title: Semi-Classical Limits of Simplicial Quantum Gravity

abstract:
  We consider the simplicial state-sum model of Ponzano and Regge as a path
integral for quantum gravity in three dimensions.
  We examine the Lorentzian geometry of a single 3-simplex and of a simplicial
manifold, and interpret an asymptotic formula for $6j$-symbols in terms of this
geometry. This extends Ponzano and Regge's similar interpretation for Euclidean
geometry.
  We give a geometric interpretation of the stationary points of this
state-sum, by showing that, at these points, the simplicial manifold may be
mapped locally into flat Lorentzian or Euclidean space. This lends weight to
the interpretation of the state-sum as a path integral, which has solutions
corresponding to both Lorentzian and Euclidean gravity in three dimensions.


title: Stationary Axisymmetric Fields as Two-Dimensional Geodesics

abstract:
  Einstein's equations for stationary axisymmetric fields are reformulated as
the equations for affine geodesics in a two--dimensional space. The affine
collineations of this space are investigated and used to relate explicit
solutions of Einstein's equations with different physical properties.
Particularly, the solutions describing the exterior fields of a dyon and a
slowly rotating body are discussed.


title: Space-time events and relativistic particle localization

abstract:
  A relation expressing the covariant transformation properties of a
relativistic position operator is derived. This relation differs from the one
existing in the literature expressing manifest covariance by some factor
ordering. The relation is derived in order for the localization of a particle
to represent a space-time event. It is shown that there exists a conflict
between this relation and the hermiticity of a positive energy position
operator.


title: The Frenet Serret Description of Gyroscopic Precession

abstract:
  The phenomenon of gyroscopic precession is studied within the framework of
Frenet-Serret formalism adapted to quasi-Killing trajectories. Its relation to
the congruence vorticity is highlighted with particular reference to the
irrotational congruence admitted by the stationary, axisymmetric spacetime.
General precession formulae are obtained for circular orbits with arbitrary
constant angular speeds. By successive reduction, different types of
precessions are derived for the Kerr - Schwarzschild - Minkowski spacetime
family. The phenomenon is studied in the case of other interesting spacetimes,
such as the De Sitter and G\"{o}del universes as well as the general
stationary, cylindrical, vacuum spacetimes.


title: Solving the Hamilton-Jacobi Equation for General Relativity

abstract:
  We demonstrate a systematic method for solving the Hamilton-Jacobi equation
for general relativity with the inclusion of matter fields. The generating
functional is expanded in a series of spatial gradients. Each term is
manifestly invariant under reparameterizations of the spatial coordinates
(``gauge-invariant''). At each order we solve the Hamiltonian constraint using
a conformal transformation of the 3-metric as well as a line integral in
superspace. This gives a recursion relation for the generating functional which
then may be solved to arbitrary order simply by functionally differentiating
previous orders. At fourth order in spatial gradients, we demonstrate solutions
for irrotational dust as well as for a scalar field. We explicitly evolve the
3-metric to the same order. This method can be used to derive the Zel'dovich
approximation for general relativity.


title: Charged Black Holes In Quadratic Theories

abstract:
  We point out that in general the Reissner-Nordstr\"om (RN) charged black
holes of general relativity are not solutions of the four dimensional quadratic
gravitational theories. They are, e.g., exact solutions of the $R+R^2$
quadratic theory but not of a theory where a $R_{ab}R^{ab}$ term is present in
the gravitational Lagrangian. In the case where such a non linear curvature
term is present with sufficiently small coupling, we obtain an approximate
solution for a charged black hole of charge $Q$ and mass $M$. For $Q\ll M$ the
validity of this solution extends down to the horizon. This allows us to
explore the thermodynamic properties of the quadratic charged black hole and we
find that, to our approximation, its thermodynamics is identical to that of a
RN black hole. However our black hole's entropy is not equal to the one fourth
of the horizon area. Finally we extend our analysis to the rotating charged
black hole and qualitatively similar results are obtained.


title: Cosmology, Time's Arrow, and That Old Double Standard

abstract:
  It is widely accepted that temporal asymmetry is largely a cosmological
problem; the task of explaining temporal asymmetry reduces in the main to that
of explaining an aspect of the condition of the early universe. However,
cosmologists who discuss these issues often make mistakes similar to those that
plagued nineteenth century discussions of the statistical foundations of
thermodynamics. In particular, they are often guilty of applying temporal
"double standards" of various kinds---e.g., in failing to recognise that
certain statistical arguments apply with equal force in either temporal
direction. This paper aims to clarify the issue as to what would count as
adequate explanation of cosmological time asymmetry. A particular concern is
the question whether it is possible to explain why entropy is low near the Big
Bang without showing that it must also be low near a Big Crunch, in the event
that the universe recollapses. I criticise some of the objections raised to
this possibility, showing that these too often depend on a temporal double
standard. I also discuss briefly some issues that arise if we take the view
seriously. (Could we observe a time- reversing future, for example?)


title: Entropy Production from Vacuum Decay

abstract:
  Using as dynamical variable the square of the radius of the Universe, we
solve analytically the Einstein equations in the framework of Robertson-Walker
models where a cosmological constant describing phenomenologically the vacuum
energy decays into radiation. Emphasis is put on the computation of the entropy
creation.


title: Leading Quantum Correction to the Newtonian Potential

abstract:
  I argue that the leading quantum corrections, in powers of the energy or
inverse powers of the distance, may be computed in quantum gravity through
knowledge of only the low energy structure of the theory. As an example, I
calculate the leading quantum corrections to the Newtonian gravitational
potential.


title: The Gauss Linking Number in Quantum Gravity

abstract:
  We show that the exponential of the Gauss (self) linking number of a knot is
a solution of the Wheeler-DeWitt equation in loop space with a cosmological
constant. Using this fact, it is straightforward to prove that the second
coefficient of the Jones Polynomial is a solution of the Wheeler-DeWitt
equation in loop space with no cosmological constant. We perform calculations
from scratch, starting from the connection representation and give details of
the proof. Implications for the possibility of generation of other solutions
are also discussed.


title: Dimensional Reduction in Quantum Gravity

abstract:
  The requirement that physical phenomena associated with gravitational
collapse should be duly reconciled with the postulates of quantum mechanics
implies that at a Planckian scale our world is not 3+1 dimensional. Rather, the
observable degrees of freedom can best be described as if they were Boolean
variables defined on a two-dimensional lattice, evolving with time. This
observation, deduced from not much more than unitarity, entropy and counting
arguments, implies severe restrictions on possible models of quantum gravity.
Using cellular automata as an example it is argued that this dimensional
reduction implies more constraints than the freedom we have in constructing
models. This is the main reason why so-far no completely consistent
mathematical models of quantum black holes have been found.
  Essay dedicated to Abdus Salam.


title:
Path Integrals, Density Matrices, and Information Flow with Closed
  Timelike Curves

abstract:
  Two formulations of quantum mechanics, inequivalent in the presence of closed
timelike curves, are studied in the context of a soluable system. It
illustrates how quantum field nonlinearities lead to a breakdown of unitarity,
causality, and superposition using a path integral. Deutsch's density matrix
approach is causal but typically destroys coherence. For each of these
formulations I demonstrate that there are yet further alternatives in
prescribing the handling of information flow (inequivalent to previous
analyses) that have implications for any system in which unitarity or coherence
are not preserved.


title: Inhomogenous Chaotic Inflation

abstract:
  A chaotic model of the early universe within the framework of the
singularity-free solutions of Einstein's equation is suggested. The evolution
of our universe at its early stage, starting out as a small domain of the
parent universe, is governed by the dynamics of a classical scalar field $\phi$
. If in any such domain, larger than Planck length,$\dot \phi$ happens to be
very large,$\phi$ may develop a dominant inhomogeneous mode,leading to an
anisotropic inflation of the universe. The particle $\phi$ is coupled to other
particles, which are produced copiously after inflation and these thermalize
leading to a rather low temperature universe $(T \geq 10^{4} $ Gev). The
electroweak B+L Baryogenesis is assumed to account for the observed baryon
asymmetry. The universe now passes through a radiation-dominated phase, leading
eventually to a matter-dominated universe, which is isotropic and homogeneous.
The model does not depend on the details of Planck scale physics.


title:
Ramsey fringes in atomic interferometry: measurability of the influence
  of space-time curvature

abstract:
  The influence od space-time curvature on quantum matter which can be
theoretically described by covariant wave equations has not been experimentally
established yet. In this paper we analyse in detail the suitability of the
Ramsey atom beam interferometer for the measurement of the phase shift caused
by the Riemannian curvature of the earth. It appears that the detection should
be possible with minor modifications of existing devices within the near
future. The paper is divided into two parts. The first one is concerned with
the derivation of general relativistic correction terms to the Pauli equation
starting from the fully covariant Dirac equation and their physical
interpretation. The inertial effects of acceleration and rotation are included.
In the second part we calculate the phase shift as seen in a laboratory resting
on the rotating earth and examine various possibilities to enlarge the
sensitivity of the apparatus to space-time curvature. Some remarks on the
Lense-Thirring effect and on gravitational waves are made. Since the two parts
may be more or less interesting for physicists with different research fields
they are written in such a way that each one may be read without much reference
to the other one.


title: Can wormholes exist?

abstract:
  Renormalized vacuum expectation values of electromagnetic stress-energy
tensor are calculated in the background spherically-symmetrical metric of the
wormhole's topology. Covariant geodesic point separation method of
regularization is used. Violation of the weak energy condition at the throat of
wormhole takes place for geometry sufficiently close to that of infinitely long
wormhole of constant radius irrespectively of the detailed form of metric. This
is an argument in favour of possibility of existence of selfconsistent wormhole
in empty space maintained by vacuum field fluctuations in the wormhole's
background.


title: Prima Facie Questions in Quantum Gravity

abstract:
  The long history of the study of quantum gravity has thrown up a complex web
of ideas and approaches. The aim of this article is to unravel this web a
little by analysing some of the {\em prima facie\/} questions that can be asked
of almost any approach to quantum gravity and whose answers assist in
classifying the different schemes. Particular emphasis is placed on (i) the
role of background conceptual and technical structure; (ii) the role of
spacetime diffeomorphisms; and (iii) the problem of time.


