title: Geodesic Structure of the 2 + 1 Black Hole

abstract:
  Null and timelike geodesics around a 2+1 black hole are determined. Complete
geodesics of both types exist in the rotating black-hole background, but not in
the spinless case. Upper and lower bounds for the radial size of the orbits are
given in all cases and the possibility of passing from one black hole exterior
spacetime to another is discussed using the Penrose diagrams. An analysis of
particle motions by means of effective potentials and orbit graphs are also
included.


title: Relaxed Bounds on the Dilaton Mass in a String Cosmology Scenario

abstract:
  We discuss bounds on the dilaton mass, following from the cosmological
amplification of the quantum fluctuations of the dilaton background, under the
assumption that such fluctuations are dominant with respect to the classical
background oscillations. We show that if the fluctuation spectrum grows with
the frequency the bounds are relaxed with respect to the more conventional case
of a flat or decreasing spectrum. As a consequence, the allowed range of masses
may become compatible with models of supersymmetry breaking, and with a
universe presently dominated by a relic background of dilaton dark matter.


title: Black Holes as Quantum Membranes

abstract:
  We propose a quantum description of black holes. The degrees of freedom to be
quantized are identified with the microscopic degrees of freedom of the
horizon, and their dynamics is governed by the action of the relatistic bosonic
membrane in $D=4$. We find that a consistent and plausible description emerges,
both at the classical and at the quantum level. We present results for the
level structure of black holes. We find a ``principal series'' of levels,
corresponding to quantization of the area of the horizon. From each level of
this principal series starts a quasi-continuum of levels due to excitations of
the membrane. We discuss the statistical origin of the black hole entropy and
the relation with Hawking radiation and with the information loss problem. The
limits of validity of the membrane approach turn out to coincide with the known
limits of validity of the thermodynamical description of black holes.


title: Towards a unification of gravity and Yang-Mills theory

abstract:
  We introduce a gauge and diffeomorphism invariant theory on Yang-Mills phase
space. The theory is well defined for an arbitrary gauge group with an
invariant bilinear form, it contains only first class constraints, and the
spacetime metric has a simple form in terms of the phase space variables. With
gauge group $SO(3,C)$, the theory equals the Ashtekar formulation of gravity
with a cosmological constant. For Lorentzian signature, the theory is complex,
and we have not found any good reality conditions. In the Euclidean signature
case, everything is real. In a weak field expansion around de Sitter spacetime,
the theory is shown to give the conventional Yang-Mills theory to the lowest
order in the fields.


title:
Quantum Gravity on a Circle and the Diffeomorphism Invariance of the
  Schrodinger Equation

abstract:
  We study a model for quantum gravity on a circle in which the notion of a
classical metric tensor is replaced by a quantum metric with an inhomogeneous
transformation law under diffeomorphisms. This transformation law corresponds
to the co--adjoint action of the Virasoro algebra, and resembles that of the
connection in Yang--Mills theory. The transformation property is motivated by
the diffeomorphism invariance of the one dimensional Schr\"odinger equation.
The quantum distance measured by the metric corresponds to the phase of a
quantum mechanical wavefunction. The dynamics of the quantum gravity theory are
specified by postulating a Riemann metric on the space $Q$ of quantum metrics
and taking the kinetic energy operator to be the resulting laplacian on the
configuration space $Q/\rm Diff_0(S^1)$. The resulting metric on the
configuration space is analyzed and found to have singularities. The
second--quantized Schr\"odinger equation is derived, some exact solutions are
found, and a generic wavefunction behavior near one of the metric singularities
is described. Finally some further directions are indicated, including an
analogue of the Yamabe problem of differential geometry.


title:
Stochastic Dynamics of Coarse-Grained Quantum Fields in Inflationary
  Universe

abstract:
  It is shown how coarse-graining of quantum field ^M theory in de Sitter space
leads to the emergence of a classical ^M stochastic description as an effective
theory in the infra-red regime. ^M The quantum state of the coarse-grained
scalar field is found to be a highly^M squeezed coherent state, whose center
performs a random walk on a^M bundle of classical trajectories.^M


title:
Squeezing and Dual Recycling in Laser Interferometric Gravitational Wave
  Detectors

abstract:
  We calculate the response of an ideal Michelson interferometer incorporating
both dual recycling and squeezed light to gravitational waves. The photon
counting noise has contributions from the light which is sent in through the
input ports as well as the vacuum modes at sideband frequencies generated by
the gravitational waves. The minimum detectable gravity wave amplitude depends
on the frequency of the wave as well as the squeezing and recycling parameters.
Both squeezing and the broadband operation of dual recycling reduce the photon
counting noise and hence the two techniques can be used together to make more
accurate phase measurements. The variance of photon number is found to be
time-dependent, oscillating at the gravity wave frequency but of much lower
order than the constant part.


title: Spherically Symmetric Gravity as a Completely Integrable System

abstract:
  It is shown - in Ashtekar's canonical framework of General Relativity - that
spherically symmetric (Schwarzschild) gravity in 4 dimensional space-time
constitutes a finite dimensional completely integrable system. Canonically
conjugate observables for asymptotically flat space-times are masses as action
variables and - surprisingly - time variables as angle variables, each of which
is associated with an asymptotic "end" of the Cauchy surfaces. The emergence of
the time observable is a consequence of the Hamiltonian formulation and its
subtleties concerning the slicing of space and time and is not in contradiction
to Birkhoff's theorem. The results are of interest as to the concept of time in
General Relativity. They can be formulated within the ADM formalism, too.
Quantization of the system and the associated Schr\"odinger equation depend on
the allowed spectrum of the masses.


title: Multiple Field Scalar-Tensor Theories of Gravity and Cosmology

abstract:
  We consider multiple scalar fields coupled to gravity, with special attention
given to two-field theories. First, the conditions necessary for these theories
to meet solar system tests are given. Next, we investigate the cosmological
evolution of the fields to see if these conditions can be met. Solutions are
found in the dust era, as well as radiation and cosmological constant dominated
epochs. The possibility of inflation in these theories is discussed. While
power law growth of the scalar fields can yield the appropriate conditions to
meet solar system constraints, these solutions are unstable.


title: Two dimensional Sen connections in general relativity

abstract:
  The two dimensional version of the Sen connection for spinors and tensors on
spacelike 2-surfaces is constructed. A complex metric $\gamma_{AB}$ on the spin
spaces is found which characterizes both the algebraic and extrinsic
geometrical properties of the 2-surface $\$ $. The curvature of the two
dimensional Sen operator $\Delta_e$ is the pull back to $\$ $ of the
anti-self-dual part of the spacetime curvature while its `torsion' is a boost
gauge invariant expression of the extrinsic curvatures of $\$ $. The difference
of the 2 dimensional Sen and the induced spin connections is the anti-self-dual
part of the `torsion'. The irreducible parts of $\Delta_e$ are shown to be the
familiar 2-surface twistor and the Weyl--Sen--Witten operators. Two Sen--Witten
type identities are derived, the first is an identity between the 2 dimensional
twistor and the Weyl--Sen--Witten operators and the integrand of Penrose's
charge integral, while the second contains the `torsion' as well. For spinor
fields satisfying the 2-surface twistor equation the first reduces to Tod's
formula for the kinematical twistor.


title: MATTERS OF GRAVITY, a newsletter for the gravity community, Number 3

abstract:
  Table of contents
  Editorial
  Correspondents
  Gravity News:
  Open Letter to gravitational physicists, Beverly Berger
  A Missouri relativist in King Gustav's Court, Clifford Will
  Gary Horowitz wins the Xanthopoulos award, Abhay Ashtekar
  Research briefs:
  Gamma-ray bursts and their possible cosmological implications, Peter Meszaros
  Current activity and results in laboratory gravity, Riley Newman
  Update on representations of quantum gravity, Donald Marolf
  Ligo project report: December 1993, Rochus E. Vogt
  Dark matter or new gravity?, Richard Hammond
  Conference reports:
  Gravitational waves from coalescing compact binaries, Curt Cutler
  Mach's principle: from Newton's bucket to quantum gravity, Dieter Brill
  Cornelius Lanczos international centenary conference, David Brown
  Third Midwest relativity conference, David Garfinkle


title:
Running Coupling Constants, Newtonian Potential and non localities in
  the Effective Action

abstract:
  We consider a quantum scalar field on an arbitrary gravitational background.
We obtain the effective {\it in-in} equations for the gravitational fields
using a covariant and non-local approximation for the effective action proposed
by Vilkovisky and collaborators. {}From these equations, we compute the quantum
corrections to the Newtonian potential. We find logarithmic corrections which
we identify as the running of the gravitational constants. This running
coincides with the renormalization group prediction only for minimal and
conformal coupling.


title: Regge calculus and Ashtekar variables

abstract:
  Spacetime discretized in simplexes, as proposed in the pioneer work of Regge,
is described in terms of selfdual variables. In particular, we elucidate the
"kinematic" structure of the initial value problem, in which 3--space is
divided into flat tetrahedra, paying particular attention to the role played by
the reality condition for the Ashtekar variables. An attempt is made to write
down the vector and scalar constraints of the theory in a simple and
potentially useful way.


title: Two dimensional Sen connections and quasi-local energy-momentum

abstract:
  The recently constructed two dimensional Sen connection is applied in the
problem of quasi-local energy-momentum in general relativity. First it is shown
that, because of one of the two 2 dimensional Sen--Witten identities, Penrose's
quasi-local charge integral can be expressed as a Nester--Witten integral.Then,
to find the appropriate spinor propagation laws to the Nester--Witten integral,
all the possible first order linear differential operators that can be
constructed only from the irreducible chiral parts of the Sen operator alone
are determined and examined. It is only the holomorphy or anti-holomorphy
operator that can define acceptable propagation laws. The 2 dimensional Sen
connection thus naturally defines a quasi-local energy-momentum, which is
precisely that of Dougan and Mason. Then provided the dominant energy condition
holds and the 2-sphere S is convex we show that the next statements are
equivalent: i. the quasi-local mass (energy-momentum) associated with S is
zero; ii.the Cauchy development $D(\Sigma)$ is a pp-wave geometry with pure
radiation ($D(\Sigma)$ is flat), where $\Sigma$ is a spacelike hypersurface
whose boundary is S; iii. there exist a Sen--constant spinor field (two spinor
fields) on S. Thus the pp-wave Cauchy developments can be characterized by the
geometry of a two rather than a three dimensional submanifold.


