title: General Laws of Black-Hole Dynamics

abstract:
  A general definition of a black hole is given, and general `laws of
black-hole dynamics' derived. The definition involves something similar to an
apparent horizon, a trapping horizon, defined as a hypersurface foliated by
marginal surfaces of one of four non-degenerate types, described as future or
past, and outer or inner. If the boundary of an inextendible trapped region is
suitably regular, then it is a (possibly degenerate) trapping horizon. The
future outer trapping horizon provides the definition of a black hole. Outer
marginal surfaces have spherical or planar topology. Trapping horizons are null
only in the instantaneously stationary case, and otherwise outer trapping
horizons are spatial and inner trapping horizons are Lorentzian. Future outer
trapping horizons have non-decreasing area form, constant only in the null
case---the `second law'. A definition of the trapping gravity of an outer
trapping horizon is given, generalizing surface gravity. The total trapping
gravity of a compact outer marginal surface has an upper bound, attained if and
only if the trapping gravity is constant---the `zeroth law'. The variation of
the area form along an outer trapping horizon is determined by the trapping
gravity and an energy flux---the `first law'.


title: The Universality of Einstein Equations

abstract:
  It is shown that for a wide class of analytic Lagrangians which depend only
on the scalar curvature of a metric and a connection, the application of the
so--called ``Palatini formalism'', i.e., treating the metric and the connection
as independent variables, leads to ``universal'' equations. If the dimension
$n$ of space--time is greater than two these universal equations are Einstein
equations for a generic Lagrangian and are suitably replaced by other universal
equations at bifurcation points. We show that bifurcations take place in
particular for conformally invariant Lagrangians $L=R^{n/2} \sqrt g$ and prove
that their solutions are conformally equivalent to solutions of Einstein
equations. For 2--dimensional space--time we find instead that the universal
equation is always the equation of constant scalar curvature; the connection in
this case is a Weyl connection, containing the Levi--Civita connection of the
metric and an additional vectorfield ensuing from conformal invariance. As an
example, we investigate in detail some polynomial Lagrangians and discuss their
bifurcations.


title: No Superluminal Expansion of the Universe

abstract:
  The apparent superluminal growth in the size of a sufficiently large part of
the universe can be ascribed to the special relativistic effect of time
dilation.


title: Conformal Fourth-Rank Gravity

abstract:
  We consider the consequences of describing the metric properties of space-
time through a quartic line element $ds^4=G_{\mu\nu\lambda\rho}dx^\mu dx^\nu
dx^\lambda dx^\rho$. The associated "metric" is a fourth-rank tensor
$G_{\mu\nu\lambda\rho}$. We construct a theory for the gravitational field
based on the fourth-rank metric $G_{\mu\nu\lambda\rho}$ which is conformally
invariant in four dimensions. In the absence of matter the fourth-rank metric
becomes of the form $G_{\mu\nu\lambda\rho}=g_{(\mu\nu}g_{\lambda\rho )}$
therefore we recover a Riemannian behaviour of the geometry; furthermore, the
theory coincides with General Relativity. In the presence of matter we can keep
Riemannianicity, but now gravitation couples in a different way to matter as
compared to General Relativity. We develop a simple cosmological model based on
a FRW metric with matter described by a perfect fluid. Our field equations
predict that the entropy is an increasing function of time. For $k_{obs}=0$ the
field equations predict $\Omega\approx 4y$, where $y={p\over\rho}$; for
$\Omega_{small}=0.01$ we obtain $y_{pred}=2.5\times 10^{-3}$. $y$ can be
estimated from the mean random velocity of typical galaxies to be
$y_{random}=1\times10^{-5}$. For the early universe there is no violation of
causality for $t>t_{class}\approx10^{19}t_{Planck}\approx 10^{-24}s$.


title:
The Extended Loop Group: An Infinite Dimensional Manifold Associated
  with the Loop Space

abstract:
  A set of coordinates in the non parametric loop-space is introduced. We show
that these coordinates transform under infinite dimensional linear
representations of the diffeomorphism group. An extension of the group of loops
in terms of these objects is proposed. The enlarged group behaves locally as an
infinite dimensional Lie group. Ordinary loops form a subgroup of this group.
The algebraic properties of this new mathematical structure are analized in
detail. Applications of the formalism to field theory, quantum gravity and knot
theory are considered.


title: The Construction of Sorkin Triangulations

abstract:
  Some time ago, Sorkin (1975) reported investigations of the time evolution
and initial value problems in Regge calculus, for one triangulation each of the
manifolds $R*S^3$ and $R^4$. Here we display the simple, local characteristic
of those triangulations which underlies the structure found by Sorkin, and
emphasise its general applicability, and therefore the general validity of
Sorkin's conclusions. We also make some elementary observations on the
resulting structure of the time evolution and initial value problems in Regge
calculus, and add some comments and speculations.


title: Microcanonical Action and the Entropy of a Rotating Black Hole

abstract:
  The authors have recently proposed a ``microcanonical functional integral"
representation of the density of quantum states of the gravitational field. The
phase of this real--time functional integral is determined by a
``microcanonical" or Jacobi action, the extrema of which are classical
solutions at fixed total energy, not at fixed total time interval as in
Hamilton's action. This approach is fully general but is especially well suited
to gravitating systems because for them the total energy can be fixed simply as
a boundary condition on the gravitational field. In this paper we describe how
to obtain Jacobi's action for general relativity. We evaluate it for a certain
complex metric associated with a rotating black hole and discuss the relation
of the result to the density of states and to the entropy of the black hole.
(Dedicated to Yvonne Choquet-Bruhat in honor of her retirement.)


title: Torsion and Nonmetricity in Scalar-Tensor Theories of Gravity

abstract:
  We show that the gravitational field equations derived from an action
composed of i) an arbitrary function of the scalar curvature and other scalar
fields plus ii) connection-independent kinetic and source terms, are identical
whether one chooses nonmetricity to vanish and have non-zero torsion or vice
versa.


title: Maxwell Fields in Spacetimes Admitting Non-Null Killing Vectors

abstract:
  We consider source-free electromagnetic fields in spacetimes possessing a
non-null Killing vector field, $\xi^a$. We assume further that the
electromagnetic field tensor, $F_{ab}$, is invariant under the action of the
isometry group induced by $\xi^a$. It is proved that whenever the two
potentials associated with the electromagnetic field are functionally
independent the entire content of Maxwell's equations is equivalent to the
relation $\n^aT_{ab}=0$. Since this relation is implied by Einstein's equation
we argue that it is enough to solve merely Einstein's equation for these
electrovac spacetimes because the relevant equations of motion will be
satisfied automatically. It is also shown that for the exceptional case of
functionally related potentials $\n^aT_{ab}=0$ implies along with one of the
relevant equations of motion that the complementary equation concerning the
electromagnetic field is satisfied.


title:
Bibliography of Publications related to Classical and Quantum Gravity in
  terms of the Ashtekar Variables

abstract:
  This bibliography attempts to give a comprehensive overview of all the
literature related to the Ashtekar variables. The original version was compiled
by Peter Huebner in 1989, and it has been subsequently updated by Gabriela
Gonzalez and Bernd Bruegmann. Information about additional literature, new
preprints, and especially corrections are always welcome.


title: The Isaacson expansion in quantum cosmology

abstract:
  This paper is an application of the ideas of the Born-Oppenheimer (or
slow/fast) approximation in molecular physics and of the Isaacson (or
short-wave) approximation in classical gravity to the canonical quantization of
a perturbed minisuperspace model of the kind examined by Halliwell and Hawking.
Its aim is the clarification of the role of the semiclassical approximation and
the backreaction in such a model. Approximate solutions of the quantum model
are constructed which are not semiclassical, and semiclassical solutions in
which the quantum perturbations are highly excited.


title: Topologica Defects and Corrections to the Nambu Action

abstract:
  The effective action of a (1+2)-dimensional defect is obtained as an
expansion in powers of the thickness.Considering non-straight solutions as the
zero order term, the corrections to the Nambu action are found to depend on the
curvature scalar and on the gaussian curvature .


title: Wave Functions of the Induced 2D-Gravity

abstract:
  We consider the induced $2$d-gravity in the minisuperspace approach. The
general solution to the Wheeler-DeWitt equation is given in terms of different
kind of Bessel functions of purely real or imaginary orders. We study the
properties of the corresponding probability distribution finding a kind of
phase transition at the critical point $\nu=0$.


title: Loop Representations for 2+1 Gravity on a Torus

abstract:
  We study the loop representation of the quantum theory for 2+1 dimensional
general relativity on a manifold, $M = {\cal T}^2 \times {\cal R}$, where
${\cal T}^2$ is the torus, and compare it with the connection representation
for this system. In particular, we look at the loop transform in the part of
the phase space where the holonomies are boosts and study its kernel. This
kernel is dense in the connection representation and the transform is not
continuous with respect to the natural topologies, even in its domain of
definition. Nonetheless, loop representations isomorphic to the connection
representation corresponding to this part of the phase space can still be
constructed if due care is taken. We present this construction but note that
certain ambiguities remain; in particular, functions of loops cannot be
uniquely associated with functions of connections.


title: Clock Time and Entropy

abstract:
  Testable conditional probabilities appear to be restricted to single
hypersurfaces (marvelous moments) and depend only on stationary observables.
Observable evolution, such as a change of entropy, should be expressed as a
dependence upon clock time, not upon inaccessible coordinate time.


title:
Non-Analytic Extension of the Kinnersley-Chitre Group for Colliding
  Plane Gravitational Waves. I

abstract:
  A program is outlined concerning the set of all solutions of the hyperbolic
Ernst equation on a two-dimensional manifold whose underlying topological space
is the same as the domain of all Ernst potentials for colliding plane
gravitational wave pairs. The aim of the program is to construct and apply a
non-trivial extension of the group of Kinnersley-Chitre transformations. This
is to be done by employing the formalism of a homogeneous Hilbert problem. In
this first paper of a series, the aforementioned program is completely carried
out for the collinear polarization case.


title:
Inconsistency between alternative approaches to Quantum Decoherence in
  special systems

abstract:
  We study the decoherence properties of a certain class of Markovian quantum
open systems from both the Decohering Histories and Environment Induced
Superselection paradigms. The class studied includes many familiar quantum
optical cases. For this class, we show that there always exists a basis which
leads to {\em exactly} consistent histories for any coarse graining {\em
irrespective} of the initial conditions. The magnitude of the off--diagonal
elements of the reduced density matrix $\rho$ in this basis however, depends on
the initial conditions. Necessary requirements for classicality as advanced by
the two paradigms are thus in direct conflict in these systems.