title: Apparent wave function collapse caused by scattering

abstract:
  Some experimental implications of the recent progress on wave function
collapse are calculated. Exact results are derived for the center-of-mass wave
function collapse caused by random scatterings and applied to a range of
specific examples. The results show that recently proposed experiments to
measure the GRW effect are likely to fail, since the effect of naturally
occurring scatterings is of the same form as the GRW effect but generally much
stronger. The same goes for attempts to measure the collapse caused by quantum
gravity as suggested by Hawking and others. The results also indicate that
macroscopic systems tend to be found in states with (Delta-x)(Delta-p) =
hbar/sqrt(2), but microscopic systems in highly tiltedly squeezed states with
(Delta-x)(Delta-p) >> hbar.


title: Comments on Dragging Effects

abstract:
  This is a reply, given at the conference ``Mach's Principle" in T\"ubingen in
July 1993, to the paper by Pfister (1993). Unfortunately the Pfister paper
itself was not sent to gr-qc.


title: Comments on Initial Value Formulation

abstract:
  This is the reply given at the conference ``Mach's Principle" at T\"ubingen
in July 1993 to the paper by Isenberg (1993a). Unfortunately the Isenberg paper
itself was not submitted to gr-qc.


title: Vassiliev Invariants and the Loop States in Quantum Gravity

abstract:
  An exposition of Vassiliev invariants is given in terms of the simplest
approach to the functional integral construction of link invariants from
Chern-Simons theory. This approach gives the top row evaluations of Vassiliev
invariants for the classical Lie algebras, and a neat point of view on the
results of Bar-Natan. It also clarifies the relation between Vassiliev
invariants and the extension of the bracket invariant to links with transverse
double points that appears in the work of Bruegmann, Gambini and Pullin on the
loop representation of quantum gravity. We see that the Vassiliev vertex is not
just a transversal intersection of Wilson loops, but rather has the structure
of Casimir insertion (up to first order of approximation) coming from the
difference formula in the functional integral. (Figures are available from the
author.)


title:
A Step Toward Pregeometry I.: Ponzano-Regge Spin Networks and the Origin
  of Spacetime Structure in Four Dimensions

abstract:
  In this paper, a candidate for pregeometry, Ponzano-Regge spin networks, will
be examined in the context of the pregeometric philosophy of Wheeler. Ponzano
and Regge were able to construct a theory for 3-dimensional quantum gravity
based on 3nj-symbols, obtaining the path integral over the metric in the
semiclassical limit. However, extension of this model to 4-dimensions has
proven to be difficult. It will be shown that the building blocks for
4-dimensional spacetime are already present in the Ponzano-Regge formalism
using a reinterpretation of the theory based on the pregeometric hypotheses of
Wheeler.


title: 2-D Gravity as Gauge Theories with Extended Groups

abstract:
  The interaction of matter with gravity in two dimensional spacetimes can be
supplemented with a geometrical force analogous to a Lorentz force produced on
a surface by a constant perpendicular magnetic field. In the special case of
constant curvature, the relevant symmetry does not lead to the de Sitter or the
Poincar\'e algebra but to an extension of them by a central element. This
richer structure suggests to construct a gauge theory of 2-D gravity that
reproduces the Jackiw-Teitelboim model and the string inspired model. Moreover
matter can be coupled in a gauge invariant fashion. Classical and quantized
results are discussed. Based on a talk given at the XXIIIth International
Conference on Differential Geometric Methods in Theoretical Physics. Ixtapa,
Mexico. September 1993.


title:
Quantum Limits for Measurements on Macroscopic Bodies : A Decoherence
  Analysis

abstract:
  We consider in this paper the quantum limits for measurements on macroscopic
bodies which are obtained in a novel way employing the concept of decoherence
coming from an analysis of the quantum mechanics of dissipative systems. Two
cases are analysed, the free mass and the harmonic oscillator, and for both
systems we compare our approach with previous treatments of such limits.


title:
Generalized boundary conditions for general relativity for the
  asymptotically flat case in terms of Ashtekar's variables

abstract:
  There is a gap that has been left open since the formulation of general
relativity in terms of Ashtekar's new variables namely the treatment of
asymptotically flat field configurations that are general enough to be able to
define the generators of the Lorentz subgroup of the asymptotical Poincar\'e
group. While such a formulation already exists for the old geometrodynamical
variables, up to now only the generators of the translation subgroup could be
defined because the function spaces of the fields considered earlier are taken
too special. The transcription of the framework from the ADM variables to
Ashtekar's variables turns out not to be straightforward due to the freedom to
choose the internal SO(3) frame at spatial infinity and due to the fact that
the non-trivial reality conditions of the Ashtekar framework reenter the game
when imposing suitable boundary conditions on the fields and the Lagrange
multipliers.


title: How to construct quantum measure in Regge calculus?

abstract:
  We propose the following way of constructing quantum measure in Regge
calculus: the full discrete Regge manifold is made continuous in some direction
by tending corresponding dimensions of simplices to zero, then functional
integral measure corresponding to the canonical quantization (with continuous
coordinate playing the role of time) can be constructed. The full discrete
measure is chosen so that it would result in canonical quantization one
whatever coordinate is made continuous. This strategy is followed in 3D case
where full discrete measure is determined in such the way practically uniquely
(in fact, family of similar measures is obtained). Averaging with the help of
the constructed measure gives finite expectation values for links.


title: The Two-Dimensional Analogue of General Relativity

abstract:
  General Relativity in three or more dimensions can be obtained by taking the
limit $\omega\rightarrow\infty$ in the Brans-Dicke theory. In two dimensions
General Relativity is an unacceptable theory. We show that the two-dimensional
closest analogue of General Relativity is a theory that also arises in the
limit $\omega\rightarrow\infty$ of the two-dimensional Brans-Dicke theory.


title: On quantization of Regge links

abstract:
  In quantum Regge calculus areas of timelike triangles possess discrete
spectrum. This is because bivectors of these triangles are variables
canonically conjugate to orthogonal connection matrices varying in the compact
group. (The scale of quantum of this spectrum is nothing but Plankian one).
This is checked in simple exactly solvable model - dimensionally reduced in
some way Regge calculus.


title: Graviton Mode Function in Inflationary Cosmology

abstract:
  We consider the production of gravitons in an inflationary cosmology by
approximating each epoch of change in the equation of state as sudden, from
which a simple analytic graviton mode function has been derived. We use this
mode function to compute the graviton spectral energy density and the
tensor-induced cosmic microwave background anisotropy. The results are then
compared to the numerical calculations which incorporate a smooth
radiation-matter phase transition. We find that the sudden approximation is a
fairly good method. Besides, in determining the frequency range and amplitude
of the mode function, we introduce a pre-inflationary radiation-dominated epoch
and use a physically sensible regularization method.


title:
Local Determination of the Light Deflection in the Sperically Symmetric
  Static Gravitational Field

abstract:
  The new method of invariant definition of the measurable angle of light
deflection in the static central symmetric gravitational field is suggested.
The predicted pure gravitational contribution to the deflection angle slightly
differs from its classical estimate and one may hope that this discrepancy
could be experimentally detected in the near future. (uuencoded,compressed
PostScript, 23 p. inc. 2 fig.)


title: The Hartle-Hawking state for the Bianchi IX model in supergravity

abstract:
  We solve the quantum constraints for homogeneous N=1 supergravity on
3-geometries with a Bianchi IX metric. Because these geometries admit Killing
vectors with the same commutation relations as the angular momentum generators,
there are two distinct definitions of homogeneity. The first of these is
well-known and has been shown by D'Eath to give the wormhole state. We show
that the alternative definition of homogeneity leads to the Hartle-Hawking ``no
boundary" state.


title: On kinematical constraints in Regge calculus

abstract:
  In the (3+1)D Hamiltonian Regge calculus (one of the coordinates, $ t$, is
continuous) conjugate variables are (defined on triangles of discrete 3D
section $ t=const$) finite connections and antisymmetric area bivectors. The
latter, however, are not independent, since triangles may have common edges.
This circumstance can be taken into account with the help of the set of
kinematical (that is, required to hold by definition of Regge manifold)
bilinear constraints on bivectors. Some of these contain derivatives over $ t$,
and taking them into account with the help of Lagrange multipliers would result
in the new dynamical variables not having analogs in the continuum theory. It
is shown that kinematical constraints with derivatives are consequences of eqs.
of motion for Regge action supplemented with the rest of these constraints
without derivatives and can be omitted; so the new dynamical variables do not
appear.


title:
On Einstein's equations for spacetimes admitting a non-null Killing
  field

abstract:
  We consider the 3-dimensional formulation of Einstein's theory for spacetimes
possessing a non-null Killing field $\xi^a$. It is known that for the vacuum
case some of the basic field equations are deducible from the others. It will
be shown here how this result can be generalized for the case of essentially
arbitrary matter fields. The systematic study of the structure of the
fundamental field equations is carried out. In particular, the existence of
geometrically preferred reference systems is shown. Using local coordinates of
this type two approaches are presented resulting resolvent systems of partial
differential equations for the basic field variables. Finally, the above
results are applied for perfect fluid spacetimes describing possible
equilibrium configurations of relativistic dissipative fluids.


title: Equivalent Quantisations of (2+1)-Dimensional Gravity

abstract:
  For spacetimes with the topology $\IR\!\times\!T^2$, the action of
(2+1)-dimensional gravity with negative cosmological constant $\La$ is written
uniquely in terms of the time-independent traces of holonomies around two
intersecting noncontractible paths on $T^2$. The holonomy parameters are
related to the moduli on slices of constant mean curvature by a time-dependent
canonical transformation which introduces an effective Hamiltonian. The
quantisation of the two classically equivalent formulations differs by terms of
order $O(\hbar^3)$, negligible for small $|\La|$.


title: The Black Holes of a General Two-Dimensional Dilaton Gravity Theory

abstract:
  A general dilaton gravity theory in 1+1 spacetime dimensions with a
cosmological constant $\lambda$ and a new dimensionless parameter $\omega$,
contains as special cases the constant curvature theory of Teitelboim and
Jackiw, the theory equivalent to vacuum planar General Relativity, the first
order string theory, and a two-dimensional purely geometrical theory. The
equations of this general two-dimensional theory admit several different black
holes with various types of singularities. The singularities can be spacelike,
timelike or null, and there are even cases without singularities. Evaluation of
the ADM mass, as a charge density integral, is possible in some situations, by
carefully subtrating the black hole solution from the corresponding linear
dilaton at infinity.


