title: Faraday lines and observables for the Einstein-Maxwell theory

abstract:
  In recent work on Einstein gravity in four dimensions using the Ashtekar
variables, non-local loop variables have played an important role in attempts
to formulate a quantum theory. The introduction of such variables is guided by
gauge invariance, and here an infinite set of loop variables is introduced for
the Hamiltonian form of the Einstein-Maxwell theory. The loops that enter the
description naturally are the (source free) electric field lines. These
variables are invariant under spatial diffeomorphisms and they also form a
closed Poisson algebra. As such they may be useful for quantization attempts
and for studying classical solutions.


title: Open Questions in Classical Gravity

abstract:
  We discuss some outstanding open questions regarding the validity and
uniqueness of the standard second order Newton-Einstein classical gravitational
theory. On the observational side we discuss the degree to which the realm of
validity of Newton's Law of Gravity can actually be extended to distances much
larger than the solar system distance scales on which the law was originally
established. On the theoretical side we identify some commonly accepted but
actually still open to question assumptions which go into the formulating of
the standard second order Einstein theory in the first place. In particular, we
show that while the familiar second order Poisson gravitational equation (and
accordingly its second order covariant Einstein generalization) may be
sufficient to yield Newton's Law of Gravity they are not in fact necessary. The
standard theory thus still awaits the identification of some principle which
would then make it necessary too. We show that current observational
information does not exclusively mandate the standard theory, and that the
conformal invariant fourth order theory of gravity considered recently by
Mannheim and Kazanas is also able to meet the constraints of data, and in fact
to do so without the need for any so far unobserved non-luminous or dark
matter.


title: Gauge fields on Riemann-Cartan space-times

abstract:
  Gauge fields are described on an Riemann-Cartan space-time by means of
tensor-valued differential forms and exterior calculus. It is shown that
minimal coupling procedure leads to a gauge invariant theory where gauge fields
interact with torsion, and that consistency conditions for the gauge fields
impose restrictions in the non-Riemannian structure of space-time. The new
results differ from the well established ones obtained by using minimal
coupling procedure at the action formulation. The sources of these differences
are pointed out and discussed.


title: Blow-Up of Test Fields Near Cauchy Horizons

abstract:
  The behaviour of test fields near a compact Cauchy horizon is investigated.
It is shown that solutions of nonlinear wave equations on Taub spacetime with
generic initial data cannot be continued smoothly to both extensions of the
spacetime through the Cauchy horizon. This is proved using an energy method.
Similar results are obtained for the spacetimes of Moncrief containing a
compact Cauchy horizon and for more general matter models.


title: Geometric Phase in Vacuum Instability:APPLICATIONS in Quantum Cosmology

abstract:
  Three different methods viz. i) a perturbative analysis of the Schr\"odinger
equation ii) abstract differential geometric method and iii) a semiclassical
reduction of the Wheeler-Dewitt equation, relating Pancharatnam phase to vacuum
instability are discussed. An improved semiclassical reduction is also shown to
yield the correct zeroth order semicalssical Einstein equations with
backreaction. This constitutes an extension of our earlier discussions on the
topic


title:
On time and the quantum-to-classical transition in Jordan-Brans-Dicke
  quantum gravity

abstract:
  Any quantum theory of gravity which treats the gravitational constant as a
dynamical variable has to address the issue of superpositions of states
corresponding to different eigenvalues. We show how the unobservability of such
superpositions can be explained through the interaction with other
gravitational degrees of freedom (decoherence). The formal framework is
canonically quantized Jordan-Brans-Dicke theory. We discuss the concepts of
intrinsic time and semiclassical time as well as the possibility of tunneling
into regions corresponding to a negative gravitational constant. We calculate
the reduced density matrix of the Jordan-Brans-Dicke field and show that the
off-diagonal elements can be sufficiently suppressed to be consistent with
experiments. The possible relevance of this mechanism for structure formation
in extended inflation is briefly discussed.


title: Gravitational Observables and Local Symmetries

abstract:
  Using a recent classification of local symmetries of the vacuum Einstein
equations, it is shown that there can be no observables for the vacuum
gravitational field (in a closed universe) built as spatial integrals of local
functions of Cauchy data and their derivatives.


title: Elliptic and circular wormholes

abstract:
  Two new exact analytical solutions of the euclidean Einstein equations for a
minimal massless scalar field and negative cosmological constant have been
obtained. These solutions are given in terms of Jacobian elliptic or circular
functions, rather than hyperbolic functions, connect large asymptotic regions
of maximally-symmetric anti-DeSitter metrics through a microscopic throat, and
correspond to negative definite components of the Ricci tensor. Therefore, they
describe wormhole-like changes of topology driven by nucleation of baby
universes. The quantum state of such elliptic and circular wormholes or handles
is discussed in the most interesting inner and asymptotic regions.


title: Black Hole with Non-Commutative Hair

abstract:
  The specific nonlinear vector $\sigma$-model coupled to Einstein gravity is
investigated. The model arises in the studies of the gravitating matter in
non-commutative geometry. The static spherically symmetric spacetimes are
identified by direct solving of the field equations. The asymptotically flat
black hole with the ``non-commutative'' vector hair appears for the special
choice of the integration constants, giving thus another counterexample to the
famous ``no-hair'' theorem.


title:
Gravitational Waves from an Axi-symmetric Source in the Nonsymmetric
  Gravitational Theory

abstract:
  We examine gravitational waves in an isolated axi--symmetric reflexion
symmetric NGT system. The structure of the vacuum field equations is analyzed
and the exact solutions for the field variables in the metric tensor are found
in the form of expansions in powers of a radial coordinate. We find that in the
NGT axially symmetric case the mass of the system remains constant only if the
system is static (as it necessarily is in the case of spherical symmetry). If
the system radiates, then the mass decreases monotonically and the energy flux
associated with waves is positive.


title: On the Constraint Algebra of Degenerate Relativity

abstract:
  As shown by Ashtekar in the mid 80's, general relativity can be extended to
incorporate degenerate metrics. This extension is not unique, however, as one
can change the form of the hamiltonian constraints and obtain an {\it
alternative} degenerate extension of general relativity that disagrees with
Ashtekar's original theory when the triads vectors are degenerate. In this
paper, the constraint algebra of a particular alternative theory is explicitly
evaluated and compared with that of Ashtekar's original degenerate extension. A
generic classification of the difference between the two theories is given in
terms of the degeneracy and surface-forming properties of the triad vectors.
(This classification is valid when the degeneracy and surface-forming
properties of the triad vectors is the same everywhere in an open set about a
point in space.) If the triad vectors are degenerate and surface-forming, then
all the secondary constraints of the alternative degenerate extension are
satisfied as a consequence of the primary constraints, and the constraints of
this theory are weaker than those of Ashtekar's. If the degenerate triad
vectors are not surface-forming, then the first secondary constraint of the
alternative theory already implies equivalence with Ashtekar's degenerate
extension. What happens when the degeneracy and surface-forming properties of
the triad vectors change from point to point is an open question.


title: From the Big Bang Theory to the Theory of a Stationary Universe

abstract:
  We consider chaotic inflation in the theories with the effective potentials
phi^n and e^{\alpha\phi}. In such theories inflationary domains containing
sufficiently large and homogeneous scalar field \phi permanently produce new
inflationary domains of a similar type. We show that under certain conditions
this process of the self-reproduction of the Universe can be described by a
stationary distribution of probability, which means that the fraction of the
physical volume of the Universe in a state with given properties (with given
values of fields, with a given density of matter, etc.) does not depend on
time, both at the stage of inflation and after it. This represents a strong
deviation of inflationary cosmology from the standard Big Bang paradigm. We
compare our approach with other approaches to quantum cosmology, and illustrate
some of the general conclusions mentioned above with the results of a computer
simulation of stochastic processes in the inflationary Universe.


title:
Recovery of information from black hole radiation by considering
  stimulated emission

abstract:
  We deal with the black hole information loss paradox by showing that the
stimulated emission component of the black hole radiation contains information
about the initial state of the system. The nonlocal behaviour that allows the
recovery of information about the matter that falls behind the horizon appears
in a natural way. We calculate the expectation value and probability
distribution of particles at ${\cal J}^+$ for a non-vacuum initial state. The
entropy of the final state is compared to that of a thermal state with the same
energy per mode. We find that the information recovered about the initial state
increases with the number $r$ of the initially incoming particles, reaching for
example over 30\% for $r = 1000$. We point out that recovering information
about the initial state, nevertheless, does not automatically imply the purity
of the final state.


title: Conformal Invariance of Black Hole Temperature

abstract:
  It is shown that the surface gravity and temperature of a stationary black
hole are invariant under conformal transformations of the metric that are the
identity at infinity. More precisely, we find a conformal invariant definition
of the surface gravity of a conformal Killing horizon that agrees with the
usual definition(s) for a true Killing horizon and is proportional to the
temperature as defined by Hawking radiation. This result is reconciled with the
intimate relation between the trace anomaly and the Hawking effect, despite the
{\it non}invariance of the trace anomaly under conformal transformations.


title: Models of Particle Detection in Regions of Spacetime

abstract:
  We investigate two models of measuring devices designed to detect a
non-relativistic free particle in a given region of spacetime. These models
predict different probabilities for a free quantum particle to enter a
spacetime region $R$ so that this notion is device dependent. The first model
is of a von Neumann coupling which we present as a contrast to the second
model. The second model is shown to be related to probabilities defined through
partitions of configuration space paths in a path integral. This study thus
provides insight into the physical situations to which such definitions of
probabilities are appropriate.


title: A Phase Space for Gravitational Radiation

abstract:
  We give a new definition, based on considerations of well-posedness for a
certain asymptotic initial value problem, of the phase space for the radiative
degrees of freedom of the gravitational field in exact General Relativity. This
space fibres over the space of final states, with the fibres being the purely
radiative degrees of freedom. The symplectic form is rigorously identified.
  The infrared sectors are shown to be the level surfaces of a moment map of an
action of the quotient group Supertranslations/Translations. A similar result
holds for Electromagnetism in Minkowski space.


