title:
Quasilocal Energy and Conserved Charges Derived from the Gravitational
  Action

abstract:
  The quasilocal energy of gravitational and matter fields in a spatially
bounded region is obtained by employing a Hamilton-Jacobi analysis of the
action functional. First, a surface stress-energy-momentum tensor is defined by
the functional derivative of the action with respect to the three-metric on
${}^3B$, the history of the system's boundary. Energy density, momentum
density, and spatial stress are defined by projecting the surface stress tensor
normally and tangentially to a family of spacelike two-surfaces that foliate
${}^3B$. The integral of the energy density over such a two-surface $B$ is the
quasilocal energy associated with a spacelike three-surface $\Sigma$ whose
intersection with ${}^3B$ is the boundary $B$. The resulting expression for
quasilocal energy is given in terms of the total mean curvature of the spatial
boundary $B$ as a surface embedded in $\Sigma$. The quasilocal energy is also
the value of the Hamiltonian that generates unit magnitude proper time
translations on ${}^3B$ in the direction orthogonal to $B$. Conserved charges
such as angular momentum are defined using the surface stress tensor and
Killing vector fields on ${}^3B$. For spacetimes that are asymptotically flat
in spacelike directions, the quasilocal energy and angular momentum defined
here agree with the results of Arnowitt-Deser-Misner in the limit that the
boundary tends to spatial infinity. For spherically symmetric spacetimes, it is
shown that the quasilocal energy has the correct Newtonian limit, and includes
a negative contribution due to gravitational binding.


title: Poincar\'e Gauge Theories for Lineal Garvity

abstract:
  We have shown that two of the most studied models of lineal gravities -
Liouville gravity and a ``string-inspired'' model exhibiting the main
characteristic features of a black-hole solution - can be formulated as gauge
invariant theories of the Poincar\'e group. The gauge invariant couplings to
matter (particles, scalar and spinor fields) and explicit solutions for some
matter field configurations, are provided. It is shown that both the models, as
well as the couplings to matter, can be obtained as suitable dimensional
reductions of a 2+1-dimensional ISO(2,1) gauge invariant theory.


title: The Microcanonical Functional Integral. I. The Gravitational Field

abstract:
  The gravitational field in a spatially finite region is described as a
microcanonical system. The density of states $\nu$ is expressed formally as a
functional integral over Lorentzian metrics and is a functional of the
geometrical boundary data that are fixed in the corresponding action. These
boundary data are the thermodynamical extensive variables, including the energy
and angular momentum of the system. When the boundary data are chosen such that
the system is described semiclassically by {\it any} real stationary
axisymmetric black hole, then in this same approximation $\ln\nu$ is shown to
equal 1/4 the area of the black hole event horizon. The canonical and grand
canonical partition functions are obtained by integral transforms of $\nu$ that
lead to "imaginary time" functional integrals. A general form of the first law
of thermodynamics for stationary black holes is derived. For the simpler case
of nonrelativistic mechanics, the density of states is expressed as a real-time
functional integral and then used to deduce Feynman's imaginary-time functional
integral for the canonical partition function.


title: Jordan-Brans-Dicke Quantum Wormholes and Coleman's Mechanism

abstract:
  We consider the quantum gravity and cosmology of a Jordan-Brans-Dicke theory,
predicted by string effective actions. We study its canonical formalism and
find that the constraint algebra is that of general relativity, as a
consequence of the general covariance of scalar-tensor theories. We also
analyze the problem of boundary conditions and propose that they must be
imposed in the Jordan frame, in which particles satisfy the strong equivalence
principle. Specifically, we discuss both Hartle-Hawking and wormhole boundary
conditions in the context of quantum cosmology. We find quantum wormhole
solutions for Jordan-Brans-Dicke gravity even in the absence of matter.
Wormholes may affect the constants of nature and, in particular, the
Brans-Dicke parameter. Following Coleman's mechanism, we find a probability
distribution which is strongly peaked at zero cosmological constant and
infinite Brans-Dicke parameter. That is, we recover general relativity as the
effective low energy theory of gravity.


title: Clifford Algebra of Two-Forms, Conformal Structures and Field Equations

abstract:
  I review the equivalence between duality operators on two-forms and conformal
structures in four dimensions, from a Clifford algebra point of view (due to
Urbantke and Harnett). I also review an application, which leads to a set of
"neighbours" of Einstein's equations. An attempt to formulate reality
conditions for the "neighbours" is discussed.


title: The Nordtvedt effect in the Trojan asteroids

abstract:
  Bounds to the Nordtvedt parameter are obtained from the motion of the first
twelve Trojan asteroids in the period 1906-1990. From the analysis performed,
we derive a value for the inverse of the Saturn mass 3497.80 \pm 0.81 and the
Nordtvedt parameter -0.56 \pm 0.48, from a simultaneous solution for all
asteroids.


title:
The Wave Function of the Universe by the New Euclidean Path-integral
  Approach in Quantum Cosmology

abstract:
  The wave function of the universe is evaluated by using the Euclidean path
integral approach. As is well known, the real Euclidean path integral diverges
because the Einstein-Hilbert action is not positive definite. In order to
obtain a finite wave function, we propose a new regularization method and
calculate the wave function of the Friedmann- Robertson-Walker type
minisuperspace model. We then consider a homogeneous but anisotropic type
minisuperspace model, which is known as the Bianch type I model. The physical
meaning of the wave function by this new regularization method is also
examined.


title: The Spacetime Approach to Quantum Mechanics

abstract:
  Feynman's sum-over-histories formulation of quantum mechanics is reviewed as
an independent statement of quantum theory in spacetime form. It is different
from the usual Schr\"odinger-Heisenberg formulation that utilizes states on
spacelike surfaces because it assigns probabilities to different sets of
alternatives. Sum-over-histories quantum mechanics can be generalized to deal
with spacetime alternatives that are not "at definite moments of time". An
example in field theory is the set of alternative ranges of values of a field
averaged over a spacetime region. An example in particle mechanics is the set
of the alternatives defined by whether a particle never crosses a fixed
spacetime region or crosses it at least once. The general notion of a set of
spacetime alternatives is a partition (coarse-graining) of the histories into
an exhaustive set of exclusive classes. With this generalization the
sum-over-histories formulation can be said to be in fully spacetime form with
dynamics represented by path integrals over spacetime histories and
alternatives defined as spacetime partitions of these histories. When
restricted to alternatives at definite moments of times this generalization is
equivalent to Schr\"odinger-Heisenberg quantum mechanics. However, the quantum
mechanics of more general spacetime alternatives does not have an equivalent
Schr\"odinger-Heisenberg formulation. We suggest that, in the quantum theory of
gravity, the general notion of "observable" is supplied by diffeomorphism
invariant partitions of spacetime metrics and matter field configurations. By
generalizing the usual alternatives so as to put quantum theory in fully
spacetime form we may be led to a covariant generalized quantum mechanics of
spacetime free from the problem of time.


title: The Dark Matter Problem in Light of Quantum Gravity

abstract:
  We show how, by considering the cumulative effect of tiny quantum
gravitational fluctuations over very large distances, it may be possible to:
($a$) reconcile nucleosynthesis bounds on the density parameter of the Universe
with the predictions of inflationary cosmology, and ($b$) reproduce the
inferred variation of the density parameter with distance. Our calculation can
be interpreted as a computation of the contribution of quantum gravitational
degrees of freedom to the (local) energy density of the Universe.


title: The Quantum Mechanics of Closed Systems

abstract:
  A pedagogical introduction is given to the quantum mechanics of closed
systems, most generally the universe as a whole. Quantum mechanics aims at
predicting the probabilities of alternative coarse-grained time histories of a
closed system. Not every set of alternative coarse-grained histories that can
be described may be consistently assigned probabilities because of quantum
mechanical interference between individual histories of the set. In the quantum
mechanics of closed systems, containing both observer and observed,
probabilities are assigned to those sets of alternative histories for which
there is negligible interference between individual histories as a consequence
of the system's initial condition and dynamics. Such sets of histories are said
to decohere. Typical mechanisms of decoherence that are widespread in our
universe are illustrated. Copenhagen quantum mechanics is an approximation to
the more general quantum framework of closed subsystems. It is appropriate when
there is an approximately isolated subsystem that is a participant in a
measurement situation in which (among other things) the decoherence of
alternative registrations of the apparatus can be idealized as exact. Since the
quantum mechanics of closed systems does not posit the existence of the
quasiclassical domain of everyday experience, the domain of the approximate
aplicability of classical physics must be explained. We describe how a
quasiclassical domain described by averages of densities of approximately
conserved quantities could be an emergent feature of an initial condition of
the universe that implies the approximate classical behavior of spacetime on
accessible scales.


title:
Unitary Equivalence of the Metric and Holonomy Formulations of 2+1
  Dimensional Quantum Gravity on the Torus

abstract:
  Recent work on canonical transformations in quantum mechanics is applied to
transform between the Moncrief metric formulation and the Witten-Carlip
holonomy formulation of 2+1-dimensional quantum gravity on the torus. A
non-polynomial factor ordering of the classical canonical transformation
between the metric and holonomy variables is constructed which preserves their
classical modular transformation properties. An extension of the definition of
a unitary transformation is briefly discussed and is used to find the inner
product in the holonomy variables which makes the canonical transformation
unitary. This defines the Hilbert space in the Witten-Carlip formulation which
is unitarily equivalent to the natural Hilbert space in the Moncrief
formulation. In addition, gravitational theta-states arising from ``large''
diffeomorphisms are found in the theory.


title: Dynamical Origin of the Lorentzian Signature of Spacetime

abstract:
  It is suggested that not only the curvature, but also the signature of
spacetime is subject to quantum fluctuations. A generalized D-dimensional
spacetime metric of the form $g_{\mu \nu}=e^a_\mu \eta_{ab} e^b_\nu$ is
introduced, where $\eta_{ab} = diag\{e^{i\theta},1,...,1\}$. The corresponding
functional integral for quantized fields then interpolates from a Euclidean
path integral in Euclidean space, at $\theta=0$, to a Feynman path integral in
Minkowski space, at $\theta=\pi$. Treating the phase $e^{i\theta}$ as just
another quantized field, the signature of spacetime is determined dynamically
by its expectation value. The complex-valued effective potential $V(\theta)$
for the phase field, induced by massless fields at one-loop, is considered. It
is argued that $Re[V(\theta)]$ is minimized and $Im[V(\theta)]$ is stationary,
uniquely in D=4 dimensions, at $\theta=\pi$, which suggests a dynamical origin
for the Lorentzian signature of spacetime.