title: 2+1 Gravity and Closed Time-Like Curves

abstract:
  In this paper we report some results obtained by applying the radial gauge to
2+1 dimensional gravity. The general features of this gauge are reviewed and it
is shown how they allow the general solution of the problem in terms of simple
quadratures. Then we concentrate on the general stationary problem providing
the explicit solving formulas for the metric and the explicit support
conditions for the energy momentum tensor. The chosen gauge allows, due to its
physical nature, to exploit the weak energy condition and in this connection it
is proved that for an open universe conical at space infinity the weak energy
condition and the absence of closed time like curves (CTC) at space infinity
imply the total absence of CTC. It is pointed out how the approach can be used
to examine cosmological solution in 2+1 dimensions.


title: Representation Theory of Analytic Holonomy C* Algebras

abstract:
  Integral calculus on the space of gauge equivalent connections is developed.
Loops, knots, links and graphs feature prominently in this description. The
framework is well--suited for quantization of diffeomorphism invariant theories
of connections.
  The general setting is provided by the abelian C* algebra of functions on the
quotient space of connections generated by Wilson loops (i.e., by the traces of
holonomies of connections around closed loops). The representation theory of
this algebra leads to an interesting and powerful ``duality'' between
gauge--equivalence classes of connections and certain equivalence classes of
closed loops. In particular, regular measures on (a suitable completion of)
connections/gauges are in 1--1 correspondence with certain functions of loops
and diffeomorphism invariant measures correspond to (generalized) knot and link
invariants. By carrying out a non--linear extension of the theory of
cylindrical measures on topological vector spaces, a faithful, diffeomorphism
invariant measure is introduced. This measure can be used to define the Hilbert
space of quantum states in theories of connections. The Wilson--loop
functionals then serve as the configuration operators in the quantum theory.


title:
Negative Energy Densities in Extended Sources Generating Closed Timelike
  Curves in General Relativity with and without Torsion

abstract:
  Near a spinning point particle in (2+1)-dimensional gravity (or near an
infinitely thin, straight, spinning string in 3+1 dimensions) there is a region
of space-time with closed timelike curves. Exact solutions for extended sources
with apparently physically acceptable energy-momentum tensors, have produced
the same exterior space-time structure. Here it is pointed out that in the case
with torsion, closed timelike curves appear only for spin densities so high
that the spin energy density is higher than the net effective energy density.
In models without torsion, the presence of closed time-like curves is related
to a heat flow of unphysical magnitude. This corroborates earlier arguments
against the possibility of closed timelike curves in space-time geometries
generated by physical sources.


title:
Weakly decaying asymptotically flat static and stationary solutions to
  the Einstein equations

abstract:
  The assumption that a solution to the Einstein equations is static (or
stationary) very strongly constrains the asymptotic behaviour of the metric. It
is shown that one need only impose very weak differentiability and decay
conditions {\it a priori} on the metric for the field equations to force the
metric to be analytic near infinity and to have the standard Schwarzschildian
falloff.


title: Trapped surfaces in spherical expanding open universes

abstract:
  Consider spherically symmetric initial data for a cosmology which, in the
large, approximates an open $k = -1 ,\Lambda = 0$ Friedmann-Lema{\^\i}tre
universe. Further assume that the data is chosen so that the trace of the
extrinsic curvature is a constant and that the matter field is at rest at this
instant of time. One expects that no trapped surfaces appear in the data if no
significant clump of excess matter is to be found. This letter confirms this
belief by displaying a necessary condition for the existence of trapped
surfaces.This necessary condition, simply stated, says that a relatively large
amount of excess matter must be concentrated in a small volume for trapped
surfaces to appear.


title: First class constraints in Regge calculus

abstract:
  Considered are I class constraints in the tetrad-connection formulation of
Regge calculus. One of these is well-known Gauss law which generates rotations
in the local frames associated with tetrahedrons in the continuous time 3D
section. Another two types of these are new, satisfied by definition of Regge
manifold and having no I class analogs in the continuum general relativity.
Constraints of the first type express vanishing of the dual squares of
antisymmetric tensors of the triangles in the 3D section thus ensuring each
such tensor being a bivector. Constraints of the second type are trigonometric
relations between areas of triangles of 3D section caused by that the set of
areas is redundant as compared to the set of linklengts.


title:
A Clifford Dyadic Superfield from Bilateral Interactions of Geometric
  Multispin Dirac Theory

abstract:
  Multivector quantum mechanics utilizes wavefunctions which are Clifford
aggregates (e.g. sum of scalar, vector, bivector). This is equivalent to multi-
spinors constructed of Dirac matrices, with the representation independent form
of the generators geometrically interpreted as the basis vectors of spacetime.
Multiple generations of particles appear as left ideals of the algebra, coupled
only by now-allowed right-side applied (dextral) operations. A generalized
bilateral (two-sided operation) coupling is proposed which includes the above
mentioned dextrad field, and the spin-gauge interaction as particular cases.
This leads to a new principle of {\it poly-dimensional covariance}, in which
physical laws are invariant under the reshuffling of coordinate geometry. Such
a multigeometric superfield equation is proposed, which is sourced by a
bilateral current. In order to express the superfield in representation and
coordinate free form, we introduce Eddington E-F {\it double-frame} numbers.
Symmetric tensors can now be represented as 4D ``dyads", which actually are
elements of a global 8D Clifford algebra. As a restricted example, the dyadic
field created by the Greider-Ross multivector current (of a Dirac electron)
describes both electromagnetic and Morris- Greider gravitational interactions.
[to appear in Proceedings edited by J. Keller, UNAM, Mexico (Kluwer Academic
Publ)]


title:
Quantum Bubble Dynamics in 2+1 Dimensional Gravity I: Geometrodynamic
  Approach

abstract:
  The Dirac quantization of a 2+1 dimensional bubble is performed. The bubble
consists of a string forming a boundary between two regions of space-time with
distinct geometries. The ADM constraints are solved and the coupling to the
string is introduced through the boundary conditions. The wave functional is
obtained and the quantum uncertainty in the radius of the ring is calculated;
this uncertainty becomes large at the Planck scale.


title: What is the Geometry of Superspace ?

abstract:
  We investigate certain properties of the Wheeler-DeWitt metric (for constant
lapse) in canonical General Relativity associated with its non-definite nature.
Contribution to the conference on Mach's principle: "From Newtons Bucket to
Quantum Gravity", July 26-30 1993, Tuebingen, Germany


title:
Wigner Functions in Curved Space-Time and Quantum Corrections to Thermal
  Equilibrium

abstract:
  A brief review of the Wigner functions method in curved space-time.
Contribution to the 3rd International Wigner Symposium, 5th-11th September
1993, Oxford, UK.


title:
A Real Polynomial Formulation of General Relativity in terms of
  Connections

abstract:
  I show in this letter that it is possible to construct a Hamiltonian
description for Lorentzian General Relativity in terms of two real $SO(3)$
connections. The constraints are simple polynomials in the basic variables. The
present framework gives us a new formulation of General Relativity that keeps
some of the interesting features of the Ashtekar formulation without the
complications associated with the complex character of the latter.


title:
Reality Conditions for Lorentzian and Euclidean Gravity in the Ashtekar
  Formulation

abstract:
  Using Ashtekar variables, we analyze Lorentzian and Euclidean gravity in
vacuum up to a constant conformal transformation. We prove that the reality
conditions are invariant under a Wick rotation of the time, and show that the
compatibility of the algebra of commutators and constraints with the involution
defined by the reality conditions restricts the possible values of the
conformal factor to be either real or purely imaginary. In the first case, one
recovers real Lorentzian general relativity. For purely imaginary conformal
factors, the classical theory can be interpreted as real Euclidean gravity. The
reality conditions associated with this Euclidean theory demand the hermiticity
of the Ashtekar connection, but the densitized triad is represented by an
anti-Hermitian operator. We also demonstrate that the Euclidean and Lorentzian
sets of reality conditions lead to inequivalent quantizations of full general
relativity. As a consequence, it seems impossible to obtain Lorentzian physical
predictions from the quantum theory constructed with the Euclidean reality
conditions.


title:
A completely solvable model with an infinite number of Dirac observables
  for a real sector of complexified Ashtekar gravity

abstract:
  We introduce a reduced model for a real sector of complexified Ashtekar
gravity that does not correspond to a subset of Einstein's gravity but for
which the programme of canonical quantization can be carried out completely,
both, via the reduced phase space approach or along the lines of the algebraic
quantization programme.\\ This model stands in a certain correspondence to the
frequently treated cylindrically symmetric waves.\\ In contrast to other models
that have been looked at up to now in terms of the new variables the reduced
phase space is infinite dimensional while the scalar constraint is genuinely
bilinear in the momenta.\\ The infinite number of Dirac observables can be
expressed in compact and explicit form in terms of the original phase space
variables.\\ They turn out, as expected, to be non-local and form naturally a
set of countable cardinality.


title:
Tunnelling geometries I. Analyticity, unitarity and instantons in
  quantum cosmology

abstract:
  We present a theory of tunnelling geometries originating from the no-boundary
quantum state of Hartle and Hawking. We reformulate the no-boundary
wavefunction in the representation of true physical variables and calculate it
in the one-loop approximation. For this purpose a special technique is
developed, which reduces the formalism of complex tunnelling geometries to the
real ones, and also the method of collective variables is applied, separating
the macroscopic collective degrees of freedom from the microscopic modes. The
quantum distribution of Lorentzian universes, defined on the space of such
collective variables, incorporates the probabilty conservation and represents
the partition function of quasi-DeSitter gravitational instantons weighted by
their Euclidean effective action. They represent closed compact manifolds
obtained by the procedure of doubling the Euclidean spacetime which nucleates
the Lorentzian universes. The over-Planckian behaviour of their distribution is
determined by the anomalous scaling of the theory on such instantons, which
serves as a criterion for the high-energy normalizability of the no-boudary
wavefunction and the validity of the semiclassical expansion.


title: Tunnelling geometries II. Reduction methods for functional determinants

abstract:
  The reduction algorithms for functional determinants of differential
operators on spacetime manifolds of different topological types are presented,
which were recently used for the calculation of the no-boundary wavefunction
and the partition function of tunnelling geometries in quantum gravity and
cosmology.


title: Junction Conditions of Friedmann-Robertson-Walker Space-Times

abstract:
  We complete a classification of junctions of two Friedmann-Robertson-Walker
space-times bounded by a spherical thin wall. Our analysis covers super-horizon
bubbles and thus complements the previous work of Berezin, Kuzumin and Tkachev.
Contrary to sub-horizon bubbles, various topology types for super-horizon
bubbles are possible, regardless of the sign of the extrinsic curvature. We
also derive a formula for the peculiar velocity of a domain wall for all types
of junction.