title: Twistors and the BMS Group

abstract:
  We compute the motions of null infinity to which the components of the
angular momentum of the gravitational field, as defined by Penrose, are
conjugate. We find that the boosts are supplemented by anomalous translations.
If $c_{ab}$ is the skew bivector determining the component of the angular
momentum in question, the anomaly is proportional to $$c_{ab}t^b\phi ^{ad}\,
,$$ where $t^a$ is a unit vector in the direction of the Bondi--Sachs momentum
and $\phi _{ab}$ is the quadrupole moment of the shear of the cut at which the
angular momentum is evaluated. This effect persists in the weak--field limit.
This surprising result is a general consequence of the requirement that angular
momentum be supertranslation--invariant in a quiescent regime, and not some
essentially twistorial peculiarity.


title: The Phase Space of 2+1 Dimensional Gravity in the Ashtekar Formulation

abstract:
  The Ashtekar formulation of 2+1 gravity differs from the geometrodynamical
and Witten descriptions when the 2-metric is degenerate. We study the phase
space of 2+1 gravity in the Ashtekar formulation to understand these degenerate
solutions to the field equations. In the process we find two new systems of
first class constraints which describe part of the degenerate sectors of the
Ashtekar formulation. One of them also generalizes the Witten constraints.
Finally we argue that the Ashtekar formulation has an arbitrarily large number
of degrees of freedom in contrast to the usual descriptions. TO GET THE FIGURES
CONTACT Barbero@suhep.phy.syr.edu or Madhavan@suhep.phy.syr.edu


title: 2D dilaton-gravity from 5D Einstein equations

abstract:
  A semiclassical two-dimensional dilaton-gravity model is obtained by
dimensional reduction of the spherically symmetric five-dimensional Einstein
equations and used to investigate black hole evaporation. It is shown that this
model prevents the formation of naked singularity and allows spacetime
wormholes to contribute the process of formation and evaporation of black
holes.


title: Gravitational Effects on Domain Walls with Curvature Correction

abstract:
  We derive the effective action for a domain wall with small thickness in
curved spacetime and show that, apart from the Nambu term, it includes a
contribution proportional to the induced curvature. We then use this action to
study the dynamics of a spherical thick bubble of false vacuum (de Sitter)
surrounded by an infinite region of true vacuum (Schwarzschild).


title:
Late-Time Behavior of Stellar Collapse and Explosions: I. Linearized
  Perturbations

abstract:
  Problem with the figures should be corrected. Apparently a broken uuencoder
was the cause.


title:
Late-Time Behavior of Stellar Collapse and Explosions: II. Nonlinear
  Evolution


title: On Singularity Free Spacetimes--II : mid Geodesic Completeness

abstract:
  We study the geodesics of the singularity free metric considered in the
preceding Paper I and show that they are complete. This once again demonstrates
the absence of singularity. The geodesic completeness is established in general
without reference to any particular matter distribution. The metric is globally
hyperbolic and causally stable. The question of inapplicability of the powerful
singularity theorems in this case is discussed.


title: Singularity Free Spacetimes -- I :Metric and Fluid Models

abstract:
  We show that the metric for the singularity free family of fluid models [3]
can be obtained by a simple and natural inhomogenisation and anisotropisation
procedure from Friedman--Robertson--Walker metric with negative curvature. The
metric is unique for cylindrically symmetric spacetime with metric potentials
being separable functions of radial and time coordinates. It turns out that
fluid models separate out into two classes, with $\rho \not= \mu p$ in general
but $\rho = 3p$ in particular and $\rho = p$. It is shown that in both the
cases radial heat flow can be incorporated without disturbing the singularity
free character of the spacetime. Further by introducing massless scalar field
it is possible to open out a narrow window for $\mu, 4 \geq \mu \geq 3$.


title:
Quantum-Mechanical Histories and the Uncertainty Principle. II.
  Fluctuations About Classical Predictability

abstract:
  This paper is concerned with two questions in the decoherent histories
approach to quantum mechanics: the emergence of approximate classical
predictability, and the fluctuations about it necessitated by the uncertainty
principle. We consider histories characterized by position samplings at $n$
moments of time. We use this to construct a probability distribution on the
value of (discrete approximations to) the field equations, $F = m \ddot x +
V'(x) $, at $n-2$ times. We find that it is peaked around $F=0$; thus classical
correlations are exhibited. We show that the width of the peak $ \Delta F$ is
largely independent of the initial state and the uncertainty principle takes
the form $2 \sigma^2 \ (\Delta F)^2 \ge { \hbar^2 / t^2 } $, where $\sigma$ is
the width of the position samplings, and $t$ is the timescale between
projections. We determine the modifications to this result when the system is
coupled to a thermal environment. We show that the thermal fluctuations become
comparable with the quantum fluctuations under the same conditions that
decoherence effects come into play. We also study an alternative measure of
classical correlations, namely the conditional probability of finding a
sequence of position samplings, given that particular initial phase space data
have occurred. We use these results to address the issue of the formal
interpretation of the probabilities for sequences of position samplings in the
decoherent histories approach to quantum mechanics. The decoherence of the
histories is also briefly discussed.


title: Testing Cosmic Censorship with Black Hole Collisions

abstract:
  There exists an upper limit on the mass of black holes when the cosmological
constant $\Lambda$ is positive. We study the collision of two black holes whose
total mass exceeds this limit. Our investigation is based on a recently
discovered exact solution describing the collision of $Q=M$ black holes with
$\Lambda > 0$. The global structure of this solution is analyzed. We find that
if the total mass is less than the extremal limit, then the black holes
coalesce. If it is greater, then a naked singularity forms to the future of a
Cauchy horizon. However, the horizon is not smooth. Generically, there is a
mild curvature singularity, which still allows geodesics to be extended. The
implications of these results for cosmic censorship are discussed.


title: Generalized Sums over Histories for Quantum Gravity I. Smooth Conifolds

abstract:
  This paper proposes to generalize the histories included in Euclidean
functional integrals from manifolds to a more general set of compact
topological spaces. This new set of spaces, called conifolds, includes
nonmanifold stationary points that arise naturally in a semiclasssical
evaluation of such integrals; additionally, it can be proven that sequences of
approximately Einstein manifolds and sequences of approximately Einstein
conifolds both converge to Einstein conifolds. Consequently, generalized
Euclidean functional integrals based on these conifold histories yield
semiclassical amplitudes for sequences of both manifold and conifold histories
that approach a stationary point of the Einstein action. Therefore sums over
conifold histories provide a useful and self-consistent starting point for
further study of topological effects in quantum gravity. Postscript figures
available via anonymous ftp at black-hole.physics.ubc.ca (137.82.43.40) in file
gen1.ps.


title:
The origin of spacetime topology and generalizations of quantum field
  theory

abstract:
  The research effort reported in this paper is directed, in a broad sense,
towards understanding the small-scale structure of spacetime. The fundamental
question that guides our discussion is ``what is the physical content of
spacetime topology?" In classical physics, if spacetime, $(X, \tau )$, has
sufficiently regular topology, and if sufficiently many fields exist to allow
us to observe all continuous functions on $X$, then this collection of
continuous functions uniquely determines both the set of points $X$ and the
topology $\tau$ on it. To explore the small-scale structure of spacetime, we
are led to consider the physical fields (the observables) not as classical
(continuous functions) but as quantum operators, and the fundamental observable
as not the collection of all continuous functions but the local algebra of
quantum field operators. In pursuing our approach further, we develop a number
of generalizations of quantum field theory through which it becomes possible to
talk about quantum fields defined on arbitrary topological spaces. Our ultimate
generalization dispenses with the fixed background topological space altogether
and proposes that the fundamental observable should be taken as a lattice (or
more specifically a ``frame," in the sense of set theory) of closed subalgebras
of an abstract $C^{\ast}$ algebra. Our discussion concludes with the definition
and some elementary


title:
Algebraic approach to quantum field theory on non-globally-hyperbolic
  spacetimes

abstract:
  The mathematical formalism for linear quantum field theory on curved
spacetime depends in an essential way on the assumption of global
hyperbolicity. Physically, what lie at the foundation of any formalism for
quantization in curved spacetime are the canonical commutation relations,
imposed on the field operators evaluated at a global Cauchy surface. In the
algebraic formulation of linear quantum field theory, the canonical commutation
relations are restated in terms of a well-defined symplectic structure on the
space of smooth solutions, and the local field algebra is constructed as the
Weyl algebra associated to this symplectic vector space. When spacetime is not
globally hyperbolic, e.g. when it contains naked singularities or closed
timelike curves, a global Cauchy surface does not exist, and there is no
obvious way to formulate the canonical commutation relations, hence no obvious
way to construct the field algebra. In a paper submitted elsewhere, we report
on a generalization of the algebraic framework for quantum field theory to
arbitrary topological spaces which do not necessarily have a spacetime metric
defined on them at the outset. Taking this generalization as a starting point,
in this paper we give a prescription for constructing the field algebra of a
(massless or massive) Klein-Gordon field on an arbitrary background spacetime.
When spacetime is globally hyperbolic, the theory defined by our construction
coincides with the ordinary Klein-Gordon field theory on a


title: Superspace Dynamics and Perturbations Around "Emptiness"

abstract:
  Superspace parametrized by gauge potentials instead of metric
three-geometries is discussed in the context of the Ashtekar variables. Among
other things, an "internal clock" for the full theory can be identified.
Gauge-fixing conditions which lead to the natural geometrical separation of
physical from gauge modes are derived with the use of the metric in
connection-superspace. A perturbation scheme about an unconventional background
which is inaccessible to conventional variables is presented. The resultant
expansion retains much of the simplicity of Ashtekar's formulation of General
Relativity.


title:
Generalized Sums over Histories for Quantum Gravity II. Simplicial
  Conifolds

abstract:
  This paper examines the issues involved with concretely implementing a sum
over conifolds in the formulation of Euclidean sums over histories for gravity.
The first step in precisely formulating any sum over topological spaces is that
one must have an algorithmically implementable method of generating a list of
all spaces in the set to be summed over. This requirement causes well known
problems in the formulation of sums over manifolds in four or more dimensions;
there is no algorithmic method of determining whether or not a topological
space is an n-manifold in five or more dimensions and the issue of whether or
not such an algorithm exists is open in four. However, as this paper shows,
conifolds are algorithmically decidable in four dimensions. Thus the set of
4-conifolds provides a starting point for a concrete implementation of
Euclidean sums over histories in four dimensions. Explicit algorithms for
summing over various sets of 4-conifolds are presented in the context of Regge
calculus. Postscript figures available via anonymous ftp at
black-hole.physics.ubc.ca (137.82.43.40) in file gen2.ps.