title: Decoherence, Chaos, and the Second Law

abstract:
  We investigate implications of decoherence for quantum systems which are
classically chaotic. We show that, in open systems, the rate of von Neumann
entropy production quickly reaches an asymptotic value which is: (i)
independent of the system-environment coupling, (ii) dictated by the dynamics
of the system, and (iii) dominated by the largest Lyapunov exponent. These
results shed a new light on the correspondence between quantum and classical
dynamics as well as on the origins of the ``arrow of time.''


title: Decoherence in Quantum Brownian Motion

abstract:
  We examine the dependence of decoherence on the spectral density of the
environment as well as on the initial state of the system. We use two simple
examples to illustrate some important effects. The simplest derivation of the
general form of the master equation for a general quantum Brownian motion is
outlined in an Appendix.


title: 5D Schwarzschild-Like Spacetimes with Arbitrary Magnetic Field

abstract:
  We find a new class of exact solutions of the five-dimensional Einstein
equations whose corresponding four-dimensional spacetime possesses a
Schwarzschild-like behavior. The electromagnetic potential depends on a
harmonic function and can be choosen to be of a monopole, dipole, etc. field.
The solutions are asymptotically flat and for vanishing magnetic field the four
metrics are of the Schwarzschild solution. The spacetime is singular in $r=2m$
for higher multipole moments, but regular for monopoles or vanishing magnetic
fields in this point. The scalar field posseses a singular behavior. #(Preprint
CINVESTAV 15/93)#


title:
Thermal states in Anti-de Sitter space-time and the role of time-like
  infinity

abstract:
  The grand-canonical thermodynamic potential for Bose and Fermi fields in
anti-de Sitter space-time is introduced and a Mellin complex representation is
given. This is used to investigate the high temperature properties of the
thermal state at finite charge. The time-like nature of spatial infinity is
shown to act as a boundary, and changes the free energy of the field in thermal
equilibrium.


title: On the physical meaning of Fermi coordinates

abstract:
  (Some Latex problems should be removed in this version) Fermi coordinates
(FC) are supposed to be the natural extension of Cartesian coordinates for an
arbitrary moving observer in curved space-time. Since their construction cannot
be done on the whole space and even not in the whole past of the observer we
examine which construction principles are responsible for this effect and how
they may be modified. One proposal for a modification is made and applied to
the observer with constant acceleration in the two and four dimensional
Minkowski space. The two dimensional case has some surprising similarities to
Kruskal space which generalize those found by Rindler for the outer region of
Kruskal space and the Rindler wedge. In perturbational approaches the
modification leads also to different predictions for certain physical systems.
As an example we consider atomic interferometry and derive the deviation of the
acceleration-induced phase shift from the standard result in Fermi coordinates.


title:
Preferred Observables, Predictability, Classicality, and the
  Environment-Induced Decoherence

abstract:
  Selection of the preferred classical set of states in the process of
decoherence -- so important for cosmological considerations -- is discussed
with an emphasis on the role of information loss and entropy. {\it Persistence
of correlations} between the observables of two systems (for instance, a record
and a state of a system evolved from the initial conditions described by that
record) in the presence of the environment is used to define classical
behavior. From the viewpoint of an observer (or any system capable of
maintaining records) {\it predictability} is a measure of such persistence.
{\it Predictability sieve} -- a procedure which employs both the statistical
and algorithmic entropies to systematically explore all of the Hilbert space of
an open system in order to eliminate the majority of the unpredictable and
non-classical states and to locate the islands of predictability including the
preferred {\it pointer basis} is proposed. Predictably evolving states of
decohering systems along with the time-ordered sequences of records of their
evolution define the effectively classical branches of the universal
wavefunction in the context of the ``Many Worlds Interpretation". The relation
between the consistent histories approach and the preferred basis is
considered. It is demonstrated that histories of sequences of events
corresponding to projections onto the states of the pointer basis are
consistent.


title:
Metric-Affine Gauge Theory of Gravity: Field Equations, Noether
  Identities, World Spinors, and Breaking of Dilation Invariance

abstract:
  In Einstein's gravitational theory, the spacetime is Riemannian, that is, it
has vanishing torsion and vanishing nonmetricity (covariant derivative of the
metric). In the gauging of the general affine group ${A}(4,R)$ and of its
subgroup ${GL}(4,R)$ in four dimensions, energy--momentum and hypermomentum
currents of matter are canonically coupled to the one--form basis and to the
connection of a metric--affine spacetime with nonvanishing torsion and
nonmetricity, respectively. Fermionic matter can be described in this framework
by half--integer representations of the $\overline{SL}(4,R)$ covering subgroup.
--- We set up a (first--order) Lagrangian formalism and build up the
corresponding Noether machinery. For an arbitrary gauge Lagrangian, the three
gauge field equations come out in a suggestive Yang-Mills like form. The
conservation--type differential identities for energy--momentum and
hypermomentum and the corresponding complexes and superpotentials are derived.
Limiting cases such as the Einstein--Cartan theory are discussed. In particular
we show, how the ${A}(4,R)$ may ``break down'' to the Poincar\'e (inhomogeneous
Lorentz) group. In this context, we present explicit models for a symmetry
breakdown in the cases of the Weyl (or homothetic) group, the ${SL}(4,R)$, or
the ${GL}(4,R)$.


title: Multi-Black-Holes in Three Dimensions

abstract:
  We construct time-dependent multi-centre solutions to three-dimensional
general relativity with zero or negative cosmological constant. These solutions
correspond to dynamical systems of freely falling black holes and conical
singularities, with a multiply connected spacetime topology. Stationary
multi-black-hole solutions are possible only in the extreme black hole case.


title:
Gravitational Waves from Mergin Compact Binaries: How Accurately Can One
  Extract the Binary's Parameters from the Inspiral Waveform?

abstract:
  The most promising source of gravitational waves for the planned detectors
LIGO and VIRGO are merging compact binaries, i.e., neutron star/neutron star
(NS/NS), neutron star/black hole (NS/BH), and black hole/black-hole (BH/BH)
binaries. We investigate how accurately the distance to the source and the
masses and spins of the two bodies will be measured from the gravitational wave
signals by the three detector LIGO/VIRGO network using ``advanced detectors''
(those present a few years after initial operation). The combination ${\cal M}
\equiv (M_1 M_2)^{3/5}(M_1 +M_2)^{-1/5}$ of the masses of the two bodies is
measurable with an accuracy $\approx 0.1\%-1\%$. The reduced mass is measurable
to $\sim 10\%-15\%$ for NS/NS and NS/BH binaries, and $\sim 50\%$ for BH/BH
binaries (assuming $10M_\odot$ BH's). Measurements of the masses and spins are
strongly correlated; there is a combination of $\mu$ and the spin angular
momenta that is measured to within $\sim 1\%$. We also estimate that distance
measurement accuracies will be $\le 15\%$ for $\sim 8\%$ of the detected
signals, and $\le 30\%$ for $\sim 60\%$ of the signals, for the LIGO/VIRGO
3-detector network.


title:
Conformal Transformations of the Wigner Function and Solutions of the
  Quantum Corrected Vlasov Equation

abstract:
  We study conformal properties of the quantum kinetic equations in curved
spacetime. A transformation law for the covariant Wigner function under
conformal transformations of a spacetime is derived by using the formalism of
tangent bundles. The conformal invariance of the quantum corrected Vlasov
equation is proven. This provides a basis for generating new solutions of the
quantum kinetic equations in the presence of gravitational and other external
fields. We use our method to find explicit quantum corrections to the class of
locally isotropic distributions, to which equilibrium distributions belong. We
show that the quantum corrected stress--energy tensor for such distributions
has, in general, a non--equilibrium structure. Local thermal equilibrium is
possible in quantum systems only if an underlying spacetime is conformally
static (not stationary). Possible applications of our results are discussed.


title: Gravitating Solitons and Hairy Black Holes

abstract:
  A brief review of recent research on soliton and black hole solutions of
Einstein's equations with nonlinear field sources is presented and some open
questions are pointed out.


title: Critical Behavior of Black Hole Formation in a Scalar Wave Collapse

abstract:
  We present a self-similar model of spherically symmetric collapse of a
massless scalar field with a parameter $p$. The black hole formation is
explicitly shown to occur only in the strong-field implosion of $p >1$. The
field evolution in the critical limit $ p \rightarrow 1 $ is compared with
numerical results found by Choptuik.


title: Cosmological Histories for the New Variables

abstract:
  Histories and measures for quantum cosmology are investigated through a
quantization of the Bianchi IX cosmology using path integral techniques. The
result, derived in the context of Ashtekar variables, is compared with earlier
work. A non-trivial correction to the measure is found, which may dominate the
classical potential for universes on the Planck scale.


title: Observables for spacetimes with two Killing field symmetries

abstract:
  The Einstein equations for spacetimes with two commuting spacelike Killing
field symmetries are studied from a Hamiltonian point of view. The complexified
Ashtekar canonical variables are used, and the symmetry reduction is performed
directly in the Hamiltonian theory. The reduced system corresponds to the field
equations of the SL(2,R) chiral model with additional constraints.
  On the classical phase space, a method of obtaining an infinite number of
constants of the motion, or observables, is given. The procedure involves
writing the Hamiltonian evolution equations as a single `zero curvature'
equation, and then employing techniques used in the study of two dimensional
integrable models. Two infinite sets of observables are obtained explicitly as
functionals of the phase space variables. One set carries sl(2,R) Lie algebra
indices and forms an infinite dimensional Poisson algebra, while the other is
formed from traces of SL(2,R) holonomies that commute with one another. The
restriction of the (complex) observables to the Euclidean and Lorentzian
sectors is discussed.
  It is also shown that the sl(2,R) observables can be associated with a
solution generating technique which is linked to that given by Geroch.


title: Self-dual gravity and the chiral model

abstract:
  The self-dual Einstein equation (SDE) is shown to be equivalent to the two
dimensional chiral model, with gauge group chosen as the group of area
preserving diffeomorphisms of a two dimensional surface. The approach given
here leads to an analog of the Plebanski equations for general self-dual
metrics, and to a natural Hamiltonian formulation of the SDE, namely that of
the chiral model.


