoms of defining time and fields.
In particular, some models with the sum of exponential potentials in the flat
spatial metric are shown to be integrable. The model with the Sine-Gordon
potential can be solved in terms of analytic continuation of the non-periodic
Toda field theory.


title:
Absorption Probability of De Sitter Horizon for Massless Fields with
  Spin

abstract:
  The evaluation of the absorption coefficients are important for particle
emission caused by Hawking radiation. In the case of cosmological particle
emission from the event horizon in De Sitter space, it is known that the scalar
wave functions are solved in terms of Legendre functions. For fields with
higher spin, the solution has been examined with low frequency approximation.
We shows that the radial equations of the fields with spin $0,1/2,1$ and $2$
can be solved analytically in terms of the hypergeometric functions. We
calculate the absorption probability using asymptotic expansion for high
frequency limit. It turns out that the absorption coefficients are universal to
all bosonic fields; They depend only on the angular momentum and not spin. In
the case of spin $1/2$ fermions, we can also find non-vanishing absorption
probability in contrast to the previously known result.


title: Anderson Localization in the Sky and Cosmological Magnetic Field

abstract:
  We discuss the Anderson localization of electromagnetic fields in the
fluctuating plasma induced by the gravitational density perturbation before the
recombination time of the Universe. Randomly distributed localized coherent
electromagnetic fields emerge in the thermal equilibrium before the
recombination time. We argue that the localized coherent electric fields
eventually produce cosmological magnetic fields after the decoupling time.