title:
Inflationary Attractors and Perturbation Spectra in Generally Coupled
  Gravity

abstract:
  A generic outcome of theories with scalar-tensor coupling is the existence of
inflationary attractors, either power-law or de Sitter. The fluctuations
arising during this phase are Gaussian and their spectrum depends on the
wavenumber $k$ according to the power-law $k^{1/(1-p)}$, where $p$ is the
inflationary power-law exponent. We investigate to which extent these
properties depend on the coupling function and on the potential. We find the
class of models in which viable attractors exist. Within this class, we find
that the cosmic expansion and the scaling of the fluctuation spectrum are
independent of the coupling function. Further, the analytical solution of the
Fokker-Planck equation shows that the deviations from Gaussianity are
negligible.


title: Generalized Symmetries of the Einstein Equations

abstract:
  We reformulate the symmetries of Gurses [Phys. Rev. Lett. 70, 367 (1993)] in
a more abstract, more geometrical manner. The type (b) transformation of
\gurses\ is related to a diffeomorphism of the differentiable manifold onto
itself. The type (c) symmetry is replaced by a more general type (c-bar)
symmetry that has the nice property that the commutator of a type (c-bar)
generator with a type (a) generator is itself of type (c-bar). We identify a
differential constraint that transformations of type (c) and (c-bar) must
satisfy, and which, in our opinion, may severely limit the usefulness of these
transformations.


title:
Radiation from a Uniformly Accelerated Charge and the Equivalence
  Principle

abstract:
  We argue that purely local experiments can distinguish a stationary charged
particle in a static gravitational field from an accelerated particle in
(gravity-free) Minkowski space. Some common arguments to the contrary are
analyzed and found to rest on a misidentification of ``energy''.


title:
Unique determination of an inner product by adjointness relations in the
  algebra of quantum observables

abstract:
  It is shown that if a representation of a *-algebra on a vector space $V$ is
an irreducible *-representation with respect to some inner product on $V$ then
under appropriate technical conditions this property determines the inner
product uniquely up to a constant factor. Ashtekar has suggested using the
condition that a given representation of the algebra of quantum observables is
a *-representation to fix the inner product on the space of physical states.
This idea is of particular interest for the quantisation of gravity where an
obvious prescription for defining an inner product is lacking. The results of
this paper show rigorously that Ashtekar's criterion does suffice to determine
the inner product in very general circumstances. Two versions of the result are
proved: a simpler one which only applies to representations by bounded
operators and a more general one which allows for unbounded operators. Some
concrete examples are worked out in order to illustrate the meaning and range
of applicability of the general theorems.


title:
The Newtonian Limit for Asymptotically Flat Solutions of the
  Vlasov-Einstein System

abstract:
  It is shown that there exist families of asymptotically flat solutions of the
Einstein equations coupled to the Vlasov equation describing a collisionless
gas which have a Newtonian limit. These are sufficiently general to confirm
that for this matter model as many families of this type exist as would be
expected on the basis of physical intuition. A central role in the proof is
played by energy estimates in unweighted Sobolev spaces for a wave equation
satisfied by the second fundamental form of a maximal foliation.


title: Loop Variable Inequalities in Gravity and Gauge Theory

abstract:
  We point out an incompleteness of formulations of gravitational and gauge
theories that use traces of holonomies around closed curves as their basic
variables. It is shown that in general such loop variables have to satisfy
certain inequalities if they are to give a description equivalent to the usual
one in terms of local gauge potentials.


title:
Critical Phenomena for Riemannian Manifolds: Simple Homotopy and
  Simplicial Quantum Gravity

abstract:
  We show how Gromov's spaces of bounded geometries provide a general
mathematical framework for addressing and solving many of the issues of
$3D$-simplicial quantum gravity. In particular, we establish entropy estimates
characterizing the asymptotic distribution of combinatorially inequivalent
triangulated $3$-manifolds, as the number of tetrahedra diverges. Moreover, we
offer a rather detailed presentation of how spaces of three-dimensional
riemannian manifolds with natural bounds on curvatures, diameter, and volume
can be used to prove that three-dimensional simplicial quantum gravity is
connected to a Gaussian model determined by the simple homotopy types of the
underlying manifolds. This connection is determined by a Gaussian measure
defined over the general linear group $GL({\bf R},\infty)$. It is shown that
the partition function of three-dimensional simplicial quantum gravity is
well-defined, in the thermodynamic limit, for a suitable range of values of the
gravitational and cosmological coupling constants. Such values are determined
by the Reidemeister-Franz torsion invariants associated with an orthogonal
representation of the fundamental groups of the set of manifolds considered.
The geometrical system considered shows also critical behavior, and in such a
case the partition function is exactly evaluated and shown to be equal to the
Reidemeister-Franz torsion. The phase structure in the thermodynamical limit is
also discussed. In particular, there are either phase transitions describing
the passage from a simple homotopy type to another, and (first order) phase
transitions within a given simple homotopy type which seem to confirm, on an
analytical ground, the picture suggested by numerical simulations.


title: Quasi-Local Gravitational Energy

abstract:
  A dynamically preferred quasi-local definition of gravitational energy is
given in terms of the Hamiltonian of a `2+2' formulation of general relativity.
The energy is well-defined for any compact orientable spatial 2-surface, and
depends on the fundamental forms only. The energy is zero for any surface in
flat spacetime, and reduces to the Hawking mass in the absence of shear and
twist. For asymptotically flat spacetimes, the energy tends to the Bondi mass
at null infinity and the \ADM mass at spatial infinity, taking the limit along
a foliation parametrised by area radius. The energy is calculated for the
Schwarzschild, Reissner-Nordstr\"om and Robertson-Walker solutions, and for
plane waves and colliding plane waves. Energy inequalities are discussed, and
for static black holes the irreducible mass is obtained on the horizon.
Criteria for an adequate definition of quasi-local energy are discussed.


title: Uncertainty Relation at Finite Temperature

abstract:
  We use the quantum Brownian model to derive the uncertainty relation for a
quantum open system. We examine how the fluctuations of a quantum system evolve
after it is brought in contact with a heat bath at finite temperature. We study
the decoherence and relaxation processes and use this example to examine 1) the
relation between quantum and thermal fluctuations; and 2) the conditions when
the two basic postulates of quantum statistical mechanics become valid.


title: Geometrodynamics vs. Connection Dynamics

abstract:
  The purpose of this review is to describe in some detail the mathematical
relationship between geometrodynamics and connection dynamics in the context of
the classical theories of 2+1 and 3+1 gravity. I analyze the standard
Einstein-Hilbert theory (in any spacetime dimension), the Palatini and
Chern-Simons theories in 2+1 dimensions, and the Palatini and self-dual
theories in 3+1 dimensions. I also couple various matter fields to these
theories and briefly describe a pure spin-connection formulation of 3+1
gravity. I derive the Euler-Lagrange equations of motion from an action
principle and perform a Legendre transform to obtain a Hamiltonian formulation
of each theory. Since constraints are present in all these theories, I
construct constraint functions and analyze their Poisson bracket algebra. I
demonstrate, whenever possible, equivalences between the theories.


title: Scalar and Spinor Fields in Signature Changing Spacetimes

abstract:
  The propagation of scalar and spinor fields in a spacetime whose metric
changes signature is analyzed. Recent work of Dray et al. on particle
production from signature change for a (massless) scalar field is reviewed, and
an attempt is made to extend their analysis to the case of a (massless)
spin-half field. In contrast to their results for a scalar field, it is shown
here---for $SL(2,C)$ spinors---that although there are inequivalent forms of
the Dirac equation that can be used to propagate a spinor in a signature
changing spacetime, none of these forms gives rise to a conserved inner product
on the space of solutions to the field equations.


title: Junction Conditions for Signature Change

abstract:
  The change of signature of a metric is explained using simple examples and
methods. The Klein-Gordon field on a signature-changing background is
discussed, and it is shown how the approach of Dray et al.\ can be corrected to
ensure that the Klein-Gordon equation holds. Isotropic cosmologies are
discussed, and it is shown how the approach of Ellis et al.\ can be corrected
to ensure that the Einstein-Klein-Gordon equations hold. A straightforward
calculation shows that a well defined Ricci tensor requires the standard
junction condition, namely vanishing of the second fundamental form of the
junction surface.


title: Exotic Black Holes?

abstract:
  Exotic smooth manifolds, ${\bf R^2\times_\Theta S^2}$, are constructed and
discussed as possible space-time models supporting the usual Kruskal
presentation of the vacuum Schwarzschild metric locally, but {\em not
globally}. While having the same topology as the standard Kruskal model, none
of these manifolds is diffeomorphic to standard Kruskal, although under certain
conditions some global smooth Lorentz-signature metric can be continued from
the local Kruskal form. Consequently, it can be conjectured that such manifolds
represent an infinity of physically inequivalent (non-diffeomorphic) space-time
models for black holes. However, at present nothing definitive can be said
about the continued satisfaction of the Einstein equations. This problem is
also discussed in the original Schwarzschild $(t,r)$ coordinates for which the
exotic region is contained in a world tube along the time-axis, so that the
manifold is spatially, but not temporally, asymptotically standard. In this
form, it is tempting to speculate that the confined exotic region might serve
as a source for some exterior solution. Certain aspects of the Cauchy problem
are also discussed in terms of ${\bf R^4_\\Theta}$\ models which are
``half-standard'', say for all $t<0,$ but for which $t$ cannot be globally
smooth.


title: Decoherence Functional and Inhomogeneities in the Early Universe

abstract:
  We investigate the quantum to classical transition of small inhomogeneous
fluctuations in the early Universe using the decoherence functional of
Gell-Mann and Hartle. We study two types of coarse graining; one due to coarse
graining the value of the scalar field and the other due to summing over an
environment. We compare the results with a previous study using an environment
and the off-diagonal rule proposed by Zurek. We show that the two methods give
different results.