title: Exact solution for scalar field collapse

abstract:
  We give an exact spherically symmetric solution for the Einstein-scalar field
system. The solution may be interpreted as an inhomogeneous dynamical scalar
field cosmology. The spacetime has a timelike conformal Killing vector field
and is asymptotically conformally flat. It also has black or white hole-like
regions containing trapped surfaces. We describe the properties of the apparent
horizon and comment on the relevance of the solution to the recently discovered
critical behaviour in scalar field collapse.


title: Generality of Inflation in a Planar Universe

abstract:
  We study a generality of an inflationary scenario by integrating the Einstein
equations numerically in a plane-symmetric spacetime. We consider the
inhomogeneous spacetimes due to (i) localized gravitational waves with a
positive cosmological constant $\Lambda$, and (ii) an inhomogeneous inflaton
field $\Phi$ with a potential $\frac12 m^2 \Phi^2$. For the case (i), we find
that any initial inhomogeneities are smoothed out even if waves collide, so
that we conclude that inhomogeneity due to gravitational waves do not prevent
the onset of inflation. As for the case (ii), if the mean value of the inflaton
field is initially as large as the condition in an isotropic and homogeneous
inflationary model (i.e., the mean value is larger than several times Planck
mass), the field is soon homogenized and the universe always evolves into de
Sitter spacetime. These support the cosmic no hair conjecture in a planar
universe. We also discuss the effects of an additional massless scalar field,
which is introduced to set initial data in usual analysis.


title: Does scalar field collapse produce `zero mass' black holes?

abstract:
  An exact one parameter ($\alpha$) family of solutions representing scalar
field collapse is presented. These solutions exhibit a type of critical
behaviour which has been discussed by Choptuik. The three possible evolutions
are outlined. For supercritical evolution (when black holes form) I show that a
quantity related to the mass of the black hole exhibits a power law dependence
on $\alpha$, for near critical evolution $M \simeq |\alpha-\alpha_{\rm
crit}|^{1/2}$. Based on the properties of the solution some comments are also
made on conjectures of Choptuik.


title: Event horizons and apparent horizons in spherically symmetric geometries

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


title: Super-Minisuperspace and New Variables

abstract:
  We consider the specialization to spatially homogenous solutions of the
  Jacobson formulation of N=1 canonical supergravity in terms of Ashtekar's new
variables.
  We find that the classical Poisson algebra of the supersymmetry constraints
is preserved by this specialization only for Bianchi type A models. The
quantization of supersymmetric Bianchi type A models is carried out in the
triad representation. We find the physical states of this quantum theory. Since
we are missing a suitable inner product on these physical states, our results
are only formal.


title:
Decoherence produces coherent states: an explicit proof for harmonic
  chains

abstract:
  We study the behavior of infinite systems of coupled harmonic oscillators as
t->infinity, and generalize the Central Limit Theorem (CLT) to show that their
reduced Wigner distributions become Gaussian under quite general conditions.
This shows that generalized coherent states tend to be produced naturally. A
sufficient condition for this to happen is shown to be that the spectral
function is analytic and nonlinear. For a rectangular lattice of coupled
oscillators, the nonlinearity requirement means that waves must be dispersive,
so that localized wave-packets become suppressed. Virtually all harmonic
heat-bath models in the literature satisfy this constraint, and we have good
reason to believe that coherent states and their generalizations are not merely
a useful analytical tool, but that nature is indeed full of them. Standard
proofs of the CLT rely heavily on the fact that probability densities are
non-negative. Although the CLT generally fails if the probability densities are
allowed to take negative values, we show that a CLT does indeed hold for a
special class of such functions. We find that, intriguingly, nature has
arranged things so that all Wigner functions belong to this class.


title: Fractal basins and chaotic trajectories in multi-black hole space-times

abstract:
  We investigate the phase-space for trajectories in multi-black hole
spacetimes. We find that complete, chaotic geodesics are well described by
Lyapunov exponents, and that the attractor basin boundary scales as a fractal
in a diffeomorphism invariant manner.


title:
Hamiltonian quantization of General Relativity with the change of
  signature

abstract:
  We show in this article how the usual hamiltonian formalism of General
Relativity should be modified in order to allow the inclusion of the Euclidean
classical solutions of Einstein's equations. We study the effect that the
dynamical change of signature has on the superspace and we prove that it
induces a passage of the signature of the supermetric from ($-+++++$) to
($+-----$). Next, all these features are more particularly studied on the
example of minisuperspaces. Finally, we consider the problem of quantization of
the Euclidean solutions. The consequences of different choices of boundary
conditions are examined.


title: The Gauge Theory of the de-Sitter Group and Ashtekar Formulation

abstract:
  By adding the Pontrjagin topological invariant to the gauge theory of the de
Sitter group proposed by MacDowell and Mansouri we obtain an action quadratic
in the field-strengths, of the Chern-Simons type, from which the Ashtekar
formulation is derived.


title: The Boulware State and the Generalised Second Law of Thermodynamics

abstract:
  We show that the appropriate vacuum state for the interior of a box with
reflecting walls being lowered adiabatically into a Schwarzschild black hole is
the Boulware state. This is concordant with the results of Unruh and Wald, who
used a different approach to obtain the stress-energy inside the box. Some
comments about an entropy bound for ordinary matter, as first conjectured by
Bekenstein, are presented.


title: A SCHR\"Odinger Equation for Mini Universes

abstract:
  We discuss how to fix the gauge in the canonical treatment of Lagrangians,
with finite number of degrees of freedom, endowed with time reparametrization
invariance. The motion can then be described by an effective Hamiltonian acting
on the gauge shell canonical space. The system is then suited for quantization.
We apply this treatment to the case of a Robertson--Walker metric interacting
with zero modes of bosonic fields and write a \S equation for the on--shell
wave function.


title: "No Hair" Theorems -- Folklore, Conjectures, Results

abstract:
  Various assumptions underlying the uniqueness theorems for black holes are
discussed. Some new results are described, and various unsatisfactory features
of the present theory are stressed.


title: Conformally Invariant Cosmology Based on Riemann-Cartan Spacetime

abstract:
  Conformally invariant GUT-like model including gravity based on Riemann -
Cartan space-time $U_4$ is considered. Cosmological scenario that follows from
the model is discussed and standard quantum gravitational formalism in the
Arnowitt-Deser-Misner form is developed. General formalism is then illustrated
on Bianchi-IX minisuperspace cosmological model. Wave functions of the universe
in the de Sitter minisuperspace model with Vilenkin and Hartle-Hawking boundary
conditions are considered and corresponding probability distributions for the
scalar field values are calculated.


title:
Is the Exponential of the Chern-Simons Action a Normalizable Physical
  State?

abstract:
  We determine the wavefunction that corresponds to the exponential of the
Chern-Simons action in a family of gravitational models provided with
cosmological constant whose non-perturbative canonical quantization is
completely known. We show that this wavefunction does not represent a proper
quantum state, because it is not normalizable with respect to the unique inner
product of Lorentzian gravity.


title: Dimension on Discrete Spaces

abstract:
  In this paper we develop some combinatorial models for continuous spaces. In
this spirit we study the approximations of continuous spaces by graphs,
molecular spaces and coordinate matrices. We define the dimension on a discrete
space by means of axioms, and the axioms are based on an obvious geometrical
background. This work presents some discrete models of n-dimensional Euclidean
spaces, n-dimensional spheres, a torus and a projective plane. It explains how
to construct new discrete spaces and describes in this connection several
three-dimensional closed surfaces with some topological singularities
  It also analyzes the topology of (3+1)-spacetime. We are also discussing the
question by R. Sorkin [19] about how to derive the system of simplicial
complexes from a system of open covering of a topological space S.


title: Arrow of time in a recollapsing quantum universe

abstract:
  We show that the Wheeler-DeWitt equation with a consistent boundary condition
is only compatible with an arrow of time that formally reverses in a
recollapsing universe. Consistency of these opposite arrows is facilitated by
quantum effects in the region of the classical turning point. Since
gravitational time dilation diverges at horizons, collapsing matter must then
start re-expanding ``anticausally" (controlled by the reversed arrow) before
horizons or singularities can form. We also discuss the meaning of the
time-asymmetric expression used in the definition of ``consistent histories".
We finally emphasize that there is no mass inflation nor any information loss
paradox in this scenario.


title: Horizon Operator Approach to Black Hole Quantization

abstract:
  The $S$-matrix Ansatz for the construction of a quantum theory of black holes
is further exploited. We first note that treating the metric tensor $g_{\m\n}$
as an operator rather than a background allows us to use a setting where
information is not lost. But then we also observe that the 'trans-Planckian'
particles (particles with kinetic energies beyond the Planck energy) need to be
addressed. It is now postulated that they can be transformed into
'cis-Planckian particles' (having energies less that the Planck energy). This
requires the existence of a delicate algebra of operators defined at a black
hole horizon. Operators describing ingoing particles are mapped onto operators
describing outgoing ones, preserving their commutator algebra. At short
distance, the transverse gravitational back reaction dictates a discrete
lattice of data points, and at large distance the algebra must reproduce known
interactions of the Standard Model of elementary particles. It is suggested
that further elaboration of these ideas requiring complete agreement with
general relativity and unitarity should lead to severe restrictions concerning
the inter-particle interactions.


title: A Gravitational Lens need not produce an Odd Number of Images

abstract:
  Given any space-time $M$ without singularities and any event $O$, there is a
natural continuous mapping $f$ of a two dimensional sphere into any space-like
slice $T$ not containing $O$. The set of future null geodesics (or the set of
past null geodesics) forms a 2-sphere $S^2$ and the map $f$ sends a point in
$S^2$ to the point in $T$ which is the intersection of the corresponding
geodesic with $T$. To require that $f$, which maps a two dimensional space into
a three dimensional space, satisfy the condition that any point in the image of
$f$ has an odd number of preimages, is to place a very strong condition on $f$.
This is exactly what happens in any case where the odd image theorem holds for
a transparent gravitational lens. It is argued here that this condition on $f$
is probably too restrictive to occur in general; and if it appears to hold in a
specific example, then some $f$ should be calculated either analytically or
numerically to provide either an illustrative example or counterexample.


title: Colliding Black Holes: The Close Limit

abstract:
  The problem of the mutual attraction and joining of two black holes is of
importance as both a source of gravitational waves and as a testbed of
numerical relativity. If the holes start out close enough that they are
initially surrounded by a common horizon, the problem can be viewed as a
perturbation of a single black hole. We take initial data due to Misner for
close black holes, apply perturbation theory and evolve the data with the
Zerilli equation. The computed gravitational radiation agrees with and extends
the results of full numerical computations.