title: Improved Energy-Momentum Currents in Metric-Affine Spacetime

abstract:
  In Minkowski spacetime it is well-known that the canonical energy-momentum
current is involved in the construction of the globally conserved currents of
energy-momentum and total angular momentum. For the construction of conserved
currents corresponding to (approximate) scale and proper conformal symmetries,
however, an improved energy-momentum current is needed. By extending the
Minkowskian framework to a genuine metric-affine spacetime, we find that the
affine Noether identities and the conformal Killing equations enforce this
improvement in a rather natural way. So far, no gravitational dynamics is
involved in our construction. The resulting dilation and proper conformal
currents are conserved provided the trace of the energy-momentum current
satisfies a (mild) scaling relation or even vanishes.


title: Classical Equations for Quantum Systems

abstract:
  The origin of the phenomenological deterministic laws that approximately
govern the quasiclassical domain of familiar experience is considered in the
context of the quantum mechanics of closed systems such as the universe as a
whole. We investigate the requirements for coarse grainings to yield decoherent
sets of histories that are quasiclassical, i.e. such that the individual
histories obey, with high probability, effective classical equations of motion
interrupted continually by small fluctuations and occasionally by large ones.
We discuss these requirements generally but study them specifically for coarse
grainings of the type that follows a distinguished subset of a complete set of
variables while ignoring the rest. More coarse graining is needed to achieve
decoherence than would be suggested by naive arguments based on the uncertainty
principle. Even coarser graining is required in the distinguished variables for
them to have the necessary inertia to approach classical predictability in the
presence of the noise consisting of the fluctuations that typical mechanisms of
decoherence produce. We describe the derivation of phenomenological equations
of motion explicitly for a particular class of models. Probabilities of the
correlations in time that define equations of motion are explicitly considered.
Fully non-linear cases are studied. Methods are exhibited for finding the form
of the phenomenological equations of motion even when these are only distantly
related to those of the fundamental action. The demonstration of the connection
between quantum-mechanical causality and causalty in classical phenomenological
equations of motion is generalized. The connections among decoherence, noise,
dissipation, and the amount of coarse graining necessary to achieve classical
predictability are investigated quantitatively.


title: Canonical Quantum Gravity and the Problem of Time

abstract:
  This is the write-up of my lectures at the NATO Summer School held in
Salamanca in June 1992. The paper deals with the problem of time in quantum
gravity. All the major schemes are reviewed. Please note that the paper is in
two parts for ease of email transmission; this is part 1. The mailer from gr-qc
may further subdivide these two sections.


title: No Time Machines from Lightlike Sources in 2+1 Gravity

abstract:
  We extend the argument that spacetimes generated by two timelike particles in
D=3 gravity (or equivalently by parallel-moving cosmic strings in D=4) permit
closed timelike curves (CTC) only at the price of Misner identifications that
correspond to unphysical boundary conditions at spatial infinity and to a
tachyonic center of mass. Here we analyze geometries one or both of whose
sources are lightlike.
  We make manifest both the presence of CTC at spatial infinity if they are
present at all, and the tachyonic character of the system: As the total energy
surpasses its tachyonic bound, CTC first begin to form at spatial infinity,
then spread to the interior as the energy increases further. We then show that,
in contrast, CTC are entirely forbidden in topologically massive gravity for
geometries generated by lightlike sources.


title: Quantum Effects in Black Hole Interiors

abstract:
  The Weyl curvature inside a black hole formed in a generic collapse grows,
classically without bound, near to the inner horizon, due to partial absorption
and blueshifting of the radiative tail of the collapse. Using a spherical
model, we examine how this growth is modified by quantum effects of conformally
coupled massless fields.


title: A Nonsingular Universe

abstract:
  We construct an effective action for gravity in which all homogeneous
solutions are nonsingular. In particular, there is neither a big bang nor a big
crunch. The action is a higher derivative modification of Einstein's theory
constructed in analogy to how the action for point particle motion in special
relativity is obtained from Newtonian mechanics.


title: Cosmological Models in Two Spacetime Dimensions

abstract:
  Various physical properties of cosmological models in (1+1) dimensions are
investigated. We demonstrate how a hot big bang and a hot big crunch can arise
in some models. In particular, we examine why particle horizons do not occur in
matter and radiation models. We also discuss under what circumstances
exponential inflation and matter/radiation decoupling can happen. Finally,
without assuming any particular equation of state, we show that physical
singularities can occur in both untilted and tilted universe models if certain
assumptions are satisfied, similar to the (3+1)-dimensional cases.


title: Towards a Singularity-Proof Scheme in Numerical Relativity

abstract:
  Progress in numerical relativity has been hindered for 30 years because of
the difficulties of avoiding spacetime singularities in numerical evolution. We
propose a scheme which excises a region inside an apparent horizon containing
the singularity. Two major ingredients of the scheme are the use of a
horizon-locking coordinate and a finite differencing which respects the causal
structure of the spacetime. Encouraging results of the scheme in the spherical
collapse case are given.


title: Is Quantum Spacetime Foam Unstable?

abstract:
  A very simple wormhole geometry is considered as a model of a mode of
topological fluctutation in Planck-scale spacetime foam. Quantum dynamics of
the hole reduces to quantum mechanics of one variable, throat radius, and
admits a WKB analysis. The hole is quantum-mechanically unstable: It has no
bound states. Wormhole wave functions must eventually leak to large radii. This
suggests that stability considerations along these lines may place strong
constraints on the nature and even the existence of spacetime foam.


title: Self-Consistence of Semi-Classical Gravity

abstract:
  Simon argued that the semi-classical theory of gravity, unless with some of
its solutions excluded, is unacceptable for reasons of both self-consistency
and experiment, and that it has to be replaced by a constrained semi-classical
theory. We examined whether the evidence is conclusive.


title: Path integration in relativistic quantum mechanics

abstract:
  The simple physics of a free particle reveals important features of the
path-integral formulation of relativistic quantum theories. The exact
quantum-mechanical propagator is calculated here for a particle described by
the simple relativistic action proportional to its proper time. This propagator
is nonvanishing outside the light cone, implying that spacelike trajectories
must be included in the path integral. The propagator matches the WKB
approximation to the corresponding configuration-space path integral far from
the light cone; outside the light cone that approximation consists of the
contribution from a single spacelike geodesic. This propagator also has the
unusual property that its short-time limit does not coincide with the WKB
approximation, making the construction of a concrete skeletonized version of
the path integral more complicated than in nonrelativistic theory.


title: SO(4) Invariant States in Quantum Cosmology

abstract:
  The phenomenon of linearisation instability is identified in models of
quantum cosmology that are perturbations of mini-superspace models. In
particular, constraints that are second order in the perturbations must be
imposed on wave functions calculated in such models. It is shown explicitly
that in the case of a model which is a perturbation of the mini-superspace
which has $S^3$ spatial sections these constraints imply that any wave
functions calculated in this model must be SO(4) invariant. (This replaces the
previous corrupted version.)


title: Chern--Simons Gravity from 3+1 Dimensional Gravity

abstract:
  In the context of a Poincar\'e gauge theoretical formulation, pure gravity in
3+1-dimensions is dimensionally reduced to gravity in 2+1-dimensions with or
without cosmological constant $\Lambda$. The dimensional reductions are
consistent with the gauge symmetries, mapping ISO(3, 1) gauge transformations
into ISO(2,1) ones. One of the reductions leads to Chern-Simons-Witten gravity.
The solutions of 2+1-gravity with $\Lambda\le 0$ (in particular the black-hole
solution recently found by Banados, Teitelboim and Zanelli) and those of
1+1-dimensional Liouville gravity, are thus mapped into 3+1-dimensional vacuum
solutions.


title: Einstein Equation with Quantum Corrections Reduced to Second Order

abstract:
  We consider the Einstein equation with first order (semiclassical) quantum
corrections. Although the quantum corrections contain up to fourth order
derivatives of the metric, the solutions which are physically relevant satisfy
a reduced equations which contain derivatives no higher than second order. We
obtain the reduced equations for a range of stress-energy tensors. These
reduced equations are suitable for numerical solution, are expected to contain
fewer numerical instabilities than the original fourth order equations, and
yield only physically relevant solutions. We give analytic and numerical
solutions or reduced equations for particular examples, including
Friedmann-Lema\^\i tre universes with cosmological constant, a spherical body
of constant density, and more general conformally flat metrics.


title: Hadamard States and Adiabatic Vacua

abstract: Reversing a slight detrimental effect of the mailer related to TeXability


title:
Sum-over-histories origin of the composition laws of relativistic
  quantum mechanics and quantum cosmology

abstract:
  The scope of the paper has been broadened to include a more complete
discussion of the following topics: The derivation of composition laws in
quantum cosmology. The connection between the existence of a composition law in
the sum over histories approach to relativistic quantum mechanics and quantum
cosmology, and the existence of a canonical formulation.


title: M\"o\ss{}bauer null redshift experiment II

abstract:
  Accurate limits for the violation of the Principle of Equivalence have been
found from the comparison of the redshifts of two identical nuclear species in
different chemical environments.


title: Wormhole Cosmology and the Horizon Problem

abstract:
  We construct an explicit class of dynamic lorentzian wormholes connecting
Friedmann-Robertson-Walker (FRW) spacetimes. These wormholes can allow two-way
transmission of signals between spatially separated regions of spacetime and
could permit such regions to come into thermal contact. The cosmology of a
network of early Universe wormholes is discussed.


title: D=3: Singularities in Gravitational Scattering of Scalar Waves

abstract:
  Family of exact spacetimes of D=3 Einstein gravity interacting with massless
scalar field is obtained by suitable dimensional reduction of a class of D=4
plane-symmetric Einstein vacua. These D=3 spacetimes describe collisions of
line-fronted asymptotically null excitations and are generically singular to
the future. The solution for the scalar field can be decomposed into the
Fourier-Bessel modes around the background solitons. The criteria of regularity
of incoming waves are found. It is shown that the appearance of the scalar
curvature singularities need not stem from singularities of incoming waves.
Moreover, in distinction to D=4 case, for all solutions with regular incoming
waves the final singularities are inevitable.


