title: A POSSIBLE SOLUTION TO THE PROBLEM OF EXTRA DIMENSIONS

abstract:
  We consider a multidimensional universe with the topology $M= \R\times
M_1\times \cdots \times M_n$, where the $M_i$ ($i>1$) are $d_i$-dimensional
Ricci flat spaces. Exploiting a conformal equivalence between minimal coupling
models and conformal coupling models, we get exact solutions for such an
universe filled by a conformally coupled scalar field. One of the solutions can
be used to describe trapped unobservable extra dimensions.


title:
On Singularities and Instability for Different Couplings between Scalar
  Field and Multidimensional Geometry

abstract:
  We consider a multidimensional model of the universe given as a
$D$-dimensional geometry, represented by a Riemannian manifold $(M,g)$ with
arbitrary signature of $g$, $M= \R\times M_1\times \cdots \times M_n$, where
the $M_i$ of dimension $d_i$ are Einstein spaces, compact for $i>1$. For
Lagrangian models $L(R,\phi)$ on $M$ which depend only on the Ricci curvature
$R$ and a scalar field $\phi$, there exists a conformal equivalence with
minimal coupling models. For certain nonminimal models we study classical
solutions and their relation to solutions in the equivalent minimal coupling
model. The domains of equivalence are separated by certain critical values of
the scalar field $\phi$. Furthermore, the coupling constant $\xi$ of the
coupling between $\phi$ and $R$ is critical at both, the minimal value $\xi=0$
and the conformal value $\xi_c=\frac{D-2}{4(D-1)}$. In different noncritical
regions of $\xi$ the solutions behave qualitatively different. Instability can
occure only in certain ranges of $\xi$. {This paper is dedicated to Prof. D. D.
Ivanenko.}


title: Increase of Black Hole Entropy in Higher Curvature Gravity

abstract:
  We examine the Zeroth Law and the Second Law of black hole thermodynamics
within the context of effective gravitational actions including higher
curvature interactions. We show that entropy can never decrease for
quasi-stationary processes in which a black hole accretes positive energy
matter, independent of the details of the gravitational action. Within a class
of higher curvature theories where the Lagrangian consists of a polynomial in
the Ricci scalar, we use a conformally equivalent theory to establish that
stationary black hole solutions with a Killing horizon satisfy the Zeroth Law,
and that the Second Law holds in general for any dynamical process. We also
introduce a new method for establishing the Second Law based on a
generalization of the area theorem, which may prove useful for a wider class of
Lagrangians. Finally, we show how one can infer the form of the black hole
entropy, at least for the Ricci polynomial theories, by integrating the changes
of mass and angular momentum in a quasistationary accretion process.


title: Towards a no hair theorem for higher order gravity

abstract:
  We use gravitational Lagrangians $R \Box \sp k R \sqrt{-g}$ and linear
combinations of them; we ask under which circumstances the de Sitter space-time
represents an attractor solution in the set of spatially flat Friedman models.
Results are: For arbitrary $k$, i.e., for arbitrarily large order of the field
equation, on can always find examples where the attractor property takes place.
Such examples necessarily need a non-vanishing $R\sp 2$-term. The main formulas
do not depend on the dimension, so one gets similar results also for
1+1-dimensional gravity and for Kaluza-Klein cosmology.


title: Divergences problem in black hole brick-wall model

abstract:
  In this work we review, in the framework of the so-called brick wall model,
the divergence problem arising in the one loop calculations of various
thermodynamical quantities, like entropy, internal energy and heat capacity.
Particularly we find that, if one imposes that entanglement entropy is equal to
the Bekenstein-Hawking one, the model gives problematic results. Then a
proposal of solution to the divergence problem is made following the zeroth law
of black hole mechanics.


title: The Use of Computer Algebra in Maxwell's Theory

abstract:
  We present a small computer algebra program for use in Maxwell's theory. The
Maxwell equations and the energy-momentum current of the electromagnetic field
are formulated in the language of exterior differential forms. The
corresponding program can be applied (in the presence of a gravitational field)
in curved Riemannian spacetime as well as in flat Minkowski spacetime in
inertial or {\em non-inertial} frames. Our program is written for the computer
algebra system REDUCE with the help of the EXCALC package for exterior
differential forms.\par The two major advantages of this modern approch to
electrodynamics --- the natural formulation, free of both metric and
coordinates, and the straightforward programming of problems --- are
illustrated by examining a number of examples ranging from the Coulomb field of
a static point charge to the Kerr--Newman solution of the Einstein--Maxwell
equations.