title: Collapse of a Circular Loop of Cosmic String

abstract:
  We study the collapse of a circular loop of cosmic string. The gravitational
field of the string is treated using the weak field approximation. The
gravitational radiation from the loop is evaluated numerically. The memtric of
the loop near the point of collapse is found analytically.


title: On Singularity Free Cosmological Models

abstract:
  In 1990 Senovilla$^1$ obtained an interestisng cosmological solution of
Einstein's equations that was free of the big-bang singularity. It represented
an inhomogeneous and anisotropic cylindrical model filled with disordered
radiation, ${\bf \rho = 3p}$. The model was valid for ${\bf t \rightarrow -
\infty }$ to ${\bf t \rightarrow \infty}$ having all physical and geometrical
invariants finite and regular for the whole of spacetime. This was the first
instance of a singularity free cosmological model satisfying all the energy and
causality conditions and remaining true to general relativity (GR).
Subsequently a family of singularity free models has been identified${\bf ^2}$.
In this letter we wish to point out that a simple and natural inhomogenisation
and anisotropisation, appropriate for cylindrical symmetry, of the
Friedman-Robertson-Walker (FRW) model with negative curvature leads to the same
singularity free family. It consists of the complete set of singularity free
general solutions of Einstein's equations for perfect fluid when cylindrically
symmetric metric potentials are assumed to be separable functions of radial and
time coordinates.


title:
Energy, Temperature, and Entropy of Black Holes Dressed with Quantum
  Fields

abstract:
  A deeper understanding of the thermal properties of black holes than we
presently have depends to a large degree on obtaining a firmer grasp of the
properties of the entropy. For such an understanding we must at least know the
basic relations among entropy, energy, and temperature of a black hole in
thermal equilibrium with quantized matter fields. Limiting attention to
spherical, uncharged (``Schwarzschild") holes, we will find that the basic
Bekenstein-Hawking relations have to be generalized when the hole is dressed by
quantum fields. Though this fact is not surprising, the corrections contain
surprises and are very instructive. My purpose here is to discuss several
aspects of this problem and to display some concrete results within the
framework of the semi-classical theory of quantum fields in curved spacetime.


title: How to Estimate Energy Lost to Gravitational Waves (revised)

abstract:
  The energy--momentum radiated in gravitational waves by an isolated source is
given by a formula of Bondi. This formula is highly non--local: the
energy--momentum is not given as the integral of a well--defined local density.
It has therefore been unclear whether the Bondi formula can be used to get
information from gravity--wave measurements. In this note, we obtain, from
local knowledge of the radiation field, a lower bound on the Bondi flux.


title: Quantum Squeezing and Cosmological Entropy Production

abstract:
  The entropy growth in a cosmological process of pair production is completely
determined by the associated squeezing parameter, and is insensitive to the
number of particles in the initial state. The total produced entropy may
represent a significant fraction of the entropy stored today in the cosmic
black-body radiation, provided pair production originates from a change in the
background metric at a curvature scale of the Planck order.


title: The Geometry and Topology of 3-Manifolds and Gravity

abstract:
  It is well known that one can parameterize 2-D Riemannian structures by
conformal transformations and diffeomorphisms of fiducial constant curvature
geometries; and that this construction has a natural setting in general
relativity theory in 2-D. I will show that a similar parameterization exists
for 3-D Riemannian structures, with the conformal transformations and
diffeomorphisms of the 2-D case replaced by a finite dimensional group of gauge
transformations. This parameterization emerges from the theory of 3-D gravity
coupled to topological matter.


title: Canonical variables and quasilocal energy in general relativity

abstract:
  Recently Brown and York have devised a new method for defining quasilocal
energy in general relativity. Their method yields expressions for the
quasilocal energy and momentum surface densities associated with the
two-boundary of a spacelike slice of a spatially bounded spacetime. These
expressions are essentially Arnowitt-Deser-Misner variables, but with canonical
conjugacy defined with respect to the time history of the two-boundary. This
paper introduces Ashtekar-type variables on the time history of the
two-boundary and shows that these variables lead to elegant alternative
expressions for the quasilocal surface densities. In addition, it is
demonstrated here that both the boundary ADM variables and the boundary
Ashtekar-type variables can be incorporated into a larger framework by
appealing to the tetrad-dependent Sparling differential forms.


title: Semiclassical Equations for Weakly Inhomogeneous Cosmologies

abstract:
  The in-in effective action formalism is used to derive the semiclassical
correction to Einstein's equations due to a massless scalar quantum field
conformally coupled to small gravitational perturbations in spatially flat
cosmological models. The vacuum expectation value of the stress tensor of the
quantum field is directly derived from the renormalized in-in effective action.
The usual in-out effective action is also discussed and it is used to compute
the probability of particle creation. As one application, the stress tensor of
a scalar field around a static cosmic string is derived and the backreaction
effect on the gravitational field of the string is discussed.


title: Classical Models of Subatomic Particles

abstract:
  We look at the program of modelling a subatomic particle---one having mass,
charge, and angular momentum---as an interior solution joined to a classical
general-relativistic Kerr-Newman exterior spacetime. We find that the
assumption of stationarity upon which the validity of the Kerr-Newman exterior
solution depends is in fact violated quantum mechanically for all known
subatomic particles. We conclude that the appropriate stationary spacetime
matched to any known subatomic particle is flat space.


title: Solution to 2+1 Gravity in DreiBein formalism

abstract:
  The reduction of the dreibein formalism of 2+1 General Relativity to the
holonomies is explicitly performed. We also show explicitly how to relate these
holonomies to a geometry classically, and how to generate these holonomies from
any initial data for 2+1 gravity obeying the constraints.


title: A Noncommutative Extension of Gravity

abstract:
  The commutative algebra of functions on a manifold is extended to a
noncommutative algebra by considering its tensor product with the algebra of
nxn complex matrices. Noncommutative geometry is used to formulate an extension
of the Einstein-Hilbert action. The result is shown to be equivalent to the
usual Kaluza-Klein theory with the manifold SUn as an internal space, in a
truncated approximation.


title: Loop Variables in Topological Gravity

abstract:
  We examine the relationship between covariant and canonical
(Ashtekar/Rovelli/Smolin) loop variables in the context of BF type topological
field theories in 2+1 and 3+1 dimensions, with respective gauge groups SO(2,1)
and SO(3,1). The latter model can be considered as the simplest topological
gravity theory in 3+1 dimensions. We carry out the canonical quantization of
this model in both the connection and loop representations, for the two spatial
topologies $T^3$ and $S^2\times S^1$.


title: Numerical Investigation of Cosmological Singularities

abstract:
  Although cosmological solutions to Einstein's equations are known to be
generically singular, little is known about the nature of singularities in
typical spacetimes. It is shown here how the operator splitting used in a
particular symplectic numerical integration scheme fits naturally into the
Einstein equations for a large class of cosmological models and thus allows
study of their approach to the singularity. The numerical method also naturally
singles out the asymptotically velocity term dominated (AVTD) behavior known to
be characteristic of some of these models, conjectured to describe others, and
probably characteristic of a subclass of the rest. The method is first applied
to the unpolarized Gowdy T$^3$ cosmology. Exact pseudo-unpolarized solutions
are used as a code test and demonstrate that a 4th order accurate
implementation of the numerical method yields acceptable agreement. For generic
initial data, support for the conjecture that the singularity is AVTD with
geodesic velocity (in the harmonic map target space) < 1 is found. A new
phenomenon of the development of small scale spatial structure is also
observed. Finally, it is shown that the numerical method straightforwardly
generalizes to an arbitrary cosmological spacetime on $T^3 \times R$ with one
spacelike U(1) symmetry.


title: Dimensionally Continued Black Holes

abstract:
  Static, spherically symmetric solutions of the field equations for a
particular dimensional continuation of general relativity with negative
cosmological constant are studied. The action is, in odd dimensions, the
Chern-Simons form for the anti-de Sitter group and, in even dimensions, the
Euler density constructed with the Lorentz part of the anti-de Sitter curvature
tensor. Both actions are special cases of the Lovelock action, and they reduce
to the Hilbert action (with negative cosmological constant) in the lower
dimensional cases $\mbox{$\cal D$}=3$ and $\mbox{$\cal D$}=4$. Exact black hole
solutions characterized by mass ($M$) and electric charge ($Q$) are found. In
odd dimensions a negative cosmological constant is necessary to obtain a black
hole, while in even dimensions, both asymptotically flat and asymptotically
anti-de Sitter black holes exist. The causal structure is analyzed and the
Penrose diagrams are exhibited.


title: Extended Gravity Theories and the Einstein-Hilbert Action

abstract:
  I discuss the relation between arbitrarily high-order theories of gravity and
scalar-tensor gravity at the level of the field equations and the action. I
show that $(2n+4)$-order gravity is dynamically equivalent to Brans-Dicke
gravity with an interaction potential for the Brans-Dicke field and $n$ further
scalar fields. This scalar-tensor action is then conformally equivalent to the
Einstein-Hilbert action with $n+1$ scalar fields. This clarifies the nature and
extent of the conformal equivalence between extended gravity theories and
general relativity with many scalar fields.


title: Entropy Bounds and Black Hole Remnants

abstract:
  We rederive the universal bound on entropy with the help of black holes while
allowing for Unruh--Wald buoyancy. We consider a box full of entropy lowered
towards and then dropped into a Reissner--Nordstr\"om black hole in equilibrium
with thermal radiation. We avoid the approximation that the buoyant pressure
varies slowly across the box, and compute the buoyant force exactly. We find,
in agreement with independent investigations, that the neutral point
generically lies very near the horizon. A consequence is that in the generic
case, the Unruh--Wald entropy restriction is neither necessary nor sufficient
for enforcement of the generalized second law. Another consequence is that
generically the buoyancy makes only a negligible contribution to the energy
bookeeping, so that the original entropy bound is recovered if the generalized
second law is assumed to hold. The number of particle species does not figure
in the entropy bound, a point that has caused some perplexity. We demonstrate
by explicit calculation that, for arbitrarily large number of particle species,
the bound is indeed satisfied by cavity thermal radiation in the thermodynamic
regime, provided vacuum energies are included. We also show directly that
thermal radiation in a cavity in $D$ dimensional space also respects the bound
regardless of the value of $D$. As an application of the bound we show that it
strongly restricts the information capacity of the posited black hole remnants,
so that they cannot serve to resolve the information paradox.