title:
Particle Production and Positive Energy Theorems for Charged Black Holes
  in deSitter

abstract:
  We study quantum mechanical and classical stability properties of
Reissner-Nordstrom deSitter spacetimes, which describe black holes with mass
$M$ and charge $Q$ in a background with cosmological constant $\Lambda \ge 0$.
There are two sources of particle production in these spacetimes; the black
hole horizon and the cosmological horizon. A scattering calculation is done to
compute the Hawking radiation in these spacetimes. We find that the flux from
the black hole horizon equals the flux from the cosmological horizon, if and
only if $|Q|=M$, indicating that this is a state of thermodynamic equilibrium.
The spectrum, however, is not thermal. We also show that spacetimes containing
a number of charge equal to mass black holes with $\Lambda \ge 0$, have
supercovariantly constant spinors, suggesting that they may be minimum energy
states in a positive energy construction. As a first step in this direction, we
present a positive energy construction for asymptotically deSitter spacetimes
with vanishing charge. Because the construction depends only on a spatial
slice, our result also holds for spacetimes which are asymptotically
Robertson-Walker.


title: van Vleck determinants: traversable wormhole spacetimes

abstract:
  Calculating the van Vleck determinant in traversable wormhole spacetimes is
an important ingredient in understanding the physical basis behind Hawking's
chronology protection conjecture. This paper presents extensive computations of
this object --- at least in the short--throat flat--space approximation. An
important technical trick is to use an extension of the usual junction
condition formalism to probe the full Riemann tensor associated with a thin
shell of matter. Implications with regard to Hawking's chronology protection
conjecture are discussed. Indeed, any attempt to transform a single isolated
wormhole into a time machine results in large vacuum polarization effects
sufficient to disrupt the internal structure of the wormhole before the onset
of Planck scale physics, and before the onset of time travel. On the other
hand, it is possible to set up a putative time machine built out of two or more
wormholes, each of which taken in isolation is not itself a time machine. Such
``Roman configurations'' are much more subtle to analyse. For some particularly
bizarre configurations (not traversable by humans) the vacuum polarization
effects can be arranged to be arbitrarily small at the onset of Planck scale
physics. This indicates that the disruption scale has been pushed down into the
Planck slop. Ultimately, for these configurations, questions regarding the
truth or falsity of Hawking's chronology protection can only be addressed by
entering the uncharted wastelands of full fledged quantum gravity.


title: Gravitational Field of a Moving Point Particle

abstract:
  The gravitational field of a moving point particle is obtained in a Lorentz
covariant form for both uncharged and charged cases. It is shown that the
general relativistic proper time interval at the location of the particle is
the same as the special relativistic one and the gravitational and
electromagnetic self forces are zero.


title:
Acoustic propagation in fluids: an unexpected example of Lorentzian
  geometry

abstract:
  It is a deceptively simple question to ask how acoustic disturbances
propagate in a non--homogeneous flowing fluid. If the fluid is barotropic and
inviscid, and the flow is irrotational (though it may have an arbitrary time
dependence), then the equation of motion for the velocity potential describing
a sound wave can be put in the (3+1)--dimensional form: d'Alembertian psi = 0.
That is partial_mu(sqrt{-g} g^{mu nu} partial_nu psi)/sqrt{-g} = 0. The
acoustic metric --- g_{mu nu}(t,x) --- governing the propagation of sound
depends algebraically on the density, flow velocity, and local speed of sound.
Even though the underlying fluid dynamics is Newtonian, non--relativistic, and
takes place in flat space + time, the fluctuations (sound waves) are governed
by a Lorentzian spacetime geometry.


title: Quantisation of 2+1 gravity for genus 2

abstract:
  In [1,2] we established and discussed the algebra of observables for $2+1$
gravity at both the classical and quantum level, and gave a systematic
discussion of the reduction of the expected number of independent observables
to $6g - 6 (g > 1)$. In this paper the algebra of observables for the case
$g=2$ is reduced to a very simple form. A Hilbert space of state vectors is
defined and its representations are discussed using a deformation of the
Euler-Gamma function. The deformation parameter $\th$ depends on the
cosmological and Planck's constants.


title:
A Kucha\v{r} Hypertime Formalism For Cylindrically Symmetric Spacetimes
  With Interacting Scalar Fields

abstract:
  The Kucha\v{r} canonical transformation for vacuum geometrodynamics in the
presence of cylindrical symmetry is applied to a general non-vacuum case. The
resulting constraints are highly non-linear and non-local in the momenta
conjugate to the Kucha\v{r} embedding variables. However, it is demonstrated
that the constraints can be solved for these momenta and thus the dynamics of
cylindrically symmetric models can be cast in a form suitable for the
construction of a hypertime functional Schr\"odinger equation.


title: Coordinate transformations in Schwarzschild singularity problem

abstract:
  A systematic approach to the coordinate transformations in the Schwarzschild
singularity problem is considered. It is shown that both singularities at r=0
and r=2m can be eliminated by suitable coordinate transformations.


title: Semi-Complex Analysis & Mathematical Physics (Corrected Version)

abstract:
  A theoretical framework based on a simple quasi-number algebra is
investigated in a treatment of space-time and gravity.


title: B^F Theory and Flat Spacetimes

abstract:
  We propose a reduced constrained Hamiltonian formalism for the exactly
soluble $B \wedge F$ theory of flat connections and closed two-forms over
manifolds with topology $\Sigma^3 \times (0,1)$. The reduced phase space
variables are the holonomies of a flat connection for loops which form a basis
of the first homotopy group $\pi_1(\Sigma^3)$, and elements of the second
cohomology group of $\Sigma^3$ with value in the Lie algebra $L(G)$. When
$G=SO(3,1)$, and if the two-form can be expressed as $B= e\wedge e$, for some
vierbein field $e$, then the variables represent a flat spacetime. This is not
always possible: We show that the solutions of the theory generally represent
spacetimes with ``global torsion''. We describe the dynamical evolution of
spacetimes with and without global torsion, and classify the flat spacetimes
which admit a locally homogeneous foliation, following Thurston's
classification of geometric structures.


title:
Testing for Preferred-Frame Effects in Gravity with Artificial Earth
  Satellites

abstract:
  As gravity is a long-range force, one might a priori expect the Universe's
global matter distribution to select a preferred rest frame for local
gravitational physics. At the post-Newtonian approximation, two parameters
suffice to describe the phenomenology of preferred-frame effects. One of them
has already been very tightly constrained (|alpha_2| < 4 x 10^-7, 90% C.L.),
but the present bound on the other one is much weaker (|alpha_1| < 5 x 10^-4,
90% C.L.). It is pointed out that the observation of particular orbits of
artificial Earth satellites has the potential of improving the alpha_1 limits
by a couple of orders of magnitude, thanks to the appearance of small divisors
which enhance the corresponding preferred-frame effects. There is a discrete
set of inclinations which lead to arbitrarily small divisors, while, among
zero-inclination (equatorial) orbits, geostationary ones are near optimal. The
main alpha_1-induced effects are: (i) a complex secular evolution of the
eccentricity vector of the orbit, describable as the vectorial sum of several
independent rotations; and (ii) a yearly oscillation in the longitude of the
satellite.


title: A Hamiltonian Formulation of Topological Gravity

abstract:
  Topological gravity is the reduction of Einstein's theory to spacetimes with
vanishing curvature, but with global degrees of freedom related to the topology
of the universe. We present an exact Hamiltonian lattice theory for topological
gravity, which admits translations of the lattice sites as a gauge symmetry.
There are additional symmetries, not present in Einstein's theory, which kill
the local degrees of freedom. We show that these symmetries can be fixed by
choosing a gauge where the torsion is equal to zero. In this gauge, the theory
describes flat space-times. We propose two methods to advance towards the holy
grail of lattice gravity: A Hamiltonian lattice theory for curved space-times,
with first-class translation constraints.


title: Gravitational Field of a Moving Spinning Point Particle

abstract:
  The gravitational and electromagnetic fields of a moving charged spinning
point particle are obtained in the Lorentz covariant form by transforming the
Kerr--Newman solution in Boyer--Lindquist coordinates to the one in the
coordinate system which resembles the isotropic coordinates and then
covariantizing it. It is shown that the general relativistic proper time at the
location of the particle is the same as the special relativistic one and the
gravitational and electromagnetic self forces vanish.


title:
Affine Projection Tensor Geometry: Decomposing the Curvature Tensor When
  the Connection is Arbitrary and the Projection is Tilted

abstract:
  This paper constructs the geometrically natural objects which are associated
with any projection tensor field on a manifold with any affine connection. The
approaches to projection tensor fields which have been used in general
relativity and related theories assume normal projection tensors of
co-dimension one and connections which are metric compatible and torsion-free.
These assumptions fail for projections onto lightlike curves or surfaces and
other situations where degenerate metrics occur as well as projections onto
two-surfaces and projections onto spacetime in the higher dimensional manifolds
of unified field theories. This paper removes these restrictive assumptions.
One key idea is to define two different ''extrinsic curvature tensors'' which
become equal for normal projections. In addition, a new family of geometrical
tensors is introduced: the cross-projected curvature tensors. In terms of these
objects, projection decompositions of covariant derivatives, the full Riemann
curvature tensor and the Bianchi identities are obtained and applied to perfect
fluids, timelike curve congruences, string congruences, and the familiar 3+1
analysis of the spacelike initial value problem of general relativity.


title: Loop Representations

abstract:
  The loop representation plays an important role in canonical quantum gravity
because loop variables allow a natural treatment of the constraints. In these
lectures we give an elementary introduction to (i) the relevant history of
loops in knot theory and gauge theory, (ii) the loop representation of Maxwell
theory, and (iii) the loop representation of canonical quantum gravity. (Based
on lectures given at the 117. Heraeus Seminar, Bad Honnef, Sept. 1993)


title: The Off-Shell Black Hole

abstract:
  The standard (Euclidean) action principle for the gravitational field implies
that for spacetimes with black hole topology, the opening angle at the horizon
and the horizon area are canonical conjugates. It is shown that the opening
angle bears the same relation to the horizon area that the time separation
bears to the mass at infinity. The dependence of the wave function on this new
degree of freedom is governed by an extended Wheeler-DeWitt equation. Summing
over all horizon areas yields the black hole entropy.