title: Gauge Field Back-reaction on a Black Hole

abstract:
  The order $\hbar$ fluctuations of gauge fields in the vicinity of a blackhole
can create a repulsive antigravity region extending out beyond the renormalized
Schwarzschild horizon. If the strength of this repulsive force increases as
higher orders in the back-reaction are included, the formation of a
wormhole-like object could occur.


title:
Positivity of Entropy in the Semi-Classical Theory of Black Holes and
  Radiation

abstract:
  Quantum stress-energy tensors of fields renormalized on a Schwarzschild
background violate the classical energy conditions near the black hole.
Nevertheless, the associated equilibrium thermodynamical entropy $\Delta S$ by
which such fields augment the usual black hole entropy is found to be positive.
More precisely, the derivative of $\Delta S$ with respect to radius, at fixed
black hole mass, is found to vanish at the horizon for {\it all} regular
renormalized stress-energy quantum tensors. For the cases of conformal scalar
fields and U(1) gauge fields, the corresponding second derivative is positive,
indicating that $\Delta S$ has a local minimum there. Explicit calculation
shows that indeed $\Delta S$ increases monotonically for increasing radius and
is positive. (The same conclusions hold for a massless spin 1/2 field, but the
accuracy of the stress-energy tensor we employ has not been confirmed, in
contrast to the scalar and vector cases). None of these results would hold if
the back-reaction of the radiation on the spacetime geometry were ignored;
consequently, one must regard $\Delta S$ as arising from both the radiation
fields and their effects on the gravitational field. The back-reaction, no
matter how "small",


title: Gauge (In)variance, Mass and Parity in D=3 Revisited

abstract:
  We analyze the degree of equivalence between abelian topologically massive,
gauge-invariant, vector or tensor parity doublets and their explicitly massive,
non-gauge, counterparts. We establish equivalence of field equations by
exploiting a generalized Stueckelberg invariance of the gauge systems. Although
the respective excitation spectra and induced source-source interactions are
essentially identical, there are also differences, most dramatic being those
between the Einstein limits of the interactions in the tensor case: the
doublets avoid the discontinuity (well-known from D=4) exhibited by Pauli-Fierz
theory.


title: Weak-Field Gravity of Circular Cosmic Strings

abstract:
  A weak-field solution of Einstein's equations is constructed. It is generated
by a circular cosmic string externally supported against collapse. The solution
exhibits a conical singularity, and the corresponding deficit angle is the same
as for a straight string of the same linear energy density. This confirms the
deficit-angle assumption made in the Frolov-Israel-Unruh derivation of the
metric describing a string loop at a moment of time symmetry.


title: Inflating Lorentzian Wormholes

abstract:
  It has been speculated that Lorentzian wormholes of the Morris- Thorne type
might be allowed by the laws of physics at submicroscopic, e.g. Planck, scales
and that a sufficiently advanced civilization might be able to enlarge them to
classical size. The purpose of this paper is to explore the possibility that
inflation might provide a natural mechanism for the enlargement of such
wormholes to macroscopic size. A new classical metric is presented for a
Lorentzian wormhole which is imbedded in a flat deSitter space. It is shown
that the throat and proper length of the wormhole inflate. The resulting
properties and stress-energy tensor associated with this metric are discussed.


title:
Gauge Formulation of the Spinning Black Hole in (2+1)-Dimensional
  Anti-de Sitter Space

abstract:
  We compute the group element of SO(2,2) associated with the spinning black
hole found by Ba\~nados, Teitelboim and Zanelli in (2+1)-dimensional anti-de
Sitter space-time. We show that their metric is built with SO(2,2) gauge
invariant quantities and satisfies Einstein's equations with negative
cosmological constant everywhere except at $r=0$. Moreover, although the metric
is singular on the horizons, the group element is continuous and possesses a
kink there.


title: Unification of Gravity and Yang-Mills Theory in (2+1)-Dimensions

abstract:
  A gauge and diffeomorphism invariant theory in (2+1)-dimensions is presented
in both first and second order Lagrangian form as well as in a Hamiltonian
form. For gauge group $SO(1,2)$, the theory is shown to describe ordinary
Einstein gravity with a cosmological constant. With gauge group
$G^{tot}=SO(1,2)\otimes G^{YM}$, it is shown that the equations of motion for
the $G^{YM}$ fields are the Yang-Mills equations. It is also shown that for
weak $G^{YM}$ Yang-Mills fields, this theory agrees with the conventional
Einstein-Yang-Mills theory to lowest order in Yang-Mills fields. Explicit
static and rotation symmetric solutions to the Einstein-Maxwell theory are
studied both for the conventional coupling and for this unified theory. In the
electric solution to the unified theory, point charges are not allowed, the
charges must have spatial extensions.


title: Discrete Symmetry, Non-Commutative Geometry and Gravity

abstract:
  We describe the geomety of a set of scalar fields coupled to gravity. We
consider the formalism of a differential Z_2-graded algebra of $2\times 2$
matrices whose elements are differential forms on space-time. The connection
and the vierbeins are extended to incorporate additional scalar and vector
fields. The resulting action describes two universes coupled in a non-minimal
way to a set of scalar fields. This picture is slightly different from the
description of general relativity in the framework of non-commutative geomety.


title: Vacuum Polarisation and the Black Hole Singularity

abstract:
  In order to investigate the effects of vacuum polarisation on mass inflation
singularities, we study a simple toy model of a charged black hole with cross
flowing radial null dust which is homogeneous in the black hole interior. In
the region $r^2 \ll e^2$ we find an approximate analytic solution to the
classical field equations. The renormalized stress-energy tensor is evaluated
on this background and we find the vacuum polarisation backreaction corrections
to the mass function $m(r)$. Asymptotic analysis of the semiclassical mass
function shows that the mass inflation singularity is much stronger in the
presence of vacuum polarisation than in the classical case.


title: The Relation between Physical and Gravitational Geometry

abstract:
  The appearance of two geometries in one and the same gravitational theory is
familiar. Usually, as in the Brans-Dicke theory or in string theory, these are
conformally related Riemannian geometries. Is this the most general relation
between the two geometries allowed by physics ? We study this question by
supposing that the physical geometry on which matter dynamics take place could
be Finslerian rather than just Riemannian. An appeal to the weak equivalence
principle and causality then leads us the conclusion that the Finsler geometry
has to reduce to a Riemann geometry whose metric - the physical metric - is
related to the gravitational metric by a generalization of the conformal
transformation.


title:
Generalized Fierz Identities and the Superselection Rule for Geometric
  Multispinors

abstract:
  The inverse problem, to reconstruct the general multivector wave function
from the observable quadratic densities, is solved for 3D geometric algebra. It
is found that operators which are applied to the right side of the wave
function must be considered, and the standard Fierz identities do not
necessarily hold except in restricted situations, corresponding to the
spin-isospin superselection rule. The Greider idempotent and Hestenes
quaterionic spinors are included as extreme cases of a single superselection
parameter.


title:
What can we learn from the study of non-perturbative quantum general
  relativity?

abstract:
  I attempt to answer the question of the title by giving an annotated list of
the major results achieved, over the last six years, in the program to
construct quantum general relativity using the Ashtekar variables and the loop
representation. A summary of the key open problems is also included. Also
included are expositions of several new results including the construction of
spatially diffeomorphism invariant observables constructed by coupling general
relativity to matter fields.


title:
Superluminary Universe: A Possible Solution to the Initial Value Problem
  in Cosmology

abstract:
  The spontaneous breaking of local Lorentz invariance in the early Universe,
associated with a first order phase transition at a critical time $t_c$,
generates a large increase in the speed of light and a superluminary
communication of information occurs, allowing all regions in the Universe to be
causally connected. This solves the horizon problem, leads to a mechanism of
monopole suppression in cosmology and can resolve the flatness problem. After
the critical time $t_c$, local Lorentz (and diffeomorphism) invariance is
restored and light travels at its presently measured speed. The kinematical and
dynamical aspects of the generation of quantum fluctuations in the
superluminary Universe are investigated. A scale invariant prediction for the
fluctuation density amplitude is obtained.


title: Dilaton Contributions to the Cosmic Gravitational Wave Background

abstract:
  We consider the cosmological amplification of a metric perturbation
propagating in a higher-dimensional Brans-Dicke background, including a non
trivial dilaton evolution. We discuss the properties of the spectral energy
density of the produced gravitons (as well as of the associated squeezing
parameter), and we show that the present observational bounds on the graviton
spectrum provide significant information on the dynamical evolution of the
early universe.


title: Quantum Gravity by the Complex Canonical Formulation

abstract:
  The basic features of the complex canonical formulation of general relativity
and the recent developments in the quantum gravity program based on it are
reviewed. The exposition is intended to be complementary to the review articles
available already and some original arguments are included. In particular the
conventional treatment of the Hamiltonian constraint and quantum states in the
canonical approach to quantum gravity is criticized and a new formulation is
proposed.


title: Gravitational Waves in the Nonsymmetric Gravitational Theory

abstract:
  We prove that the flux of gravitational radiation from an isolated source in
the Nonsymmetric Gravitational Theory is identical to that found in Einstein's
General Theory of Relativity.


title: Tunneling in Anisotropic Cosmological Models

abstract:
  Tunneling rate is investigated in homogenous and anisotropic cosmologies. The
calculations is done by two methods: Euclidean and Hamiltonian approaches. It
is found that the probability decreases exponentialy as anisotropy is
increased.


title: Spin effects in the inspiral of coalescing compact binaries

abstract:
  We derive the contributions of spin-orbit and spin-spin coupling to the
gravitational radiation from coalescing binary systems of spinning compact
objects. We calculate spin effects in the symmetric, trace-free radiative
multipoles that determine the gravitational waveform, and the rate of energy
loss. Assuming a balance between energy radiated and orbital energy lost, we
determine the spin effects in the evolution of the orbital frequency and
orbital radius. Assuming that a laser interferometric gravitational observatory
can track the gravitational-wave frequency (twice the orbital frequency) as it
sweeps through its sensitive bandwidth between about 10 Hz and one kHz, we
estimate the accuracy with which the spins of the component bodies can be
determined from the gravitational-wave signal.