title:
Can the Gravitational Wave Background from Inflation be Detected
  Locally?

abstract:
  The Cosmic Background Explorer (COBE) detection of microwave background
anisotropies may contain a component due to gravitational waves generated by
inflation. It is shown that the gravitational waves from inflation might be
seen using `beam-in-space' detectors, but not the Laser Interferometer Gravity
Wave Observatory (LIGO). The central conclusion, dependent only on weak
assumptions regarding the physics of inflation, is a surprising one. The larger
the component of the COBE signal due to gravitational waves, the {\em smaller}
the expected local gravitational wave signal.


title:
Effective Potential of a Black Hole in Thermal Equilibrium with Quantum
  Fields

abstract:
  Expectation values of one-loop renormalized thermal equilibrium stress-energy
tensors of free conformal scalars, spin-${1 \over 2}$ fermions and U(1) gauge
fields on a Schwarzschild black hole background are used as sources in the
semi-classical Einstein equation. The back-reaction and new equilibrium metric
are solved for at $O({\hbar})$ for each spin field. The nature of the modified
black hole spacetime is revealed through calculations of the effective
potential for null and timelike orbits. Significant novel features affecting
the motions of both massive and massless test particles show up at lowest order
in $\epsilon= (M_{Pl}/M)^2 < 1$, where $M$ is the renormalized black hole mass,
and $M_{Pl}$ is the Planck mass. Specifically, we find the tendency for
\underline{stable} circular photon orbits, an increase in the black hole
capture cross sections, and the existence of a gravitationally repulsive region
associated with the black hole which is generated from the U(1) back-reaction.
We also consider the back-reaction arising from multiple fields, which will be
useful for treating a black hole in thermal equilibrium with field ensembles
belonging to gauge theories.


title: Black Hole Entropy is Noether Charge

abstract:
  We consider a general, classical theory of gravity in $n$ dimensions, arising
from a diffeomorphism invariant Lagrangian. In any such theory, to each vector
field, $\xi^a$, on spacetime one can associate a local symmetry and, hence, a
Noether current $(n-1)$-form, ${\bf j}$, and (for solutions to the field
equations) a Noether charge $(n-2)$-form, ${\bf Q}$. Assuming only that the
theory admits stationary black hole solutions with a bifurcate Killing horizon,
and that the canonical mass and angular momentum of solutions are well defined
at infinity, we show that the first law of black hole mechanics always holds
for perturbations to nearby stationary black hole solutions. The quantity
playing the role of black hole entropy in this formula is simply $2 \pi$ times
the integral over $\Sigma$ of the Noether charge $(n-2)$-form associated with
the horizon Killing field, normalized so as to have unit surface gravity.
Furthermore, we show that this black hole entropy always is given by a local
geometrical expression on the horizon of the black hole. We thereby obtain a
natural candidate for the entropy of a dynamical black hole in a general theory
of gravity. Our results show that the validity of the ``second law" of black
hole mechanics in dynamical evolution from an initially stationary black hole
to a final stationary state is equivalent to the positivity of a total Noether
flux, and thus may be intimately related to the positive energy properties of
the theory. The relationship between the derivation of our formula for black
hole entropy and the derivation via ``Euclidean methods" also is explained.


title: Bianchi Cosmologies: New Variables and a Hidden Supersymmetry

abstract:
  We find a supersymmetrization of the Bianchi IX cosmology in terms of
Ashtekar's new variables. This provides a framework for connecting the recent
results of Graham and those of Ryan and Moncrief for quantum states of this
model. These states are also related with the states obtained particularizing
supergravity for a minisuperspace. Implications for the general theory are also
briefly discussed.


title: The physical hamiltonian in nonperturbative quantum gravity

abstract:
  A quantum hamiltonian which evolves the gravitational field according to time
as measured by constant surfaces of a scalar field is defined through a
regularization procedure based on the loop representation, and is shown to be
finite and diffeomorphism invariant. The problem of constructing this
hamiltonian is reduced to a combinatorial and algebraic problem which involves
the rearrangements of lines through the vertices of arbitrary graphs. This
procedure also provides a construction of the hamiltonian constraint as a
finite operator on the space of diffeomorphism invariant states as well as a
construction of the operator corresponding to the spatial volume of the
universe.


title: Recollapse of the closed Tolman spacetimes

abstract:
  The closed-universe recollapse conjecture is studied for the spherically
symmetric spacetimes. It is proven that there exists an upper bound to the
lengths of timelike curves in any Tolman spacetime that possesses $S^3$ Cauchy
surfaces and whose energy density is positive. Furthermore, an explicit bound
is constructed from the initial data for such a spacetime.


title: The Stability of the Minisuperspace

abstract:
  The stability of the minisuperspace model of the early universe is studied by
solving the Wheeler-DeWitt equation numerically. We consider a system of
Einstein gravity with a scalar field. When we solve the Wheeler-DeWitt
equation, we pick up some inhomogeneous wave modes from the infinite number of
modes adequately: degrees of freedom of the superspace are restricted to a
finite one. We show that the minisuperspace is stable when a scale factor ($a$)
of the universe is larger than a few times of the Planck length, while it
becomes unstable when $a$ is comparable to the Planck length.


title: Aspects of the Decoherent Histories Approach to Quantum Mechanics

abstract:
  I give an informal overview of the decoherent histories approach to quantum
mechanics, due to Griffiths, to Omn\`es, and to Gell-Mann and Hartle is given.
Results on the connections between decoherence, records, correlation and
entropy are described. The emphasis of the presentation is on understanding the
broader meaning of the conditions of consistency and decoherence, and in
particular, the extent to which they permit one to assign definite properties
to the system. The quantum Brownian motion model is briefly discussed. (To
appear in proceedings of the workshop, "Stochastic Evolution of Quantum States
in Open Systems and Measurement Processes", Budapest, March, 1993, edited by
L.Diosi).


title: Quantum Logic and the Histories Approach to Quantum Theory

abstract:
  An extended analysis is made of the Gell-Mann and Hartle axioms for a
generalised `histories' approach to quantum theory. Emphasis is placed on
finding equivalents of the lattice structure that is employed in standard
quantum logic. Particular attention is given to `quasi-temporal' theories in
which the notion of time-evolution is less rigid than in conventional
Hamiltonian physics; theories of this type are expected to arise naturally in
the context of quantum gravity and quantum field theory in a curved space-time.
The quasi-temporal structure is coded in a partial semi-group of `temporal
supports' that underpins the lattice of history propositions. Non-trivial
examples include quantum field theory on a non globally-hyperbolic spacetime,
and a simple cobordism approach to a theory of quantum topology.
  It is shown how the set of history propositions in standard quantum theory
can be realised in such a way that each history proposition is represented by a
genuine projection operator. This provides valuable insight into the possible
lattice structure in general history theories, and also provides a number of
potential models for theories of this type.


title: Quantum Measurement, Gravitation, and Locality

abstract:
  This essay argues that when measurement processes involve energies of the
order of the Planck scale, the fundamental assumption of locality may no longer
be a good approximation. Idealized position measurements of two distinguishable
spin-$0$ particles are considered. The measurements alter the space-time metric
in a fundamental manner governed by the commutation relations $[x_i\,\,p_j]=
i\hbar\,\delta_{ij}$ and the classical field equations of gravitation. This
{\it in-principle} unavoidable change in the space-time metric destroys the
commutativity (and hence locality) of position measurement operators.


title: Properties of 3-manifolds for relativists

abstract:
  In canonical quantum gravity certain topological properties of 3-manifolds
are of interest. This article gives an account of those properties which have
so far received sufficient attention, especially those concerning the
diffeomorphism groups of 3-manifolds. We give a summary of these properties and
list some old and new results concerning them. The appendix contains a
discussion of the group of large diffeomorphisms of the $l$-handle 3-manifold.


title:
The Quantum Propagator for a Nonrelativistic Particle in the Vicinity of
  a Time Machine

abstract:
  We study the propagator of a non-relativistic, non-interacting particle in
any non-relativistic ``time-machine'' spacetime of the type shown in Fig.~1: an
external, flat spacetime in which two spatial regions, $V_-$ at time $t_-$ and
$V_+$ at time $t_+$, are connected by two temporal wormholes, one leading from
the past side of $V_-$ to t the future side of $V_+$ and the other from the
past side of $V_+$ to the future side of $V_-$. We express the propagator
explicitly in terms of those for ordinary, flat spacetime and for the two
wormholes; and from that expression we show that the propagator satisfies
completeness and unitarity in the initial and final ``chronal regions''
(regions without closed timelike curves) and its propagation from the initial
region to the final region is unitary. However, within the time machine it
satisfies neither completeness nor unitarity. We also give an alternative proof
of initial-region-to-final-region unitarity based on a conserved current and
Gauss's theorem. This proof can be carried over without change to most any
non-relativistic time-machine spacetime; it is the non-relativistic version of
a theorem by Friedman, Papastamatiou and Simon, which says that for a free
scalar field, quantum mechanical unitarity follows from the fact that the
classical evolution preserves the Klein-Gordon inner product.


title: Exact Superstring Motivated Cosmological Models

abstract:
  We present a number of new, exact scalar field cosmologies where the
potential consists of two or more exponential terms. Such potentials are
motivated by supergravity or superstring models formulated in higher
dimensional spacetimes that have been compactified to (3+1)-dimensions. We have
found solutions in both curved and flat Robertson Walker spacetimes. These
models have a diverse range of properties and often possess several distinct
phases, with a smooth transition between ordinary and inflationary expansion.
While exponential potentials typically produce powerlaw inflation, we find
models where the inflationary period contains eras of both powerlaw and
exponential growth.


title: Squeezed States and Uncertainty Relation at Finite Temperature

abstract:
  We use the quantum Brownian model to derive the uncertainty relation for a
quantum open system in an arbitrarily-squeezed initial state interacting with
an environment at finite temperature. We examine the relative importance of the
quantum and thermal fluctuations in the evolution of the system towards
equilibrium with the aim of clarifying the meaning of quantum, classical and
thermal. We show that upon contact with the bath the system evolves from a
quantum-dominated state to a thermal-dominated state in a time which is the
same as the decoherence time calculated before in the context of quantum to
classical transitions. We also use these results to deduce the conditions when
the two basic postulates of quantum statistical mechanics become valid.


title: Why is Spacetime Lorentzian?