title:
Naked Singularities in Spherically Symmetric Inhomogeneous Tolman-Bondi
  Dust Cloud Collapse

abstract:
  We investigate the occurrence and nature of naked singularity for the
inhomogeneous gravitational collapse of Tolman-Bondi dust clouds.It is shown
that the naked singularities form at the center of the collapsing cloud in a
wide class of collapse models which includes the earlier cases considered by
Eardley and Smarr and Christodoulou. This class also contains self-similar as
well as non-self-similar models. The structure and strength of this singularity
is examined and the question is investigated as to when a non-zero measure set
of non-spacelike trajectories could be emitted from the singularity as opposed
to isolated trajectories coming out. It is seen that the weak energy condition
and positivity of energy density ensures that the families of non-spacelike
trajectories come out of the singularity. The curvature strength of the naked
singularity is examined which provides an important test for its physical
significance and powerful curvature growth near the naked singularity is
pointed out for several subclasses considered. The conditions are discussed for
the naked singularity to be globally naked. Implications for the basic issue of
the final fate of gravitational collapse are considered once the
inhomogeneities in the matter distribution are taken into account. It is argued
that a physical formulation for the cosmic censorship may be evolved which
avoids the features above. Possibilities in this direction are discussed while
indicating that the analysis presented here should be useful for any possible
rigorous formulation of the cosmic censorship hypothesis.


title: Motion of Inertial Observers Through Negative Energy

abstract:
  Recent research has indicated that negative energy fluxes due to quantum
coherence effects obey uncertainty principle-type inequalities of the form
$|\Delta E|\,{\Delta \tau} \lprox 1\,$. Here $|\Delta E|$ is the magnitude of
the negative energy which is transmitted on a timescale $\Delta \tau$. Our main
focus in this paper is on negative energy fluxes which are produced by the
motion of observers through static negative energy regions. We find that
although a quantum inequality appears to be satisfied for radially moving
geodesic observers in two and four-dimensional black hole spacetimes, an
observer orbiting close to a black hole will see a constant negative energy
flux. In addition, we show that inertial observers moving slowly through the
Casimir vacuum can achieve arbitrarily large violations of the inequality. It
seems likely that, in general, these types of negative energy fluxes are not
constrained by inequalities on the magnitude and duration of the flux. We
construct a model of a non-gravitational stress-energy detector, which is
rapidly switched on and off, and discuss the strengths and weaknesses of such a
detector.


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

abstract:
  Cosmological perturbations generated quantum-mechanically (as a particular
case, during inflation) possess statistical properties of squeezed quantum
states. The power spectra of the perturbations are modulated and the angular
distribution of the produced temperature fluctuations of the CMBR is quite
specific. An exact formula is derived for the angular correlation function of
the temperature fluctuations caused by squeezed gravitational waves. The
predicted angular pattern can, in principle, be revealed by the COBE-type
observations.


title:
Bianchi Cosmological Models in the Minimum Quadratic Poincare Gauge
  Theory of Gravity

abstract:
  Within the framework of the minimum quadratic Poincare gauge theory of
gravity in the Riemann-Cartan spacetime the dynamics of homogeneous anisotropic
Bianchi types I-IX spinning-fluid cosmological models is investigated. A basic
equation set for these models is obtained and analyzed. In particular, exact
solutions for the Bianchi type-I spinning-fluid and Bianchi type-V
perfect-fluid models are found in analytic form.


title: Gravity-Wave Watching

abstract:
  It is suggested that gravity waves could, in several cases, be detected by
means of already (or shortly to be) available technology, independently of
current efforts of detection. The present is a follow-up on a recently
suggested detection strategy based on gravity-wave-induced deviations of null
geodesics. The new development is that a way was found to probe the waves close
to the source, where they are several orders of magnitude larger than on the
Earth. The effect translates into apparent shifts in stellar angular positions
that could be as high as $10^{-7}$ arcsec, which is just about the present
theoretical limit of detectability. (Calculation improved; results unchanged.)


title: Proof of the Thin Sandwich Conjecture

abstract:
  We prove that the Thin Sandwich Conjecture in general relativity is valid,
provided that the data $(g_{ab},\dot g_{ab})$ satisfy certain geometric
conditions. These conditions define an open set in the class of possible data,
but are not generically satisfied. The implications for the ``superspace''
picture of the Einstein evolution equations are discussed.


title: A New Discretization of Classical and Quantum General Relativity

abstract:
  We propose a new discrete approximation to the Einstein equations, based on
the Capovilla-Dell-Jacobson form of the action for the Ashtekar variables. This
formulation is analogous to the Regge calculus in that the curvature has
support on sets of measure zero. Both a Lagrangian and Hamiltonian formulation
are proposed and we report partial results about the constraint algebra of the
Hamiltonian formulation. We find that the discrete versions of the
diffeomorphism constraints do not commute with each other or with the
Hamiltonian constraint.


title: Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime

abstract:
  These are the author's lectures at the 1992 Les Houches Summer School,
"Gravitation and Quantizations". They develop a generalized sum-over-histories
quantum mechanics for quantum cosmology that does not require either a
preferred notion of time or a definition of measurement. The "post-Everett"
quantum mechanics of closed systems is reviewed. Generalized quantum theories
are defined by three elements (1) the set of fine-grained histories of the
closed system which are its most refined possible description, (2) the allowed
coarse grainings which are partitions of the fine-grained histories into
classes, and (3) a decoherence functional which measures interference between
coarse grained histories. Probabilities are assigned to sets of alternative
coarse-grained histories that decohere as a consequence of the closed system's
dynamics and initial condition. Generalized sum-over histories quantum theories
are constructed for non-relativistic quantum mechanics, abelian gauge theories,
a single relativistic world line, and for general relativity. For relativity
the fine-grained histories are four-metrics and matter fields. Coarse grainings
are four-dimensional diffeomorphism invariant partitions of these. The
decoherence function is expressed in sum-over-histories form. The quantum
mechanics of spacetime is thus expressed in fully spacetime form. The
coarse-grainings are most general notion of alternative for quantum theory
expressible in spacetime terms. Hamiltonian quantum mechanics of matter fields
with its notion of unitarily evolving state on a spacelike surface is recovered
as an approximation to this generalized quantum mechanics appropriate for those
initial conditions and coarse-grainings such that spacetime geometry


title: Global Structure of a Black-Hole Cosmos and its Extremes

abstract:
  We analyze the global structure of a family of Einstein-Maxwell solutions
parametrized by mass, charge and cosmological constant. In a qualitative
classification there are: (i) generic black-hole solutions, describing a
Wheeler wormhole in a closed cosmos of spatial topology $S^2\times S^1$; (ii)
generic naked-singularity solutions, describing a pair of ``point" charges in a
closed cosmos; (iii) extreme black-hole solutions, describing a pair of
``horned" particles in an otherwise closed cosmos; (iv) extreme
naked-singularity solutions, in which a pair of point charges forms and then
evaporates, in a way which is not even weakly censored; and (v) an
ultra-extreme solution. We discuss the properties of the solutions and of
various coordinate systems, and compare with the Kastor-Traschen
multi-black-hole solutions.


title: Semiclassical Gravity Theory and Quantum Fluctuations

abstract:
  We discuss the limits of validity of the semiclassical theory of gravity in
which a classical metric is coupled to the expectation value of the stress
tensor. It is argued that this theory is a good approximation only when the
fluctuations in the stress tensor are small. We calculate a dimensionless
measure of these fluctuations for a scalar field on a flat background in
particular cases, including squeezed states and the Casimir vacuum state. It is
found that the fluctuations are small for states which are close to a coherent
state, which describes classical behavior, but tend to be large otherwise. We
find in all cases studied that the energy density fluctuations are large
whenever the local energy density is negative. This is taken to mean that the
gravitational field of a system with negative energy density, such as the
Casimir vacuum, is not described by a fixed classical metric but is undergoing
large metric fluctuations. We propose an operational scheme by which one can
describe a fluctuating gravitational field in terms of the statistical behavior
of test particles. For this purpose we obtain an equation of the form of the
Langevin equation used to describe Brownian motion.


title: Maximal Hypersurfaces in Asymptotically Stationary Space-Times

abstract:
  Existence of maximal hypersurfaces and of foliations by maximal hypersurfaces
is proven in two classes of asymptotically flat spacetimes which possess a one
parameter group of isometries whose orbits are timelike ``near infinity''. The
first class consists of strongly causal asymptotically flat spacetimes which
contain no ``black hole or white hole" (but may contain ``ergoregions" where
the Killing orbits fail to be timelike). The second class of spacetimes possess
a black hole and a white hole, with the black and white hole horizons
intersecting in a compact 2-surface $S$.


title: General covariance, loops and matter

abstract:
  A four dimensional generally covariant field theory is presented which
describes non-dynamical three geometries coupled to scalar fields. The theory
has an infinite number of physical observables (or constants of the motion)
which are constructed from loops made from scalar field configurations. The
Poisson algebra of these observables is closed and is the same as that for the
3+1 gravity loop variables in the Ashtekar formalism. The theory also has
observables that give the areas of open surfaces and the volumes of finite
regions. Solutions to all the Hamilton-Jacobi equations for the theory and the
Dirac quantization conditions in the coordinate representation are given. These
solutions are holonomies based on matter loops. A brief discussion of the loop
space representation for the quantum theory is also given together with some
implications for the quantization of 3+1 gravity.


title: Can quantum wormholes set $Lam$ 0

abstract:
  We find the quantum analogues of Carlini-Mijic wormholes and consider their
application to the cosmological constant problem. In a simple model with
$\Lambda$ only we differ with the results of Strominger.


title: Canonical Quantum Gravity

abstract:
  This is a review of the aspirations and disappointments of the canonical
quantization of geometry. I compare the two chief ways of looking at canonical
gravity, geometrodynamics and connection dynamics. I capture as much of the
classical theory as I can by pictorial visualization. Algebraic aspects
dominate my description of the quantization program. I address the problem of
observables. The reader is encouraged to follow the broad outlines and not
worry about the technical details.


title: Gurses' Type (b) Transformations are Neighborhood-Isometries

abstract:
  Following an idea close to one given by C. G. Torre (private communication),
we prove that Riemannian spaces (M,g) and (M,h) that are related by a Gurses
type (b) transformation [M. Gurses, Phys. Rev. Lett. 70, 367 (1993)] or,
equivalently, by a Torre-Anderson generalized diffeomorphism [C. G. Torre and
I. M. Anderson, Phys. Rev. Lett. xx, xxx (1993)] are neighborhood-isometric,
i.e., every point x in M has a corresponding diffeomorphism phi of a
neighborhood V of x onto a generally different neighborhood W of x such that
phi*(h|W) = g|V.


title: The Fourth Root of Gravity

abstract:
  By attaching basis vectors to the components of matter fields, one may render
free action densities fully covariant. Both the connection and the tetrads are
quadratic forms in these basis vectors. The metric of spacetime, which is
quadratic in the tetrads, is then quartic in the basis vectors.