title: Evolution of Topological Defects During Inflation

abstract:
  Topological defects can be formed during inflation by phase transitions as
well as by quantum nucleation. We study the effect of the expansion of the
Universe on the internal structure of the defects. We look for stationary
solutions to the field equations, i.e. solutions that depend only on the proper
distance from the defect core. In the case of very thin defects, whose core
dimensions are much smaller than the de Sitter horizon, we find that the
solutions are well approximated by the flat space solutions. However, as the
flat space thickness parameter $\delta_0$ increases we notice a deviation from
this, an effect that becomes dramatic as $\delta_0$ approaches $(H)^{-1}/{\sqrt
2}$. Beyond this critical value we find no stationary solutions to the field
equations. We conclude that only defects that have flat space thicknesses less
than the critical value survive, while thicker defects are smeared out by the
expansion.


title:
Observation of critical phenomena and self-similarity in the
  gravitational collapse of radiation fluid

abstract:
  We observe critical phenomena in spherical collapse of radiation fluid. A
sequence of spacetimes $\cal{S}[\eta]$ is numerically computed, containing
models ($\eta\ll 1$) that adiabatically disperse and models ($\eta\gg 1$) that
form a black hole. Near the critical point ($\eta_c$), evolutions develop a
self-similar region within which collapse is balanced by a strong,
inward-moving rarefaction wave that holds $m(r)/r$ constant as a function of a
self-similar coordinate $\xi$. The self-similar solution is known and we show
near-critical evolutions asymptotically approaching it. A critical exponent
$\beta \simeq 0.36$ is found for supercritical ($\eta>\eta_c$) models.


title: Post-Newtonian Expansion of the Ingoing-Wave Regge-Wheeler Function

abstract:
  We present a method of post-Newtonian expansion to solve the homogeneous
Regge-Wheeler equation which describes gravitational waves on the Schwarzschild
spacetime. The advantage of our method is that it allows a systematic iterative
analysis of the solution. Then we obtain the Regge-Wheeler function which is
purely ingoing at the horizon in closed analytic form, with accuracy required
to determine the gravitational wave luminosity to (post)$^{4}$-Newtonian order
(i.e., order $v^8$ beyond Newtonian) from a particle orbiting around a
Schwarzschild black hole. Our result, valid in the small-mass limit of one
body, gives an important guideline for the study of coalescing compact
binaries. In particular, it provides basic formulas to analytically calculate
detailed waveforms and luminosity, including the tail terms to
(post)$^3$-Newtonian order, which should be reproduced in any other
post-Newtonian calculations.


title: No Quantum Super-Minisuperspace with $\Lambda \ne 0$

abstract:
  We show that the quantum super-minisuperspace of N=1 supergravity with
$\Lambda \ne 0 $ has no non-trivial physical states for class A Bianchi models.
Hence, in super quantum cosmology, the vanishing of $\Lambda$ is a condition
for the existence of the universe. We argue that this result implies that in
full supergravity with $\Lambda$ there are no non-trivial physical states with
a finite number of fermionic fields. We use the Jacobson canonical formulation.


title: Axisymmetric Stationary Solutions as Harmonic Maps

abstract:
  We present a method for generating exact solutions of Einstein equations in
vacuum using harmonic maps, when the spacetime possesses two commutating
Killing vectors. This method consists in writing the axisymmetric stationry
Einstein equations in vacuum as a harmonic map which belongs to the group
SL(2,R), and decomposing it in its harmonic "submaps". This method provides a
natural classification of the solutions in classes (Weil's class, Lewis' class
etc).


title: Instability of Gravitating Sphalerons

abstract:
  We prove the instability of the gravitating regular sphaleron solutions of
the $SU(2)$ Einstein-Yang-Mills-Higgs system with a Higgs doublet, by studying
the frequency spectrum of a class of radial perturbations. With the help of a
variational principle we show that there exist always unstable modes. Our
method has the advantage that no detailed knowledge of the equilibrium solution
is required. It does, however, not directly apply to black holes.


title: Adjointness Relations as a Criterion for Choosing an Inner Product

abstract:
  This is a contribution to the forthcoming book "Canonical Gravity: {}From
Classical to Quantum" edited by J. Ehlers and H. Friedrich. Ashtekar's
criterion for choosing an inner product in the quantisation of constrained
systems is discussed. An erroneous claim in a previous paper is corrected and a
cautionary example is presented.


title: Gravity and Yang-Mills Theory: Two Faces of the Same Theory?

abstract:
  We introduce a gauge and diffeomorphism invariant theory on the Yang-Mills
phase space. The theory is well defined for an arbitrary gauge group with an
invariant bilinear form, it contains only first class constraints, and the
spacetime metric has a simple form in terms of the phase space variables. With
gauge group $SO(3,C)$, the theory equals the Ashtekar formulation of gravity
with a cosmological constant. For Lorentzian signature, the theory is complex,
and we have not found any good reality conditions. In the Euclidean signature
case, everything is real. In a weak field expansion around de Sitter spacetime,
the theory is shown to give the conventional Yang-Mills theory to the lowest
order in the fields. We show that the coupling to a Higgs scalar is
straightforward, while the naive spinor coupling does not work. We have not
found any way of including spinors that gives a closed constraint algebra. For
gauge group $U(2)$, we find a static and spherically symmetric solution.


title: Geometrodynamics of Schwarzschild Black Holes

abstract:
  The curvature coordinates $T,R$ of a Schwarz\-schild spacetime are turned
into canonical coordinates $T(r), {\sf R}(r)$ on the phase space of spherically
symmetric black holes. The entire dynamical content of the Hamiltonian theory
is reduced to the constraints requiring that the momenta $P_{T}(r), P_{\sf
R}(r)$ vanish. What remains is a conjugate pair of canonical variables $m$ and
$p$ whose values are the same on every embedding. The coordinate $m$ is the
Schwarzschild mass, and the momentum $p$ the difference of parametrization
times at right and left infinities. The Dirac constraint quantization in the
new representation leads to the state functional $\Psi (m; T, {\sf R}] = \Psi
(m)$ which describes an unchanging superposition of black holes with different
masses. The new canonical variables may be employed in the study of collapsing
matter systems.


title: The Impossibility of Steady-State Inflation

abstract:
  Inflation is known to be generically eternal to the future: the false vacuum
is thermalized in some regions of space, while inflation continues in other
regions. Here, we address the question of whether inflation can also be eternal
to the past. We argue that such a steady-state picture is impossible and,
therefore, that inflation must have had a beginning. First, it is shown that
the old inflationary model is not past-eternal. Next, some necessary conditions
are formulated for inflationary spacetimes to be past-eternal and
future-eternal. It is then shown that these conditions cannot simultaneously
hold in physically reasonable open universes.


title: A Spinor Model for Quantum Cosmology

abstract:
  The question of the interpretation of Wheeler-DeWitt solutions in the context
of cosmological models is addressed by implementing the Hamiltonian constraint
as a spinor wave equation in minisuperspace. We offer a relative probability
interpretation based on a non-closed vector current in this space and a
prescription for a parametrisation of classical solutions in terms of classical
time. Such a prescription can accommodate classically degenerate metrics
describing manifolds with signature change. The relative probability density,
defined in terms of a Killing vector of the Dewitt metric on minisuperspace,
should permit one to identify classical loci corresponding to geometries for a
classical manifold. This interpretation is illustrated in the context of a
quantum cosmology model for two-dimensional dilaton gravity.


title:
On the Relation between Classical and Quantum Cosmology in a
  2-Dimensional Dilaton-Gravity Model

abstract:
  We analyse the classical and quantum theory of a scalar field interacting
with gravitation in two dimensions. We describe a class of analytic solutions
to the Wheeler-DeWitt equation from which we are able to synthesise states that
give prominence to a set of classical cosmologies. These states relate in a
remarkable way to the general solution of the classical field equations. We
express these relations, without approximation, in terms of a metric and a
closed form on the domain of quantum states.


title: Theory of Local Times II. Another formulation and examples

abstract:
  The model of a stationary universe and the notion of local times presented in
[10] are reviewed with some alternative formulation of the consistent
unification of the Riemannian and Euclidean geometries of general relativity
and quantum mechanics. The method of unification adopted in the present paper
is by constructing a vector bundle $X\times R^6$ or $X\times R^4$ with $X$
being the observer's reference frame and $R^6$ or $R^4$ being the unobservable
inner space(-time) within each observer's local system. Some applications of
our theory to two concrete examples of human size and of cosmological size are
discussed, as well as the uncertainty of time in our context is calculated.


title: Quantum gravity and minimum length

abstract:
  The existence of a fundamental scale, a lower bound to any output of a
position measurement, seems to be a model-independent feature of quantum
gravity. In fact, different approaches to this theory lead to this result. The
key ingredients for the appearance of this minimum length are quantum
mechanics, special relativity and general relativity. As a consequence,
classical notions such as causality or distance between events cannot be
expected to be applicable at this scale. They must be replaced by some other,
yet unknown, structure.


title: The isolation of gravitational instantons: Flat tori V flat R^4

abstract:
  The role of topology in the perturbative solution of the Euclidean Einstein
equations about flat instantons is examined.


title: Approaches to Quantum Cosmology

abstract:
  Different proposals for the wave function of the universe are analyzed, with
an emphasis on various forms of the tunneling proposal. The issues discussed
include the equivalence of the Lorentzian path integral and outgoing-wave
proposals, the definitions of the outgoing waves and of superspace boundaries,
topology change and the corresponding modification of the Wheeler-DeWitt
equation. Also discussed are the "generic" boundary conditions and the third
quantization approach.


title: Dynamics of Apparent and Event Horizons

abstract:
  The dynamics of apparent and event horizons of various black hole spacetimes,
including those containing distorted, rotating and colliding black holes, are
studied. We have developed a powerful and efficient new method for locating the
event horizon, making possible the study of both types of horizons in numerical
relativity. We show that both the event and apparent horizons, in all dynamical
black hole spacetimes studied, oscillate with the quasinormal frequency.


title: The Gauss Map and 2+1 Gravity

abstract:
  We prove that the Gauss map of a surface of constant mean curvature embedded
in Minkowski space is harmonic. This fact will then be used to study 2+1
gravity for surfaces of genus higher than one. By considering the energy of the
Gauss map, a canonical transform between the ADM reduced variables and holonomy
variables can be constructed. This allows one to solve (in principle) for the
evolution in the ADM variables without having to explicitly solve the
constraints first.