title: Cauchy horizon singularity without mass inflation

abstract:
  A perturbed Reissner-Nordstr\"om-de Sitter solution is used to emphasize the
nature of the singularity along the Cauchy horizon of a charged spherically
symmetric black hole. For these solutions, conditions may prevail under which
the mass function is bounded and yet the curvature scalar
$R_{\alpha\beta\gamma\delta} R^{\alpha\beta\gamma\delta}$ diverges.


title: Chaotic Friedmann-Robertson-Walker Cosmology

abstract:
  We show that the dynamics of a spatially closed Friedmann - Robertson -
Walker Universe conformally coupled to a real, free, massive scalar field, is
chaotic, for large enough field amplitudes. We do so by proving that this
system is integrable under the adiabatic approximation, but that the
corresponding KAM tori break up when non adiabatic terms are considered. This
finding is confirmed by numerical evaluation of the Lyapunov exponents
associated with the system, among other criteria. Chaos sets strong limitations
to our ability to predict the value of the field at the Big Crunch, from its
given value at the Big Bang. (Figures available on request)


title:
Thawing the Frozen Formalism: The Difference Between Observables and
  What We Observe

abstract:
  In a parametrized and constrained Hamiltonian system, an observable is an
operator which commutes with all (first-class) constraints, including the
super-Hamiltonian. The problem of the frozen formalism is to explain how
dynamics is possible when all observables are constants of the motion. An
explicit model of a measurement-interaction in a parametrized Hamiltonian
system is used to elucidate the relationship between three definitions of
observables---as something one observes, as self-adjoint operators, and as
operators which commute with all of the constraints. There is no inconsistency
in the frozen formalism when the measurement process is properly understood.
The projection operator description of measurement is criticized as an
over-idealization which treats measurement as instantaneous and
non-destructive. A more careful description of measurement necessarily involves
interactions of non-vanishing duration. This is a first step towards a more
even-handed treatment of space and time in quantum mechanics. (This paper was
written for the festschrift of Dieter Brill.)


title: Cosmic Censorship in 2-Dimensional Dilaton Gravity

abstract:
  The global structure of 2-dimensional dilaton gravity is studied, attending
in particular to black holes and singularities. A gravitational energy is
defined and shown to be positive at spatial singularities and negative at
temporal singularities. Trapped points are defined, and it is shown that
spatial singularities are trapped and temporal singularities are not. Thus a
local form of cosmic censorship holds for positive energy. In an analogue of
gravitational collapse to a black hole, matter falling into an initially flat
space creates a spatial curvature singularity which is cloaked in a spatial or
null apparent horizon with non-decreasing energy and area.


title: Galilean Theories of Gravitation

abstract:
  A generalization of Newtonian gravitation theory is obtained by a suitable
limiting procedure from the ADM action of general relativity coupled to a
mass-point. Three particular theories are discussed and it is found that two of
them are invariant under an extended Galilei gauge group.


title: Exotic Differentiable Structures and General Relativity

abstract:
  We review recent developments in differential topology with special concern
for their possible significance to physical theories, especially general
relativity. In particular we are concerned here with the discovery of the
existence of non-standard (``fake'' or ``exotic'') differentiable structures on
topologically simple manifolds such as $S^7$, \R and $S^3\times {\bf R^1}.$
Because of the technical difficulties involved in the smooth case, we begin
with an easily understood toy example looking at the role which the choice of
complex structures plays in the formulation of two-dimensional vacuum
electrostatics. We then briefly review the mathematical formalisms involved
with differentiable structures on topological manifolds, diffeomorphisms and
their significance for physics. We summarize the important work of Milnor,
Freedman, Donaldson, and others in developing exotic differentiable structures
on well known topological manifolds. Finally, we discuss some of the geometric
implications of these results and propose some conjectures on possible physical
implications of these new manifolds which have never before been considered as
physical models.


title: Quantum Vacuum Instability Near Rotating Stars

abstract:
  We discuss the Starobinskii-Unruh process for the Kerr black hole. We show
how this effect is related to the theory of squeezed states. We then consider a
simple model for a highly relativistic rotating star and show that the
Starobinskii-Unruh effect is absent.


title:
Dark Matter and Non-Newtonian Gravity From General Relativity on a
  Stringy Background

abstract:
  An exact solution of Einstein's field equations for a static spherically
symmetric medium with a radially boost invariant energy-momentum tensor is
presented. In the limit of an equation of state corresponding to a distribution
of radially directed strings there is a $1/r$ correction to Newton's force law.
At large distances and small accelerations this law coincides with the
phenomenological force law invented by Milgrom in order to explain the flat
rotation curves of galaxies without introducing dark matter. The present model
explaines why the critical acceleration of Milgrom is of the same order of
magnitude as the Hubble parameter.


title:
On Cosmological Isotropy, Quantum Cosmology and the Weyl Curvature
  Hypothesis

abstract:
  The increasing entropy, large-scale isotropy and approximate flatness of the
universe are considered in the context of signature change, which is a
classical model of quantum tunnelling in quantum cosmology. The signature
change hypothesis implies an initial inflationary epoch, the magnetic half of
the Weyl curvature hypothesis, and a close analogue of the conformal
singularity hypothesis. Adding the electric half of the Weyl curvature
hypothesis yields, for a perfect fluid, only homogeneous and isotropic
cosmologies. In the cosmological-constant case, the unique solution is the
Vilenkin tunnelling solution, which gives a de Sitter cosmology.


title: Weak-Field Gravity of Revolving Circular Cosmic Strings

abstract:
  A weak-field solution of Einstein's equations is constructed. It is generated
by a circular cosmic string revolving in its plane about the centre of the
circle. (The revolution is introduced to prevent the string from collapsing.)
This solution exhibits a conical singularity, and the corresponding deficit
angle is the same as for a straight string of the same linear energy density,
irrespective of the angular velocity of the string.


title:
The Coherent State Representation of Quantum Fluctuations in the Early
  Universe

abstract:
  Using the squeezed state formalism the coherent state representation of
quantum fluctuations in an expanding universe is derived. It is shown that this
provides a useful alternative to the Wigner function as a phase space
representation of quantum fluctuations. The quantum to classical transition of
fluctuations is naturally implemented by decohering the density matrix in this
representation. The entropy of the decohered vacua is derived. It is shown that
the decoherence process breaks the physical equivalence between vacua that
differ by a coordinate dependent phase generated by a surface term in the
Lagrangian. In particular, scale invariant power spectra are only obtained for
a special choice of surface term.


title: Magnetically Charged Black Holes and their Stability

abstract:
  We study magnetically charged black holes in the Einstein-Yang-Mills-Higgs
theory in the limit of infinitely strong coupling of the Higgs field. Using
mixed analytical and numerical methods we give a complete description of static
spherically symmetric black hole solutions, both abelian and nonabelian. In
particular, we find a new class of extremal nonabelian solutions. We show that
all nonabelian solutions are stable against linear radial perturbations. The
implications of our results for the semiclassical evolution of magnetically
charged black holes are discussed.


title: Black Hole Tunneling Entropy and the Spectrum of Gravity

abstract:
  The tunneling approach for entropy generation in quantum gravity is applied
to black holes. The area entropy is recovered and shown to count only a tiny
fraction of the black hole degeneracy. The latter stems from the extension of
the wave function outside the barrier. In fact the semi-classical analysis
leads to infinite degeneracy. Evaporating black holes leave then infinitely
degenerate "planckons" remnants which can neither decay into, nor be formed
from, ordinary matter in a finite time. Quantum gravity opens up at the Planck
scale into an infinite Hilbert space which is expected to provide the
ultraviolet cutoff required to render the theory finite in the sector of large
scale physics.


title: A Nonlinear Model of a Quantum Minisuperspace System with Back Reaction

abstract:
  We consider the quantum evolution of the space-independent mode of a $\lambda
{\phi}^4$ theory as a minisuperspace in the space of all $\phi$. The motion of
the wave packet in the minisuperspace is then compared to the motion of a wave
packet in a larger minisuperspace consisting of the original minisuperspace
plus one space-dependent mode. By comparing the motion of the two packets we
develop criteria that tell us when the quantum evolution in the
space-independent minisuperspace gives us useful information about the true
evolution in the larger minisuperspace. These criteria serve as a toy model for
similar(but much more complex) criteria that will tell us whether or when
quantized gravitational minisuperspaces can possibly give any useful
information about quantum gravity.


title: Collisions of Einstein-Conformal Scalar Waves

abstract:
  A large class of solutions of the Einstein-conformal scalar equations in
D=2+1 and D=3+1 is identified. They describe the collisions of asymptotic
conformal scalar waves and are generated from Einstein-minimally coupled scalar
spacetimes via a (generalized) Bekenstein transformation. Particular emphasis
is given to the study of the global properties and the singularity structure of
the obtained solutions. It is shown, that in the case of the absence of pure
gravitational radiation in the initial data, the formation of the final
singularity is not only generic, but is even inevitable.


title: Inhomogeneous and anisotropic cosmologies

abstract:
  This is a review of cosmological models prepared for the Pont d'Oye workshop
on the origin of structure in the universe. The classes of models are discussed
in turn, and then some of their uses are considered.


title: Anisotropic and inhomogeneous cosmologies

abstract:
  This review was given at the 65th birthday meeting of D.W. Sciama, The
Renaissance of General Relativity and Cosmology, to be published by Cambridge
University Press. It presents progress in the understanding of non-standard
relativistic cosmologies during Sciama's career, organized by the areas of
application rather than the mathematical types of the models.


title: (1+1)-Dimensional Methods for General Relativity

abstract:
  This is an article contributed to the Brill Festschrift, in honor of the 60th
birthday of Prof. D.R. Brill, which will appear in the Vol.2 of the Proceedings
of the International Symposia on Directions in General Relativity. In this
article we present the (1+1)-dimensional method for studying general relativity
of 4-dimensions. We first discuss the general formalism, and subsequently draw
attention to the algebraically special class of space-times, following the
Petrov classification. It is shown that this class of space-times can be
described by the (1+1)-dimensional Yang-Mills action interacting with matter
fields, with the spacial diffeomorphisms of the 2-surface as the gauge
symmetry. The constraint appears polynomial in part, whereas the non-polynomial
part is a non-linear sigma model type in (1+1)-dimensions. It is also shown
that the representations of $w_{\infty}$-gravity appear naturally as special
cases of this description, and we discuss briefly the $w_{\infty}$-geometry in
term of the fibre bundle.