title: Stationary Universe

abstract:
  If the Universe contains at least one inflationary domain with a sufficiently
large and homogeneous scalar field, then this domain permanently produces new
inflationary domains of all possible types. 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. This represents a strong deviation of inflationary
cosmology from the standard Big Bang paradigm.


title: Unique family of consistent histories in the Caldeira-Leggett model

abstract:
  Based on the standard statistical interpretation of mixed quantum states, a
unique family of consistent histories has been constructed for the quantum
Brownian motion in the Caldeira-Leggett reservoir. Analytic solutions have been
shown in the Markovian regime: they are uniquely defined coherent wave packets
travelling near classical trajectories.


title: Condensation of Matter and Trapped Surfaces in Quasi-Polar Gauge

abstract:
  We continue the investigation of formation of trapped surfaces in strongly
curved , conformally flat geometries. Initial data in quasi-polar gauges rather
then maximal ones are considered. This implies that apparent horizons coincide
with minimal surfaces. Necessary and sufficient conditions for the formation of
trapped surfaces are given. These results can be generalized to include the
case with gravitational radiation. We found that mass of a body inside a fixed
volume is bounded from above if geometry of a Cauchy slice is smooth.


title: Relic Gravitational Waves and Limits on Inflation

abstract:
  It is shown that only a narrow class of inflationary models can possibly
agree with the available observational data on the anisotropy of the cosmic
microwave background radiation (CMBR). These models may be governed by
``matter'' with the effective equation of state $-1.2 <p/ \epsilon < -0.6$
which includes the De-Sitter case $p/ \epsilon = -1$.


title:
On ``hyperboloidal'' Cauchy data for vacuum Einstein equations and
  obstructions to smoothness of ``null infinity''

abstract:
  Various works have suggested that the Bondi--Sachs--Penrose decay conditions
on the gravitational field at null infinity are not generally representative of
asymptotically flat space--times. We have made a detailed analysis of the
constraint equations for ``asymptotically hyperboloidal'' initial data and find
that log terms arise generically in asymptotic expansions. These terms are
absent in the corresponding Bondi--Sachs--Penrose expansions, and can be
related to explicit geometric quantities. We have nevertheless shown that there
exists a large class of ``non--generic'' solutions of the constraint equations,
the evolution of which leads to space--times satisfying the
Bondi--Sachs--Penrose smoothness conditions.


title: Gravitational Radiation, Inspiraling Binaries, and Cosmology

abstract:
  We show how to measure cosmological parameters using observations of
inspiraling binary neutron star or black hole systems in one or more
gravitational wave detectors. To illustrate, we focus on the case of fixed mass
binary systems observed in a single Laser Interferometer Gravitational-wave
Observatory (LIGO)-like detector. Using realistic detector noise estimates, we
characterize the rate of detections as a function of a threshold
signal-to-noise ratio $\rho_0$, the Hubble constant $H_0$, and the binary
``chirp'' mass. For $\rho_0 = 8$, $H_0 = 100$ km/s/Mpc, and $1.4 \msun$ neutron
star binaries, the sample has a median redshift of $0.22$. Under the same
assumptions but independent of $H_0$, a conservative rate density of coalescing
binaries ($8\times10^{-8}\,{\rm yr}^{-1}\,{\rm Mpc}^{-3}$) implies LIGO will
observe $\sim 50\,{\rm yr}^{-1}$ binary inspiral events. The precision with
which $H_0$ and the deceleration parameter $q_0$ may be determined depends on
the number of observed inspirals. For fixed mass binary systems, $\sim 100$
observations with $\rho_0 = 10$ in the LIGO detector will give $H_0$ to 10\% in
an Einstein-DeSitter cosmology, and 3000 will give $q_0$ to 20\%. For the
conservative rate density of coalescing binaries, 100 detections with $\rho_0 =
10$ will require about 4~yrs.


title:
Nonlinear evolution of density perturbations using approximate constancy
  of gravitational potential

abstract:
  During the evolution of density inhomogeneties in an $\Omega=1$, matter
dominated universe, the typical density contrast changes from $\delta\simeq
10^{-4}$ to $\delta\simeq 10^2$. However, during the same time, the typical
value of the gravitational potential generated by the perturbations changes
only by a factor of order unity. This significant fact can be exploited to
provide a new, powerful, approximation scheme for studying the formation of
nonlinear structures in the universe. This scheme, discussed in this paper,
evolves the initial perturbation using a Newtonian gravitational potential
frozen in time. We carry out this procedure for different intial spectra and
compare the results with the Zeldovich approximation and the frozen flow
approximation (proposed by Mattarrese et al. recently). Our results are in far
better agreement with the N-body simulations than the Zeldovich approximation.
It also provides a dynamical explanation for the fact that pancakes remain thin
during the evolution. While there is some superficial similarity between the
frozen flow results and ours, they differ considerably in the velocity
information. Actual shell crossing does occur in our approximation; also there
is motion of particles along the pancakes leading to further clumping. These
features are quite different from those in frozen flow model. We also discuss
the evolution of the two-point correlation function in various approximations.


title:
Scaling properties of the gravitational clustering in the nonlinear
  regime

abstract:
  The growth of density perturbations in an expanding universe in the
non-linear regime is investigated. The underlying equations of motion are cast
in a suggestive form, and motivate a conjecture that the scaled pair velocity,
$h(a,x)\equiv -[v/(\dot{a}x)]$ depends on the expansion factor $a$ and comoving
coordinate $x$ only through the density contrast $\sigma(a,x)$. This leads to
the result that the true, non-linear, density contrast
$<(\delta\rho/\rho)^{2}_{x}>^{1/2}=\sigma(a,x)$ is a universal function of the
density contrast $\sigma_L(a,l)$, computed in the linear theory and evaluated
at a scale $l$ where $l=x(1+\sigma^2)^{1/3}$. This universality is supported by
existing numerical simulations with scale-invariant initial conditions having
different power laws. We discuss a physically motivated ansatz
$h(a,x)=h[\sigma^2(a,x)]$ and use it to compute the non-linear density contrast
at any given scale analytically. This provides a promising method for analysing
the non-linear evolution of density perturbations in the universe and for
interpreting numerical simulations.


title: Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology

abstract:
  We investigate the origin of the arrow of time in quantum mechanics in the
context of quantum cosmology. The ``Copenhagen'' quantum mechanics of measured
subsystems incorporates a fundamental arrow of time. Extending discussions of
Aharonov, Bergmann and Lebovitz, Griffiths, and others we investigate a
generalized quantum mechanics for cosmology that utilizes both an initial and a
final density matrix to give a time-neutral formulation without a fundamental
arrow of time. Time asymmetries can arise for particular universes from
differences between their initial and final conditions. Theories for both would
be a goal of quantum cosmology. A special initial condition and a final
condition of indifference would be sufficient to explain the observed time
asymmetries of the universe. In this essay we ask under what circumstances a
completely time symmetric universe, with T-symmetric initial and final
condition, could be consistent with the time asymmetries of the limited domain
of our experience. We discuss the approach to equilibrium, the electromagnetic
system, and T-violation in the weak interactions in such universes.
  The decoherence of alternatives that is necessary for the prediction of
probabilities in the quantum mechanics of closed systems is the origin of a
fundamental limitation on quantum cosmologies with initial and final
conditions. The initial and final density matrices cannot both be pure; if they
are there is no decoherence and no prediction.


title: Operative Time Definition and Principal Uncertainity

abstract:
  Arguments are given that time must be defined in an operative manner,i.e., by
constructing devices which can serve as clocks.The investigation of such
devices leads to the conclusion that there is a principal uncertainity of time
if one considers periods which are not large compared with the Planck time.
Thus,according to the old (classical) concept,time cannot be well-defined at
this scale.The uncertainity of time leads to a breakdown of Special and General
relativity in the Planck regime;the same happens with causality. We present
arguments that the classical concept of time,which treats t simply as a real
parameter,must be replaced by a new one.


title:
An Information-Theoretic Measure of Uncertainty due to Quantum and
  Thermal Fluctuations

abstract:
  We study an information-theoretic measure of uncertainty for quantum systems.
It is the Shannon information $I$ of the phase space probability distribution
$\la z | \rho | z \ra $, where $|z \ra $ are coherent states, and $\rho$ is the
density matrix. The uncertainty principle is expressed in this measure as $I
\ge 1$. For a harmonic oscillator in a thermal state, $I$ coincides with von
Neumann entropy, $- \Tr(\rho \ln \rho)$, in the high-temperature regime, but
unlike entropy, it is non-zero at zero temperature. It therefore supplies a
non-trivial measure of uncertainty due to both quantum and thermal
fluctuations. We study $I$ as a function of time for a class of non-equilibrium
quantum systems consisting of a distinguished system coupled to a heat bath. We
derive an evolution equation for $I$. For the harmonic oscillator, in the
Fokker-Planck regime, we show that $I$ increases monotonically. For more
general Hamiltonians, $I$ settles down to monotonic increase in the long run,
but may suffer an initial decrease for certain initial states that undergo
``reassembly'' (the opposite of quantum spreading). Our main result is to
prove, for linear systems, that $I$ at each moment of time has a lower bound
$I_t^{min}$, over all possible initial states. This bound is a generalization
of the uncertainty principle to include thermal fluctuations in non-equilibrium
systems, and represents the least amount of uncertainty the system must suffer
after evolution in the presence of an environment for time $t$.


title: Action functionals for relativistic perfect fluids

abstract:
  Action functionals describing relativistic perfect fluids are presented. Two
of these actions apply to fluids whose equations of state are specified by
giving the fluid energy density as a function of particle number density and
entropy per particle. Other actions apply to fluids whose equations of state
are specified in terms of other choices of dependent and independent fluid
variables. Particular cases include actions for isentropic fluids and
pressureless dust. The canonical Hamiltonian forms of these actions are
derived, symmetries and conserved charges are identified, and the boundary
value and initial value problems are discussed. As in previous works on perfect
fluid actions, the action functionals considered here depend on certain
Lagrange multipliers and Lagrangian coordinate fields. Particular attention is
paid to the interpretations of these variables and to their relationships to
the physical properties of the fluid.


title: No Time Asymmetry from Quantum Mechanics

abstract:
  With CPT-invariant initial conditions that commute with CPT-invariant final
conditions, the respective probabilities (when defined) of a set of histories
and its CPT reverse are equal, giving a CPT-symmetric universe. This leads me
to question whether the asymmetry of the Gell-Mann--Hartle decoherence
functional for ordinary quantum mechanics should be interpreted as an asymmetry
of {\it time} .