title: Penrose Inequality for Gravitational Waves

abstract:
  We investigate axially symmetric asymptotically flat vacuum self-gravitating
system. A class of initial data with apparent horizon was numerically
constructed. The examined solutions satisfy the Penrose inequality. The prior
analysis of a massive system and the present results suggest that either
massive or sourcefree configurations fulfill the Penrose inequality.


title: Conformal Killing Vectors in Five-Dimensional Space

abstract:
  The solutions of generalized Killing equation have been obtained for line
element with initial $t^2 \oplus so(3)$ symmetry. The coefficients of the
metric $g$ corresponding to these vector fields are written down.


title: Optimal Filters for the Detection of Continuous Gravitational Waves

abstract:
  We determine the transfer functions of two kinds of filters that can be used
in the detection of continuous gravitational radiation. The first one optimizes
the signal-to-noise ratio, and the second reproduces the wave with minimum
error. We analyse the behaviour of these filters in connection with actual
detection schemes.


title:
Landau Level Ground--State Degeneracy, and Its Relevance for a General
  Quantization Procedure

abstract:
  The quantum dynamics of a two-dimensional charged spin $1/2$ particle is
studied for general, symmetry--free curved surfaces and general, nonuniform
magnetic fields that are, when different from zero, orthogonal to the defining
two surface. Although higher Landau levels generally lose their degeneracy
under such general conditions, the lowest Landau level, the ground state,
remains degenerate. Previous discussions of this problem have had less
generality and/or used supersymmetry, or else have appealed to very general
mathematical theorems from differential geometry. In contrast our discussion
relies on simple and standard quantum mechanical concepts.
  The mathematical similarity of the physical problem at hand and that of a
phase-space path integral quantization scheme of a general classical system is
emphasized. Adopting this analogy in the general case leads to a general
quantization procedure that is invariant under general coordinate
transformations-- completely unlike any of the conventional quantization
prescriptions -- and therefore generalizes the concept of quantization to new
and hitherto inaccesible situations.
  In a complementary fashion , the so-obtained picture of general quantization
helps to derive useful semiclassical formulas for the Hall current in the case
of a filling factor equal to one for a general surface and magnetic field.


title: Spacetime structure and Quantum physics

abstract:
  A description of electromagnetism as four-dimensional spacetime structure
leads to the dynamics of a charged particle being determined only by the
four-vector potential and the existence of an electromagnetic field depending
on the topological structure of the background spacetime. When the spacetime
structure of electromagnetism is complex it is possible to connect spacetime
structure and quantum physics via the method of path integration. (This paper
is a consequence of an attempt to incorporate gravitation into electromagnetism
by describing gravity as a coupling of two electromagnetic fields.)


title: On Physical Equivalence between Nonlinear Gravity Theories

abstract:
  We argue that in a nonlinear gravity theory, which according to well-known
results is dynamically equivalent to a self-gravitating scalar field in General
Relativity, the true physical variables are exactly those which describe the
equivalent general-relativistic model (these variables are known as Einstein
frame). Whenever such variables cannot be defined, there are strong indications
that the original theory is unphysical. We explicitly show how to map, in the
presence of matter, the Jordan frame to the Einstein one and backwards. We
study energetics for asymptotically flat solutions. This is based on the
second-order dynamics obtained, without changing the metric, by the use of a
Helmholtz Lagrangian. We prove for a large class of these Lagrangians that the
ADM energy is positive for solutions close to flat space. The proof of this
Positive Energy Theorem relies on the existence of the Einstein frame, since in
the (Helmholtz--)Jordan frame the Dominant Energy Condition does not hold and
the field variables are unrelated to the total energy of the system.


title: On black hole singularities in quantum gravity

abstract:
  We show that absence of space-like boundaries in 1+1 dimensional dilaton
gravity implies a catastrophic event at the end point of black hole
evaporation. The proof is completely independent of the physics at Planck
scales, which suggests that the same will occur in any theory of quantum
gravity which only admits trivial space-time topologies.


title:
On the principles of description of time and space relationships in
  frames of general relativity

abstract:
  The problem of the referring of space and time relationships between physical
objects in a curved space-time is discussed. The basic notions of column and
weak column that could constitute the basis for consistent general relativistic
description of measurements of space and time relations are introduced and the
corresponding equations are derived. A column of observers is proposed to
realize still vague notion of `non-inertial frame of reference' in case of
curved space-time, the criterion distinguishing `inertial columns' is suggested
as well. A number of solutions of column equations is described. They are
applied for calculation of gravitational, inertial (or gravitational-inertial
in more general situation) and ``external" forces and the strength of
gravitational field in several cases of physical interest. In particular, the
`general relativistic' version of Newton's law of inverse squares is derived in
case of the interaction of test particle with a static central symmetric body.


title:
Compact Three Dimensional Black Hole: Topology Change and Closed
  Timelike Curve (minor changes)

abstract:
  We present a compactified version of the 3-dimensional black hole recently
found by considering extra identifications and determine the analytical
continuation of the solution beyond its coordinate singularity by extending the
identifications to the extended region of the spacetime. In the extended region
of the spacetime, we find a topology change and non-trivial closed timelike
curves both in the ordinary 3-dimensional black hole and in the compactified
one. Especially, in the case of the compactified 3-dimensional black hole, we
show an example of topology change from one double torus to eight spheres with
three punctures.


title: Causal Feature of Central Singularity and Gravitational Mass

abstract:
  Mass of singularity is defined, and its relation to whether the singularity
is spacelike, timelike or null is discussed for spherically symmetric
spacetimes.
  It is shown that if the mass of singularity is positive
  (negative) the singularity is non-timelike (non-spacelike).
  The connection between the sign of the mass and the force on a particle is
also discussed.


title:
Representations of the $SU(N)$ $T$-algebra and the loop representation
  in $1+1$-dimensions

abstract:
  We consider the phase-space of Yang-Mills on a cylindrical space-time ($S^1
\times {\bf R}$) and the associated algebra of gauge-invariant functions, the
$T$-variables. We solve the Mandelstam identities both classically and
quantum-mechanically by considering the $T$-variables as functions of the
eigenvalues of the holonomy and their associated momenta. It is shown that
there are two inequivalent representations of the quantum $T$-algebra. Then we
compare this reduced phase space approach to Dirac quantization and find it to
give essentially equivalent results. We proceed to define a loop representation
in each of these two cases. One of these loop representations (for $N=2$) is
more or less equivalent to the usual loop representation.


title:
Squeezed Vacua and the Quantum Statistics of Cosmological Particle
  Creation

abstract:
  We use the language of squeezed states to give a systematic description of
two issues in cosmological particle creation: a) Dependence of particle
creation on the initial state specified. We consider in particular the number
state, the coherent and the squeezed state. b) The relation of spontaneous and
stimulated particle creation and their dependence on the initial state. We also
present results for the fluctuations in particle number in anticipation of its
relevance to defining noise in quantum fields and the vacuum susceptibility of
spacetime.


title: The semiclassical approximation to quantum gravity

abstract:
  A detailed review is given of the semiclassical approximation to quantum
gravity in the canonical framework. This includes in particular the derivation
of the functional Schr\"odinger equation and a discussion of semiclassical time
as well as the derivation of quantum gravitational correction terms to the
Schr\"odinger equation. These terms are used to calculate energy shifts for
fields in De~Sitter space and non-unitary contributions in black hole
evaporation. Emphasis is also put on the relevance of decoherence and
correlations in semiclassical gravity. The back reaction of non-gravitational
quantum fields onto the semiclassical background and the emergence of a Berry
connection on superspace is also discussed in this framework.


title: Periodic Solutions of the Einstein Equations for Binary Systems

abstract:
  This revision includes clarified exposition and simplified analysis.
Solutions of the Einstein equations which are periodic and have standing
gravitational waves are valuable approximations to more physically realistic
solutions with outgoing waves. A variational principle is found which has the
power to provide an accurate estimate of the relationship between the mass and
angular momentum of the system, the masses and angular momenta of the
components, the rotational frequency of the frame of reference in which the
system is periodic, the frequency of the periodicity of the system, and the
amplitude and phase of each multipole component of gravitational radiation.
Examination of the boundary terms of the variational principle leads to
definitions of the effective mass and effective angular momentum of a periodic
geometry which capture the concepts of mass and angular momentum of the source
alone with no contribution from the gravitational radiation. These effective
quantities are surface integrals in the weak-field zone which are independent
of the surface over which they are evaluated, through second order in the
deviations of the metric from flat space.


title: Predictability in Quantum Gravity and Black Hole Evaporation

abstract:
  A possible resolution of the information loss paradox for black holes is
proposed in which a phase transition occurs when the temperature of an
evaporating black hole equals a critical value, $T_c$, and Lorentz invariance
and diffeomorphism invariance are spontaneously broken. This allows a
generalization of Schr\"odinger's equation for the quantum mechanical density
matrix, such that a pure state can evolve into a mixed state, because in the
symmetry broken phase the conservation of energy-momentum is spontaneously
violated. TCP invariance is also spontaneously broken together with time
reversal invariance, allowing the existence of white holes, which are black
holes moving backwards in time. Domain walls would form which separate the
black holes and white holes (anti-black holes) in the broken symmetry regime,
and the system could evolve into equilibrium producing a balance of information
loss and gain.


title: Time-Dependent Open String Solutions in 2+1 Dimensional Gravity

abstract:
  We find general, time-dependent solutions produced by open string sources
carrying no momentum flow in 2+1 dimensional gravity. The local Poincar\'e
group elements associated with these solutions and the coordinate
transformations that transform these solutions into Minkowski metric are
obtained. We also find the relation between these solutions and the planar wall
solutions in 3+1 dimensions.


title: Quantum Kinetic Equations and Cosmology

abstract:
  We analyse quantum--kinetic effects in the early Universe. We show that
quantum corrections to the Vlasov equation give rise to a dynamical variation
of the gravitational constant. The value of the gravitational constant at the
Grand Unification epoch is shown to differ from its present value to about
$10^{-4} \div 10^{-3} \% $.