title: String Instabilities in Black Hole Spacetimes

abstract:
  We study the emergence of string instabilities in $D$ - dimensional black
hole spacetimes (Schwarzschild and Reissner - Nordstr\o m), and De Sitter space
(in static coordinates to allow a better comparison with the black hole case).
We solve the first order string fluctuations around the center of mass motion
at spatial infinity, near the horizon and at the spacetime singularity. We find
that the time components are always well behaved in the three regions and in
the three backgrounds. The radial components are {\it unstable}: imaginary
frequencies develop in the oscillatory modes near the horizon, and the
evolution is like $(\tau-\tau_0)^{-P}$, $(P>0)$, near the spacetime
singularity, $r\to0$, where the world - sheet time $(\tau-\tau_0)\to0$, and the
proper string length grows infinitely. In the Schwarzschild black hole, the
angular components are always well - behaved, while in the Reissner - Nordstr\o
m case they develop instabilities inside the horizon, near $r\to0$ where the
repulsive effects of the charge dominate over those of the mass. In general,
whenever large enough repulsive effects in the gravitational background are
present, string instabilities develop. In De Sitter space, all the spatial
components exhibit instability. The infalling of the string to the black hole
singularity is like the motion of a particle in a potential
$\gamma(\tau-\tau_0)^{-2}$ where $\gamma$ depends on the $D$ spacetime
dimensions and string angular momentum, with $\gamma>0$ for Schwarzschild and
$\gamma<0$ for Reissner - Nordstr\o m black holes. For $(\tau-\tau_0)\to0$ the
string ends trapped by the black hole singularity.


title: Bianchi Cosmological Models and Gauge Symmetries

abstract:
  We analyze carefully the problem of gauge symmetries for Bianchi models, from
both the geometrical and dynamical points of view. Some of the geometrical
definitions of gauge symmetries (=``homogeneity preserving diffeomorphisms'')
given in the literature do not incorporate the crucial feature that local gauge
transformations should be independent at each point of the manifold of the
independent variables ( = time for Bianchi models), i.e, should be arbitrarily
localizable ( in time). We give a geometrical definition of homogeneity
preserving diffeomorphisms that does not possess this shortcoming. The proposed
definition has the futher advantage of coinciding with the dynamical definition
based on the invariance of the action ( in Lagrangian or Hamiltonian form). We
explicitly verify the equivalence of the Lagrangian covariant phase space with
the Hamiltonian reduced phase space. Remarks on the use of the Ashtekar
variables in Bianchi models are also given.


title: Event horizons and apparent horizons in spherically symmetric geometries

abstract:
  Spherical configurations that are very massive must be surrounded by apparent
horizons. These in turn, when placed outside a collapsing body, must propagate
outward with a velocity equal to the velocity of radially outgoing photons.
That proves, within the framework of (1+3) formalism and without resorting to
the Birkhoff theorem, that apparent horizons coincide with event horizons.


title: Observing binary inspiral in gravitational radiation: One interferometer

abstract:
  We investigate the sensitivity of individual LIGO/VIRGO-like interferometers
and the precision with which they can determine the characteristics of an
inspiralling binary system. Since the two interferometers of the LIGO detector
share nearly the same orientation, their joint sensitivity is similar to that
of a single, more sensitive interferometer. We express our results for a single
interferometer of both initial and advanced LIGO design, and also for the LIGO
detector in the limit that its two interferometers share exactly the same
orientation. We approximate the evolution of a binary system as driven
exclusively by leading order quadrupole gravitational radiation. To assess the
sensitivity, we calculate the rate at which sources are expected to be
observed, the range to which they are observable, and the precision with which
characteristic quantities describing the observed binary system can be
determined. Assuming a conservative rate density for coalescing neutron star
binary systems we expect that the advanced LIGO detector will observe
approximately 69~yr${}^{-1}$ with an amplitude SNR greater than 8. Of these,
approximately 7~yr${}^{-1}$ will be from binaries at distances greater than
950~Mpc. We explore the sensitivity of these results to a tunable parameter in
the interferometer design (the recycling frequency). The optimum choice of the
parameter is dependent on the goal of the observations, e.g., maximizing the
rate of detections or maximizing the precision of measurement. We determine the
optimum parameter values for these two cases.


title: On the Definition of Decoherence

abstract:
  We examine the relationship between the decoherence of quantum-mechanical
histories of a closed system (as discussed by Gell-Mann and Hartle) and
environmentally-induced diagonalization of the density operator for an open
system. We study a definition of decoherence which incorporates both of these
ideas, and show that it leads to a consistent probabilistic interpretation of
the reduced density operator.


title: Time Symmetric Quantum Cosmology and Our Universe

abstract:
  We investigate the time neutral formulation of quantum cosmology of Gell-Mann
and Hartle. In particular we study the proposal discussed by them that our
Universe corresponds to the time symmetric decoherence functional with initial
and final density matrix of low entropy. We show that our Universe does not
correspond to this proposal by investigating the behaviour of small
inhomogeneous perturbations around a Friedman-Robertson-Walker model. These
perturbations cannot be time symmetric if they were small at the Big Bang.


title: Real Tunneling Solutions and the Hartle-Hawking Wave Function

abstract:
  A real tunneling solution is an instanton for the Hartle-Hawking path
integral with vanishing extrinsic curvature (vanishing ``momentum'') at the
boundary. Since the final momentum is fixed, its conjugate cannot be specified
freely; consequently, such an instanton will contribute to the wave function at
only one or a few isolated spatial geometries. I show that these geometries are
the extrema of the Hartle-Hawking wave function in the semiclassical
approximation, and provide some evidence that with a suitable choice of time
parameter, these extrema are the maxima of the wave function at a fixed time.


title: Decoherence Functional and Probability Interpretation

abstract:
  We confirm that the diagonal elements of the Gell-Mann and Hartle's
decoherence decoherence functional are equal to the relative frequencies of the
results of many identical experiments, when a set of alternative histories
decoheres. We consider both cases of the pure and mixed initial states.


title: What is the True Description of Charged Black Holes?

abstract:
  If string theory describes nature, then charged black holes are not described
by the Reissner-Nordstrom solution. This solution must be modified to include a
massive dilaton. In the limit of vanishing dilaton mass, the new solution can
be found by a generalization of the Harrison transformation for the
Einstein-Maxwell equations. These two solution generating transformations and
the resulting black holes are compared. It is shown that the extremal black
hole with massless dilaton can be viewed as the ``square root" of the extremal
Reissner-Nordstrom solution. When the dilaton mass is included, extremal black
holes are repulsive, and it is energetically favorable for them to bifurcate
into smaller holes. (To appear in the Festschrift for Dieter Brill)


title: Cosmology, Oscillating Physics and Oscilllating Biology

abstract:
  According to recent reports there is an excess correlation and an apparent
regularity in the galaxy one-dimensional polar distribution with a
characteristic scale of 128 $h^{-1}$ Mpc. This aparent spatial periodicity can
be naturally explained by a time oscillation of the gravitational constant $G$.
On the other hand, periodic growth features of bivalve and coral fossiles
appear to show a periodic component in the time dependence of the number of
days per year. In this letter we show that a time oscillating gravitational
constant with similar period and amplitude can explain such a feature.


title:
Entropy Production in the Cosmological Amplification of the Vacuum
  Fluctuations

abstract:
  We estimate the entropy associated to a background of squeezed cosmic
gravitons, and we argue that the process of cosmological pair production from
the vacuum may explain the large amount of entropy of our present universe.


title:
The Reduction of the State Vector and Limitations on Measurement in the
  Quantum Mechanics of Closed Systems

abstract:
  Measurement is a fundamental notion in the usual approximate quantum
mechanics of measured subsystems. Probabilities are predicted for the outcomes
of measurements. State vectors evolve unitarily in between measurements and by
reduction of the state vector at measurements. Probabilities are computed by
summing the squares of amplitudes over alternatives which could have been
measured but weren't. Measurements are limited by uncertainty principles and by
other restrictions arising from the principles of quantum mechanics. This essay
examines the extent to which those features of the quantum mechanics of
measured subsystems that are explicitly tied to measurement situations are
incorporated or modified in the more general quantum mechanics of closed
systems in which measurement is not a fundamental notion. There, probabilities
are predicted for decohering sets of alternative time histories of the closed
system, whether or not they represent a measurement situation. Reduction of the
state vector is a necessary part of the description of such histories.
Uncertainty principles limit the possible alternatives at one time from which
histories may be constructed. Models of measurement situations are exhibited
within the quantum mechanics of the closed system containing both measured
subsystem and measuring apparatus. Limitations are derived on the existence of
records for the outcomes of measurements when the initial density matrix of the
closed system is highly impure. (Festschrift for Dieter Brill).


title:
Massive Spin-5/2 Fields Coupled to Gravity: Tree-Level Unitarity vs. the
  Equivalence Principle

abstract:
  I show that the gravitational scattering amplitudes of a spin-5/2 field with
mass $m\ll M_{Pl}$ violate tree-level unitarity at energies
$\sqrt{s}\approx\sqrt{mM_{Pl}}$ if the coupling to gravity is minimal.
Unitarity up to energies $\sqrt{s}\approx M_{Pl}$ is restored by adding a
suitable non-minimal term, which gives rise to interactions violating the
(strong) equivalence principle. These interactions are only relevant at
distances $d\lequiv 1/m$.


title:
"Are Black Holes in Brans-Dicke Theory precisely the same as in General
  Relativity?"

abstract:
  We study a three-parameters family of solutions of the Brans-Dicke field
equations. They are static and spherically symmetric. We find the range of
parameters for which this solution represents a black hole different from the
Schwarzschild one. We find a subfamily of solutions which agrees with
experiments and observations in the solar system. We discuss some astrophysical
applications and the consequences on the "no hair" theorems for black holes.


title: On Self-Dual Gravity I

abstract:
  (One typo corrected and one incorrect statement removed. Extra details on
conserved quantities and symmetry algebras added).