abstract:
  We expand on the idea that spacetime signature should be treated as a
dynamical degree of freedom in quantum field theory. It has been argued that
the probability distribution for signature, induced by massless free fields, is
peaked at the Lorentzian value uniquely in D=4 dimensions. This argument is
reviewed, and certain consistency constraints on the generalized signature
(i.e. the tangent space metric
$\eta_{ab}(x)=\mbox{diag}[e^{i\theta(x)},1,1,1]$) are derived. It is shown that
only one dynamical "Wick angle" $\theta(x)$ can be introduced in the
generalized signature, and the magnitude of fluctuations away from Lorentzian
signature $\delta \theta = \pi - \theta$ is estimated to be of order
$(l_P/R)^3$, where $l_P$ is the Planck length, and $R$ is the length scale of
the Universe. For massless fields, the case of D=2 dimensions and the case of
supersymmetry are degenerate, in the sense that no signature is preferred. Mass
effects lift this degeneracy, and we show that a dynamical origin of Lorentzian
signature is also possible for (broken) supersymmetry theories in D=6
dimensions, in addition to the more general non-supersymmetric case in D=4
dimensions.


title: Did the Pseudo-Sphere Universe have a Beginning?

abstract:
  A calculation of the no-boundary wave-function of the universe is put forward
for a spacetime with negative curvature. A semi-classical Robertson-Walker
approximation is attempted and two solutions to the field equations, one
Lorentzian and the other a tunneling one are found. The regularity of those
solutions are analysed explicitly, both in 2+1 and 3+1 dimensions and a conical
singularity is found at the origin of the time axis, contradicting the
no-boundary assumption.


title: No New Symmetries of the Vacuum Einstein Equations

abstract:
  In this note we examine some recently proposed solutions of the linearized
vacuum Einstein equations. We show that such solutions are {\it not} symmetries
of the Einstein equations, because of a crucial integrability condition.


title: The use of exp(iS[x]) in the sum over histories

abstract:
  The use of $\sum \exp(iS[x])$ as the generic form for a sum over histories in
configuration space is discussed critically and placed in its proper context.
The standard derivation of the sum over paths by discretizing the paths is
reviewed, and it is shown that the form $\sum \exp(iS[x])$ is justified only
for Schrodinger-type systems which are at most second order in the momenta.
Extending this derivation to the relativistic free particle, the causal Green's
function is expressed as a sum over timelike paths, and the Feynman Green's
function is expressed both as a sum over paths which only go one way in time
and as a sum over paths which move forward and backward in time. The weighting
of the paths is shown not to be $\exp(iS[x])$ in any of these cases. The role
of the inner product and the operator ordering of the wave equation in defining
the sum over histories is discussed.


title:
How to determine approximate Mixmaster parameters from numerical
  evolution of Einstein's equations

abstract:
  To assess the validity of the Belinskii, Khalatnikov, and Lifshitz (BKL)
approximation to Mixmaster dynamics, it would be useful to evaluate the BKL
discrete parameters as a byproduct of the numerical solution of Einstein's
equations. An algorithm to do this and results for a typical trajectory are
presented.


title: On the mechanism of trapped surface formation

abstract:
  By a combination of analytical and numerical methods, the density profile of
a momentarily at rest spherical star is varied, and the corresponding response
in the area of the spherical shells is monitored. It is shown that the inner
apparent horizon (if it exists) must lie within or at most on the star's
surface, while no such restriction is found for the outer apparent horizon.
However, an apparent horizon lying in the vacuum region will always have non
vanishing area, as long as the ADM mass of the system is non zero. Furthermore
for density profiles not decreasing inwards, it appears that all spherical
trapped surfaces lie on a thick spherical shell. Finally for a uniform density
star a simple criterion is found, relating density and proper radius that
guarantees the presence or absence of trapped regions.


title:
Solution space of 2+1 gravity on ${\bf R} \times T^2$ in Witten's
  connection formulation

abstract:
  We investigate the space ${\cal M}$ of classical solutions to Witten's
formulation of 2+1 gravity on the manifold ${\bf R} \times T^2$. ${\cal M}$ is
connected, unlike the spaces of classical solutions in the cases where $T^2$ is
replaced by a higher genus surface. Although ${\cal M}$ is neither Hausdorff
nor a manifold, removing from ${\cal M}$ a set of measure zero yields a
manifold which is naturally viewed as the cotangent bundle over a non-Hausdorff
base space~${\cal B}$. We discuss the relation of the various parts of ${\cal
M}$ to spacetime metrics, and various possibilities of quantizing~${\cal M}$.
There exist quantizations in which the exponentials of certain momentum
operators, when operating on states whose support is entirely on the part of
${\cal B}$ corresponding to conventional spacetime metrics, give states whose
support is entirely outside this part of~${\cal B}$. Similar results hold when
the gauge group ${\rm SO}_0(2,1)$ is replaced by ${\rm SU}(1,1)$.


title: Particle Creation in a universe filled by radiation and dust-like matter

abstract:
  In this article the particle creation process of scalar and spin 1/2
particles in a spatially open cosmological model associated with a universe
filled by radiation and dustlike matter. The Klein-Gordon and Dirac equations
are solved via separation of variables. After comparing the{\it \ in }and% {\it
\ out} vacua, we obtain that the number of created particles corresponds to
  Planckian and Fermi-Dirac distributions for the scalar and Dirac cases


title:
Quantum mechanical composition laws in reparameterization invariant
  systems

abstract:
  This paper gives a brief description of the derivation of a composition law
for the propagator of a relativistic particle, in a sum over histories
quantization. The extension of this derivation to the problem of finding a
composition law for quantum cosmology is also discussed. (For the proceedings
of Journees Relativistes 93)


title:
Integrals of Motion in the Two Killing Vector Reduction of General
  Relativity

abstract:
  We apply the inverse scattering method to the midi-superspace models that are
characterized by a two-parameter Abelian group of motions with two spacelike
Killing vectors. We present a formulation that simplifies the construction of
the soliton solutions of Belinski\v i and Zakharov. Furthermore, it enables us
to obtain the zero curvature formulation for these models. Using this, and
imposing periodic boundary conditions corresponding to the Gowdy models when
the spatial topology is a three torus $T ^3$, we show that the equation of
motion for the monodromy matrix is an evolution equation of the Heisenberg
type. Consequently, the eigenvalues of the monodromy matrix are the generating
functionals for the integrals of motion. Furthermore, we utilise a suitable
formulation of the transition matrix to obtain explicit expressions for the
integrals of motion. This involves recursion relations which arise in solving
an equation of Riccati type. In the case when the two Killing vectors are
hypersurface orthogonal the integrals of motion have a particularly simple
form.


title: Multiplicative Noise: Applications in Cosmology and Field Theory

abstract:
  Physical situations involving multiplicative noise arise generically in
cosmology and field theory. In this paper, the focus is first on exact
nonlinear Langevin equations, appropriate in a cosmologica setting, for a
system with one degree of freedom. The Langevin equations are derived using an
appropriate time-dependent generalization of a model due to Zwanzig. These
models are then extended to field theories and the generation of multiplicative
noise in such a context is discussed. Important issues in both the cosmological
and field theoretic cases are the fluctuation-dissipation relations and the
relaxation time scale. Of some importance in cosmology is the fact that
multiplicative noise can substantially reduce the relaxation time. In the field
theoretic context such a noise can lead to a significant enhancement in the
nucleation rate of topological defects.


title: Energy Radiation of Charged Particles in Conformally Flat Spacetimes

abstract:
  Original abstract: Consider the worldline of a charged particle in a static
spacetime. Contraction of the time-translation Killing field with the retarded
electromagnetic energy-momentum tensor gives a conserved electromagnetic energy
vector which can be used to define the radiated electromagnetic energy. This
note points out that for a conformally flat spacetime, the radiated energy is
the same as for a flat spacetime (i.e. Minkowski space). This appears to be
inconsistent with an equation of motion for such particles derived by DeWitt
and Brehme and later corrected by Hobbs [End of original abstract]
  New abstract: Same as old abstract with last sentence deleted. The body of
the paper is the same as previously. A new Appendix 2 has been added discussing
implications to the previous arguments of recent work of Sonego (J. Math. Phys.
40 (1999), 3381-3394) and of Quinn and Wald (Phys. Rev. D 60 (1999),
gr-qc/9610053).


title: Quantum Gravity and Non-unitarity in Black Hole Evaporation

abstract:
  We discuss the relevance of quantum gravitational corrections to the
functional Schr\"odinger equation for the information loss paradox in black
hole evaporation. These corrections are found from the Wheeler-DeWitt equation
through a semiclassical expansion scheme. The dominant contribution in the
final evaporation stage, when the black hole approaches the Planck regime, is a
term which explicitly violates unitarity in the non-gravitational sector. While
pure states remain pure, there is an increase in the degree of purity for
non-pure states in this sector. This result holds irrespective of whether full
quantum gravity respects unitarity or not.


title: Quantum cosmology and the emergence of a classical world

abstract:
  This paper gives an elementary introduction to some of the conceptual
problems of quantum cosmology. Contents: 1. Why quantum cosmology? 2. Time in
quantum gravity 3.Decoherence and the recovery of the Schrodinger equation 4.
The direction of time


title: Nicolai Maps for Quantum Cosmology

abstract:
  We construct Nicolai maps for $N=2$ supersymmetric extensions of
minisuperspace models. It is shown that Nicolai maps exist for only a very
restricted set of states. In the models considered these are the two states
corresponding to the empty and the filled fermion sectors. The form of the
Nicolai maps in these sectors is given explicitly, and it is shown that they
have a natural stochastic interpretation. This result also suggests a
probabilistic interpretation of the wave function.


title: New Types of Thermodynamics from $(1+1)$-Dimensional Black Holes

abstract:
  For normal thermodynamic systems superadditivity $\S$, homogeneity $\H$ and
concavity $\C$ of the entropy hold, whereas for $(3+1)$-dimensional black holes
the latter two properties are violated. We show that $(1+1)$-dimensional black
holes exhibit qualitatively new types of thermodynamic behaviour, discussed
here for the first time, in which $\C$ always holds, $\H$ is always violated
and $\S$ may or may not be violated, depending of the magnitude of the black
hole mass. Hence it is now seen that neither superadditivity nor concavity
encapsulate the meaning of the second law in all situations.