title: A Non-singular Theory of Gravity

abstract:
  We present a geometrical gravitational theory which reduces to Einstein's
theory for weak gravitational potentials and which has a singularity-free
analog of the Schwarzschild metric.


title:
Minimal Closed Set of Observables in the Theory of Cosmological
  Perturbations

abstract:
  The theory of perturbation of Friedman-Robertson-Walker (FRW) cosmology is
analysed exclusively in terms of observable quantities. Although this can be a
very complete and general procedure we limit our presentation here to the case
of irrotational perturbations for simplicity. We show that the electric part of
Weyl conformal tensor {\bf $E$} and the shear {\bf $\Sigma$} constitute the two
basic perturbed variables in terms of which all remaining observable quantities
can be described. Einstein\rq s equations of General Relativity reduce to a
closed set of dynamical system for {\bf $E$} and {\bf $\Sigma$}. The basis for
a gauge-invariant Hamiltonian treatment of the Perturbation Theory in the FRW
background is then set up.


title:
Particle creation in a colliding plane wave spacetime: wave packet
  quantization

abstract:
  We use wave packet mode quantization to compute the creation of massless
scalar quantum particles in a colliding plane wave spacetime. The background
spacetime represents the collision of two gravitational shock waves followed by
trailing gravitational radiation which focus into a Killing-Cauchy horizon. The
use of wave packet modes simplifies the problem of mode propagation through the
different spacetime regions which was previously studied with the use of
monocromatic modes. It is found that the number of particles created in a given
wave packet mode has a thermal spectrum with a temperature which is inversely
proportional to the focusing time of the plane waves and which depends on the
mode trajectory.


title:
Discrete Self-Similiarity and Critical Point Behavior in Fluctuations
  About Extremal Black Holes

abstract:
  The issues of scaling symmetry and critical point behavior are studied for
fluctuations about extremal charged black holes. We consider the scattering and
capture of the spherically symmetric mode of a charged, massive test field on
the background spacetime of a black hole with charge $Q$ and mass $M$. The
spacetime geometry near the horizon of a $|Q|=M$ black hole has a scaling
symmetry, which is absent if $|Q|<M$, a scale being introduced by the surface
gravity. We show that this symmetry leads to the existence of a self-similiar
solution for the charged field near the horizon, and further, that there is a
one parameter family of discretely self-similiar solutions . The scaling
symmetry, or lack thereof, also shows up in correlation length scales, defined
in terms of the rate at which the influence of an external source coupled to
the field dies off. It is shown by constructing the Greens functions, that an
external source has a long range influence on the extremal background, compared
to a correlation length scale which falls off exponentially fast in the $|Q|<M$
case. Finally it is shown that in the limit of $\Delta \equiv (1-{Q^2 \overM^2}
)^{1\over 2} \rightarrow 0$ in the background spacetime, that infinitesimal
changes in the black hole area vary like $\Delta ^{1\over 2}$.


title: Collapse of Kaluza-Klein Bubbles

abstract:
  Kaluza-Klein theory admits ``bubble" configurations, in which the
circumference of the fifth dimension shrinks to zero on some compact surface. A
three parameter family of such bubble initial data at a moment of time-symmetry
(some including a magnetic field) has been found by Brill and Horowitz,
generalizing the (zero-energy) ``Witten bubble" solution. Some of these data
have negative total energy. We show here that all the negative energy bubble
solutions start out expanding away from the moment of time symmetry, while the
positive energy bubbles can start out either expanding or contracting. Thus it
is unlikely that the negative energy bubbles would collapse and produce a naked
singularity.


title: Is the gravitational action additive?

abstract:
  The gravitational action is not always additive in the usual sense. We
provide a general prescription for the change in action that results when
different portions of the boundary of a spacetime are topologically identified.
We discuss possible implications for the superposition law of quantum gravity.
We present a definition of `generalized additivity' which does hold for
arbitrary spacetime composition.


title: Structure of the Inner Singularity of a Spherical Black Hole

abstract:
  We review the evidence for and against the possibility that the inner
singularity of a black hole contains a lightlike segment which is locally mild
and characterized by mass inflation.


title: Time (a-)symmetry in a recollapsing quantum universe

abstract:
  It is argued that Hawking's `greatest mistake' may not have been a mistake at
all. According to the canonical quantum theory of gravity for Friedmann type
universes, any time arrows of general nature can only be correlated with that
of the expansion. For recollapsing universes this seems to be facilitated in
part by quantum effects close to their maximum size. Because of the resulting
thermodynamical symmetry between expansion and (formal) collapse, black holes
must formally become `white' during the collapse phase (while physically only
expansion of the universe and black holes can be observed). It is conjectured
that the quantum universe remains completely singularity-free in this way
(except for the homogeneous singularity) if an appropriate boundary condition
for the wave function is able to exclude {\it past} singularities (as is often
assumed).


title: Observing Binary Inspiral with LIGO

abstract:
  Gravitational radiation from a binary neutron star or black hole system leads
to orbital decay and the eventual coalescence of the binary's components.
During the last several minutes before the binary components coalesce, the
radiation will enter the bandwidth of the United States Laser Inteferometer
Gravitational-wave Observatory (LIGO) and the French/Italian VIRGO
gravitational radiation detector. The combination of detector sensitivity,
signal strength, and source density and distribution all point to binary
inspiral as the most likely candidate for observation among all the anticipated
sources of gravitational radiation for LIGO/VIRGO. Here I review briefly some
of the questions that are posed to theorists by the impending observation of
binary inspiral.


title: Geodesic Motion in the 5D Magnetized Schwarzschild-Like Solutions

abstract:
  Geodesics for a 5D magnetized Schwarzschild-like solution are analyzed by
reducing the problem to the motion of a test particle in an effective
potential. In absence of magnetic field comparison is established with
Schwarzschild's geometry. Embedding diagrams are constructed in order to
visualize the geometry of the metric. The study performed here is also valid,
when the electromagnetic interactions are neglected, for the low energy
superstring theory and the Brans-Dicke theory.


title:
A test of a kind of the equivalence principle by long-baseline
  neutrino-oscillation experiments

abstract:
  Possible breakdown of the universality of the gravitational couplings to
different neutrino flavors can be tested in long-baseline neutrino-oscillation
experiments, such as a proposed experiment at SOUDAN 2 or one at the DUMAND
project. Such a breakdown could be detected with sensitivity to the order of
$10^{-14}$ or $10^{-15}$. For generic case of neutrino oscillations, it is
emphasized that one can identify the spin of the particle which mediates the
force causing the oscillation, by investigating the energy spectrum of the
outgoing charged leptons. (based on talk presented at the Workshop on General
Relativity and Gravitation held at Univ. of Tokyo, January 17-20, 1994)


title: Large Squeezing Behavior of Cosmological Entropy Generation

abstract:
  We consider the generation of entropy when particle pairs are created at a
cosmological level. Making a reduction via the particle number basis, we
compute the classical limit for the entropy generation due to the evolution of
the matter field fluctuations (squeeze transformation), obtaining that it is
linear in the squeeze parameter for a general class of initial states. We also
discuss the dependence of the generated entropy on the coarse graining
criteria.


title: Lensing Properties of Lightlike Current Carrying Cosmic Strings

abstract:
  The lensing properties of superconducting cosmic strings endowed with a time
dependent pulse of lightlike current are investigated. The metric outside the
core of the string belongs to the $pp$--wave class, with a deficit angle. We
study the field theoretic bosonic Witten model coupled to gravity, and we show
that the full metric (both outside and inside the core) is a Taub-Kerr-Shild
generalization of that for the static string with no current. It is shown that
the double image due to the deficit angle evolves in an unambiguous way as a
pulse of lightlike current passes between the source and the observer.
Observational consequences of this signature of the existence of cosmic strings
are briefly discussed.


title: Some Spinor-Curvature Identities

abstract:
  We describe a class of spinor-curvature identities which exist for Riemannian
or Riemann-Cartan geometries. Each identity relates an expression quadratic in
the covariant derivative of a spinor field with an expression linear in the
curvature plus an exact differential. Certain special cases in 3 and 4
dimensions which have been or could be used in applications to General
Relativity are noted.


title: Thermodynamics and Evaporation of the 2+1-D Black Hole

abstract:
  The properties of canonical and microcanonical ensembles of a black hole with
thermal radiation and the problem of black hole evaporation in 3-D are studied.
In 3-D Einstein-anti-de Sitter gravity we have two relevant mass scales,
$m_c=1/G$, and $m_p=(\hbar^2\Lambda/G)^{1/3}$, which are particularly relevant
for the evaporation problem. It is argued that in the `weak coupling' regime
$\Lambda<(\hbar G)^{-2}$, the end point of an evaporating black hole formed
with an initial mass $m_0>m_p$, is likely to be a stable remnant in equilibrium
with thermal radiation. The relevance of these results for the information
problem and for the issue of back reaction is discussed. In the `strong
coupling' regime, $\Lambda>(\hbar G)^{-2}$ a full fledged quantum gravity
treatment is required. Since the total energy of thermal states in anti-de
Sitter space with reflective boundary conditions at spatial infinity is bounded
and conserved, the canonical and microcanonical ensembles are well defined. For
a given temperature or energy black hole states are locally stable. In the weak
coupling regime black hole states are more probable then pure radiation states.


title:
Some Properties of Noether Charge and a Proposal for Dynamical Black
  Hole Entropy

abstract:
  We consider a general, classical theory of gravity with arbitrary matter
fields in $n$ dimensions, arising from a diffeomorphism invariant Lagrangian,
$\bL$. We first show that $\bL$ always can be written in a ``manifestly
covariant" form. We then show that the symplectic potential current
$(n-1)$-form, $\th$, and the symplectic current $(n-1)$-form, $\om$, for the
theory always can be globally defined in a covariant manner. Associated with
any infinitesimal diffeomorphism is a Noether current $(n-1)$-form, $\bJ$, and
corresponding Noether charge $(n-2)$-form, $\bQ$. We derive a general
``decomposition formula" for $\bQ$. Using this formula for the Noether charge,
we prove that the first law of black hole mechanics holds for arbitrary
perturbations of a stationary black hole. (For higher derivative theories,
previous arguments had established this law only for stationary perturbations.)
Finally, we propose a local, geometrical prescription for the entropy,
$S_{dyn}$, of a dynamical black hole. This prescription agrees with the Noether
charge formula for stationary black holes and their perturbations, and is
independent of all ambiguities associated with the choices of $\bL$, $\th$, and
$\bQ$. However, the issue of whether this dynamical entropy in general obeys a
``second law" of black hole mechanics remains open. In an appendix, we apply
some of our results to theories with a nondynamical metric and also briefly
develop the theory of stress-energy pseudotensors.