title: Static solutions of the spherically symmetric Vlasov-Einstein system

abstract:
  The Vlasov-Einstein system describes the evolution of an ensemble of
particles (such as stars in a galaxy, galaxies in a galaxy cluster etc.)
interacting only by the gravitational field which they create collectively and
which obeys Einstein's field equations. The matter distribution is described by
the Vlasov or Liouville equation for a collisionless gas. Recent investigations
seem to indicate that such a matter model is particularly suited in a general
relativistic setting and may avoid the formation of naked singularities, as
opposed to other matter models. In the present note we consider the
Vlasov-Einstein system in a spherically symmetric setting and prove the
existence of static solutions which are asymptotically flat and have finite
total mass and finite extension of the matter. Among these there are smooth,
singularity-free solutions, which have a regular center and may have isotropic
or anisotropic pressure, and solutions, which have a Schwarzschild-singularity
at the center. The paper extends previous work, where smooth, globally defined
solutions with regular center and isotropic pressure were considered.


title: On completeness of orbits of Killing vector fields

abstract:
  A Theorem is proved which reduces the problem of completeness of orbits of
Killing vector fields in maximal globally hyperbolic, say vacuum, space--times
to some properties of the orbits near the Cauchy surface. In particular it is
shown that all Killing orbits are complete in maximal developements of
asymptotically flat Cauchy data, or of Cauchy data prescribed on a compact
manifold. This result gives a significant strengthening of the uniqueness
theorems for black holes.


title: On the limits of Brans-Dicke spacetimes: a coordinate-free approach

abstract:
  We investigate the limit of Brans-Dicke spacetimes as the scalar field
coupling constant omega tends to infinity applying a coordinate-free technique.
We obtain the limits of some known exact solutions. It is shown that these
limits may not correspond to similar solutions in the general relativity
theory.


title:
Environment--Induced Decoherence, Classicality and Consistency of
  Quantum Histories

abstract:
  We prove that for an open system, in the Markovian regime, it is always
possible to construct an infinite number of non trivial sets of histories that
exactly satisfy the probability sum rules. In spite of being perfectly
consistent, these sets manifest a very non--classical behavior: they are quite
unstable under the addition of an extra instant to the list of times defining
the history. To eliminate this feature --whose implications for the
interpretation of the formalism we discuss-- and to achieve the stability that
characterizes the quasiclassical domain, it is necessary to separate the
instants which define the history by time intervals significantly larger than
the typical decoherence time. In this case environment induced superselection
is very effective and the quasiclassical domain is characterized by histories
constructed with ``pointer projectors''.


title: Covariant perturbations of domain walls in curved spacetime

abstract:
  A manifestly covariant equation is derived to describe the perturbations in a
domain wall on a given background spacetime. This generalizes recent work on
domain walls in Minkowski space and introduces a framework for examining the
stability of relativistic bubbles in curved spacetimes.


title:
Perturbations of a topological defect as a theory of scalar fields
  interacting with an external vector potential

abstract: This is a revised version of gr-qc/9304033


title: Trapped Surfaces in Vacuum Spacetimes

abstract:
  An earlier construction by the authors of sequences of globally regular,
asymptotically flat initial data for the Einstein vacuum equations containing
trapped surfaces for large values of the parameter is extended, from the time
symmetric case considered previously, to the case of maximal slices. The
resulting theorem shows rigorously that there exists a large class of initial
configurations for non-time symmetric pure gravitational waves satisfying the
assumptions of the Penrose singularity theorem and so must have a singularity
to the future.


title:
Non-standard phase space variables, quantization, and path integrals, or
  little ado about much

abstract: Contribution to the Misner Festshrift, no abstract.


title: The Cayley-Hamilton theorem for supermatrices

abstract:
  Starting from the expression for the superdeterminant of (xI-M), where M is
an arbitrary supermatrix, we propose a definition for the corresponding
characteristic polynomial and we prove that each supermatrix satisfies its
characteristic equation. Depending upon the factorization properties of the
basic polynomials whose ratio defines the above mentioned determinant we are
able to construct polynomials of lower degree which are also shown to be
annihilated by the supermatrix. Some particular cases and examples are
considered.


title: Calculation of X-Ray Signals from Karolyhazy Hazy Space-Time

abstract:
  Karolyhazy's hazy space-time model, invented for breaking down macroscopic
interferences, employs wave-like gravity disturbances. If so, then electric
charges would radiate permanently. Here we discuss the observational
consequences of the radiation. We find that such radiation is excluded by
common experimental situations.


title:
Comment on Consistent Interpretation of Quantum Mechanics Using Quantum
  Trajectories

abstract:
  Recently, Griffiths presented a generalization of the consistent history
approach to quantum mechanics. I can easily construct all possible complete
families satisfying Griffiths' "noninterference conditions". Since only trivial
families exist one may conclude that Griffiths' proposal has not got farther
than the ordinary theory of quantum measurement.


title:
Quantum-Mechanical Histories and the Uncertainty Principle:
  I.Information-Theoretic Inequalities

abstract:
  This paper is generally concerned with understanding how the uncertainty
principle arises in formulations of quantum mechanics, such as the decoherent
histories approach, whose central goal is the assignment of probabilities to
histories. We first consider histories characterized by position or momentum
projections at two moments of time. Both exact and approximate (Gaussian)
projections are studied. Shannon information is used as a measure of the
uncertainty expressed in the probabilities for these histories. We derive a
number of inequalities in which the uncertainty principle is expressed as a
lower bound on the information of phase space distributions derived from the
probabilities for two-time histories. We go on to consider histories
characterized by position samplings at $n$ moments of time. We derive a lower
bound on the information of the joint probability for $n$ position samplings.
Similar bounds are derived for histories characterized by samplings of other
variables. All lower bounds on the information of histories have the general
form $\ln \left( V_H / V_S \right) $, where $V_H$ is a volume element of
history space, which we define, and $V_S$ is the volume of that space probed by
the projections. We thus obtain a concise and general form of the uncertainty
principle referring directly to the histories description of the system, and
making no reference to notions of phase space.


title: Saddle points of stringy action

abstract:
  It is shown that Einstein-Yang-Mills-dilaton theory has a countable family of
static globally regular solutions which are purely magnetic but uncharged. The
discrete spectrum of masses of these solutions is bounded from above by the
mass of extremal Gibbons-Maeda solution. As follows from linear stability
analysis all solutions are unstable.


title:
Non-Perturbative Canonical Quantization of Minisuperspace Models:
  Bianchi Types I and II

abstract:
  We carry out the quantization of the full type I and II Bianchi models
following the non-perturbative canonical quantization program. These
homogeneous minisuperspaces are completely soluble, i.e., it is possible to
obtain the general solution to their classical equations of motion in an
explicit form. We determine the sectors of solutions that correspond to
different spacetime geometries, and prove that the parameters employed to
describe the different physical solutions define a good set of coordinates in
the phase space of these models. Performing a transformation from the Ashtekar
variables to this set of phase space coordinates, we endow the reduced phase
space of each of these systems with a symplectic structure. The symplectic
forms obtained for the type I and II Bianchi models are then identified as
those of the cotangent bundles over ${\cal L}^+_{(+,+)}\times S^2\times S^1$
and ${\cal L}^+_{(+,+)}\times S^1$, respectively. We construct a closed
*-algebra of Dirac observables in each of these reduced phase spaces, and
complete the quantization program by finding unitary irreducible
representations of these algebras. The real Dirac observables are represented
in this way by self-adjoint operators, and the spaces of quantum physical
states are provided with a Hilbert structure.


title: On the Definition of Averagely Trapped Surfaces

abstract:
  Previously suggested definitions of averagely trapped surfaces are not
well-defined properties of 2-surfaces, and can include surfaces in flat
space-time. A natural definition of averagely trapped surfaces is that the
product of the null expansions be positive on average. A surface is averagely
trapped in the latter sense if and only if its area $A$ and Hawking mass $M$
satisfy the isoperimetric inequality $16\pi M^2 > A$, with similar inequalities
existing for other definitions of quasi-local energy.


title:
An algebraic approach to the quantization of cosntrained systems: finite
  dimensional examples

abstract:
  From the point of view of canonical quantum gravity, it has become imperative
to find a framework for quantization which provides a {\em general}
prescription to find the physical inner product, and is flexible enough to
accommodate non-canonical variables. In this dissertation I consider an
algebraic formulation of the Dirac approach to the quantization of constrained
systems, due to A. Ashtekar. The Dirac quantization program is augmented by a
general principle to find the inner product on physical states. Essentially,
the Hermiticity conditions on physical operators determine this inner product.
I also clarify the role in quantum theory of possible algebraic identities
between the elementary variables. I use this approach to quantize various
finite dimensional systems. Some of these models test the new aspects of the
algebraic framework. Others bear qualitative similarities to \gr, and may give
some insight into the pitfalls lurking in \qg. In (spatially compact) general
relativity, the Hamiltonian is constrained to vanish. I present various
approaches one can take to obtain an interpretation of the quantum theory of
such ``dynamically constrained'' systems. I apply some of these ideas to the
Bianchi I cosmology, and analyze the issue of the initial singularity in
quantum theory.


title:
Completeness of Wilson loop functionals on the moduli space of $SL(2,C)$
  and $SU(1,1)$-connections

abstract:
  The structure of the moduli spaces $\M := \A/\G$ of (all, not just flat)
$SL(2,C)$ and $SU(1,1)$ connections on a n-manifold is analysed. For any
topology on the corresponding spaces $\A$ of all connections which satisfies
the weak requirement of compatibility with the affine structure of $\A$, the
moduli space $\M$ is shown to be non-Hausdorff. It is then shown that the
Wilson loop functionals --i.e., the traces of holonomies of connections around
closed loops-- are complete in the sense that they suffice to separate all
separable points of $\M$. The methods are general enough to allow the
underlying n-manifold to be topologically non-trivial and for connections to be
defined on non-trivial bundles. The results have implications for canonical
quantum general relativity in 4 and 3 dimensions.


title: Functional Change of Variables in the Wheeler--De Witt Equation

abstract:
  I present a new way to solve the Wheeler--de Witt equation using the
invariance of the classical lagrangian under reparametrization. This property
allows one to introduce an arbitrary function for each degree of freedom of the
wave function $\Psi$: this arbitrariness can be used to fix the asymptotic
behaviour of $\Psi$ so as to obtain a wave function representing a closed
universe or a wormhole. These considerations are applied in detail to the
Kantowsky--Sachs spacetime.