title: Selfgravitating Yang-Mills solitons and their Chern-Simons numbers

abstract:
  We present a classification of the possible regular, spherically symmetric
solutions of the Einstein-Yang-Mills system which is based on a bundle
theoretical analysis for arbitrary gauge groups. It is shown that such solitons
must be of magnetic type, at least if the magnetic Yang-Mills charge vanishes.
Explicit expressions for the Chern-Simons numbers of these selfgravitating
Yang-Mills solitons are derived, which involve only properties of irreducible
root systems and some information about the asymptotics of the solutions. It
turns out, as an example, that the Chern-Simons numbers are always
half-integers or integers for the gauge groups $SU(n)$. Possible physical
implications of these results, which are based on analogies with the unstable
sphaleron solution of the electroweak theory, are briefly indicated.


title: Quantum Fluctuations of Black Hole Geometry

abstract:
  By using the minisuperspace model for the interior metric ofstatic black
holes, we solve the Wheeler-DeWitt equation to study quantum mechanics of the
horizon geometry. Our basic idea is to introduce the gravitational mass and the
expansions of null rays as quantum operators. Then, the exact wave function is
found as a mass eigenstate, and the radius of the apparent horizon is
quantum-mechanically defined. In the evolution of the metric variables, the
wave function changes from a WKB solution giving the classical trajectories to
a tunneling solution. By virtue of the quantum fluctuations of the metric
evolution beyond the WKB approximation, we can observe a static black hole
state with the apparent horizon separating from the event horizon.


title: Fate of Inhomogeneity in Schwarzschild-deSitter Space-time

abstract:
  We investigate the global structure of the space time with a spherically
symmetric inhomogeneity using a metric junction, and classify all possible
types. We found that a motion with a negative gravitational mass is possible
although the energy condition of the matter is not violated. Using the result,
formation of black hole and worm hole during the inflationary era is discussed.


title: Local Structure of Numerically Generated Worm Hole Spacetime

abstract:
  We investigate the evolution of the apparent horizons in a numerically
gererated worm hole spacetime. The behavior of the apparent horizons is
affected by the dynamics of the matter field. By using the local mass of the
system, we interpret the evolution of the worm hole structure. Figures are
available by mail to author.


title: The Quantum Stress Tensor in the Three Dimensional Black Hole

abstract:
  The quantum stress tensor $<T_{\mu\nu}>$ is calculated in the 2+1 dimensional
black hole found by Banados, Teitelboim, and Zanelli. The Greens function, from
which $<T_{\mu\nu}> $ is derived, is obtained by the method of images. For the
non-rotating black hole, it is shown that $<T_{\mu\nu}>$ is finite on the event
horizon, but diverges at the singularity. For the rotating solution, the stress
tensor is finite at the outer horizon, but diverges near the inner horizon.
This suggests that the inner horizon is quantum mechanically unstable against
the formation of a singularity.


title: Dynamical Origin of the Entropy of a Black Hole

abstract:
  Modes of physical fields which are located inside a horizon and which cannot
be observed by a distant observer are identified with dynamical degrees of
freedom of a black hole. A new invariant statistical mechanical definition of a
black-hole's entropy is proposed. It is shown that the main contribution to the
entropy is given by thermally excited `invisible' modes propagating in the
close vicinity of the horizon. A calculation based on the proposed definition
yields a value of the entropy which is in good agreement with the usually
adopted value.


title: Notes on the (2+1)-Dimensional Wheeler-DeWitt Equation

abstract:
  In contrast to other approaches to (2+1)-dimensional quantum gravity, the
Wheeler-DeWitt equation appears to be too complicated to solve explicitly, even
for simple spacetime topologies. Nevertheless, it is possible to obtain a good
deal of information about solutions and their interpretation. In particular,
strong evidence is presented that Wheeler-DeWitt quantization is not equivalent
to reduced phase space quantization.


title: MATTERS OF GRAVITY, a newsletter for the gravity community, number 2

abstract:
  Table of contents:
  Editorial 1
  Correspondents 3
  Some recent work in general relativistic Astrophysics 4
  Two dimensional black holes 6
  Resonant-mass gravitational wave detectors: an update 8
  Universality and scaling in gravitational collapse 9
  Gravitational Wave memories upgraded 11
  Conference report: quantum aspects of black holes 13
  Conference report: knots and quantum gravity 14
  Conference report: deterministic chaos in GR 17


title: A Cosmological Constant Limits the Size of Black Holes

abstract:
  In a space-time with cosmological constant $\Lambda>0$ and matter satisfying
the dominant energy condition, the area of a black or white hole cannot exceed
$4\pi/\Lambda$. This applies to event horizons where defined, i.e. in an
asymptotically deSitter space-time, and to outer trapping horizons (cf.
apparent horizons) in any space-time. The bound is attained if and only if the
horizon is identical to that of the degenerate `Schwarzschild-deSitter'
solution. This yields a topological restriction on the event horizon, namely
that components whose total area exceeds $4\pi/\Lambda$ cannot merge. We
discuss the conjectured isoperimetric inequality and implications for the
cosmic censorship conjecture.


title:
Wigner function and quantum kinetic theory in curved space-time and
  external fields

abstract:
  A new definition of the Wigner function for quantum fields coupled to curved
space--time and an external Yang--Mills field is studied on the example of a
scalar and a Dirac fields. The definition uses the formalism of the tangent
bundles and is explicitly covariant and gauge invariant. Derivation of
collisionless quantum kinetic equations is carried out for both quantum fields
by using the first order formalism of Duffin and Kemmer. The evolution of the
Wigner function is governed by the quantum corrected Liouville--Vlasov equation
supplemented by the generalized mass--shell constraint. The structure of the
quantum corrections is perturbatively found in all adiabatic orders. The lowest
order quantum--curvature corrections coincide with the ones found by Winter.


title: Physical States in d=3,N=2 Supergravity

abstract:
  To clarify some issues raised by D'Eath's recent proposal for the physical
states of $N=1$ supergravity in four dimensions, we study pure (topological)
$N=2$ supergravity in three dimensions, which is formally very similar, but
much easier to solve. The wave functionals solving the quantum constraints can
be understood in terms of arbitrary functions on the space of moduli and
supermoduli, which is not Hausdorff. We discuss the implications for the wave
functionals and show that these are not amenable to expansions in fermionic
coordinates, but can serve as lowest-order solutions to the quantum constraints
in an expansion in $\hbar$ in more realistic theories.


title: The Mixmaster Spacetime, Geroch's Transformation and Constants of Motion

abstract:
  We show that for $U(1)$-symmetric spacetimes on $S^3 \times R$ a constant of
motion associated with the well known Geroch transformation, a functional
$K[h_{ij},\pi^{ij}]$, quadratic in gravitational momenta, is strictly positive
in an open subset of the set of all $U(1)$-symmetric initial data, and
therefore not weakly zero. The Mixmaster initial data appear to be on the
boundary of that set. We calculate the constant of motion perturbatively for
the Mixmaster spacetime and find it to be proportional to the minisuperspace
Hamiltonian to the first order in the Misner anisotropy variables, i.e. weakly
zero. Assuming that $K$ is exactly zero for the Mixmaster spacetime, we show
that Geroch's transformation, when applied to the Mixmaster spacetime, gives a
new \mbox{$U(1)$-symmetric} solution of the vacuum Einstein equations, globally
defined on \mbox{$S^2 \times S^1 \times R$},which is non-homogeneous and
presumably exhibits Mixmaster-like complicated dynamical behavior.


title: Quantum State and Spontaneous Symmetry Breaking in Gravity

abstract:
  A spontaneous symmetry breaking mechanism is used in quantum gravity to
obtain a convergent positive definite density-matrix as the most general
quantum state of Euclidean wormholes


title: Blackbody Distribution for Wormholes

abstract:
  By assuming that only (i) bilocal vertex operators which are diagonal with
respect to the basis for local field operators, and (ii) the convergent
elements with nonzero positive energy of the density matrix representing the
quantum state of multiply-connected wormholes, contribute the path integral
that describes the effects of wormholes on ordinary matter fields at low
energy, it is obtained that the probability measure for multiply connected
wormholes with nondegenerate energy spectrum is given in terms of a Planckian
probability distribution for the momenta of a quantum field $\frac{1}{2}\alpha^
{2}$, where the $\alpha$'s are the Coleman parameters, rather than a classical
gaussian distribution law, and that an observable classical universe can exist
if, and only if, such multiply connected wormholes are allowed to occur.


title:
The Dispersion of Newton's Constant: A Transfer Matrix Formulation of
  Quantum Gravity

abstract:
  A transfer matrix formalism applicable to certain reparametrization invariant
theories, including quantum gravity, is proposed. In this formulation it is
found that every stationary state in quantum gravity satisfies a Wheeler-DeWitt
equation, but each with a different value of the Planck mass; the value
$m_{Planck}^4$ turns out to be proportional to the eigenvalue of the evolution
operator. As a consequence, the fact that the Universe is non-stationary
implies that it is not in an eigenstate of Newton's constant.


title: Black Holes in Einstein-Lovelock Gravity

abstract:
  Static, spherically symmetric solutions of the field equations for a
particular dimensional continuation of general relativity with negative
cosmological constant are found. In even dimensions the solution has many
similarities with the \Sch\ metric. In odd dimensions, the equations of motion
are explicitly anti de-Sitter invariant, and the solution is alike in many ways
to the 2+1 black hole.


title:
Unitarity and Causality in Generalized Quantum Mechanics for Non-Chronal
  Spacetimes

abstract:
  Spacetime must be foliable by spacelike surfaces for the quantum mechanics of
matter fields to be formulated in terms of a unitarily evolving state vector
defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike
surfaces, as in the case of spacetimes with closed timelike curves, a more
general formulation of quantum mechanics is required. In such generalizations
the transition matrix between alternatives in regions of spacetime where states
{\it can} be defined may be non-unitary. This paper describes a generalized
quantum mechanics whose probabilities consistently obey the rules of
probability theory even in the presence of such non-unitarity. The usual notion
of state on a spacelike surface is lost in this generalization and familiar
notions of causality are modified. There is no signaling outside the light
cone, no non-conservation of energy, no ``Everett phones'', and probabilities
of present events do not depend on particular alternatives of the future.
However, the generalization is acausal in the sense that the existence of
non-chronal regions of spacetime in the future can affect the probabilities of
alternatives today. The detectability of non-unitary evolution and violations
of causality in measurement situations are briefly considered. The evolution of
information in non-chronal spacetimes is described.