title: Lectures in (2+1)-Dimensional Gravity

abstract:
  These lectures briefly review our current understanding of classical and
quantum gravity in three spacetime dimensions, concentrating on the quantum
mechanics of closed universes and the (2+1)-dimensional black hole. Three
formulations of the classical theory and three approaches to quantization are
discussed in some detail, and a number of other approaches are summarized. An
extensive, although by no means complete, list of references is included.
(Lectures given at the First Seoul Workshop on Gravity and Cosmology, February
24-25, 1995.)


title: Three dimensional numerical relativity: the evolution of black holes

abstract:
  We report on a new 3D numerical code designed to solve the Einstein equations
for general vacuum spacetimes. This code is based on the standard 3+1 approach
using cartesian coordinates. We discuss the numerical techniques used in
developing this code, and its performance on massively parallel and vector
supercomputers. As a test case, we present evolutions for the first 3D black
hole spacetimes. We identify a number of difficulties in evolving 3D black
holes and suggest approaches to overcome them. We show how special treatment of
the conformal factor can lead to more accurate evolution, and discuss
techniques we developed to handle black hole spacetimes in the absence of
symmetries. Many different slicing conditions are tested, including geodesic,
maximal, and various algebraic conditions on the lapse. With current
resolutions, limited by computer memory sizes, we show that with certain lapse
conditions we can evolve the black hole to about $t=50M$, where $M$ is the
black hole mass. Comparisons are made with results obtained by evolving
spherical initial black hole data sets with a 1D spherically symmetric code. We
also demonstrate that an ``apparent horizon locking shift'' can be used to
prevent the development of large gradients in the metric functions that result
from singularity avoiding time slicings. We compute the mass of the apparent
horizon in these spacetimes, and find that in many cases it can be conserved to
within about 5\% throughout the evolution with our techniques and current
resolution.


title: Four Dimensional Quantum Topology Changes of Spacetimes

abstract:
  We investigate topology changing processes in the WKB approximation of four
dimensional quantum cosmology with a negative cosmological constant. As
Riemannian manifolds which describe quantum tunnelings of spacetime we consider
constant negative curvature solutions of the Einstein equation i.e. hyperbolic
geometries. Using four dimensional polytopes, we can explicitly construct
hyperbolic manifolds with topologically non-trivial boundaries which describe
topology changes. These instanton-like solutions are constructed out of
8-cell's, 16-cell's or 24-cell's and have several points at infinity called
cusps. The hyperbolic manifolds are non-compact because of the cusps but have
finite volumes. Then we evaluate topology change amplitudes in the WKB
approximation in terms of the volumes of these manifolds. We find that the more
complicated are the topology changes, the more likely are suppressed.


title: Experimental Signatures of Quantum Gravity

abstract:
  I review several different calculations, coming from string theory,
nonperturbative quantum gravity and analyses of black holes that lead to
predictions of phenomena that would uniquely be signatures of quantum
gravitational effects.
  These include: 1) deviations from a thermal spectra for evaporating black
holes, 2) upper limits on the entropy and energy content of bounded regions, 3)
suppression of ultra-high energy scattering amplitudes, consistent with a
modified uncertainty principle, 4) physical volumes and areas have discrete
spectra, 5), violations of $CPT$ and universal violations of $CP$, 6) otherwise
inexplicable conditions on the initial state of the universe or otherwise
inexplicable correlations between cosmological and microscopic parameters.
Consideration of all of these together suggests the possibility of connections
between perturbative and nonperturbative approaches to quantum gravity.


title:
Self-Forces on Electric and Magnetic Linear Sources in the Space-Time of
  a Cosmic String

abstract:
  In this paper we calculate the magnetic and electric self-forces, induced by
the conical structure of a cosmic string space-time, on a long straight wire
which presents either a constant current or a linear charge density. We also
show how these self-forces are related by a Lorentz tranformation and, in this
way, explain what two different inertial observers detect in their respective
frames.


title: Trapped surfaces in cosmological spacetimes

abstract:
  We investigate the formation of trapped surfaces in cosmological spacetimes,
using constant mean curvature slicing. Quantitative criteria for the formation
of trapped surfaces demonstrate that cosmological regions enclosed by trapped
surfaces may have matter density exceeding significantly the background matter
density of the flat and homogeneous cosmological model.


title:
The constant mean curvature slices of asymptotically flat spherical
  spacetimes

abstract:
  We investigate the formation of trapped surfaces in asymptotically flat
spherical spacetimes, using constant mean curvature slicing.