title:
Unique Quantum Paths by Continuous Diagonalization of the Density
  Operator

abstract:
  In this short note we show that for a Markovian open quantum system it is
always possible to construct a unique set of perfectly consistent Schmidt
paths, supporting quasi-classicality. Our Schmidt process, elaborated several
years ago, is the $\Delta t\to 0$ limit of the Schmidt chain constructed very
recently by Paz and Zurek.


title:
Invariant Connections with Torsion on Group Manifolds and Their
  Application in Kaluza-Klein Theories

abstract:
  Invariant connections with torsion on simple group manifolds $S$ are studied
and an explicit formula describing them is presented. This result is used for
the dimensional reduction in a theory of multidimensional gravity with
curvature squared terms on $M^{4} \times S$. We calculate the potential of
scalar fields, emerging from extra components of the metric and torsion, and
analyze the role of the torsion for the stability of spontaneous
compactification.


title: About a Super-Ashtekar-Renteln Ansatz

abstract:
  The Ashtekar-Renteln Ansatz gives the self-dual solutions to the Einstein
equation. A direct generalization of the Ashtekar-Renteln An\-satz to N=1
supergravity is given both in the canonical and in the covariant formulation
and a geometrical property of the solutions is pointed out. (Changes: the
covariant formulation and some comments about a wave function has been added)


title: Gravitational form factors of the neutrino

abstract:
  The gravitational properties of the neutrino is studied in the weak field
approximation. By imposing the hermiticity condition, CPT and CP invariance on
the \em tensor matrix element, we shown that the allowed gravitational form
factors for Dirac and Majorana neutrinos are very different. In a CPT and CP
invariant theory, the \em tensor for a Dirac neutrino of the same specie is
characterized by four gravitational form factors. As a result of CPT
invariance, the \em tensor for a Majorana neutrino of the same specie has five
form factors. In a CP invariant theory, if the initial and final Majorana
neutrinos have the same (opposite) CP parity, then only tensor (pseudo-tensor)
type transition are allowed.


title: Holomorphic quantum mechanics with a quadratic Hamiltonian constraint

abstract:
  A finite dimensional system with a quadratic Hamiltonian constraint is Dirac
quantized in holomorphic, antiholomorphic and mixed representations. A unique
inner product is found by imposing Hermitian conjugacy relations on an operator
algebra. The different representations yield drastically different Hilbert
spaces. In particular, all the spaces obtained in the antiholomorphic
representation violate classical expectations for the spectra of certain
operators, whereas no such violation occurs in the holomorphic representation.
A subset of these Hilbert spaces is also recovered in a configuration space
representation. A propagation amplitude obtained from an (anti)holomorphic path
integral is shown to give the matrix elements of the identity operators in the
relevant Hilbert spaces with respect to an overcomplete basis of
representation-dependent generalized coherent states. Relation to quantization
of spatially homogeneous cosmologies is discussed in view of the no-boundary
proposal of Hartle and Hawking and the new variables of Ashtekar.


title: Form Connections

abstract:
  Riemannian geometry in four dimensions naturally leads to an SL(3) connection
that annihilates a basis for self-dual two-forms. Einstein's equations may be
written in terms of an SO(3) connection, with SO(3) chosen as an appropriate
subgroup of SL(3). We show how a set of "neighbours" of Einstein's equations
arises because the subgroup may be chosen in different ways. An explicit
example of a non-Einstein metric obtained in this way is given. Some remarks on
three dimensional space-times are made.


title:
Cosmological Constant and Gravitational Repulsion Effect: 1. Homogeneous
  models with radiation

abstract:
  Within the framework of the minimum quadratic Poincare gauge theory of
gravity in the Riemann-Cartan spacetime we study the influence of gravitational
vacuum energy density (a cosmological constant) on the dynamics of various
gravitating systems. It is shown that the inclusion of the cosmological term
can lead to gravitational repulsion. For some simple cases of spatially
homogeneous cosmological models with radiation we obtain non-singular solutions
in form of elementary functions and elliptic integrals.


title: The Quantum Sphaleron

abstract:
  A gravitational instanton is found that can tunnel into a new more stable
vacuum phase where diffeomorphism invariance is broken and pitchfork
bifurcations develop. This tunnelling process involves a double sphaleron-like
transition which is associated with an extra level of quantization which is
above that is contained in quantum field theory.


title: Average Entropy of a Subsystem

abstract:
  If a quantum system of Hilbert space dimension $mn$ is in a random pure
state, the average entropy of a subsystem of dimension $m\leq n$ is conjectured
to be $S_{m,n}=\sum_{k=n+1}^{mn}\frac{1}{k}-\frac{m-1}{2n}$ and is shown to be
$\simeq \ln m - \frac{m}{2n}$ for $1\ll m\leq n$. Thus there is less than
one-half unit of information, on average, in the smaller subsystem of a total
system in a random pure state.


title: Canonical Quantization of Gravitating Point Particles in 2+1 Dimensions

abstract:
  A formalism previously introduced by the author using tesselated Cauchy
surfaces is applied to define a quantized version of gravitating point
particles in 2+1 dimensions. We observe that this is the first model whose
quantum version automatically discretizes time. But also spacelike distances
are discretized in a very special way.


title:
On the Distributional Nature of the Energy Momentum Tensor of a Black
  Hole or What Curves the Schwarzschild Geometry ?

abstract:
  Using distributional techniques we calculate the energy--momentum tensor of
the Schwarzschild geometry. It turns out to be a well--defined
tensor--distribution concentrated on the $r=0$ region which is usually excluded
from space--time. This provides a physical interpretation for the curvature of
this geometry.


title: Singularity Free Inhomogeneous Models with Heat Flow

abstract:
  We present a class of singularity free exact cosmological solutions of
Einstein's equations describing a perfect fluid with heat flow. It is obtained
as generalization of the Senovilla class [1] corresponding to incoherent
radiation field. The spacetime is cylindrically symmetric and globally regular.


title: Actions for Gravity, with Generalizations: A Review

abstract:
  Related to the classical Ashtekar Hamiltonian, there have been discoveries
regarding new classical actions for gravity in (2+1)- and (3+1)-dimensions, and
also generalizations of Einstein's theory of gravity. In this review, I will
try to clarify the relations between the new and old actions for gravity, and
also give a short introduction to the new generalizations. The new
results/treatments in this review are: 1. A more detailed constraint analysis
of the Hamiltonian formulation of the Hilbert- Palatini Lagrangian in
(3+1)-dimensions. 2. The canonical transformation relating the Ashtekar- and
the ADM-Hamiltonian in (2+1)-dimensions is given. 3. There is a discussion
regarding the possibility of finding a higher dimensional Ashtekar formulation.
There are also two clarifying figures (in the beginning of chapter 2 and 3,
respectively) showing the relations between different action-formulations for
Einstein gravity in (2+1)- and (3+1)-dimensions.


title: Quantum Mechanics, Common Sense and the Black Hole Information Paradox

abstract:
  The purpose of this paper is to analyse, in the light of information theory
and with the arsenal of (elementary) quantum mechanics (EPR correlations,
copying machines, teleportation, mixing produced in sub-systems owing to a
trace operation, etc.) the scenarios available on the market to resolve the
so-called black-hole information paradox. We shall conclude that the only
plausible ones are those where either the unitary evolution of quantum
mechanics is given up, in which information leaks continuously in the course of
black-hole evaporation through non-local processes, or those in which the world
is polluted by an infinite number of meta-stable remnants.


title:
Massless Minimally Coupled Fields in De Sitter Space: O(4)-Symmetric
  States Versus De Sitter Invariant Vacuum

abstract:
  The issue of de Sitter invariance for a massless minimally coupled scalar
field is revisited. Formally, it is possible to construct a de Sitter invariant
state for this case provided that the zero mode of the field is quantized
properly. Here we take the point of view that this state is physically
acceptable, in the sense that physical observables can be computed and have a
reasonable interpretation. In particular, we use this vacuum to derive a new
result: that the squared difference between the field at two points along a
geodesic observer's space-time path grows linearly with the observer's proper
time for a quantum state that does not break de Sitter invariance. Also, we use
the Hadamard formalism to compute the renormalized expectation value of the
energy momentum tensor, both in the O(4) invariant states introduced by Allen
and Follaci, and in the de Sitter invariant vacuum. We find that the vacuum
energy density in the O(4) invariant case is larger than in the de Sitter
invariant case.


title: Can Gravitational Waves Prevent Inflation?

abstract:
  To investigate the cosmic no hair conjecture, we analyze numerically
1-dimensional plane symmetrical inhomogeneities due to gravitational waves in
vacuum spacetimes with a positive cosmological constant. Assuming periodic
gravitational pulse waves initially, we study the time evolution of those waves
and the nature of their collisions. As measures of inhomogeneity on each
hypersurface, we use the 3-dimensional Riemann invariant ${\cal I}\equiv
{}~^{(3)\!}R_{ijkl}~^{(3)\!}R^{ijkl}$ and the electric and magnetic parts of
the Weyl tensor. We find a temporal growth of the curvature in the waves'
collision region, but the overall expansion of the universe later overcomes
this effect. No singularity appears and the result is a ``no hair" de Sitter
spacetime. The waves we study have amplitudes between $0.020\Lambda \leq {\cal
I}^{1/2} \leq 125.0\Lambda$ and widths between $0.080l_H \leq l \leq 2.5l_H$,
where $l_H=(\Lambda/3)^{-1/2}$, the horizon scale of de Sitter spacetime. This
supports the cosmic no hair conjecture.


title: An illustration of 2+1 gravity loop transform troubles

abstract:
  A nonperturbative approach to quantum gravity that has generated much
discussion is the attempt to construct a ``loop representation." Despite it's
success in linear quantum theories and a part of 2+1 quantum gravity, it has
recently been noticed that difficulties arise with loop representations in a
different ``sector" of 2+1 gravity. The problems are related to the use of the
``loop transform" in the construction of the loop representation. We illustrate
these difficulties by exploring an analogy based on the Mellin transform which
allows us to work in a context that is both mathematically and physically
simple and that does not require an understanding either of loop
representations or of 2+1 gravity.


title: Initial conditions and unitarity in unimodular quantum cosmology

abstract:
  We consider quantization of the positive curvature Friedmann cosmology in the
unimodular modification of Einstein's theory, in which the spacetime
four-volume appears as an explicit time variable. The Hamiltonian admits
self-adjoint extensions that give unitary evolution in the Hilbert space
associated with the Schr\"odinger equation. The semiclassical estimate to the
no-boundary wave function of Hartle and Hawking is found. If this estimate is
accurate, there is a continuous flux of probability into the configuration
space from vanishing three-volume, and the no-boundary wave function evolves
nonunitarily. Generalizations of these results hold in a class of anisotropic
cosmologies. (Talk given at the 5th Canadian Conference on General Relativity
and Relativistic Astrophysics, Waterloo, Ontario, Canada, May 1993.)