title: Exponential-Potential Scalar Field Universes I: The Bianchi I Models

abstract:
  We obtain a general exact solution of the Einstein field equations for the
anisotropic Bianchi type I universes filled with an exponential-potential
scalar field and study their dynamics. It is shown, in agreement with previous
studies, that for a wide range of initial conditions the late-time behaviour of
the models is that of a power-law inflating FRW universe. This property, does
not hold, in contrast, when some degree of inhomogeneity is introduced, as
discussed in our following paper II.


title:
Exponential-Potential Scalar Field Universes II: The Inhomogeneous
  Models

abstract:
  We obtain exact solutions for the Einstein equations with an
exponential-potential scalar field (\(V=\Lambda e^{k\phi}\)) which represent
simple inhomogeneous generalizations of Bianchi I cosmologies. Studying these
equations numerically we find that in most of the cases there is a certain
period of inflationary behaviour for \(k^2<2\). We as well find that for
\(k^2>2\) the solutions homogenize generically at late times. Yet, {\em none of
the solutions} isotropize. For some particular values of the integration
constants we find a multiple inflationary behaviour for which the deceleration
and the inflationary phases interchange each other several times during the
history of the model.


title: Formation of Solitonic Stars Through Gravitational Cooling

abstract:
  We studied the formation of compact bosonic objects through a dissipationless
cooling mechanism. Implications of the existence of this mechanism are
discussed, including the abundance of bosonic stars in the universe, and the
possibility of ruling out the axion as a dark matter candidate.


title: The Collision of Two Black Holes

abstract:
  We study the head-on collision of two equal mass, nonrotating black holes. We
consider a range of cases from holes surrounded by a common horizon to holes
initially separated by about $20M$, where $M$ is the mass of each hole. We
determine the waveforms and energies radiated for both the $\ell = 2$ and
$\ell=4$ waves resulting from the collision. In all cases studied the normal
modes of the final black hole dominate the spectrum. We also estimate
analytically the total gravitational radiation emitted, taking into account the
tidal heating of horizons using the membrane paradigm, and other effects. For
the first time we are able to compare analytic calculations, black hole
perturbation theory, and strong field, nonlinear numerical calculations for
this problem, and we find excellent agreement.


title: Quantum Dynamics of Lorentzian Spacetime Foam

abstract:
  A simple spacetime wormhole, which evolves classically from zero throat
radius to a maximum value and recontracts, can be regarded as one possible mode
of fluctuation in the microscopic ``spacetime foam'' first suggested by
Wheeler. The dynamics of a particularly simple version of such a wormhole can
be reduced to that of a single quantity, its throat radius; this wormhole thus
provides a ``minisuperspace model'' for a structure in Lorentzian-signature
foam. The classical equation of motion for the wormhole throat is obtained from
the Einstein field equations and a suitable equation of state for the matter at
the throat. Analysis of the quantum behavior of the hole then proceeds from an
action corresponding to that equation of motion. The action obtained simply by
calculating the scalar curvature of the hole spacetime yields a model with
features like those of the relativistic free particle. In particular the
Hamiltonian is nonlocal, and for the wormhole cannot even be given as a
differential operator in closed form. Nonetheless the general solution of the
Schr\"odinger equation for wormhole wave functions, i.e., the wave-function
propagator, can be expressed as a path integral. Too complicated to perform
exactly, this can yet be evaluated via a WKB approximation. The result
indicates that the wormhole, classically stable, is quantum-mechanically
unstable: A Feynman-Kac decomposition of the WKB propagator yields no spectrum
of bound states. Though an initially localized wormhole wave function may
oscillate for many classical expansion/recontraction periods, it must
eventually leak to large radius values. The possibility of such a mode unstable
against growth, combined with


title: Exact Dirac Quantization of All 2-D Dilaton Gravity Theories

abstract:
  The most general dilaton gravity theory in 2 spacetime dimensions is
considered. A Hamiltonian analysis is performed and the reduced phase space,
which is two dimensional, is explicitly constructed in a suitable
parametrization of the fields. The theory is then quantized via the Dirac
method in a functional Schrodinger representation. The quantum constraints are
solved exactly to yield the (spatial) diffeomorphism invariant quantum wave
functional for all theories considered. This wave function depends explicitly
on the (single) configuration space coordinate as well as on the imbedding of
space into spacetime (i.e. on the choice of time).


title: Dirac spinor in a nonstationary Godel-type cosmological Universe

abstract:
  In the present article we solve, via separation of variables, the massless
Dirac equation in a nonstationary rotating, causal G\"odel-type cosmological
universe, having a constant rotational speed in all the points of the space. We
compute the frequency spectrum. We show that the spectrum of massless Dirac
particles is discrete and unbounded.


title: Geometric Structures and Loop Variables in (2+1)-Dimensional Gravity

abstract:
  This paper is a review of the relationship between the metric formulation of
(2+1)-dimensional gravity and the loop observables of Rovelli and Smolin. I
emphasize the possibility of reconstructing the geometry, via the theory of
geometric structures, from the values of the loop variables. I close with a
brief discussion of implications for quantization, particularly for covariant
canonical approaches to quantum gravity.


title: Early Direct Detection of Gravity Waves

abstract:
  Recently, the possibility has emerged of an early detection of astrophysical
gravity waves. In certain astronomical configurations, and through a new
light-deflection effect, gravity waves can cause apparent shifts in stellar
angular positions as large as $10^{-7}arcsec$. In these same configurations,
the magnitude of the gravity-wave-induced time-delay effect can exceed
$10^{-14}$. Both these figures lie just at present-day theoretical limits of
detectability. For instance, cases are described where the very faint
neutron-star gravity waves could soon become detectable. The detection meant
here involves direct observations of the very wave-forms.


title: Nonlinear Evolution of Density Perturbations

abstract:
  : From the epoch of recombination $(z\approx 10^3)$ till today, the typical
density contrasts have grown by a factor of about $10^6$ in a Friedmann
universe with $\Omega=1$. However, during the same epoch the typical
gravitational potential has grown only by a factor of order unity. We present
theoretical arguments explaining the origin of this approximate constancy of
gravitational potential. This fact can be exploited to provide a new, powerful,
approximation scheme to study the formation of nonlinear structures in the
universe. The essential idea of this method is to evolve the initial
distribution of particles using a gravitational potential frozen in time
(Frozen Potential Approximation). This approximation provides valuable insight
into understanding various features of nonlinear evolution; for example, it
provides a simple explanation as to why pancakes remain thin during the
evolution even in the absence of any artificial, adhesion-like, damping terms.
We compare the trajectories of particles in various approximations. We also
discuss a few applications of the frozen potential approximation.


title: Non-Singular Constant Curvature Two-Dimensional Black Hole

abstract:
  We show that the two-dimensional theory of Teitelboim and Jackiw has a black
hole solution, with two surprising properties: first, it has constant
curvature, and second, is free of spacetime singularities. The maximally
extended spacetime consists of an infinite chain of universes connected by
timelike wormholes.


title: Reality Conditions in Nonperturbative Quantum Cosmology

abstract:
  We carry out the nonperturbative canonical quantization of several types of
cosmological models that have already been studied in the geometrodynamic
formulation using the complex path-integral approach. We establish a relation
between the choices of complex contours in the path integral and the sets of
reality conditions for which the metric representation is well defined, proving
that the ambiguity in the selection of complex contours disappears when one
imposes suitable reality conditions. In most of the cases, the wave functions
defined by means of the path integral turn out to be non-normalizable and
cannot be accepted as proper quantum states. Moreover, the wave functions of
the Universe picked out in quantum cosmology by the no-boundary condition and
the tunneling proposals do not belong, in general, to the Hilbert space of
quantum states. Finally, we show that different sets of reality conditions can
lead to equivalent quantum theories. This fact enables us to extract physical
predictions corresponding to Lorentzian gravity from quantum theories
constructed with other than Lorentzian reality conditions.


title: Green's function for gravitational waves in FRW spacetimes

abstract:
  A method for calculating the retarded Green's function for the gravitational
wave equation in Friedmann-Roberson-Walker spacetimes, within the formalism of
linearized Einstein gravity is developed. Hadamard's general solution to
Cauchy's problem for second-order, linear partial differential equations is
applied to the FRW gravitational wave equation. The retarded Green's function
may be calculated for any FRW spacetime, with curved or flat spatial sections,
for which the functional form of the Ricci scalar curvature $R$ is known. The
retarded Green's function for gravitational waves propagating through a
cosmological fluid composed of both radiation and dust is calculated
analytically for the first time. It is also shown that for all FRW spacetimes
in which the Ricci scalar curvatures does not vanish, $R \neq 0$, the Green's
function violates Huygens' principle; the Green's function has support inside
the light-cone due to the scatter of gravitational waves off the background
curvature.


title:
Black Hole Entropy and the Dimensional Continuation of the Gauss-Bonnet
  Theorem

abstract:
  The Euclidean black hole has topology $\Re^2 \times {\cal S}^{d-2}$. It is
shown that -in Einstein's theory- the deficit angle of a cusp at any point in
$\Re^2$ and the area of the ${\cal S}^{d-2}$ are canonical conjugates. The
black hole entropy emerges as the Euler class of a small disk centered at the
horizon multiplied by the area of the ${\cal S}^{d-2}$ there.These results are
obtained through dimensional continuation of the Gauss-Bonnet theorem. The
extension to the most general action yielding second order field equations for
the metric in any spacetime dimension is given.


title: Einstein-Cartan theory of gravity revisited

abstract:
  The role of space-time torsion in general relativity is reviewed in
accordance with some recent results on the subject. It is shown that, according
to the connection compatibility condition, the usual Riemannian volume element
is not appropriate in the presence of torsion. A new volume element is proposed
and used in the Lagrangian formulation for Einstein-Cartan theory of gravity.
  The dynamical equations for the space-time geometry and for matter fields are
obtained, and some of their new predictions and features are discussed. In
particular, one has that torsion propagates and that gauge fields can interact
with torsion without the breaking of gauge invariance. It is shown also that
the new Einstein-Hilbert action for Einstein-Cartan theory may provide a
physical interpretation for dilaton gravity in terms of the non-riemannian
structure of space-time.