title: Reduced Hamiltonians

abstract:
  We resurrect a standard construction of analytical mechanics dating from the
last century. The technique allows one to pass from any dynamical system whose
first order evolution equations are known, and whose bracket algebra is not
degenerate, to a system of canonical variables and a non-zero Hamiltonian that
generates their evolution. We advocate using this method to infer a canonical
formalism, as a prelude to quantization, for systems in which the naive
Hamiltonian is constrained to vanish. The construction agrees with the usual
results for gauge theories and can be applied as well to gravity, {\it even
when the spatial manifold is closed.} As an example, we construct such a
reduced Hamiltonian in perturbation theory around a flat background on the
manifold $T^3 \times R$. The resulting Hamiltonian is positive semidefinite and
agrees with the A.D.M. energy in the limit that deviations from flat space
remain localized as the toroidal radii become infinite.


title: Multivector Solutions to the Hyper-Holomorphic Massive Dirac Equation

abstract:
  Attention is given to the interface of mathematics and physics, specifically
noting that fundamental principles limit the usefulness of otherwise perfectly
good mathematical general integral solutions. A new set of multivector
solutions to the meta-monogenic (massive) Dirac equation is constructed which
form a Hilbert space. A new integral solution is proposed which involves
application of a kernel to the right side of the function, instead of to the
left as usual. This allows for the introduction of a multivector generalization
of the Feynman Path Integral formulation, which shows that particular
``geometric groupings'' of solutions evolve in the manner to which we ascribe
the term ``quantum particle''. Further, it is shown that the role of usual $i$
is subplanted by the unit time basis vector, applied on the right side of the
functions. Summary of talk, to appear in: Proceedings of the 17th Annual
Lecture Series in the Mathematical Sciences, April 8-10, 1993, University of
Arkansas, `Clifford Algebas in Analysis', J. Ryan, editor (CRC Press, expected
1994)


title: Eternal inflation and the initial singularity

abstract:
  It is shown that a physically reasonable spacetime that is eternally
inflating to the future must possess an initial singularity.


title: On Black Hole Entropy

abstract:
  Two techniques for computing black hole entropy in generally covariant
gravity theories including arbitrary higher derivative interactions are
studied. The techniques are Wald's Noether charge approach introduced recently,
and a field redefinition method developed in this paper. Wald's results are
extended by establishing that his local geometric expression for the black hole
entropy gives the same result when evaluated on an arbitrary cross-section of a
Killing horizon (rather than just the bifurcation surface). Further, we show
that his expression for the entropy is not affected by ambiguities which arise
in the Noether construction. Using the Noether charge expression, the entropy
is evaluated explicitly for black holes in a wide class of generally covariant
theories. Further, it is shown that the Killing horizon and surface gravity of
a stationary black hole metric are invariant under field redefinitions of the
metric of the form $\bar{g}_{ab}\equiv g_{ab} + \Delta_{ab}$, where
$\Delta_{ab}$ is a tensor field constructed out of stationary fields. Using
this result, a technique is developed for evaluating the black hole entropy in
a given theory in terms of that of another theory related by field
redefinitions. Remarkably, it is established that certain perturbative, first
order, results obtained with this method are in fact {\it exact}. The possible
significance of these results for the problem of finding the statistical origin
of black hole entropy is discussed.}


title:
Cosmological "Ground State" Wave Functions in Gravity and
  Electromagnetism

abstract:
  The coincidence of quantum cosmology solutions generated by solving a
Euclidean version of the Hamilton-Jacobi equation for gravity and by using the
complex canonical transformation of the Ashtekar variables is discussed. An
examination of similar solutions for the free electromagnetic field shows that
this coincidence is an artifact of the homogeneity of the cosmological space.
(This paper will appear in a festchrift volume for Jerzy Plebanski)


title: Curvature and Flatness in a Brans-Dicke Universe

abstract:
  The evolution of a universe with Brans-Dicke gravity and nonzero curvature is
investigated here. We present the equations of motion and their solutions
during the radiation dominated era. In a Friedman-Robertson-Walker cosmology we
show explicitly that the three possible values of curvature $\kappa=+1,0,-1$
divide the evolution of the Brans-Dicke universe into dynamically distinct
classes just as for the standard model. Subsequently we discuss the flatness
problem which exists in Brans-Dicke gravity as it does in the standard model.
In addition, we demonstrate a flatness problem in MAD Brans-Dicke gravity. In
general, in any model that addresses the horizon problem, including inflation,
there are two components to the flatness issue: i) at the Planck epoch
curvature gains importance, and ii) during accelerated expansion curvature
becomes less important and the universe flattens. In many cases the universe
must be very flat at the Planck scale in order for the accelerated epoch to be
reached, thus there can be a residual flatness problem.


title:
Solutions to the Wheeler-Dewitt Equation Inspired by the String
  Effective Action

abstract:
  The Wheeler-DeWitt equation is derived from the bosonic sector of the
heterotic string effective action assuming a toroidal compactification. The
spatially closed, higher dimensional Friedmann-Robertson-Walker (FRW) cosmology
is investigated and a suitable change of variables rewrites the equation in a
canonical form. Real- and imaginary-phase exact solutions are found and a
method of successive approximations is employed to find more general power
series solutions. The quantum cosmology of the Bianchi IX universe is also
investigated and a class of exact solutions is found.


title: Time Gravity and Quantum Mechanics

abstract:
  Time plays different roles in quantum mechanics and gravity. These roles are
examined and the problems that the conflict in the roles presents for quantum
gravity are briefly summarised.


title:
Distributional Energy-Momentum Tensor of the Kerr-Newman Space-Time
  Family

abstract:
  Using the Kerr-Schild decomposition of the metric tensor that employs the
algebraically special nature of the Kerr-Newman space-time family, we calculate
the energy-momentum tensor. The latter turns out to be a well-defined
tensor-distribution with disk-like support.


title: Extended Loops: A New Arena for Nonperturbative Quantum Gravity

abstract:
  We propose a new representation for gauge theories and quantum gravity. It
can be viewed as a generalization of the loop representation. We make use of a
recently introduced extension of the group of loops into a Lie Group. This
extension allows the use of functional methods to solve the constraint
equations. It puts in a precise framework the regularization problems of the
loop representation. It has practical advantages in the search for quantum
states. We present new solutions to the Wheeler-DeWitt equation that reinforce
the conjecture that the Jones Polynomial is a state of nonperturbative quantum
gravity.


title: Nonsymmetric Gravity has Unacceptable Global Asymptotics

abstract:
  We analyze the radiative aspects of nonsymmetric gravity theory to show that,
in contrast to General Relativity, its nonstationary solutions cannot
simultaneously exhibit acceptable asymptotic behavior at both future and past
null infinity: good behavior at future null infinity is only possible through
the use of advanced potentials with concomitant unphysical behavior at past
null infinity.


title: Gravity, Non-Commutative Geometry and the Wodzicki Residue

abstract:
  We derive an action for gravity in the framework of non-commutative geometry
by using the Wodzicki residue. We prove that for a Dirac operator $D$ on an $n$
dimensional compact Riemannian manifold with $n\geq 4$, $n$ even, the Wodzicki
residue Res$(D^{-n+2})$ is the integral of the second coefficient of the heat
kernel expansion of $D^{2}$. We use this result to derive a gravity action for
commutative geometry which is the usual Einstein Hilbert action and we also
apply our results to a non-commutative extension which, is given by the tensor
product of the algebra of smooth functions on a manifold and a finite
dimensional matrix algebra. In this case we obtain gravity with a cosmological
constant.


title: Ashtekar Variables in Classical General Realtivity

abstract:
  This paper contains an introduction into Ashtekar's reformulation of General
Relativity in terms of connection variables. To appear in "Canonical Gravity -
From Classical to Quantum", ed. by J. Ehlers and H. Friedrich, Springer Verlag
(1994).


title: Quantum Gravitational Collapse of a Charged Dust Shell

abstract:
  A simple self gravitating system --- a thin spherical shell of charged
pressureless matter --- is naively quantized as a test case of quantum
gravitational collapse. The model is interpreted in terms of an inner product
on the positive energy states. An S-matrix is constructed describing scattering
between negatively and positively infinite radius.


title: Uncertainty Relation for a Quantum Open System

abstract:
  We derive the uncertainty relation for a quantum open system comprised of a
Brownian particle interacting with a bath of quantum oscillators at finite
temperature. We examine how the quantum and thermal fluctuations of the
environment contribute to the uncertainty in the canonical variables of the
system. We show that upon contact with the bath (assumed ohmic in this paper)
the system evolves from a quantum-dominated state to a thermal-dominated state
in a time which is the same as the decoherence time in similar models in the
discussion of quantum to classical transition. This offers some insight into
the physical mechanisms involved in the environment-induced decoherence
process. We obtain closed analytic expressions for this generalized uncertainty
relation under the conditions of high temperature and weak damping separately.
We also consider under these conditions an arbitrarily-squeezed initial state
and show how the squeeze parameter enters in the generalized uncertainty
relation. Using these results we examine the transition of the system from a
quantum pure state to a nonequilibrium quantum statistical state and to an
equilibrium quantum statistical state. The three stages are marked by the
decoherence time and the relaxation time respectively. With these observations
we explicate the physical conditions when the two basic postulates of quantum
statistical mechanics become valid. We also comment on the inappropriateness in
the usage of the word classicality in many decoherence studies of quantum to
classical transition.