title: Topological Censorship

abstract:
  All three-manifolds are known to occur as Cauchy surfaces of asymptotically
flat vacuum spacetimes and of spacetimes with positive-energy sources. We prove
here the conjecture that general relativity does not allow an observer to probe
the topology of spacetime: any topological structure collapses too quickly to
allow light to traverse it. More precisely, in a globally hyperbolic,
asymptotically flat spacetime satisfying the null energy condition, every
causal curve from $\scri^-$ to ${\scri}^+$ is homotopic to a topologically
trivial curve from $\scri^-$ to ${\scri}^+$. (If the Poincar\'e conjecture is
false, the theorem does not prevent one from probing fake 3-spheres).


title: Anomalous Fermion Production in Gravitational Collapse

abstract:
  The Dirac equation is solved in the Einstein-Yang-Mills background found by
Bartnik and McKinnon. We find a normalizable zero-energy fermion mode in the
$s$-wave sector. As shown recently, their solution corresponds to a
gravitational sphaleron which mediates transitions between topologically
distinct vacua. Since the Bartnik-McKinnon solution is unstable, it will either
collapse to form a black hole or radiate away its energy. In either case, as
the Chern-Simons number of the configuration changes, there will be an
accompanying anomalous change in fermion number.


title:
New Restrictions on Spatial Topology of the Universe from Microwave
  Background Temperature Fluctuations

abstract:
  If the Universe has the topology of a 3-torus ($T^3$), then it follows from
recent data on large-scale temperature fluctuations $\Delta T/T$ of the cosmic
microwave background that either the minimal size of the torus is at least of
the order of the present cosmological horizon, or the large-scale $\Delta T/T$
pattern should have a symmetry plane (in case of the effective $T^1$ topology)
or a symmetry axis (in case of the effective $T^2$ topology), the latter
possibility being probably excluded by the data.


title: Six ways to quantize (2+1)-dimensional gravity

abstract:
  We do not yet know how to quantize gravity in 3+1 dimensions, but in lower
dimensions we face the opposite problem: many of the approaches originally
developed for (3+1)-dimensional gravity can be successfully implemented in 2+1
dimensions, but the resulting quantum theories are not all equivalent. In this
talk, I discuss six such approaches --- reduced phase space ADM quantization,
the Chern-Simons/connection representation, covariant canonical quantization,
the loop representation, the Wheeler-DeWitt equation, and lattice methods ---
for the simple case of a spacetime whose spatial topology is that of a torus. A
comparison of the resulting quantum theories can provide some useful insights
into the conceptual issues that underlie quantum gravity in any number of
dimensions. (Talk given at the Fifth Canadian Conference on General Relativity
and Relativistic Astrophysics, Waterloo, Ontario, May 1993)


title:
Gravitational waves in general relativity: XIV. Bondi expansions and the
  ``polyhomogeneity'' of \Scri

abstract:
  The structure of polyhomogeneous space-times (i.e., space-times with metrics
which admit an expansion in terms of $r^{-j}\log^i r$) constructed by a
Bondi--Sachs type method is analysed. The occurrence of some log terms in an
asymptotic expansion of the metric is related to the non--vanishing of the Weyl
tensor at Scri. Various quantities of interest, including the Bondi mass loss
formula, the peeling--off of the Riemann tensor and the Newman--Penrose
constants of motion are re-examined in this context.


title: The First Law of Black Hole Mechanics

abstract:
  A simple proof of a strengthened form of the first law of black hole
mechanics is presented. The proof is based directly upon the Hamiltonian
formulation of general relativity, and it shows that the the first law
variational formula holds for arbitrary nonsingular, asymptotically flat
perturbations of a stationary, axisymmetric black hole, not merely for
perturbations to other stationary, axisymmetric black holes. As an application
of this strengthened form of the first law, we prove that there cannot exist
Einstein-Maxwell black holes whose ergoregion is disjoint from the horizon.
This closes a gap in the black hole uniqueness theorems.


title:
Mass Formulas for Stationary Einstein-Yang-Mills Black Holes and a
  Simple Proof of Two Staticity Theorems

abstract:
  We derive two new integral mass formulas for stationary black holes in
Einstein-Yang-Mills theory. From these we derive a formula for $ \J \Omega -Q V
$, from which it follows immediately that any stationary, nonrotating,
uncharged black hole is static and has vanishing electric field on the static
slices. In the Einstein-Maxwell case, we have, in addition, the ``generalized
Smarr mass formula", for which we provide a new, simple derivation. When
combined with the other two formulas, we obtain a simple proof that nonrotating
Einstein-Maxwell black holes must be static and have vanishing magnetic field
on the static slices. Our mass formulas also can be generalized to cases with
other types of matter fields, and we describe the nature of these
generalizations.


title:
A Proposal for Solving the ``Problem of Time" in Canonical Quantum
  Gravity

abstract:
  The "problem of time" in canonical quantum gravity refers to the difficulties
involved in defining a Hilbert space structure on states -- and local
observables on this Hilbert space -- for a theory in which the spacetime metric
is treated as a quantum field, so no classical metrical or causal structure is
present on spacetime. We describe an approach -- much in the spirit of ideas
proposed by Misner, Kuchar and others -- to defining states and local
observables in quantum gravity which exploits the analogy between the
Hamiltonian formulation of general relativity and that of a relativistic
particle. In the case ofminisuperspace models, a concrete theory is obtained
which appears to be mathematically and physically viable, although it contains
some radical features with regard to the presence of an "arrow of time". The
viability of this approach in the case ofinfinitely many degrees of freedom
rests on a number of fairlywell defined issues, which, however, remain
unresolved. As a byproduct of our analysis, the theory of a relativistic
particle in curved spacetime is developed.


title:
Solutions to the Wheeler DeWitt Constraint of Canonical Gravity Coupled
  to Scalar Matter Fields

abstract:
  It is shown that the Wheeler DeWitt constraint of canonical gravity coupled
to Klein Gordon scalar fields and expressed in terms of Ashtekar's variables
admits formal solutions which are parametrized by loops in the three
dimensional hypersurface and which are extensions of the well known Wilson loop
solutions found by Jacobson, Rovelli and Smolin.


title:
Compactification to Non-symmetric Homogeneous Space in Multidimensional
  Einstein-Yang-Mills Theory

abstract:
  We study ten-dimensional Einstein-Yang-Mills model with the space of extra
dimensions being a non-symmetric homogeneous space with the invariant metric
parametrized by two scales. Dimensional reduction of the model is carried out
and the scalar potential of the reduced theory is calculated. In a cosmological
setting minima of the potential in the radiation-dominated period that followed
the inflation are found and their stability is analyzed. The compactifying
solution is shown to be stable for the appropriate values of parameters.


title: Hilbert space of wormholes

abstract:
  Wormhole boundary conditions for the Wheeler--DeWitt equation can be derived
from the path integral formulation. It is proposed that the wormhole wave
function must be square integrable in the maximal analytic extension of
minisuperspace. Quantum wormholes can be invested with a Hilbert space
structure, the inner product being naturally induced by the minisuperspace
metric, in which the Wheeler--DeWitt operator is essentially self--adjoint.
This provides us with a kind of probabilistic interpretation. In particular,
giant wormholes will give extremely small contributions to any wormhole state.
We also study the whole spectrum of the Wheeler--DeWitt operator and its role
in the calculation of Green's functions and effective low energy interactions.


title: Consistency of the Nonsymmetric Gravitational Theory

abstract:
  The NGT field equations with sources are expanded first about a flat
Minkowski background and then about a GR background to first-order in the
antisymmetric part of the fundamental tensor, $g_{\mu\nu}$. From the general,
static spherically symmetric solution of the field equation in empty space, we
establish that there are two conserved charges $m$ and $\ell^2$ corresponding
to the two basic gauge invariances of NGT. There is no direct contribution to
the flux of gravitational waves from the antisymmetric, $g_{[\mu\nu]}$, sector
in the linearized, lowest order of approximation, nor in the non-linear theory.
It is demonstrated that the flux of gravitational waves is finite in magnitude
and positive definite for solutions of the field equations which satisfy the
boundary condition of asymptotic flatness.


title:
Phase-Space Decoherence: a comparison between Consistent Histories and
  Environment Induced Superselection

abstract:
  We examine the decoherence properties of a quantum open system as modeled by
a quantum optical system in the Markov regime. We look for decoherence in both
the Environment Induced Superselection (EIS) and Consistent Histories (CH)
frameworks. We propose a general measure of the coherence of the reduced
density matrix and find that EIS decoherence occurs in a number of bases for
this model. The degree of ``diagonality'' achieved increases with bath
temperature. We evaluate the Decoherence Functional of Consistent Histories for
coarse grained phase space two-time projected histories. Using the measures
proposed by Dowker and Halliwell we find that the consistency of the histories
improves with increasing bath temperature, time and final grain size and
decreases with initial grain size. The peaking increases with increasing grain
size and decreases with increasing bath temperature. Adopting the above
proposed measure of ``coherence'' to the Decoherence Functional gives similar
results. The results agree in general with expectations while the anomalous
dependence of the consistency on the initial grain size is discussed.


title: Local and global gravitational aspects of domain wall space-times

abstract:
  Local and global gravitational effects induced by eternal vacuum domain walls
are studied. We concentrate on thin walls between non-equal and non-positive
cosmological constants on each side of the wall. These vacuum domain walls fall
in three classes depending on the value of their energy density $\sigma$: (1)\
extreme walls with $\sigma = \sigma_{{\text{ext}}}$ are planar, static walls
corresponding to supersymmetric configurations, (2)\ non-extreme walls with
$\sigma = \sigma_{{\text{non}}} > \sigma_{{\text{ext}}}$ correspond to
expanding bubbles with observers on either side of the wall being {\em
inside\/} the bubble, and (3)\ ultra-extreme walls with $\sigma =
\sigma_{{\text{ultra}}} < \sigma_{{\text{ext}}}$ represent the bubbles of false
vacuum decay. On the sides with less negative cosmological constant, the
extreme, non-extreme, and ultra-extreme walls exhibit no, repulsive, and
attractive effective ``gravitational forces,'' respectively. These
``gravitational forces'' are global effects not caused by local curvature.
Since the non-extreme wall encloses observers on both sides, the supersymmetric
system has the lowest gravitational mass accessable to outside observers. It is
conjectured that similar positive mass protection occurs in all physical
systems and that no finite negative mass object can exist inside the universe.
We also discuss the global space-time structure of these singularity free
space-times and point out intriguing analogies with the causal structure of
black holes.