title:
A Positive Mass Theorem Based on the Focusing and Retardation of Null
  Geodesics

abstract:
  A positive mass theorem for General Relativity Theory is proved. The proof is
4-dimensional in nature, and relies completely on arguments pertaining to
causal structure, the basic idea being that positive energy-density focuses
null geodesics, and correspondingly retards them, whereas a negative total mass
would advance them. Because it is not concerned with what lies behind horizons,
this new theorem applies in some situations not covered by previous positivity
theorems. Also, because geodesic focusing is a global condition, the proof
might allow a generalisation to semi-classical gravity, even though quantum
violations of local energy conditions can occur there.


title: Time, measurement and information loss in quantum cosmology

abstract:
  An error in the gauge fixed quantization of section 3 is corrected. The
result is a much simpler treatment of the clock field, leading to a
simplification of the gauge fixed quantum theory and the treatment of the
semiclassical limit.


title: The Origin of Time Asymmetry

abstract:
  It is argued that the observed Thermodynamic Arrow of Time must arise from
the boundary conditions of the universe. We analyse the consequences of the no
boundary proposal, the only reasonably complete set of boundary conditions that
has been put forward. We study perturbations of a Friedmann model containing a
massive scalar field but our results should be independent of the details of
the matter content. We find that gravitational wave perturbations have an
amplitude that remains in the linear regime at all times and is roughly time
symmetric about the time of maximum expansion. Thus gravitational wave
perturbations do not give rise to an Arrow of Time. However density
perturbations behave very differently. They are small at one end of the
universe's history, but grow larger and become non linear as the universe gets
larger. Contrary to an earlier claim, the density perturbations do not get
small again at the other end of the universe's history. They therefore give
rise to a Thermodynamic Arrow of Time that points in a constant direction while
the universe expands and contracts again. The Arrow of Time does not reverse at
the point of maximum expansion. One has to appeal to the Weak Anthropic
Principle to explain why we observe the Thermodynamic Arrow to agree with the
Cosmological Arrow, the direction of time in which the universe is expanding.


title: Jacobi's Action and the Density of States

abstract:
  The authors have introduced recently a ``microcanonical functional integral"
which yields directly the density of states as a function of energy. The phase
of the functional integral is Jacobi's action, the extrema of which are
classical solutions at a given energy. This approach is 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, however, we ignore gravity and illustrate the use of Jacobi's action by
computing the density of states for a nonrelativistic harmonic oscillator.
(Festschrift for Dieter Brill)


title: Comments on Closed Bianchi Models

abstract:
  We show several kinematical properties that are intrinsic to the Bianchi
models with compact spatial sections. Especially, with spacelike hypersurfaces
being closed, (A) no anisotropic expansion is allowed for Bianchi type V and
VII(A\not=0), and (B) type IV and VI(A\not=0,1) does not exist. In order to
show them, we put into geometric terms what is meant by spatial homogeneity and
employ a mathematical result on 3-manifolds. We make clear the relation between
the Bianchi type symmetry of space-time and spatial compactness, some part of
which seem to be unnoticed in the literature. Especially, it is shown under
what conditions class B Bianchi models do not possess compact spatial sections.
Finally we briefly describe how this study is useful in investigating global
dynamics in (3+1)-dimensional gravity.


title: On the configuration space topology in general relativity

abstract:
  The configuration-space topology in canonical General Relativity depends on
the choice of the initial data 3-manifold. If the latter is represented as a
connected sum of prime 3-manifolds, the topology receives contributions from
all configuration spaces associated to each individual prime factor. There are
by now strong results available concerning the diffeomorphism group of prime
3-manifolds which are exploited to examine the topology of the configuration
spaces in terms of their homotopy groups. We explicitly show how to obtain
these for the class of homogeneous spherical primes, and communicate the
results for all other known primes except the non-sufficiently large ones of
infinite fundamental group.


title: Black Holes with a Generalized Gravitational Action

abstract:
  Microscopic black holes are sensitive to higher dimension operators in the
gravitational action. We compute the influence of these operators on the
Schwarzschild solution using perturbation theory. All (time reversal invariant)
operators of dimension six are included (dimension four operators don't alter
the Schwarzschild solution). Corrections to the relation between the Hawking
temperature and the black hole mass are found. The entropy is calculated using
the Gibbons-Hawking prescription for the Euclidean path integral and using
naive thermodynamic reasoning. These two methods agree, however, the entropy is
not equal to 1/4 the area of the horizon.


title: An Anisotropic Wormhole:TUNNELLING in Time and Space

abstract:
  We discuss the structure of a gravitational euclidean instanton obtained
through coupling of gravity to electromagnetism. Its topology at fixed $t$ is
$S^1\times S^2$. This euclidean solution can be interpreted as a tunnelling to
a hyperbolic space (baby universe) at $t=0$ or alternatively as a static
wormhole that joins the two asymptotically flat spaces of a
Reissner--Nordstr\"om type solution with $M=0$.


title:
Avoiding degenerate coframes in an affine gauge approach to quantum
  gravity

abstract:
  In quantum models of gravity, it is surmized that configurations with
degenerate coframes could occur during topology change of the underlying
spacetime structure. However, the coframe is not the true Yang--Mills type
gauge field of the translations, since it lacks the inhomogeneous gradient term
in the gauge transformations. By explicitly restoring this ``hidden" piece
within the framework of the affine gauge approach to gravity, one can avoid the
metric or coframe degeneracy which would otherwise interfere with the
integrations within the path integral. This is an important advantage for
quantization.


title:
Topological Defects in Gravitational Theories with Non Linear
  Lagrangians

abstract:
  The gravitational field of monopoles, cosmic strings and domain walls is
studied in the quadratic gravitational theory $R+\alpha R^2$ with $\alpha
|R|\ll 1$, and is compared with the result in Einstein's theory. The metric
aquires modifications which correspond to a short range `Newtonian' potential
for gauge cosmic strings, gauge monopoles and domain walls and to a long range
one for global monopoles and global cosmic strings. In this theory the
corrections turn out to be attractive for all the defects. We explain, however,
that the sign of these corrections in general depends on the particular higher
order derivative theory and topological defect under consideration. The
possible relevance of our results to the study of the evolution of topological
defects in the early universe is pointed out.


title: Singularity Free Inhomogeneous Cosmological Stiff Fluid Models

abstract:
  We present a singularity free class of inhomogeneous cylindrical universes
filled with stiff perfect fluid $(\rho = p)$. Its matter free $ (\rho = 0)$
limit yield two distinct vacuum spacetimes which can be considered as analogues
of Kasner solution for inhomogeneous singularity free spacetime.


title: Complex Numbers, Quantum Mechanics and the Beginning of Time

abstract:
  A basic problem in quantizing a field in curved space is the decomposition of
the classical modes in positive and negative frequency. The decomposition is
equivalent to a choice of a complex structure in the space of classical
solutions. In our construction the real tunneling geometries provide the link
between the this complex structure and analytic properties of the classical
solutions in a Riemannian section of space. This is related to the Osterwalder-
Schrader approach to Euclidean field theory.


title: Dynamics and Collision of Massive Shells in Curved Backgrounds

abstract:
  We analyse the dynamics of the collision of two spherical massive shells in a
generally spherically symmetric background, obtaining an expression from the
conservation law that imposes a constraint between the different parameters
involved. We study the light-like limit and make some comparisons of the
predictions of our master equation with the results obtained in the case of
collision of light-like shells, like the short life of white holes or the mass
inflation phenomena. We present some particular cases of the constraint
equation.


title:
Two-loop effective potential in quantum field theory in curved
  space-time

abstract:
  The method of the calculation of effective potential (in linear curvature
approximation and at any loop) in massless gauge theory in curved space- time
by the direct solution of RG equation is given.The closed expression for
two-loop effective potential is obtained.Two-loop effective potential in scalar
self-interacting theory is written explicitly.Some comments about it as well as
about two-loop effective potential in standard model are presented.


title: On limits of spacetimes -- a coordinate-free approach

abstract:
  A coordinate-free approach to limits of spacetimes is developed. The limits
of the Schwarzschild metric as the mass parameter tends to 0 or $\infty$ are
studied, extending previous results. Besides the known Petrov type D and 0
limits, three vacuum plane-wave solutions of Petrov type N are found to be
limits of the Schwarzschild spacetime.


title: Quantum Theory of Black Holes

abstract:
  A solvable 2-dimensional conformally invariant midi-superspace model for
black holes is obtained by imposing spherical symmetry in 4-dimensional
conformally invariant Einstein gravity. The Wheeler-DeWitt equation for the
theory is solved exactly to obtain the unique quantum wave functional for an
isolated black hole with fixed mass. By suitably relaxing the boundary
conditions, a non-perturbative ansatz is obtained for the wave functional of a
black hole interacting with its surroundings.


title:
The renormalization group for non-renormalizable theories: Einstein
  gravity with a scalar field

abstract:
  We develop a renormalization-group formalism for non-renormalizable theories
and apply it to Einstein gravity theory coupled to a scalar field with the
Lagrangian $L=\sqrt{g} [R U(\phi)-{1/2} G(\phi) g^{\mu\nu} \partial_{\mu}\phi
\partial_{\nu}\phi- V(\phi)]$, where $U(\phi), G(\phi)$ and $V(\phi)$ are
arbitrary functions of the scalar field. We calculate the one-loop counterterms
of this theory and obtain a system of renormalization-group equations in
partial derivatives for the functions $U, G$ and $V$ playing the role of
generalized charges which substitute for the usual charges in multicharge
theories. In the limit of a large but slowly varying scalar field and small
spacetime curvature this system gives the asymptotic behaviour of the
generalized charges compatible with the conventional choice of these functions
in quantum cosmological applications. It also demonstrates in the
over-Planckian domain the existence of the Weyl-invariant phase of gravity
theory asymptotically free in gravitational and cosmological constants.


title:
The Structure of Naked Singularity in Self-similar Gravitational
  Collapse II

abstract:
  Generalizing the results of Joshi and Dwivedi in Commun.Math.Phys. 146, p.333
(1992), it is pointed out that strong curvature naked singularities could occur
in the self-similar gravitational collapse of any form of matter satisfying the
weak energy condition for the positivity of mass-energy density.