title: On a Quantum Universe Filled with Yang - Mills Radiation

abstract:
  We investigate the properties of a quantum Robertson - Walker universe
described by the Wheeler -- DeWitt equation. The universe is filled with a
quantum Yang -- Mills uniform field. This is then a quantum mini copy of the
standard model of our universe. We discuss the interpretation of the Wheeler --
DeWitt wave function using the correspondence principle to connect
$\vert\psi\vert^2$ for large quantum numbers to the classical probability for a
radiation dominated universe. This can be done in any temporal gauge. The
correspondence principle determines the Schr\"odinger representation of the
momentum associated to the gravitational degree of freedom. We also discuss the
measure in the mini--superspace needed to ensure invariance of the quantum
description under change of the temporal gauge. Finally, we examine the
behaviour of $\vert\psi\vert^2$ in inflationary conditions.


title: Anti-Gravity Bounds and the Ricci Tensor

abstract:
  Recently Penrose, Sorkin and Woolgar have developed a new technique for
proving the positive mass theorem in general relativity. We extend their result
to produce a new inequality relating the mass, electric and scalar charges in
theories coupling to a dilaton in the usual way. Using a five dimensional
formalism, our result provides new information not available from the existing
techniques. The main result may be simply expressed as
  M + g\Sigma \ge { \sqrt{1+g^2} |Q| \over \sqrt {4\pi G} } . where `M' is the
A.D.M. mass, `Q' is the electric charge, `\Sigma' the scalar charge and `g' is
the dilaton coupling parameter.


title: Self-dual gravity as a two dimensional theory and conservation laws

abstract:
  Starting from the Ashtekar Hamiltonian variables for general relativity, the
self-dual Einstein equations (SDE) may be rewritten as evolution equations for
three divergence free vector fields given on a three dimensional surface with a
fixed volume element.
  From this general form of the SDE, it is shown how they may be interpreted as
the field equations for a two dimensional field theory. It is further shown
that these equations imply an infinite number of non-local conserved currents.
  A specific way of writing the vector fields allows an identification of the
full SDE with those of the two dimensional chiral model, with the gauge group
being the group of area preserving diffeomorphisms of a two dimensional
surface. This gives a natural Hamiltonian formulation of the SDE in terms of
that of the chiral model. The conservation laws using the explicit chiral model
form of the equations are also given.


title: Regge calculus in the canonical form

abstract:
  (3+1) (continuous time) Regge calculus is reduced to Hamiltonian form. The
constraints are classified, classical and quantum consequences are discussed.
As basic variables connection matrices and antisymmetric area tensors are used
supplemented with appropriate bilinear constraints. In these variables the
action can be made quasipolinomial with $\arcsin$ as the only deviation from
polinomiality. In comparison with analogous formalism in the continuum theory
classification of constraints changes: some of them disappear, the part of I
class constraints including Hamiltonian one become II class (and vice versa,
some new constraints arise and some II class constraints become I class). As a
result, the number of the degrees of freedom coincides with the number of links
in 3-dimensional leaf of foliation. Moreover, in empty space classical dynamics
is trivial: the scale of timelike links become zero and spacelike links are
constant.


title: On polinomial formulations of general relativity

abstract:
  As basic variables in general relativity (GR) are chosen antisymmetric
connection and bivectors - bilinear in tetrad area tensors subject to
appropriate (bilinear) constraints. In canonical formalism we get theory with
polinomial constraints some of which are II class. On partial resolving the
latter we get another polinomial formulation. Separating self- and antiselfdual
parts of antisymmetric tensors we come to Ashtekar constraints including those
known as "reality conditions" which connect self- and antiselfdual sectors of
the theory. These conditions form second class system and cannot be simply
imposed on quantum states (or taken as initial conditions in classical theory).
Rather these should be taken into account in operator sence by forming
corresponding Dirac brackets. As a result, commutators between canonical
variables are no longer polinomial, and even separate treatment of self- and
antiselfdual sectors is impossible.


title: Black Hole Evaporation without Information Loss

abstract:
  An approach to black hole quantization is proposed wherein it is assumed that
quantum coherence is preserved. A consequence of this is that the Penrose
diagram describing gravitational collapse will show the same topological
structure as flat Minkowski space. After giving our motivations for such a
quantization procedure we formulate the background field approximation, in
which particles are divided into "hard" particles and "soft" particles. The
background space-time metric depends both on the in-states and on the
out-states. We present some model calculations and extensive discussions. In
particular, we show, in the context of a toy model, that the $S$-matrix
describing soft particles in the hard particle background of a collapsing star
is unitary, nevertheless, the spectrum of particles is shown to be
approximately thermal. We also conclude that there is an important topological
constraint on functional integrals.


title:
Inverse Square Law of Gravitation in (2+1)-Dimensional Space-Time as a
  Consequence of Casimir Energy

abstract:
  The gravitational effect of vacuum polarization in space exterior to a
particle in (2+1)-dimensional Einstein theory is investigated. In the weak
field limit this gravitational field corresponds to an inverse square law of
gravitational attraction, even though the gravitational mass of the quantum
vacuum is negative. The paradox is resolved by considering a particle of finite
extension and taking into account the vacuum polarization in its interior.


title: Scalar field quantization on the 2+1 dimensional black hole background

abstract:
  The quantization of a massless conformally coupled scalar field on the 2+1
dimensional Anti de Sitter black hole background is presented. The Green's
function is calculated, using the fact that the black hole is Anti de Sitter
space with points identified, and taking into account the fact that the black
hole spacetime is not globally hyperbolic. It is shown that the Green's
function calculated in this way is the Hartle-Hawking Green's function. The
Green's function is used to compute $\langle T^\mu_\nu \rangle$, which is
regular on the black hole horizon, and diverges at the singularity. A particle
detector response function outside the horizon is also calculated and shown to
be a fermi type distribution. The back-reaction from $\langle T_{\mu\nu}
\rangle$ is calculated exactly and is shown to give rise to a curvature
singularity at $r=0$ and to shift the horizon outwards. For $M=0$ a horizon
develops, shielding the singularity. Some speculations about the endpoint of
evaporation are discussed.


title: General Relativity as a Theory of Two Connections

abstract:
  We show in this paper that it is possible to formulate General Relativity in
a phase space coordinatized by two $SO(3)$ connections. We analyze first the
Husain-Kucha\v{r} model and find a two connection description for it.
Introducing a suitable scalar constraint in this phase space we get a
Hamiltonian formulation of gravity that is close to the Ashtekar one, from
which it is derived, but has some interesting features of its own. Among them a
possible mechanism for dealing with the degenerate metrics and a neat way of
writing the constraints of General Relativity.


title: Local Position Invariance and Vacuum Energy Shifts

abstract:
  We discuss tests of the Einstein Equivalence Principle due to energies which
are purely quantum mechanical in origin. In particular, we consider using Lamb
Shift energies to test for possible quantum violations of Local Position
Invariance. (to appear in the Proceedings of the 5th Canadian Conference on
General Relativity and Relativistic Astrophysics, University of Waterloo, May
13-- 15, 1993) (acknowledgements changed to correct an omission in the
originally submitted version)


title:
Cosmological Rotation of Quantum-Mechanical Origin and Anisotropy of the
  Microwave Background

abstract:
  It is shown that rotational cosmological perturbations can be generated in
the early Universe, similarly to gravitational waves. The generating mechanism
is quantum-mechanical in its nature, and the created perturbations should now
be placed in squeezed vacuum quantum states. The physical conditions under
which the phenomenon can occur are formulated. The generated perturbations can
contribute to the large-angular-scale anisotropy of the cosmic microwave
background radiation. An exact formula is derived for the angular correlation
function of the temperature variations caused by the quantum-mechanically
generated rotational perturbations. The multipole expansion begins from the
dipole component. The comparison with the case of gravitational waves is made.


title:
Canonical Quantization of Spherically Symmetric Gravity in Ashtekar's
  Self-Dual Representation

abstract:
  We show that the quantization of spherically symmetric pure gravity can be
carried out completely in the framework of Ashtekar's self-dual representation.
Consistent operator orderings can be given for the constraint functionals
yielding two kinds of solutions for the constraint equations, corresponding
classically to globally nondegenerate or degenerate metrics. The physical state
functionals can be determined by quadratures and the reduced Hamiltonian system
possesses 2 degrees of freedom, one of them corresponding to the classical
Schwarzschild mass squared and the canonically conjugate one representing a
measure for the deviation of the nonstatic field configurations from the static
Schwarzschild one. There is a natural choice for the scalar product making the
2 fundamental observables self-adjoint. Finally, a unitary transformation is
performed in order to calculate the triad-representation of the physical state
functionals and to provide for a solution of the appropriately regularized
Wheeler-DeWitt equation.


title:
On the solution of the initial value constraints for general relativity
  coupled to matter in terms of Ashtekar's variables

abstract:
  The method of solution of the initial value constraints for pure canonical
gravity in terms of Ashtekar's new canonical variables due to CDJ is further
developed in the present paper. There are 2 new main results : 1) We extend the
method of CDJ to arbitrary matter-coupling again for non-degenerate metrics :
the new feature is that the 'CDJ-matrix' adopts a nontrivial antisymmetric part
when solving the vector constraint and that the Klein-Gordon-field is used,
instead of the symmetric part of the CDJ-matrix, in order to satisfy the scalar
constraint. 2) The 2nd result is that one can solve the general initial value
constraints for arbitrary matter coupling by a method which is completely
independent of that of CDJ. It is shown how the Yang-Mills and gravitational
Gauss constraints can be solved explicitely for the corresponding electric
fields. The rest of the constraints can then be satisfied by using either
scalar or spinor field momenta. This new trick might be of interest also for
Yang-Mills theories on curved backgrounds.


title: The Constraints of 2+1 Quantum Gravity

abstract:
  To appear in proceedings of II Workshop on ``Constraints Theory and
Quantisation Methods''Montepulciano (Siena) 1993}
  General discussion of the constraints of 2+1 gravity, with emphasis on two
approaches, namely the second order and first order formalisms, and comparison
with the four dimensional theory wherever possible. Introduction to an operator
algebra approach that has been developed in the last few years in collaboration
with T.Regge, and discussion of the quantisation of the g=1 case.


title: Stability of Non-Abelian Black Holes

abstract:
  Two types of self-gravitating particle solutions found in several theories
with non-Abelian fields are smoothly connected by a family of non-trivial black
holes. There exists a maximum point of the black hole entropy, where the
stability of solutions changes. This criterion is universal, and the changes in
stability follow from a catastrophe-theoretic analysis of the potential
function defined by black hole entropy.