title:
Classification of Multivector Theories and the Modification of the
  Postulates of Physics

abstract:
  We propose a graded classification of the entire field of multivector
physics, including all alternative points of view. The (often tacit) postulates
of different types of formulations are contrasted, summarizing their
consequences. Specifically, spin-gauge formulations of gravitation and GUT
which assume standard column spinors will require unnecessarily large matrix
algebras. An extreme generalization is introduced, where wavefunctions are
multivectors, in which multiple generations of particles naturally appear
without resorting to increasing the size of the algebra. Further, this allows
for two-sided (bilateral) operators, which can accomodate in excess of 10 times
more gauge fields without increasing the algebraic representation. As this
generalization encompasses all the essential features of the other categories,
it is proposed to be the best path to new physics. [Summary of talk at 3rd
International Conf on Clifford Algebras and Their Appl. in Physics, Deinze,
Belgium May 1993].


title: Pull Back Invariant Matter Couplings

abstract:
  An algorithm is described for the construction of actions for scalar, spinor,
and vector gauge fields that remains well-defined when the metric is degenerate
and that involve no contravariant tensor fields. These actions produce the
standard matter dynamics and coupling to gravity when tetrad is nondegenerate,
but have the property that all fields that appear in them can be pulled back
through an arbitrary map of degree one and that this pull back leave the action
invariant when the map has degree one.


title: Deflationary Universe Scenario

abstract:
  We show that it is possible to realize an inflationary scenario even without
conversion of the false vacuum energy to radiation. Such cosmological models
have a deflationary stage in which $Ha^2$ is decreasing and radiation produced
by particle creation in an expanding Universe becomes dominant. The preceding
inflationary stage ends since the inflaton potential becomes steep. False
vacuum energy is finally (partly) converted to the inflaton kinetic energy ,
the potential energy rapidly decreases and the Universe comes to the
deflationary stage with a scale factor $a(t) \propto t^{1/3}$. Basic features
and observational consequences of this scenario are indicated.


title:
Analytic Solutions for Cosmological Perturbations in Multi-Dimensional
  Space-Time

abstract:
  We obtain analytic solutions for the density contrast and the anisotropic
pressure in a multi-dimensional FRW cosmology with collisionless, massless
matter. These are compared with perturbations of a perfect fluid universe. To
describe the metric perturbations we use manifest gauge invariant metric
potentials. The matter perturbations are calculated by means of (automatically
gauge invariant) finite temperature field theory, instead of kinetic theory.
(Talk given at the Journ\'ees Relativistes '93, 5 -- 7 April, Brussels,
Belgium)


title: Superluminal Black Holes

abstract:
  The new solution of the Einstein equations in empty space is presented. The
solution is constructed using Schwarzschild solution but essentially differs
from it. The basic properties of the solution are: the existence of a horizon
which is a hyperboloid of one sheet moving along its axis with superluminal
velocity, right signature of the metric outside the horizon and
Minkovsky-flatness of it at infinity outside the horizon. There is also a
discussion in the last chapter, including comparing with recent astronomical
observations.


title: Cosmic Censorship for Some Spatially Homogeneous Cosmological Models

abstract:
  The global properties of spatially homogeneous cosmological models with
collisionless matter are studied. It is shown that as long as the mean
curvature of the hypersurfaces of homogeneity remains finite no singularity can
occur in finite proper time as measured by observers whose worldlines are
orthogonal to these hypersurfaces. Strong cosmic censorship is then proved for
the Bianchi I, Bianchi IX and Kantowski-Sachs symmetry classes.


title: Gravitation vs. Rotation in 2+1 Dimensions

abstract:
  We investigate rotation and rotating structures in (2+1)-dimensional Einstein
gravity. We show that rotation generally leads to pathological physical
situations.


title: Quasiclassical Equations of Motion for Nonlinear Brownian Systems

abstract:
  Following the formalism of Gell-Mann and Hartle, phenomenological equations
of motion are derived from the decoherence functional formalism of quantum
mechanics, using a path-integral description. This is done explicitly for the
case of a system interacting with a ``bath'' of harmonic oscillators whose
individual motions are neglected. The results are compared to the equations
derived from the purely classical theory. The case of linear interactions is
treated exactly, and nonlinear interactions are compared using classical and
quantum perturbation theory.


title: The Fourth Law of Black Hole Thermodynamics

abstract:
  We show that black holes fulfill the scaling laws arising in critical
transitions. In particular, we find that in the transition from negative to
positive values the heat capacities $C_{JQ}$, $C_{\Omega Q}$ and $C_{J\Phi}$
give rise to critical exponents satisfying the scaling laws. The three
transitions have the same critical exponents as predicted by the universality
Hypothesis. We also briefly discuss the implications of this result with
regards to the connections among gravitation, quantum mechanics and statistical
physics.


title: Squeezed Thermal Vacuum and the Maximum Scale for Inflation

abstract:
  We consider the stimulated emission of gravitons from an initial state of
thermal equilibrium, under the action of the cosmic gravitational background
field. We find that the low-energy graviton spectrum is enhanced if compared
with spontaneous creation from the vacuum; as a consequence, the scale of
inflation must be lowered, in order not to exceed the observed CMB quadrupole
anisotropy. This effect is particularly important for models based on a
symmetry-breaking transition which require, as initial condition, a state of
thermal equilibrium at temperatures of the order of the inflation scale.


title: Topology, Decoherence, and Semiclassical Gravity

abstract:
  We address the issue of recovering the time-dependent Schr\"{o}dinger
equation from quantum gravity in a natural way. To reach this aim it is
necessary to understand the nonoccurrence of certain superpositions in quantum
gravity.
  We explore various possible explanations and their relation. These are the
delocalisation of interference terms through interaction with irrelevant
degrees of freedom (decoherence), gravitational anomalies, and the possibility
of $\theta$ states. The discussion is carried out in both the geometrodynamical
and connection representation of canonical quantum gravity.


title: Supersymmetric Homogeneous Quantum Cosmologies Coupled to a Scalar Field

abstract:
  Recent work on $N=2$ supersymmetric Bianchi type IX cosmologies coupled to a
scalar field is extended to a general treatment of homogeneous quantum
cosmologies with explicitely solvable momentum constraints, i.e. Bianchi types
I, II, VII, VIII besides the Bianchi type IX, and special cases, namely the
Friedmann universes, the Kantowski-Sachs space, and Taub-NUT space. Besides the
earlier explicit solution of the Wheeler DeWitt equation for Bianchi type IX,
describing a virtual wormhole fluctuation, an additional explicit solution is
given and identified with the `no-boundary state'.


title:
Canonical Quantum Supergravity in Three Dimensions, (some lines lost
  during submission)

abstract:
  We discuss the canonical treatment and quantization of matter coupled
supergravity in three dimensions, with special emphasis on $N=2$ supergravity.
We then analyze the quantum constraint algebra; certain operator ordering
ambiguities are found to be absent due to local supersymmetry. We show that the
supersymmetry constraints can be partially solved by a functional analog of the
method of characteristics. We also consider extensions of Wilson loop integrals
of the type previously found in ordinary gravity, but now with connections
involving the bosonic and fermionic matter fields in addition to the
gravitational connection. In a separate section of this paper, the canonical
treatment and quantization of non-linear coset space sigma models are discussed
in a self contained way.


title:
Dirac equation in some homogeneous$sqace-times, separation of variables
  and exact solutions

abstract:
  In the present article, using a further generalization of the algebraic
method of separation of variables, the Dirac equation is separated in a family
of space-times where it is not possible to find a complete set of first order
commuting differential operators. After separating variables, the Dirac
equation is reduced to a set of coupled ordinary differential equations and
some exact solutions corresponding to cosmological backgrounds and
gravitational waves are computed in terms of hypergeometric functions. By
passing, the Klein Gordon equation in this background field is discussed.


title:
A regularity theorem for solutions of the spherically symmetric
  Vlasov-Einstein system

abstract:
  In a previous paper two of the authors (G. R. and A. D. R.) showed that there
exist global, classical solutions of the spherically symmetric Vlasov-Einstein
system for small initial data. The present paper continues this investigation
and allows also large initial data. It is shown that if a solution of the
spherically symmetric Vlasov-Einstein system develops a singularity at all then
the first singularity has to appear at the center of symmetry. The result adds
weight to the conjecture that cosmic censorship holds if one replaces dust as
matter model for which naked singularities do form by a collisionless gas
described by the Vlasov equation. The main tool is an estimate which shows that
a solution is global if all the matter remains away from the center of
symmetry.


title:
Global existence of classical solutions to the Vlasov-Poisson system in
  a three dimensional, cosmological setting

abstract:
  The initial value problem for the Vlasov-Poisson system is by now well
understood in the case of an isolated system where, by definition, the
distribution function of the particles as well as the gravitational potential
vanish at spatial infinity. Here we start with homogeneous solutions, which
have a spatially constant, non-zero mass density and which describe the mass
distribution in a Newtonian model of the universe. These homogeneous states can
be constructed explicitly, and we consider deviations from such homogeneous
states, which then satisfy a modified version of the Vlasov-Poisson system. We
prove global existence and uniqueness of classical solutions to the
corresponding initial value problem for initial data which represent spatially
periodic deviations from homogeneous states.


title: The No-Hair Conjecture in 2D Dilaton Supergravity

abstract:
  We study two dimensional dilaton gravity and supergravity following
hamiltonian methods. Firstly, we consider the structure of constraints of 2D
dilaton gravity and then the 2D dilaton supergravity is obtained taking the
squere root of the bosonic constraints. We integrate exactly the equations of
motion in both cases and we show that the solutions of the equation of motion
of 2D dilaton supergravity differs from the solutions of 2D dilaton gravity
only by boundary conditions on the fermionic variables, i.e. the black holes of
2D dilaton supergravity theory are exactly the same black holes of 2D bosonic
dilaton gravity modulo supersymmetry transformations. This result is the
bidimensional analogue of the no-hair theorem for supergravity.


title: Entropy in Black Hole Pair Production

abstract:
  Pair production of Reissner-Nordstrom black holes in a magnetic field can be
described by a euclidean instanton. It is shown that the instanton amplitude
contains an explicit factor of $e^{A/4}$, where $A$ is the area of the event
horizon. This is consistent with the hypothesis that $e^{A/4}$ measures the
number of black hole states.