title:
GENERAL RELATIVISTIC EFFECTS ON THE INDUCED ELECTRIC FIELD EXTERIOR TO
  PULSARS

abstract:
  The importance of general relativity to the induced electric field exterior
to pulsars has been investigated by assuming aligned vacuum and non-vacuum
magnetosphere models. For this purpose the stationary and axisymmetric vector
potential in Schwarzschild geometry has been considered and the corresponding
expressions for the induced electric field due to the rotation of the magnetic
dipole have been derived for both vacuum and non-vacuum conditions. Due to the
change in the magnetic dipole field in curved spacetime the induced electric
field also changes its magnitude and direction and increases significantly near
the surface of the star. As a consequence the surface charge density, the
acceleration of charged particles in vacuum magnetospheres and the space charge
density in non-vacuum magnetosphere greatly increase near the surface of the
star. The results provide the most general feature of the important role played
by gravitation and could have several potentially important implications for
the production of high-energy radiation from pulsars.


title: Magnetically Charged Black Holes with Hair

abstract:
  In these lectures the properties of magnetically charged black holes are
described. In addition to the standard Reissner-N\"ordstrom solution, there are
new types of static black holes that arise in theories containing electrically
charged massive vector mesons. These latter solutions have nontrivial matter
fields outside the horizon; i.e., they are black holes with hair. While the
solutions carrying unit magnetic charge are spherically symmetric, those with
more than two units of magnetic charge are not even axially symmetric. These
thus provide the first example of time-independent black hole solutions that
have no rotational symmetry.


title: Logico-algebraic approach to spacetime quantization

abstract:
  In the last decades the logico-algebraic approach to quantum mechanics turned
to be a successful tool to render the quantum mechanical formalism on a steady
operationalistic background. The algebraic approach to general relativity first
proposed by Geroch is used to build a smearing procedure for events in the
quantized theory of spacetime. It stems from the notion of basic algebra which
possesses both the differential structure (as functional algebras) and
non-commutativity (as algebras of observables in quantum theories). The main
essence of this formalism is that it deprives the notion of spacetime as event
support of its fundamental status making it relative to the measurement
performed. Before the observation is executed, it is pointless to speak of
events as points of spacetime: there is no underlying manifold. Only when an
eigen-subalgebra of the basic algebra is outlined as eigenstate of the
observable, it gives rise to its functional representation on the appropriate
set thought of as spacetime.


title: The Unholey Solution to Black Hole Information Loss

abstract:
  The simplest solution to the black hole information loss problem is to
eliminate black holes. Modifications of Einstein gravity which accomplish this
are discussed and the possibility that string theory is free of black holes is
considered.


title: Static Black Hole Solutions without Rotational Symmetry

abstract:
  We construct static black hole solutions that have no rotational symmetry.
These arise in theories, including the standard electroweak model, that include
charged vector mesons with mass $m\ne 0$. In such theories, a magnetically
charged Reissner-Nordstrom black hole with horizon radius less than a critical
value of the order of $m^{-1}$ is classically unstable against the development
of a nonzero vector meson field just outside the horizon, indicating the
existence of static black hole solutions with vector meson hair. For the case
of unit magnetic charge, spherically symmetric solutions of this type have
previously been studied. For other values of the magnetic charge, general
arguments show that any new solution with hair cannot be spherically symmetric.
In this paper we develop and apply a perturbative scheme (which may have
applicability in other contexts) for constructing such solutions in the case
where the Reissner-Nordstrom solution is just barely unstable. For a few low
values of the magnetic charge the black holes retain a rotational symmetry
about a single axis, but this axial symmetry disappears for higher charges.
While the vector meson fields vanish exponentially fast at distances greater
than $O(m^{-1})$, the magnetic field and the metric have higher multipole
components that decrease only as powers of the distance from the black hole.


title:
Numerical Solutions of the Einstein-Yang-Mills System with Cosmological
  Constant

abstract:
  Numerical evidence for a cosmological version of the Bartnik-McKinnon family
of particle-like solutions of the Einstein-Yang-Mills system is presented. Our
solutions are also static, but space has the topology of a three-sphere. By
adjusting the cosmological constant we found numerically a spherically
symmetric solution which can be regarded as an excitation of the unique
SO(4)-invariant solution. We expect that for each node number there exists such
a solution without a cosmological horizon.