title:
Quantum Brownian Motion in a Bath of Parametric Oscillators: A model for
  system-field interactions

abstract:
  The quantum Brownian motion paradigm provides a unified framework where one
can see the interconnection of some basic quantum statistical processes like
decoherence, dissipation, particle creation, noise and fluctuation. We treat
the case where the Brownian particle is coupled linearly to a bath of time
dependent quadratic oscillators. While the bath mimics a scalar field, the
motion of the Brownian particle modeled by a single oscillator could be used to
depict the behavior of a particle detector, a quantum field mode or the scale
factor of the universe. An important result of this paper is the derivation of
the influence functional encompassing the noise and dissipation kernels in
terms of the Bogolubov coefficients. This method enables one to trace the
source of statistical processes like decoherence and dissipation to vacuum
fluctuations and particle creation, and in turn impart a statistical mechanical
interpretation of quantum field processes. With this result we discuss the
statistical mechanical origin of quantum noise and thermal radiance from black
holes and from uniformly- accelerated observers in Minkowski space as well as
from the de Sitter universe discovered by Hawking, Unruh and Gibbons-Hawking.
We also derive the exact evolution operator and master equation for the reduced
density matrix of the system interacting with a parametric oscillator bath in
an initial squeezed thermal state. These results are useful for decoherence and
backreaction studies for systems and processes of interest in semiclassical
cosmology and gravity. Our model and results are also expected to be useful for
related problems in quantum optics. %\pacs
{05.40.+j,03.65.Sq,98.80.Cq,97.60.Lf}


title: Noise and Fluctuations in Semiclassical Gravity

abstract:
  We continue our earlier investigation of the backreaction problem in
semiclassical gravity with the Schwinger-Keldysh or closed-time-path (CTP)
functional formalism using the language of the decoherent history formulation
of quantum mechanics. Making use of its intimate relation with the
Feynman-Vernon influence functional (IF) method, we examine the statistical
mechanical meaning and show the interrelation of the many quantum processes
involved in the backreaction problem, such as particle creation, decoherence
and dissipation. We show how noise and fluctuation arise naturally from the CTP
formalism. We derive an expression for the CTP effective action in terms of the
Bogolubov coefficients and show how noise is related to the fluctuations in the
number of particles created. In so doing we have extended the old framework of
semiclassical gravity, based on the mean field theory of Einstein equation with
a source given by the expectation value of the energy-momentum tensor, to that
based on a Langevin-type equation, where the dynamics of fluctuations of
spacetime is driven by the quantum fluctuations of the matter field. This
generalized framework is useful for the investigation of quantum processes in
the early universe involving fluctuations, vacuum stability and phase transtion
phenomena and the non-equilibrium thermodynamics of black holes. It is also
essential to an understanding of the transition from any quantum theory of
gravity to classical general relativity. \pacs{pacs numbers:
04.60.+n,98.80.Cq,05.40.+j,03.65.Sq}


title: Poincar\'{e} gauge theory of gravity

abstract:
  A Poincar\'{e} gauge theory of (2+1)-dimensional gravity is developed.
Fundamental gravitational field variables are dreibein fields and Lorentz gauge
potentials, and the theory is underlain with the Riemann-Cartan space-time. The
most general gravitational Lagrangian density, which is at most quadratic in
curvature and torsion tensors and invariant under local Lorentz transformations
and under general coordinate transformations, is given. Gravitational field
equations are studied in detail, and solutions of the equations for weak
gravitational fields are examined for the case with a static, \lq \lq spin"less
point like source. We find, among other things, the following: (1)Solutions of
the vacuum Einstein equation satisfy gravitational field equations in the
vacuum in this theory. (2)For a class of the parameters in the gravitational
Lagrangian density, the torsion is \lq \lq frozen" at the place where \lq \lq
spin" density of the source field is not vanishing. In this case, the field
equation actually agrees with the Einstein equation, when the source field is
\lq \lq spin"less. (3)A teleparallel theory developed in a previous paper is
\lq \lq included as a solution" in a limiting case. (4)A Newtonian limit is
obtainable, if the parameters in the Lagrangian density satisfy certain
conditions.


title:
On the alternative description of complex holomorphic and Lorentz
  geometries in four dimensions

abstract:
  The equivalence of a conformal metric on 4-dimensional space-time and a local
field of 3-dimensional subspaces of the space of 2-forms over space-time is
discussed and the basic notion of transection is introduced. Corresponding
relation is spread to the metric case in terms of notion of normalized ordered
oriented transection field. As a result, one obtains a possibility to handle
the metric geometry without any references to the metric tensor itself on a
distinct base which nevertheless contains all the information on metricity.
Moreover, the notion of space-time curvature is provided with its natural
counterpart in the transection `language' in a form of curvature endomorphism
as well. To globalize the local constructions introduced, a certain fiber
bundle is defined whose sections are equivalent to normalized ordered oriented
transection fields and locally to the metric tensor on space-time. The
criterion distinguishing the Lorentz geometry is discussed. The resulting
alternative method of the description of space-time metricity, dealing with
exterior forms foliation alone, seems to be of a power compatible with one of
the standard concept based on the metric tensor.


title:
On the alternative description of complex holomorphic and Lorentz
  geometries in four dimensions. II. Appendix

abstract:
  This supplementary part of the paper gr-qc 9312038 contains the necessary
proofs of the claims stated in the main part.


title:
Application of the Lagrange-Souriau form method to the case of
  source-free electromagnetic field

abstract:
  The recent method of the description of classical fields in terms of
Lagrange-Souriau form is applied to the case of source-free electromagnetic
field in order to check its computational capabilities. The relevant
calculations are represented in all details and yield a useful data for
comparisons of the method with more usual approaches in this simple and
transparent case.


title: Gauge Theory of Quantum Gravity

abstract:
  A gauge theory of quantum gravity is formulated, in which an internal, field
dependent metric is introduced which non-linearly realizes the gauge fields on
the non-compact group $SL(2,C)$, while linearly realizing them on $SU(2)$.
Einstein's $SL(2,C)$ invariant theory of gravity emerges at low energies, since
the extra degrees of freedom associated with the quadratic curvature and the
internal metric only dominate at high energies. In a fixed internal metric
gauge, only the the $SU(2)$ gauge symmetry is satisfied, the particle spectrum
is identified and the Hamiltonian is shown to be bounded from below. Although
Lorentz invariance is broken in this gauge, it is satisfied in general. The
theory is quantized in this fixed, broken symmetry gauge as an $SU(2)$ gauge
theory on a lattice with a lattice spacing equal to the Planck length. This
produces a unitary and finite theory of quantum gravity.


title: Another positivity proof and gravitational energy localizations

abstract:
  Two locally positive expressions for the gravitational Hamiltonian, one using
4-spinors the other special orthonormal frames, are reviewed. A new quadratic
3-spinor-curvature identity is used to obtain another positive expression for
the Hamiltonian and thereby a localization of gravitational energy and positive
energy proof. These new results provide a link between the other two methods.
Localization and prospects for quasi-localization are discussed.


title: Quantum Mechanics as Quantum Measure Theory

abstract:
  The additivity of classical probabilities is only the first in a hierarchy of
possible sum-rules, each of which implies its successor. The first and most
restrictive sum-rule of the hierarchy yields measure-theory in the Kolmogorov
sense, which physically is appropriate for the description of stochastic
processes such as Brownian motion. The next weaker sum-rule defines a {\it
generalized measure theory} which includes quantum mechanics as a special case.
The fact that quantum probabilities can be expressed ``as the squares of
quantum amplitudes'' is thus derived in a natural manner, and a series of
natural generalizations of the quantum formalism is delineated. Conversely, the
mathematical sense in which classical physics is a special case of quantum
physics is clarified. The present paper presents these relationships in the
context of a ``realistic'' interpretation of quantum mechanics.


title: Ashtekar's New Variables and Positive Energy

abstract:
  We discuss earlier unsuccessful attempts to formulate a positive
gravitational energy proof in terms of the New Variables of Ashtekar. We also
point out the difficulties of a Witten spinor type proof. We then use the
special orthonormal frame gauge conditions to obtain a locally positive
expression for the New Variables Hamiltonian and thereby a ``localization'' of
gravitational energy as well as a positive energy proof.


title: Geometrical Constraints on the Cosmological Constant

abstract:
  The cosmological constant problem is examined under the assumption that the
extrinsic curvature of the space-time contributes to the vacuum. A compensation
mechanism based on a variable cosmological term is proposed. Under a suitable
hypothesis on the behavior of the extrinsic curvature, we find that an
initially large $\Lambda(t)$ rolls down rapidly to zero during the early stages
of the universe. Using perturbation analysis, it is shown that such vacuum
behaves essentially as a spin-2 field which is independent of the metric.


title:
Steady states of harmonic oscillator chains and shortcomings of harmonic
  heat baths

abstract:
  We study properties of steady states (states with time-independent density
operators) of systems of coupled harmonic oscillators. Formulas are derived
showing how adiabatic change of the Hamiltonian transforms one steady state
into another. It is shown that for infinite systems, sudden change of the
Hamiltonian also tends to produce steady states, after a transition period of
oscillations. These naturally arising steady states are compared to the
maximum-entropy state (the thermal state) and are seen not to coincide in
general. The approach to equilibrium of subsystems consisting of n coupled
harmonic oscillators has been widely studied, but only in the simple case where
n=1. The power of our results is that they can be applied to more complex
subsustems, where n>1. It is shown that the use of coupled harmonic oscillators
as heat baths models is fraught with some problems that do not appear in the
simple n=1 case. Specifically, the thermal states that are though to be
achievable through hard-sphere collisions with heat-bath particles can
generally NOT be achieved with harmonic coupling to the heat-bath particles,
except approximately when the coupling is weak.


title:
Does a domain wall emit gravitational waves? -- General-relativistic
  perturbative treatment

abstract:
  The behavior of gravitational wave perturbations on a locally Minkowskian
spacetime background containing a planar domain wall is investigated in the
gauge-invariant general relativistic framework. It is shown that for this
particular background the domain wall does not emit gravitational waves
spontaneously by its free oscillation in the first order, although it scatters
incidental gravitational waves.


title:
Stationary Solutions in 2+1 Dimensional Gravity and Closed Time-Like
  Curves

abstract:
  We apply the reduced radial gauge to give the general solution of the metric
in 2+1 dimensions in term of quadratures. It allows a complete controll on the
support of the source. We use the result to prove that for a general stationary
universe, conical at infinity, the weak energy condition and the absence of CTC
at space infinity prevent the occurrrence of any CTC.


title: 5D Axisymmetric Stationary Solutions as Harmonic Maps

abstract:
  We present the complete scheme of the application of the one-and two
dimensional subspace and subgroups method to five-dimensional gravity with a
$G_{3}$ group of motion. We do so in the space time and in the potential space
formalisms. From this method one obtains the Kramer, Belinsky-Ruffini,
Dobiasch-Maison, Cl\'{e}ment, Gross-Perry-Sorkin solutions etc. as special
cases.


title: Entropy generation in 2+1-dimensional Gravity

abstract:
  The tunneling approach, for entropy generation in quantum gravity, is shown
to be valid when applied to 3-D general relativity. The entropy of de Sitter
and Reissner-Nordstr\"om external event horizons and of the 3-D black hole
obtained by Ba\~nados et. al. is rederived from tunneling of the metric to
these spacetimes. The analysis for spacetimes with an external horizon is
carried out in a complete analogy with the 4-D case. However, we find
significant differences for the black hole. In particular the initial
configuration that tunnels to a 3-D black hole may not to yield an infinitely
degenerate object, as in 4-D Schwarzschild black hole. We discuss the possible
relation to the evaporation of the 3-D black hole.