title: Towards the Theory of Stationary Universe

abstract:
  This talk presents some progress achieved in collaboration with A.Linde and
D.Linde towards understanding the true nature of the global spatial structure
of the Universe as well as the most general stationary characteristics of its
time-dependent state with eternally growing total volume.


title: Cosmology with Nonminimal Derivative Couplings

abstract:
  We study a theory which generalizes the nonminimal coupling of matter to
gravity by including derivative couplings. This leads to several interesting
new dynamical phenomena in cosmology. In particular, the range of parameters in
which inflationary attractors exist is greatly expanded. We also numerically
integrate the field equations and draw the phase space of the model in second
order approximation. The model introduced here may display different
inflationary epochs, generating a non-scale-invariant fluctuation spectrum
without the need of two or more fields. Finally, we comment on the bubble
spectrum arising during a first-order phase transition occurring in our model.


title: Finite, diffeomorphism invariant observables in quantum gravity

abstract:
  Two sets of spatially diffeomorphism invariant operators are constructed in
the loop representation formulation of quantum gravity. This is done by
coupling general relativity to an anti- symmetric tensor gauge field and using
that field to pick out sets of surfaces, with boundaries, in the spatial three
manifold. The two sets of observables then measure the areas of these surfaces
and the Wilson loops for the self-dual connection around their boundaries. The
operators that represent these observables are finite and background
independent when constructed through a proper regularization procedure.
Furthermore, the spectra of the area operators are discrete so that the
possible values that one can obtain by a measurement of the area of a physical
surface in quantum gravity are valued in a discrete set that includes integral
multiples of half the Planck area. These results make possible the construction
of a correspondence between any three geometry whose curvature is small in
Planck units and a diffeomorphism invariant state of the gravitational and
matter fields. This correspondence relies on the approximation of the classical
geometry by a piecewise flat Regge manifold, which is then put in
correspondence with a diffeomorphism invariant state of the gravity-matter
system in which the matter fields specify the faces of the triangulation and
the gravitational field is in an eigenstate of the operators that measure their
areas.


title: Geometry of the 2+1 Black Hole

abstract:
  The geometry of the spinning black holes of standard Einstein theory in 2+1
dimensions, with a negative cosmological constant and without couplings to
matter, is analyzed in detail. It is shown that the black hole arises from
identifications of points of anti-de Sitter space by a discrete subgroup of
$SO(2,2)$. The generic black hole is a smooth manifold in the metric sense. The
surface $r=0$ is not a curvature singularity but, rather, a singularity in the
causal structure. Continuing past it would introduce closed timelike lines.
However, simple examples show the regularity of the metric at $r=0$ to be
unstable: couplings to matter bring in a curvature singularity there. Kruskal
coordinates and Penrose diagrams are exhibited. Special attention is given to
the limiting cases of (i) the spinless hole of zero mass, which differs from
anti-de Sitter space and plays the role of the vacuum, and (ii) the spinning
hole of maximal angular momentum . A thorough classification of the elements of
the Lie algebra of $SO(2,2)$ is given in an Appendix.


title: Decoherence of Correlation Histories

abstract:
  We use a $\lambda\Phi^4$ scalar quantum field theory to illustrate a new
approach to the study of quantum to classical transition. In this approach, the
decoherence functional is employed to assign probabilities to consistent
histories defined in terms of correlations among the fields at separate points,
rather than the field itself. We present expressions for the quantum amplitudes
associated with such histories, as well as for the decoherence functional
between two of them. The dynamics of an individual consistent history may be
described by a Langevin-type equation, which we derive. \noindent {\it
Dedicated to Professor Brill on the occasion of his sixtieth birthday, August
1993}


title: Towards a Nonsingular Universe

abstract:
  A unified theory of all forces should be nonsingular. In such a unified
theory, Einstein's general relativity will be a very low curvature effective
theory. At larger curvatures, new terms will become important. The question
then arises as to whether it is possible to construct an effective action for
gravity which leads to a nonsingular theory. In this work, we construct an
effective action for gravity in which all homogenerous and isotropic solutions
are nonsingular. In particular, there is neither a big bang nor a big crunch.
Preliminary work indicates that our construction provides a theory in which
anisotropies decrease at large curvatures, and in which the inside of a black
hole is singularity free.


title:
The quantum behavior of general time dependent quadratic systems
  linearly coupled to a bath

abstract:
  In this paper we solve for the quantum propagator of a general time dependent
system quadratic in both position and momentum, linearly coupled to an infinite
bath of harmonic oscillators. We work in the regime where the quantum optical
master equation is valid. We map this master equation to a Schroedinger
equation on Super-Hilbert space and utilize Lie Algebraic techniques to solve
for the dynamics in this space. We then map back to the original Hilbert space
to obtain the solution of the quantum dynamics. The Lie Algebraic techniques
used are preferable to the standard Wei-Norman methods in that only coupled
systems of first order ordinary differential equations and purely algebraic
equations need only be solved. We look at two examples.


title: Quantum Cosmology

abstract:
  An elementary review of quantum cosmology. (Talk given at Texas/Pascos 1992
at Berkeley)


title:
Proof of the Generalized Second Law for Quasistationary Semiclassical
  Black Holes

abstract:
  A simple direct explicit proof of the generalized second law of black hole
thermodynamics is given for a quasistationary semiclassical black hole.


title: Impossible Measurements on Quantum Fields

abstract:
  It is shown that the attempt to extend the notion of ideal measurement to
quantum field theory leads to a conflict with locality, because (for most
observables) the state vector reduction associated with an ideal measurement
acts to transmit information faster than light. Two examples of such
information-transfer are given, first in the quantum mechanics of a pair of
coupled subsystems, and then for the free scalar field in flat spacetime. It is
argued that this problem leaves the Hilbert space formulation of quantum field
theory with no definite measurement theory, removing whatever advantages it may
have seemed to possess vis a vis the sum-over-histories approach, and
reinforcing the view that a sum-over-histories framework is the most promising
one for quantum gravity.


title:
A more accurate analytic calculation of the spectrum of cosmological
  perturbations produced during inflation

abstract:
  Formulae are derived for the spectra of scalar curvature perturbations and
gravitational waves produced during inflation, special cases of which include
power law inflation, natural inflation in the small angle approximation and
inflation in the slow roll approximation.


title: The Initial Value Problem in Light of Ashtekar's Variables

abstract:
  The form of the initial value constraints in Ashtekar's hamiltonian
formulation of general relativity is recalled, and the problem of solving them
is compared with that in the traditional metric variables. It is shown how the
general solution of the four diffeomorphism constraints can be obtained
algebraically provided the curvature is non-degenerate, and the form of the
remaining (Gauss law) constraints is discussed. The method is extended to cover
the case when matter is included, using an approach due to Thiemann. The
application of the method to vacuum Bianchi models is given. The paper
concludes with a brief discussion of alternative approaches to the initial
value problem in the Ashtekar formulation.


title: Fluctuation, Dissipation and Irreversibility in Cosmology

abstract:
  We discuss the appearance of time-asymmetric behavior in physical processes
in cosmology and in the dynamics of the Universe itself. We begin with an
analysis of the nature and origin of irreversibility in well-known physical
processes such as dispersion, diffusion, dissipation and mixing, and make the
distinction between processes whose irreversibility arises from the stipulation
of special initial conditions, and those arising from the system's interaction
with a coarse-grained environment. We then study the irreversibility associated
with quantum fluctuations in cosmological processes like particle creation and
the `birth of the Universe'. We suggest that the backreaction effect of such
quantum processes can be understood as the manifestation of a
fluctuation-dissipation relation relating fluctuations of quantum fields to
dissipations in the dynamics of spacetime. For the same reason it is shown that
dissipation is bound to appear in the dynamics of minisuperspace cosmologies.
This provides a natural course for the emergence of a cosmological and
thermodynamic arrow of time and suggests a meaningful definition of
gravitational entropy. We conclude with a discussion on the criteria for the
choice of coarse-grainings and the stability of persistent physical structures.
Invited Talk given at the Conference on The Physical Origin of Time-Asymmetry
Huelva, Spain, Oct. 1991, Proceedings eds. J. J. Halliwell, J. Perez-Mercader
and W. H. Zurek, Cambridge University Press, 1993


title: Symmetric solutions of Einstein-Yang-Mills equations

abstract:
  Symmetric gauge fields and invariant metrics in homogeneous spaces are found.
Their use for finding exact solutions of the Einstein-Yang-Mills (EYM)
equations is discussed.


title: Brill Waves

abstract:
  Brill waves are the simplest (non-trivial) solutions to the vacuum
constraints of general relativity. They are also rich enough in structure to
allow us believe that they capture, at least in part, the generic properties of
solutions of the Einstein equations. As such, they deserve the closest
attention. This article illustrates this point by showing how Brill waves can
be used to investigate the structure of conformal superspace. This article is
written as a contribution to the Dieter Brill Festschrift.


title: Mathematical Problems of Non-perturbative Quantum General Relativity

abstract:
  The purpose of these lectures is to discuss in some detail a new,
non-perturbative approach to quantum gravity. I would like to present the basic
ideas, outline the key results that have been obtained so far and indicate
where we are headed and what the hopes are. The audience at this summer school
had a diverse background; many came from high energy physics, some from
mathematical physics and the rest from general relativity. Therefore, I have
tried to keep the technicalities --particularly proofs and even the number of
equations-- to a minimum. My hope is that a research student in any of these
three fields should be able to get a bird's eye view of the entire program. In
particular, I have kept all three perspectives in mind while discussing the
difficulties one encounters and strategies one adopts and in evaluating the
successes and limitations of the program.


title: Minisuperspace as a Quantum Open System

abstract:
  We trace the development of ideas on dissipative processes in chaotic
cosmology and on minisuperspace quantum cosmology from the time Misner proposed
them to current research. We show 1) how the effect of quantum processes like
particle creation in the early universe can address the issues of the isotropy
and homogeneity of the observed universe, 2) how viewing minisuperspace as a
quantum open system can address the issue of the validity of such
approximations customarily adopted in quantum cosmology, and 3) how invoking
statistical processes like decoherence and correlation when considered together
can help to establish a theory of quantum fields in curved spacetime as the
semiclassical limit of quantum gravity. {\it Dedicated to Professor Misner on
the occasion of his sixtieth birthday, June 1992.} To appear in the Proceedings
of a Symposium on {\it Directions in General Relativity}, College Park, May
1993, Volume 1, edited by B. L. Hu, M. P. Ryan and C. V. Vishveshwara
(Cambridge University Press 1993)~~~~umdpp 93-60


title: Minisuperspaces: Symmetries and Quantization

abstract:
  In several of the class A Bianchi models, minisuperspaces admit symmetries.
It is pointed out that they can be used effectively to complete the Dirac
quantization program. The resulting quantum theory provides a useful platform
to investigate a number of conceptual and technical problems of quantum
gravity.