title: Triad formulations of Canonical Gravity without a fixed reference frame

abstract:
  One can simplify the triad formulations of canonical gravity by abandoning
any relation to a fixed coordinate system. That means in case of the \ADM
formalism that one can determine the momentum by direct derivation of the
Lagrange-3-form w.r.t the time-derivative of the triad-1-forms, thus the
momentum is most naturally a 2-form. We apply this concept to the Palatini
formulation where we can closely follow Dirac's concept to find and eliminate
the second class constraints. Following the same way for the Ashtekar theory it
will turn out to be equivalent to two successive canonical transformations
where the first makes explicit use of the spatial dimension being 3 and the
second is usually hidden in the use of densities. At the end we can give a
simple version of the reality constraints.


title: Stress-Energy-Momentum Tensors in Constraint Field Theories

abstract:
  One has not any conventional energy-momentum conservation law in Lagrangian
field theory, but relations involving different stress-energy-momentum tensors
associated with different connections. It is not obvious how to choose the true
energy-momentum tensor. This problem is solved in the framework of the
multimomentum Hamiltonian formalism which provides the adequate description of
constraint field systems. The goal is that, for different solutions of the same
constraint field model, one should choose different stress-energy-momentum
tensors in general. Gauge theory illustrates this result. The
stress-energy-momentum tensors of affine-metric gravity are examined.


title:
Domain Wall Spacetimes: Instability of Cosmological Event and Cauchy
  Horizons

abstract:
  The stability of cosmological event and Cauchy horizons of spacetimes
associated with plane symmetric domain walls are studied. It is found that both
horizons are not stable against perturbations of null fluids and massless
scalar fields; they are turned into curvature singularities. These
singularities are light-like and strong in the sense that both the tidal forces
and distortions acting on test particles become unbounded when theses
singularities are approached.


title: Inflationary Cosmology from Noncommutative Geometry

abstract:
  In the framework of the Connes-Lott model based on noncommutative geometry,
the basic features of a gauge theory in the presence of gravity are reviewed,
in order to show the possible physical relevance of this scheme for
inflationary cosmology. These models naturally contain at least two scalar
fields, interacting with each other whenever more than one fermion generation
is assumed. In this paper we propose to investigate the behaviour of these two
fields (one of which represents the distance between the copies of a
two-sheeted space-time) in the early stages of the universe evolution. In
particular the simplest abelian model, which preserves the main characteristics
of more complicate gauge theories, is considered and the corresponding
inflationary dynamics is studied. We find that a chaotic inflation is naturally
favoured, leading to a field configuration in which no symmetry breaking occurs
and the final distance between the two sheets of space-time is smaller the
greater the number of $e$-fold in each sheet.


title:
Conservation laws for systems of extended bodies in the first
  post-Newtonian approximation.

abstract:
  The general form of the global conservation laws for $N$-body systems in the
first post-Newtonian approximation of general relativity is considered. Our
approach applies to the motion of an isolated system of $N$ arbitrarily
composed and shaped, weakly self-gravitating, rotating, deformable bodies and
uses a framework recently introduced by Damour, Soffel and Xu (DSX). We succeed
in showing that seven of the first integrals of the system (total mass-energy,
total dipole mass moment and total linear momentum) can be broken up into a sum
of contributions which can be entirely expressed in terms of the basic
quantities entering the DSX framework: namely, the relativistic individual
multipole moments of the bodies, the relativistic tidal moments experienced by
each body, and the positions and orientations with respect to the global
coordinate system of the local reference frames attached to each body. On the
other hand, the total angular momentum of the system does not seem to be
expressible in such a form due to the unavoidable presence of irreducible
nonlinear gravitational effects.


title: Black hole entropy: departures from area law

abstract:
  The thermodynamic and euclidean functional integral approaches to black hole
entropy are discussed. The existence of some freedom in the definition of the
entropy is pointed out and the possibility of a departure from the
semiclassical expression discussed in the light of quantum corrections. The
semiclassical area dependence of the entropy of matter in the background of a
black hole is also reviewed and shown to break down in the case of extremal
black holes. The cutoff dependence is shown to be different for the extreme
dilatonic and Reissner - Nordstrom black holes.


title: Quantum Dynamics Beyond the Gaussian Approximation

abstract:
  The time dependent quantum variational principle is emerging as an important
means of studying quantum dynamics, particularly in early universe scenarios.
To date all investigations have worked within a Gaussian framework. Here we
present an improved method which is demonstrated to be superior to the Gaussian
approach and may be naturally extended to the field--theoretic case.