title: A Periodic Analog of the Schwarzschild Solution

abstract:
  We construct a new exact solution of Einstein's equations in vacuo in terms
of Weyl canonical coordinates. This solution may be interpreted as a black hole
in a space-time which is periodic in one direction and which behaves
asymptotically like the Kasner solution with Kasner index equal to $4M L^{-1}$,
where $L$ is the period and $M$ is the mass of the black hole. Outside the
horizon, the solution is free of singularities and approaches the Schwarzschild
solution as $L \rightarrow \infty$.


title: Chaos and Quantum Chaos in Cosmological Models

abstract:
  Spatially homogeneous cosmological models reduce to Hamiltonian systems in a
low dimensional Minkowskian space moving on the total energy shell $H=0$. Close
to the initial singularity some models (those of Bianchi type VIII and IX) can
be reduced further, in a certain approximation, to a non-compact triangular
billiard on a 2-dimensional space of constant negative curvature with a
separately conserved positive kinetic energy. This type of billiard has long
been known as a prototype chaotic dynamical system. These facts are reviewed
here together with some recent results on the energy level statistics of the
quantized billiard and with direct explicit semi-classical solutions of the
Hamiltonian cosmological model to which the billiard is an approximation. In
the case of Bianchi type IX models the latter solutions correspond to the
special boundary conditions of a `no-boundary state' as proposed by Hartle and
Hawking and of a `wormhole' state.


title: Dilaton Production in String Cosmology

abstract:
  We consider the coupled evolution of density, (scalar) metric and dilaton
perturbations in the transition from a ``stringy" phase of growing curvature
and gravitational coupling to the standard radiation-dominated cosmology. We
show that dilaton production, with a spectrum tilted towards large frequencies,
emerges as a general property of this scenario. We discuss the
frame-independence of the dilaton spectrum and of the inflationary properties
of the metric background by using, as model of source, a pressureless gas of
weakly interacting strings, which is shown to provide an approximate but
consistent solution to the full system of background equations and string
equations of motion. We combine various cosmological bounds on a growing
dilaton spectrum with the bound on the dilaton mass obtained from tests of the
equivalence principle, and we find allowed windows compatible with a universe
presently dominated by a relic background of dilatonic dark matter.


title: Kinetic vs. Thermal-Field-Theory Approach to Cosmological Perturbations

abstract:
  A closed set of equations for the evolution of linear perturbations of
homogeneous, isotropic cosmological models can be obtained in various ways. The
simplest approach is to assume a macroscopic equation of state, e.g.\ that of a
perfect fluid. For a more refined description of the early universe, a
microscopic treatment is required. The purpose of this paper is to compare the
approach based on classical kinetic theory to the more recent
thermal-field-theory approach. It is shown that in the high-temperature limit
the latter describes cosmological perturbations supported by collisionless,
massless matter, wherein it is equivalent to the kinetic theory approach. The
dependence of the perturbations in a system of a collisionless gas and a
perfect fluid on the initial data is discussed in some detail. All singular and
regular solutions are found analytically.


title:
Gravitational Waves from Inspiralling Compact Binaries: A Post-Newtonian
  Approach

abstract:
  Inspiralling binary systems of neutron stars or black holes are promising
sources of gravitational radiation detectable by large-scale laser
interferometric gravitational observatories, such as the US LIGO and
Italian-French VIRGO projects. Accurate theoretical gravitational-waveform
templates will be needed to carry out matched filtering data analysis of the
detectors' output once they are on the air by the end of this decade. For all
but the final, strongly general relativistic coalescence of the two bodies,
high-order post-Newtonian methods are playing a major role in the theorists'
efforts to develop the needed templates. This paper discusses the foundations
of this method, and provides a compendium of useful formulae and results.
Figures available upon request. (Invited talk given at the 8th
Nishinomiya-Yukawa Memorial Symposium, October 28, 1993.)


title: About Loop States in Supergravity

abstract:
  The Wilson loop functionals in terms of Ashtekar's variables were the first
(formal) solutions to the quantized hamiltonian constraint of canonical
gravity. Here it is shown that the same functionals also solve the supergravity
constraints and some evidence is presented that they are artificially generated
by multiplying the constraints by the metric determinant, which has become a
widely accepted procedure. Using the same method in 2+1 dimensional gravity and
supergravity leads to wrong results, e.g.~2+1 gravity is no longer a purely
topological theory. As another feature of the densitized constraints it turns
out that the classical theory desribed by them is not invariant under space
time diffeomorphisms.


title:
Covariant algebraic calculation of the one-loop effective potential in
  non-Abelian gauge theory and a new approach to stability problem

abstract:
  We use our recently proposed algebraic approach for calculating the heat
kernel associated with the Laplace operator to calculate the one-loop effective
action in the non-Abelian gauge theory. We consider the most general case of
arbitrary space-time dimension, arbitrary compact simple gauge group and
arbitrary matter and assume a covariantly constant gauge field strength of the
most general form, having many independent color and space-time invariants
(Savvidy type chromomagnetic vacuum) and covariantly constant scalar fields as
a background. The explicit formulas for all the needed heat kernels and
zeta-functions are obtained. We propose a new method to study the vacuum
stability and show that the background field configurations with covariantly
constant chromomagnetic fields can be stable only in the case when more than
one independent field invariants are present and the values of these invariants
differ not greatly from each other. The role of space-time dimension is
analyzed in this connection and it is shown that this is possible only in
space-times with dimensions not less than five $d\geq 5$.


title:
Covariant methods for calculating the low-energy effective action in
  quantum field theory and quantum gravity

abstract:
  We continue the development of the effective covariant methods for
calculating the heat kernel and the one-loop effective action in quantum field
theory and quantum gravity. The status of the low-energy approximation in
quantum gauge theories and quantum gravity is discussed in detail on the basis
of analyzing the local Schwinger - De Witt expansion. It is argued that the
low-energy limit, when defined in a covariant way, should be related to
background fields with covariantly constant curvature, gauge field strength and
potential. Some new approaches for calculating the low-energy heat kernel
assuming a covariantly constant background are proposed. The one-loop
low-energy effective action in Yang-Mills theory in flat space with arbitrary
compact simple gauge group and arbitrary matter on a covariantly constant
background is calculated. The stability problem of the chromomagnetic
(Savvidy-type) vacuum is analyzed. It is shown, that this type of vacuum
structure can be stable only in the case when more than one background
chromomagnetic fields are present and the values of these fields differ not
greatly from each other.This is possible only in space-times of dimension not
less than five $d\geq 5$.


title: Radiation Field on Superspace

abstract:
  We study the dynamics of multiwormhole configurations within the framework of
the Euclidean Polyakov approach to string theory, incorporating a modification
to the Hamiltonian which makes it impossible to interpret the Coleman Alpha
parameters of the effective interactions as a quantum field on superspace,
reducible to an infinite tower of fields on space-time. We obtain a Planckian
probability measure for the Alphas that allows $\frac{1}{2}\alpha^{2}$ to be
interpreted as the energy of the quanta of a radiation field on superspace
whose values may still fix the coupling constants.


title: Overview and Outlook

abstract:
  This report is based on the talk given by the author in the concluding
session of the workshop on Canonical Methods in Classical and Quantum General
Relativity, held a Bad-Honef, Germany, in September 93. It contains an
assessment of the canonical approach in general, an overview of recent
developments within the canonical approach based on connections and loops, and
some suggestions for future work.


title: Quasilocal energy conditions

abstract:
  The classical value of the Hamiltonian for a system with timelike boundary
has been interpreted as a quasilocal energy. This quasilocal energy is not
positive definite. However, we derive a `quasilocal dominant energy condition'
which is the natural consequence of the local dominant energy condition. We
discuss some implications of this quasilocal energy condition. In particular,
we find that it implies a `quasilocal weak energy condition'.


title: A Connection Approach to Numerical Relativity

abstract:
  We discuss a general formalism for numerically evolving initial data in
general relativity in which the (complex) Ashtekar connection and the
Newman-Penrose scalars are taken as the dynamical variables. In the generic
case three gauge constraints and twelve reality conditions must be solved. The
analysis is applied to a Petrov type \{1111\} planar spacetime where we find a
spatially constant volume element to be an appropriate coordinate gauge choice.


title: Global structure of Witten's 2+1 gravity on ${\bf R}\times T^2$

abstract:
  We investigate the space ${\cal M}$ of classical solutions to Witten's
formulation of 2+1 gravity on the manifold ${\bf R} \times T^2$. ${\cal M}$ is
connected, but neither Hausdorff nor a manifold. However, removing from ${\cal
M}$ a set of measure zero yields a connected manifold which is naturally viewed
as the cotangent bundle over a non-Hausdorff base space. Avenues towards
quantizing the theory are discussed in view of the relation between spacetime
metrics and the various parts of~${\cal M}$. (Contribution to the proceedings
of the Lanczos Centenary Conference, Raleigh, NC, December 12--17, 1993.)


title: Integration on the space of Connections Modulo Gauge Transformations

abstract:
  A summary of the known results on integration theory on the space of
connections modulo gauge transformations is presented and its significance to
quantum theories of gauge fields and gravity is discussed. The emphasis is on
the underlying ideas rather than the technical subtleties.


title: Backreaction in Semiclassical Cosmolgy: The Einstein Langevin Equation

abstract:
  Using the influence functional formalism we show how to derive a generalized
Einstein equation in the form of a Langevin equation for the description of the
backreaction of quantum fields and their fluctuations on the dynamics of curved
spacetimes. We show how a functional expansion on the influence functional
gives the cumulants of the stochastic source, and how these cumulants enter in
the equations of motion as noise sources. We derive an expression for the
influence functional in terms of the Bogolubov coefficients governing the
creation and annihilation operators of the Fock spaces at different times, thus
relating it to the difference in particle creation in different histories. We
then apply this to the case of a free quantum scalar field in a spatially flat
Friedmann- Robertson-Walker universe and derive the Einstein-Langevin equations
for the scale factor for these semiclassical cosmologies. This approach based
on statistical field theory extends the conventional theory of semiclassical
gravity based on a semiclassical Einstein equation with a source given by the
average value of the energy momentum tensor, thus making it possible to probe
into the statistical properties of quantum fields like noise, fluctuations,
entropy, decoherence and dissipation. Recognition of the stochastic nature of
semiclassical gravity is an essential step towards the investigation of the
behavior of fluctuations, instability and phase transition processes associated
with the crossover to quantum gravity.