title: Minisuperspaces: Observables and Quantization

abstract:
  A canonical transformation is performed on the phase space of a number of
homogeneous cosmologies to simplify the form of the scalar (or, Hamiltonian)
constraint. Using the new canonical coordinates, it is then easy to obtain
explicit expressions of Dirac observables, i.e.\ phase space functions which
commute weakly with the constraint. This, in turn, enables us to carry out a
general quantization program to completion. We are also able to address the
issue of time through ``deparametrization'' and discuss physical questions such
as the fate of initial singularities in the quantum theory. We find that they
persist in the quantum theory {\it inspite of the fact that the evolution is
implemented by a 1-parameter family of unitary transformations}. Finally,
certain of these models admit conditional symmetries which are explicit already
prior to the canonical transformation. These can be used to pass to quantum
theory following an independent avenue. The two quantum theories --based,
respectively, on Dirac observables in the new canonical variables and
conditional symmetries in the original ADM variables-- are compared and shown
to be equivalent.


title: Karolyhazy's quantum space-time generates neutron star density in vacuum

abstract:
  By simple arguments, we have shown that Karolyhazy's model overestimates the
quantum uncertainty of the space-time geometry and leads to absurd physical
consequences. The given model can thus not account for gradual violation of
quantum coherence and can not predict tiny experimental effects either.


title:
Quantum and Thermal Fluctuations, Uncertainty Principle, Decoherence and
  Classicality*

abstract:
  We scrutize the commonly used criteria for classicality and examine their
underlying issues. The two major issues we address here are that of decoherence
and fluctuations. We borrow the insights gained in the study of the
semiclassical limit of quantum cosmology to discuss the three criteria of
classicality for a quantum closed system: adiabaticity, correlation and
decoherence. We then use the Brownian model as a paradigm of quantum open
systems to discuss the relation of quantum and thermal fluctuations and their
role in the transition from quantum to classical. We derive the uncertainty
relation at finite temperature. We study how the fluctuations of a quantum
system evolve after it is brought in contact with a heat bath and analyse the
decoherence and relaxation processes. From the effect of fluctuations on
decoherence we show the relation between these two sets of criteria of
classicality. Finally, we briefly comment on the issue of nonintegrability in
quantum open systems.


title: Critical Dynamics in the Early Universe

abstract:
  Methods and concepts for the study of phase transitions mediated by a
time-dependent order-parameter field in curved spacetimes are discussed. A
practical example is the derivation of an effective (quasi-)potential for the
description of `slow-roll' inflation in the early universe. We first summarize
our early results on viewing the symmetry behavior of constant background
fields in curved but static spacetimes as finite size effect, and the use of
derivative expansions for constructing effective actions for slowly-varying
background fields. We then introduce the notion of dynamical finite size effect
to explain how an exponential expansion of the scale factor imparts a finite
size to the system and how the symmetry behavior in de Sitter space can be
understood qualitatively in this light. We reason why the exponential inflation
can be described equivalently by a scale transformation, thus rendering this
special class of dynamics as effectively static. Finally we show how, in this
view, one can treat the class of `slow-roll' inflation as a dynamic
perturbation off the effectively static class of exponential inflation and
understand it as a dynamical critical phenomenon in cosmology.


title: Quantum Statistical Processes in the Early Universe

abstract:
  We show how the concept of quantum open system and the methods in
non-equilibrium statistical mechanics can be usefully applied to studies of
quantum statistical processes in the early universe. We first sketch how noise,
fluctuation, dissipation and decoherence processes arise in a wide range of
cosmological problems. We then focus on the origin and nature of noise in
quantum fields and spacetime dynamics. We introduce the concept of
geometrodynamic noise and suggest a statistical mechanical definition of
gravitational entropy. We end with a brief discussion of the theoretical
appropriateness to view the physical universe as an open system.


title: Do Black Holes Exist?

abstract:
  The problem of information loss in black hole formation and the associated
violations of basic laws of physics, such as conservation of energy, causality
and unitarity, are avoided in the nonsymmetric gravitational theory, if the NGT
charge of a black hole and its mass satisfy an inequality that does not violate
any known experimental data and allows the existence of white dwarfs and
neutron stars.


title: Symmetries of the Einstein Equations

abstract:
  Generalized symmetries of the Einstein equations are infinitesimal
transformations of the spacetime metric that formally map solutions of the
Einstein equations to other solutions. The infinitesimal generators of these
symmetries are assumed to be local, \ie at a given spacetime point they are
functions of the metric and an arbitrary but finite number of derivatives of
the metric at the point. We classify all generalized symmetries of the vacuum
Einstein equations in four spacetime dimensions and find that the only
generalized symmetry transformations consist of: (i) constant scalings of the
metric (ii) the infinitesimal action of generalized spacetime diffeomorphisms.
Our results rule out a large class of possible ``observables'' for the
gravitational field, and suggest that the vacuum Einstein equations are not
integrable.


title: On the Cosmology of Massive Vector Fields with SO(3) Global Symmetry

abstract: A relevant reference ([14]) has been added.


title: A Pictorial History of Some Gravitational Instantons

abstract:
  Four-dimensional Euclidean spaces that solve Einstein's equations are
interpreted as WKB approximations to wavefunctionals of quantum geometry. These
spaces are represented graphically by suppressing inessential dimensions and
drawing the resulting figures in perspective representation of
three-dimensional space, some of them stereoscopically. The figures are also
related to the physical interpretation of the corresponding quantum processes.


title: Quantum Effects In Cosmology

abstract:
  Contents:
  Introduction. The Present State of the Universe.
  What Can We Expect From a Complete Cosmological Theory?
  An Overview of Quantum Effects in Cosmology.
  Parametric (Superadiabatic) Amplification of Classical Waves.
  Graviton Creation in the Inflationary Universe.
  Quantum States of a Harmonic Oscillator.
  Squeezed Quantum States of Relic Gravitons and Primordial Density
Perturbations.
  Quantum Cosmology, Minisuperspace Models and Inflation.
  From the Space of Classical Solutions to the Space of Wave Functions.
  On the Probability of Quantum Tunneling From "Nothing".
  Duration of Inflation


title: A Model of Topological Affine Gravity in Two Dimensions

abstract:
  A model of two--dimensional gravity with an action depending only on a linear
connection is considered. This model is a topological one, in the sense that
the classical action does not contain a metric or zweibein at all. A metric and
an additional vector field are instead introduced in the process of solving
equations of motion for the connection. They satisfy the constant curvature
equation. It is shown that the general solution of these equations of motion
can be described by using the space of orbits under the action of the Weyl
group in the functional space containing all pairs formed by a metric and a
vectorfield. It is shown also that this model admits an equivalent description
by using a family of actions depending on the metric and the connection as
independent variables.


title: A Cosmological Theory without Singularities

abstract:
  A theory of gravitation is constructed in which all homogeneous and isotropic
solutions are nonsingular, and in which all curvature invariants are bounded.
All solutions for which curvature invariants approach their limiting values
approach de Sitter space. The action for this theory is obtained by a higher
derivative modification of Einstein's theory. We expect that our model can
easily be generalized to solve the singularity problem also for anisotropic
cosmologies.


title: The Scalar Field Equation in the Presence of Signature Change

abstract:
  We consider the (massless) scalar field on a 2-dimensional manifold with
metric that changes signature from Lorentzian to Euclidean. Requiring a
conserved momentum in the spatially homogeneous case leads to a particular
choice of propagation rule. The resulting mix of positive and negative
frequencies depends only on the total (conformal) size of the spacelike regions
and not on the detailed form of the metric. Reformulating the problem using
junction conditions, we then show that the solutions obtained above are the
unique ones which satisfy the natural distributional wave equation everywhere.
We also give a variational approach, obtaining the same results from a natural
Lagrangian.
  (PACS numbers 04.20.Cv and 02.40.+m.)


title: String-Like Structures in Complex Kerr Geometry

abstract:
  The Kerr geometry is represented as being created by a source moving along an
analytical complex world-line. The equivalence of this complex world-line and
an Euclidean version of complex strings (hyperbolic strings) is discussed. It
is shown that the complex Kerr source satisfies the corresponding string
equations. The boundary conditions of the complex Euclidean strings require an
orbifold-like structure of the world-sheet. The related orbifold-like structure
of the Kerr geometry is discussed.


title:
The Quantization of the Spacetime Geometry Generated by Planckian Energy
  Particles

abstract:
  We study the quantization of the curved spacetime created by
ultrarelativistic particles at Planckian energies. We consider a minisuperspace
model based on the classical shock wave metric generated by these particles,
and for which the Wheeler - De Witt equation is solved exactly. The wave
function of the geometry is a Bessel function whose argument is the classical
action. This allows us to describe not only the semiclassical regime
$(S\to\infty),$ but also the strong quantum regime $(S\to0).$ We analyze the
interaction with a scalar field $\phi$ and apply the third quantization
formalism to it. The quantum gravity effects make the system to evolve from a
highly curved semiclassical geometry (a gravitational wave metric) into a
strongly quantum state represented by a weakly curved geometry (essentially
flat spacetime).


title:
Motion and Trajectories of Particles Around Three-Dimensional Black
  Holes

abstract:
  The motion of relativistic particles around three dimensional black holes
following the Hamilton-Jacobi formalism is studied. It follows that the
Hamilton-Jacobi equation can be separated and reduced to quadratures in analogy
with the four dimensional case. It is shown that: a) particles are trapped by
the black hole independently of their energy and angular momentum, b) matter
alway falls to the centre of the black hole and cannot understake a motion with
stables orbits as in four dimensions. For the extreme values of the angular
momentum of the black hole, we were able to find exact solutions of the
equations of motion and trajectories of a test particle.