title: Fermions in Quantum Gravity

abstract:
  We study the quantum fermions+gravity system, that is, the gravitational
counterpart of QED. We start from the standard Einstein-Weyl theory,
reformulated in terms of Ashtekar variables; and we construct its non-
perturbative quantum theory by extending the loop representation of general
relativity. We construct the fermion equivalent to the loop variables. Not
surprisingly, fermions can be incorporated in the loop representation simply by
including open curves into ''Loop space''. We explicitely construct the
diffeomorphism and hamiltonain operators. The first can be fully solved as in
pure gravity. The second is constructed by using a background-independent
regularization technique. The theory retains the clean geometrical features of
the pure quantum gravity. In particular, the hamiltonian constraint admits the
same simple geometrical interpretation as its pure gravity counterpart. Quite
surprisingly, a simple action codes the full dynamics of the interacting
theory. To unravel the dynamics of the theory we study the evolution of the
fermion-gravity system in the physical-time defined by an additional coupled
(''clock''-) scalar field. We construct the Hamiltonian operator that evolves
the system in this physical time. We show that this Hamiltonian is finite,
diffeomorphism invariant, and has a simple geometrical action. The theory
fermions+gravity evolving in the clock time is finally given by the
combinatorial and geometrical action of this Hamiltonian on a set of graphs
with a finite number of end points. This action defines the "topological
Feynman rules" of the theory.


title:
A Proposal of Positive-Definite Local Gravitational Energy Density in
  General Relativity

abstract:
  We propose a 4-dimensional Kaluza-Klein approach to general relativity in the
(2,2)-splitting of space-time using the double null gauge. The associated
Lagrangian is equivalent to the Einstein-Hilbert Lagrangian, since it yields
the same field equations as the E-H Lagrangian does. It is describable as a
(1+1)-dimensional Yang-Mills type gauge theory coupled to (1+1)-dimensional
matter fields, where the minimal coupling associated with the diffeomorphism
group of the 2-dimensional spacelike fibre space automatically appears. Written
in the first-order formalism, our Lagrangian density directly yields a non-zero
local Hamiltonian density, where the associated time function is the retarded
time. From this Hamiltonian density, we obtain a positive-definite local
gravitational energy density. In the asymptotically flat space-times, the
volume integrals of the proposed local gravitational energy density over
suitable 3-dimensional hypersurfaces correctly reproduce the Bondi and the ADM
surface integral, at null and spatial infinity, respectively, supporting our
proposal. We also obtain the Bondi mass-loss formula as a negative-definite
flux integral of a bilinear in the gravitational currents at null infinity.


title: A Perturbative Method to solve fourth-order Gravity Field Equations

abstract:
  We develop a method for solving the field equations of a quadratic
gravitational theory coupled to matter. The quadratic terms are written as a
function of the matter stress tensor and its derivatives in such a way to have,
order by order, a set of Einstein field equations with an effective
$T_{\mu\nu}$. We study the cosmological scenario recovering the de Sitter exact
solution, and the first order (in the coupling constants $\alpha$ and $\beta$
appearing in the gravitational Lagrangian) solution to the gauge cosmic string
metric and the charged black hole. For this last solution we discuss the
consequences on the thermodynamics of black holes, and in particular, the
entropy - area relation which gets additional terms to the usual ${1\over4} A$
value.


title:
Trapped surfaces and the Penrose inequality in spherically symmetric
  geometries

abstract:
  We demonstrate that the Penrose inequality is valid for spherically symmetric
geometries even when the horizon is immersed in matter. The matter field need
not be at rest. The only restriction is that the source satisfies the weak
energy condition outside the horizon. No restrictions are placed on the matter
inside the horizon. The proof of the Penrose inequality gives a new necessary
condition for the formation of trapped surfaces. This formulation can also be
adapted to give a sufficient condition. We show that a modification of the
Penrose inequality proposed by Gibbons for charged black holes can be broken in
early stages of gravitational collapse. This investigation is based exclusively
on the initial data formulation of General Relativity.


title: On the dynamics of generators of Cauchy horizons

abstract:
  We discuss various features of the dynamical system determined by the flow of
null geodesic generators of Cauchy horizons. Several examples with non--trivial
(``chaotic'', ``strange attractors'', etc.) global behaviour are constructed.
Those examples are relevant to the ``chronology protection conjecture'', and
they show that the occurrence of ``fountains'' is {\em not} a generic feature
of Cauchy horizons.


title:
How to calculate a decoherence matrix numerically and the microscopic
  mechanism for decoherence in the Caldeira-Leggett model

abstract:
  A central object in the interpretation of quantum mechanics of closed systems
with decoherent histories is the decoherence matrix. But only for a very small
number of models one is able to give explicit expressions for its elements. So
numerical methods are required. Unfortunately the dimensions of this matrices
are usually very high, which makes also a direct numerical calculation
impossible. A solution of this problem would be given by a method which only
calculates the dominant matrix elements. This includes to make a decision about
the dominance of an element before it will be calculated. In this paper I will
develop an algorithm that combines the numerical calculation of the elements of
the decoherence matrix with a permanent estimation, so that finally the
dominant elements will be calculated only. As an example I apply this procedure
to the Caldeira- Leggett-modell.


title: Wilson Loops and Black Holes in 2+1 Dimensions

abstract:
  In 2+1 dimensional Chern-Simons gravity, Wilson loops in the three
dimensional Anti de Sitter group, $SO(2,2)$, reproduce the spinning black hole
of Ba\~nados, Teitelboim and Zanelli (BTZ) by naturally duplicating the
necessary identification of points of a four dimensional globally $SO(2,2)$
invariant space in which the hole appears as an embedding.


title: Nonsymmetric Gravity Does Have Acceptable Global Asymptotics

abstract:
  ``Reports of my death are greatly exaggerated''
  - Mark Twain. We consider the claim by Damour, Deser and McCarthy that
nonsymmetric gravity theory has unacceptable global asymptotics. We explain why
this claim is incorrect.


title: Instability of Einstein-Yang-Mills Solitons for Arbitrary Gauge Groups

abstract:
  We prove that static, spherically symmetric, asymptotically flat, regular
solutions of the Einstein-Yang-Mills equations are unstable for arbitrary gauge
groups. The proof involves the following main steps. First, we show that the
frequency spectrum of a class of radial perturbations is determined by a
coupled system of radial "Schroedinger equations". Eigenstates with negative
eigenvalues correspond to exponentially growing modes. Using the variational
principle for the ground state it is then proven that there always exist
unstable modes (at least for "generic" solitons). This conclusion is reached
without explicit knowledge of the possible equilibrium solutions.


title: Energy Fluctuations Generated by Inflation

abstract:
  The energy density correlation function $C(x,y)=<\rho(x)\rho(y)>-<\rho>^2$
and its Fourier transform generated by the gravitational tidal forces of the
inflationary de Sitter expansion are derived for a massless or light ($m<<H$)
neutral scalar field $\Phi$ without self--interactions, minimally coupled to
gravity. The field has no classical background component, $<\Phi>=0$. Every
observationally relevant mode (which has today $\lambda_{phys}<H_0^{-1}$) had
at early times $R/k_{phys}^2\to0$, and is taken to be initially in the
Minkowski vacuum state. Our computation of $C(x,y)$, which involves four field
operators, is finite and unambiguous at each step, since we use the following
two tools: (1) We use a normal ordered energy density operator N$[\rho]$ and
show that any normal ordering N gives the same finite result. (2) Since
$C(x,y)$ has the universal $|x-y|^{-8}$ short--distance behaviour, the Fourier
transform can only be performed after smearing the energy density operator in
space and time with a smearing scale $\tau$. The resulting energy density
fluctuations are non--Gaussian, but obey a $\chi^2$--distribution. The power
spectrum $\dk$ involves a smearing scale $\tau$, and we choose $\tau=k^{-1}$.
For massless scalars we obtain $k^3\dk\sim H^4k^4$ on super--horizon scales
$k<H$. For light scalars with masses $m\ll H$ a plateau appears on the largest
scales $k<\sqrt{m^3/H}$, the result is $k^3\dk\sim m^6H^2(k/H)^{4m^2/3H^2}$. On
sub--horizon scales $k>H$ we have the universal law $k^3\dk\sim k^8$.


title: Homotopy Invariants and Time Evolution in (2+1)-Dimensional Gravity

abstract:
  We establish the relation between the ISO(2,1) homotopy invariants and the
polygon representation of (2+1)-dimensional gravity. The polygon closure
conditions, together with the SO(2,1) cycle conditions, are equivalent to the
ISO(2,1) cycle conditions for the representa- tions of the fundamental group in
ISO(2,1). Also, the symplectic structure on the space of invariants is closely
related to that of the polygon representation. We choose one of the polygon
variables as internal time and compute the Hamiltonian, then perform the
Hamilton-Jacobi transformation explicitly. We make contact with other authors'
results for g = 1 and g = 2 (N = 0).


title: Canonical Quantization of (2+1)-Dimensional Gravity

abstract:
  We consider the quantum dynamics of both open and closed two- dimensional
universes with ``wormholes'' and particles. The wave function is given as a sum
of freely propagating amplitudes, emitted from a network of mapping class
images of the initial state. Interference between these amplitudes gives
non-trivial scattering effects, formally analogous to the optical diffraction
by a multidimensional grating; the ``bright lines'' correspond to the most
probable geometries.


title: On the existence of singularity-free solutions in quartic gravity

abstract:
  We study a general field theory of a scalar field coupled to gravitation
through a quadratic Gauss-Bonnet term $\xi({\phi})$$R_{GB}^2$. We show that,
under mild assumptions about the function $\xi(\phi)$, the classical solutions
in a spatially flat FRW background include singularity - free solutions.


title: Exact Conformal Scalar Field Cosmologies

abstract:
  New exact solutions of Einstein's gravity coupled to a self-interacting
conformal scalar field are derived in this work. Our approach extends a
solution-generating technique originally introduced by Bekenstein for massless
conformal scalar fields. Solutions are obtained for a
Friedmann-Robertson-Walker geometry both for the cases of zero and non-zero
curvatures, and a variety of interesting features are found. It is shown that
one class of solutions tends asymptotically to a power-law inflationary
behaviour $S(t)\sim t^p$ with $p>1$, while another class exhibits a late time
approach to the $S(t)\sim t$ behaviour of the coasting models. Bouncing models
which avoid an initial singularity are also obtained. A general discussion of
the asymptotic behaviour and of the possibility of occurrence of inflation is
provided.