title: ROTATING NEUTRON STAR MODELS WITH MAGNETIC FIELD

abstract:
  We present the first numerical solutions of the coupled Einstein-Maxwell
equations describing rapidly rotating neutron stars endowed with a magnetic
field. These solutions are fully relativistic and self-consistent, all the
effects of the electromagnetic field on the star's equilibrium (Lorentz force,
spacetime curvature generated by the electromagnetic stress-energy) being taken
into account. The magnetic field is axisymmetric and poloidal. Five dense
matter equations of state are employed. The partial differential equation
system is integrated by means of a pseudo-spectral method. Various tests passed
by the numerical code are presented. The effects of the magnetic field on
neutron stars structure are then investigated, especially by comparing
magnetized and non-magnetized configurations with the same baryon number. The
deformation of the star induced by the magnetic field is important only for
huge values of B (B>10^{10} T). The maximum mass as well as the maximum
rotational velocity are found to increase with the magnetic field. The maximum
allowable poloidal magnetic field is of the order of 10^{14} T (10^{18} G) and
is reached when the magnetic pressure is comparable to the fluid pressure at
the centre of the star. For such values, the maximum mass of neutron stars is
found to increase by 13 to 29 % (depending upon the EOS) with respect to the
maximum mass of non-magnetized stars.


title: On a Harmonic Property of the Einstein Manifold Curvature

abstract:
  The harmonicity condition of the curvature 2-form of a pseudo- Riemannian
manifold is formulated on the basis of annulment of this form by the de
Rham-Lichnerowicz Laplacian. The following theorem is proved: The curvature
2-form of any Einstein manifold is harmonic.


title: TOPOLOGY CHANGE AND QUANTUM PHYSICS

abstract:
  The role of topology in elementary quantum physics is discussed in detail. It
is argued that attributes of classical spatial topology emerge from properties
of state vectors with suitably smooth time evolution. Equivalently, they emerge
from considerations on the domain of the quantum Hamiltonian, this domain being
often specified by boundary conditions in elementary quantum physics. Several
examples are presented where classical topology is changed by smoothly altering
the boundary conditions. When the parameters labelling the latter are treated
as quantum variables, quantum states need not give a well-defined classical
topology, instead they can give a quantum superposition of such topologies. An
existing argument of Sorkin based on the spin-statistics connection and
indicating the necessity of topology change in quantum gravity is recalled. It
is suggested therefrom and our results here that Einstein gravity and its minor
variants are effective theories of a deeper description with additional novel
degrees of freedom. Other reasons for suspecting such a microstructure are also
summarized.


title: Vanishing Hawking Radiation from a Uniformly Accelerated Black Hole

abstract:
  We consider quantum fields around uniformly accelerated black holes. At a
particular value of the acceleration, the Bogolubov transformation which would
be responsible for the late-time Hawking radiation, is found to be trivial.
When this happens, Hawking's thermal radiation, Doppler-shifted or not, is
absent to the asymptotic inertial observers despite the nonzero Hawking
temperature, while the co-moving observers find the black hole radiance exactly
balanced by the acceleration heat bath. After a brief comparison to the
classical system of a uniformly accelerated charge, we close with two important
comments. (Phys. Rev. Lett. 75 (1995) 382)


title: POINTLESS SPACES IN GENERAL RELATIVITY

abstract:
  The new approach to quantize the gravity based on the notion of differential
algebra is suggested. It is shown that the differential geometry of this object
can not be described in terms of points. The spatialization procedure giving
rise to points by loosing a part of the entire structure is discussed. The
counterpart of the traditional objects of differential geometry are studied.


title: General Relativity as an Attractor in Scalar-Tensor Stochastic Inflation

abstract:
  Quantum fluctuations of scalar fields during inflation could determine the
very large-scale structure of the universe. In the case of general
scalar-tensor gravity theories these fluctuations lead to the diffusion of
fundamental constants like the Planck mass and the effective Brans--Dicke
parameter, $\omega$. In the particular case of Brans--Dicke gravity, where
$\omega$ is constant, this leads to runaway solutions with infinitely large
values of the Planck mass. However, in a theory with variable $\omega$ we find
stationary probability distributions with a finite value of the Planck mass
peaked at exponentially large values of $\omega$ after inflation. We conclude
that general relativity is an attractor during the quantum diffusion of the
fields.