title: Fermi Coordinates for Weak Gravitational Fields

abstract:
  A Reference is corrected. (We derive the Fermi coordinate system of an
observer in arbitrary motion in an arbitrary weak gravitational field valid to
all orders in the geodesic distance from the worldline of the observer. In flat
space-time this leads to a generalization of Rindler space for arbitrary
acceleration and rotation. The general approach is applied to the special case
of an observer resting with respect to the weak gravitational field of a static
mass distribution. This allows to make the correspondence between general
relativity and Newtonian gravity more precise.)


title: Fermion emission in a two-dimensional black hole space-time

abstract:
  We investigate massless fermion production by a two-dimensional dilatonic
black hole. Our analysis is based on the Bogoliubov transformation relating the
outgoing fermion field observed outside the black hole horizon to the incoming
field present before the black hole creation. It takes full account of the fact
that the transformation is neither invertible nor unitarily implementable. The
particle content of the outgoing radiation is specified by means of inclusive
probabilities for the detection of sets of outgoing fermions and antifermions
in given states. For states localized near the horizon these probabilities
characterize a thermal equilibrium state. The way the probabilities become
thermal as one approaches the horizon is discussed in detail.


title: Quantum Master Equation of Particle in Gas Environment

abstract:
  The evolution of the reduced density operator $\rho$ of Brownian particle is
discussed in single collision approach valid typically in low density gas
environments. This is the first succesful derivation of quantum friction caused
by {\it local} environmental interactions. We derive a Lindblad master equation
for $\rho$, whose generators are calculated from differential cross section of
a single collision between Brownian and gas particles, respectively. The
existence of thermal equilibrium for $\rho$ is proved. Master equations
proposed earlier are shown to be particular cases of our one.


title: Decoherent Histories and Quantum State Diffusion

abstract:
  We demonstrate a close connection between the decoherent histories (DH)
approach to quantum mechanics and the quantum state diffusion (QSD) picture,
for open quantum systems described by a master equation of Lindblad form. The
(physically unique) set of variables that localize in the QSD picture also
define an approximately decoherent set of histories in the DH approach. The
degree of localization is related to the degree of decoherence, and the
probabilities for histories prescribed by each approach are essentially the
same.


title: Hawking Radiation from Black Holes Formed During Quantum Tunneling

abstract:
  We study the behaviour of scalar fields on background geometries which
undergo quantum tunneling. The two examples considered are a moving mirror in
flat space which tunnels through a potential barrier, and a false vacuum bubble
which tunnels to form a black hole. WKB approximations to the Schrodinger and
Wheeler-DeWitt equations are made, leading one to solve field equations on the
Euclidean metric solution interpolating between the classically allowed
geometries. The state of the field after tunneling can then be determined using
the method of non-unitary Bogolubov transformations developed by Rubakov. It is
shown that the effect of the tunneling is to damp any excitations initially
present, and, in the case of the black hole, that the behaviour of fields on
the Euclidean Kruskal manifold ensures that the late time radiation will be
thermal at the Hawking temperature.


title: Open and Closed Universes, Initial Singularities and Inflation

abstract:
  The existence of initial singularities in expanding universes is proved
without assuming the timelike convergence condition. The assumptions made in
the proof are ones likely to hold both in open universes and in many closed
ones. (It is further argued that at least some of the expanding closed
universes that do not obey a key assumption of the theorem will have initial
singularities on other grounds.) The result is significant for two reasons:
(a)~previous closed-universe singularity theorems have assumed the timelike
convergence condition, and (b)~the timelike convergence condition is known to
be violated in inflationary spacetimes. An immediate consequence of this
theorem is that a recent result on initial singularities in open,
future-eternal, inflating spacetimes may now be extended to include many closed
universes. Also, as a fringe benefit, the time-reverse of the theorem may be
applied to gravitational collapse.


title:
The Cosmic No-Hair Theorem and the Nonlinear Stability of Homogeneous
  Newtonian Cosmological Models

abstract:
  The validity of the cosmic no-hair theorem is investigated in the context of
Newtonian cosmology with a perfect fluid matter model and a positive
cosmological constant. It is shown that if the initial data for an expanding
cosmological model of this type is subjected to a small perturbation then the
corresponding solution exists globally in the future and the perturbation
decays in a way which can be described precisely. It is emphasized that no
linearization of the equations or special symmetry assumptions are needed. The
result can also be interpreted as a proof of the nonlinear stability of the
homogeneous models. In order to prove the theorem we write the general solution
as the sum of a homogeneous background and a perturbation. As a by-product of
the analysis it is found that there is an invariant sense in which an
inhomogeneous model can be regarded as a perturbation of a unique homogeneous
model. A method is given for associating uniquely to each Newtonian
cosmological model with compact spatial sections a spatially homogeneous model
which incorporates its large-scale dynamics. This procedure appears very
natural in the Newton-Cartan theory which we take as the starting point for
Newtonian cosmology.


title: Orbital Tests of Relativistic Gravity using Artificial Satellites

abstract:
  We reexamine non-Einsteinian effects observable in the orbital motion of
low-orbit artificial Earth satellites. The motivations for doing so are
twofold: (i) recent theoretical studies suggest that the correct theory of
gravity might contain a scalar contribution which has been reduced to a small
value by the effect of the cosmological expansion; (ii) presently developed
space technologies should soon give access to a new generation of satellites
endowed with drag-free systems and tracked in three dimensions at the
centimeter level. Our analysis suggests that such data could measure two
independent combinations of the Eddington parameters (beta - 1) and (gamma - 1)
at the 10^-4 level and probe the time variability of Newton's "constant" at the
d(ln G)/dt ~ 10^-13 yr^-1 level. These tests would provide well-needed
complements to the results of the Lunar Laser Ranging experiment, and of the
presently planned experiments aiming at measuring (gamma -1). In view of the
strong demands they make on the level of non- gravitational perturbations,
these tests might require a dedicated mission consisting of an optimized
passive drag-free satellite.


title: The Problem of Time and Quantum Black Holes

abstract:
  We discuss the derivation of the so-called semi-classical equations for both
mini-superspace and dilaton gravity. We find that there is no systematic
derivation of a semi-classical theory in which quantum mechanics is formulated
in a space-time that is a solution of Einstein's equation, with the expectation
value of the matter stress tensor on the right-hand side. The issues involved
are related to the well-known problems associated with the interpretation of
the Wheeler-deWitt equation in quantum gravity, including the problem of time.
We explore the de Broglie-Bohm interpretation of quantum mechanics (and field
theory) as a way of spontaneously breaking general covariance, and thereby
giving meaning to the equations that many authors have been using to analyze
black hole evaporation. We comment on the implications for the ``information
loss" problem.


title:
Post-Newtonian Limits and Gravitational Radiation from the Superstring
  Effective Action

abstract:
  We consider the gravitational sector of the superstring effective action with
axion-matter couplings. The field equations are developed in the post-Newtonian
scheme and approximate solutions for a spinning point mass and a cosmic string
are presented. Furthermore, assuming vanishing axion mass and vanishing
potential for the dilaton, we consider the gravitational radiation in the
leading $O(\alpha'^0)$ order. We find that the total luminosity of a radiative
source has monopole and dipole components besides the standard quadrupole one.
These components may possibly be checked in binary systems.


title: A Fluctuation-Dissipation Relation for Semiclassical Cosmology

abstract:
  Using the concept of open systems where the classical geometry is treated as
the system and the quantum matter field as the environment, we derive a
fluctuation-dissipation theorem for semiclassical cosmology. This theorem which
exists under very general conditions for dissipations in the dynamics of the
system, and the noise and fluctuations in the environment, can be traced to the
formal mathematical relation between the dissipation and noise kernels of the
influence functional depicting the open system, and is ultimately a consequence
of the unitarity of the closed system. In particular, for semiclassical
gravity, it embodies the backreaction effect of matter fields on the dynamics
of spacetime. The backreaction equation derivable from the influence action is
in the form of a Einstein-Langevin equation. It contains a dissipative term in
the equation of motion for the dynamics of spacetime and a noise term related
to the fluctuations of particle creation in the matter field. Using the
well-studied model of a quantum scalar field in a Bianchi Type-I universe we
illustrate how this Langevin equation and the noise term are derived and show
how the creation of particles and the dissipation of anisotropy during the
expansion of the universe can be understood as a manifestation of this
fluctuation-dissipation relation.


title:
Linearly Positive Histories: Probabilities for a Robust Family of
  Sequences of Quantum Events

abstract:
  Nonnegative probabilities that obey the sum rules may be assigned to a much
wider family of sets of histories than decohering histories. The resulting {\it
linearly positive histories} avoid the highly restrictive decoherence
conditions and yet give the same probabilities when those conditions apply.
Thus linearly positive histories are a broad extension of decohering histories.
Moreover, the resulting theory is manifestly time-reversal invariant.


title: On Infrared Effects in de~Sitter Background

abstract:
  We have estimated higher order quantum gravity corrections to de~Sitter
spacetime. Our results suggest that, while the classical spacetime metric may
be distorted by the graviton self-interactions, the corrections are relatively
weaker than previously thought, possibly growing like a power rather than
exponentially in time.


title: Total Mass-Momentum of Arbitrary Initial-Data Sets in General Relativity

abstract:
  For an asymptotically flat initial-data set in general relativity, the total
mass-momentum may be interpreted as a Hermitian quadratic form on the complex,
two-dimensional vector space of ``asymptotic spinors''. We obtain a
generalization to an arbitrary initial-data set. The mass-momentum is retained
as a Hermitian quadratic form, but the space of ``asymptotic spinors'' on which
it is a function is modified. Indeed, the dimension of this space may range
from zero to infinity, depending on the initial data. There is given a variety
of examples and general properties of this generalized mass-momentum.


title:
Consequences of Propagating Torsion in Connection-Dynamic Theories of
  Gravity

abstract:
  We discuss the possibility of constraining theories of gravity in which the
connection is a fundamental variable by searching for observational
consequences of the torsion degrees of freedom. In a wide class of models, the
only modes of the torsion tensor which interact with matter are either a
massive scalar or a massive spin-1 boson. Focusing on the scalar version, we
study constraints on the two-dimensional parameter space characterizing the
theory. For reasonable choices of these parameters the torsion decays quickly
into matter fields, and no long-range fields are generated which could be
discovered by ground-based or astrophysical experiments.


title:
On Possible Measurement of Gravitational Interaction Parameters on Board
  a Satellite

abstract:
  The recently suggested SEE (Satellite Energy Exchange) method of measuring
the gravitational constant $G$, possible equivalence principle violation
(measured by the E\"{o}tv\"{o}s parameter $\eta$) and the hypothetic 5th force
parameters $\alpha$ and $\lambda$ on board a drag-free Earth's satellite is
discussed and further developed. Various particle trajectories near a heavy
ball are numerically simulated. Some basic sources of error are analysed. The
$G$ measurement procedure is modelled by noise insertion to a ``true''
trajectory. It is concluded that the present knowledge of $G, \alpha$ (for
$\lambda \geq 1$ m) and $\eta$ can be improved by at least two orders of
magnitude.


title: Scattering of Fermions off Dilaton Black Holes

abstract:
  We discuss how various properties of dilaton black holes depend on the
dilaton coupling constant $a$. In particular we investigate the $a$-dependence
of certain mass parameters both outside and in the extremal limit and discuss
their relation to thermodynamical quantities. To further illuminate the role of
the coupling constant $a$ we look at a massless point particle in a dilaton
black hole geometry as well as the scattering of (neutral) fermions. In this
latter case we find that the scattering potential vanishes for the zero angular
momentum mode which seems to indicate a catastrophic deradiation when $a>1$.


title: Quantum Statistical Field Theory in Gravitation and Cosmology

abstract:
  We describe how the concepts of quantum open systems and the methods of
closed-time-path (CTP) effective action and influence functional (IF) can be
usefully applied to the analysis of statistical mechanical problems involving
quantum fields in gravitation and cosmology. In the first lecture we discuss in
general terms the relevance of open system concepts in the description of a
variety of physical processes, and outline the basics of the CTP and IF
formalisms. In the second lecture we illustrate the IF method with a model of
two interacting quantum fields, deriving the influence action via a
perturbative expansion involving the closed-time-path Green functions. We show
how noise of quantum fields can be defined and derive a general fluctuation-
dissipation relation for quantum fields. In the third lecture we discuss the
problem of backreaction in semiclassical gravity with the example of a scalar
field in a Bianchi Type-I universe. We show that the CTP effective action not
only yields a real and causal equation of motion with a dissipative term
depicting the effect of particle creation, as was found earlier, it also
contains a noise term measuring the fluctuations in particle number and
governing the metric fluctuations. The particle creation-backreaction problem
can be understood as a manifestation of a fluctuation-dissipation relation for
quantum fields in dynamic spacetimes, generalizing Sciama's observation for
black hole Hawking radiation. A more complete description of semiclassical
gravity is given by way of an Einstein-Langevin equation, the conventional
theory based on the expectation value of the energy momentum tensor being its


title: Self - Interaction Force for the Particle in the Cone Space - Time

abstract:
  The force acting on the charged particle moving along an arbitrary trajectory
near the straight cosmic string is calculated. This interaction leads to the
scattering of particles by the cosmic string. The scattering cross section is
considered.


title: The Birkhoff Theorem in Multidimensional Gravity

abstract:
  The validity conditions for the extended Birkhoff theorem in multidimensional
gravity with $n$ internal spaces are formulated, with no restriction on
space-time dimensionality and signature. Examples of matter sources and
geometries for which the theorem is valid are given. Further generalization of
the theorem is discussed.


title: Multidimensional Cosmology with $m$-Component Perfect Fluid

abstract:
  A cosmological model describing the evolution of $n$ Einstein spaces $(n>1)$
with $m$-component perfect-fluid matter is considered. When all spaces are
Ricci-flat and for any $\alpha$-th component the pressures in all spaces are
proportional to the density: $p_{i}^{(\alpha)} = (1- h_{i}^{(\alpha)})
\rho^{(\alpha)}$, $h_{i}^{(\alpha)}$ = const, the Einstein and Wheeler-DeWitt
equations are integrated in the cases: i) $m=1$, for all $h_{i}^{(\alpha)}$;
ii) $m > 1$, for some special sets of $h_{i}^{(\alpha)}$. For $m=1$ the quantum
wormhole solutions are also obtained. \\


title:
Dirac versus Reduced Quantization of the Poincar\'{e} Symmetry in Scalar
  Electrodynamics

abstract:
  The generators of the Poincar\'{e} symmetry of scalar electrodynamics are
quantized in the functional Schr\"{o}dinger representation. We show that the
factor ordering which corresponds to (minimal) Dirac quantization preserves the
Poincar\'{e} algebra, but (minimal) reduced quantization does not. In the
latter, there is a van Hove anomaly in the boost-boost commutator, which we
evaluate explicitly to lowest order in a heat kernel expansion using zeta
function regularization. We illuminate the crucial role played by the gauge
orbit volume element in the analysis. Our results demonstrate that preservation
of extra symmetries at the quantum level is sometimes a useful criterion to
select between inequivalent, but nevertheless self-consistent, quantization
schemes.


title: Failure of Standard Conservation Laws at a Classical Change of Signature

abstract:
  The Divergence Theorem as usually stated cannot be applied across a change of
signature unless it is re-expressed to allow for a finite source term on the
signature change surface. Consequently all conservation laws must also be
`modified', and therefore insistence on conservation of matter across such a
surface cannot be physically justified. The Darmois junction conditions
normally ensure conservation of matter via Israel's identities for the jump in
the energy-momentum density, but not when the signature changes. Modified
identities are derived for this jump when a signature change occurs, and the
resulting surface effects in the conservation laws are calculated. In general,
physical vector fields experience a jump in at least one component, and a
source term may therefore appear in the corresponding conservation law. Thus
current is also not conserved. These surface effects are a consequence of the
change in the character of physical law. The only way to recover standard
conservation laws is to impose restrictions that no realistic cosmological
model can satisfy.


title: The Patchwork Divergence Theorem

abstract:
  The divergence theorem in its usual form applies only to suitably smooth
vector fields. For vector fields which are merely piecewise smooth, as is
natural at a boundary between regions with different physical properties, one
must patch together the divergence theorem applied separately in each region.
We give an elegant derivation of the resulting "patchwork divergence theorem"
which is independent of the metric signature in either region, and which is
thus valid if the signature changes.
  (PACS numbers 4.20.Cv, 04.20.Me, 11.30.-j, 02.40.Hw)


title: Localized Exotic Smoothness

abstract:
  Gompf's end-sum techniques are used to establish the existence of an infinity
of non-diffeomorphic manifolds, all having the same trivial ${\bf R^4}$
topology, but for which the exotic differentiable structure is confined to a
region which is spatially limited. Thus, the smoothness is standard outside of
a region which is topologically (but not smoothly) ${\bf B^3}\times {\bf R^1}$,
where ${\bf B^3}$ is the compact three ball. The exterior of this region is
diffeomorphic to standard ${\bf R^1}\times {\bf S^2}\times{\bf R^1}$. In a
space-time diagram, the confined exoticness sweeps out a world tube which, it
is conjectured, might act as a source for certain non-standard solutions to the
Einstein equations. It is shown that smooth Lorentz signature metrics can be
globally continued from ones given on appropriately defined regions, including
the exterior (standard) region. Similar constructs are provided for the
topology, ${\bf S^2}\times {\bf R^2}$ of the Kruskal form of the Schwarzschild
solution. This leads to conjectures on the existence of Einstein metrics which
are externally identical to standard black hole ones, but none of which can be
globally diffeomorphic to such standard objects. Certain aspects of the Cauchy
problem are also discussed in terms of ${\bf R^4_\Theta}$\models which are
``half-standard'', say for all $t<0,$ but for which $t$ cannot be globally
smooth.


title: Particle-like solutions to topologically massive gravity

abstract:
  The solution of topologically massive gravity with cosmological constant is
reduced, for space-times with two commuting Killing vectors, to a
special-relativistic dynamical problem. This approach is applied to the
construction of a class of exact sourceless, horizonless solutions asymptotic
to the BTZ extreme black holes.


title:
On "asymptotically flat" space-times with $G_{2}$-invariant Cauchy
  surfaces

abstract:
  In this paper we study space-times which evolve out of Cauchy data
$(\Sigma,{}^3g,K)$ invariant under the action of a two-dimensional commutative
Lie group. Moreover $(\Sigma,{}^3g,K)$ are assumed to satisfy certain
completeness and asymptotic flatness conditions in spacelike directions. We
show that asymptotic flatness and energy conditions exclude all topologies and
group actions except for a cylindrically symmetric $R^3$, or a periodic
identification thereof along the $z$-axis. We prove that asymptotic flatness,
energy conditions and cylindrical symmetry exclude the existence of compact
trapped surfaces. Finally we show that the recent results of Christodoulou and
Tahvildar-Zadeh concerning global existence of a class of wave-maps imply that
strong cosmic censorship holds in the class of asymptotically flat
cylindrically symmetric electro-vacuum space-times.


title: Black Hole Thermodynamics in a Box

abstract:
  Simple calculations indicate that the partition function for a black hole is
defined only if the temperature is fixed on a finite boundary. Consequences of
this result are discussed. (Contribution to the Proceedings of the Lanczos
Centenary Conference.)


title: Reference Fluids as Standards of Space and Time

abstract:
  The idea that spacetime points are to be identified by a fleet of
clock--carrying particles can be traced to the earliest days of general
relativity. Such a fleet of clocks can be described phenomenologically as a
reference fluid. One approach to the problem of time consists in coupling the
metric to a reference fluid and solving the super--Hamiltonian constraint for
the momentum conjugate to the clock time variable. The resolved constraint
leads to a functional Schr\"{o}dinger equation and formally to a conserved
inner product. The reference fluid that is described phenomenologically as
incoherent dust has the extraordinary property that the true Hamiltonian
density for the coupled system depends only on the gravitational variables. The
dust particles also endow space with a privileged system of coordinates that
allows the supermomentum constraint to be solved explicitly. (Contribution to
the Proceedings of the Lanczos Centenary Conference.)