title: On matching conditions for cosmological perturbations

abstract:
  We derive the matching conditions for cosmological perturbations in a
Friedmann Universe where the equation of state undergoes a sharp jump, for
instance as a result of a phase transition. The physics of the transition which
is needed to follow the fate of the perturbations is clarified. We dissipate
misleading statements made recently in the literature concerning the
predictions of the primordial fluctuations from inflation and confirm standard
results. Applications to string cosmology are considered.


title: QUANTUM ASPECTS OF 2+1 GRAVITY

abstract:
  We review and systematize recent attempts to canonically quantize general
relativity in 2+1 dimensions, defined on space-times $\R\times\Sigma^g$, where
$\Sigma^g$ is a compact Riemann surface of genus $g$. The emphasis is on
quantizations of the classical connection formulation, which use Wilson loops
as their basic observables, but also results from the ADM formulation are
summarized. We evaluate the progress and discuss the possible quantum
(in)equivalence of the various approaches.


title:
A comparison of Noether charge and Euclidean methods for Computing the
  Entropy of Stationary Black Holes

abstract:
  The entropy of stationary black holes has recently been calculated by a
number of different approaches. Here we compare the Noether charge approach
(defined for any diffeomorphism invariant Lagrangian theory) with various
Euclidean methods, specifically, (i) the microcanonical ensemble approach of
Brown and York, (ii) the closely related approach of Ba\~nados, Teitelboim, and
Zanelli which ultimately expresses black hole entropy in terms of the Hilbert
action surface term, (iii) another formula of Ba\~nados, Teitelboim and Zanelli
(also used by Susskind and Uglum) which views black hole entropy as conjugate
to a conical deficit angle, and (iv) the pair creation approach of Garfinkle,
Giddings, and Strominger. All of these approaches have a more restrictive
domain of applicability than the Noether charge approach. Specifically,
approaches (i) and (ii) appear to be restricted to a class of theories
satisfying certain properties listed in section 2; approach (iii) appears to
require the Lagrangian density to be linear in the curvature; and approach (iv)
requires the existence of suitable instanton solutions. However, we show that
within their domains of applicability, all of these approaches yield results in
agreement with the Noether charge approach. In the course of our analysis, we
generalize the definition of Brown and York's quasilocal energy to a much more
general class of diffeomorphism invariant, Lagrangian theories of gravity. In
an appendix, we show that in an arbitrary diffeomorphism invariant theory of
gravity, the ``volume term" in the ``off-shell" Hamiltonian associated with a
time evolution vector field $t^a$ always can be expressed as the spatial
integral of $t^a {\cal C}_a$, where ${\cal C}_a = 0$ are the constraints
associated with the diffeomorphism invariance.


title:
THE UNIQUENESS THEOREM FOR ROTATING BLACK HOLE SOLUTIONS OF
  SELF-GRAVITATING HARMONIC MAPPINGS

abstract:
  We consider rotating black hole configurations of self-gravitating maps from
spacetime into arbitrary Riemannian manifolds. We first establish the
integrability conditions for the Killing fields generating the stationary and
the axisymmetric isometry (circularity theorem). Restricting ourselves to
mappings with harmonic action, we subsequently prove that the only stationary
and axisymmetric, asymptotically flat black hole solution with regular event
horizon is the Kerr metric. Together with the uniqueness result for
non-rotating configurations and the strong rigidity theorem, this establishes
the uniqueness of the Kerr family amongst all stationary black hole solutions
of self-gravitating harmonic mappings.


title: Nontrivial Fermion States in Supersymmetric Minisuperspace

abstract:
  In this lecture supersymmetric minisuperspace models of any Bianchi type
within class A of the classification of Ellis and McCallum are considered. The
algebra of the supersymmetry generators, the Lorentz generators, the
diffeomorphism generators and the Hamiltonian generator is determined
explicitely and found to close. Different from earlier work it is established
that physical states, which are annihilated by all these generators, exist in
{\it all } sectors of these models with fixed even fermion number. A state in
the 4-fermion sector of the Bianchi type IX model is considered as a specific
example, which satisfies the `no-boundary' condition of Hartle and Hawking. The
conclusion is that supersymmetric minisuperspace models have a much richer
manifold of physical states than had been recognized before.


title: REMARKS CONCERNING THE GEOMETRIES OF GRAVITY AND GAUGE FIELDS

abstract:
  An important limitation is shown in the analogy between the Aharonov-Bohm
effect and the parallel transport on a cone. It illustrates a basic difference
between gravity and gauge fields due to the existence of the solder form for
the space-time geometry. This difference is further shown by the observability
of the gravitational phase for open paths. This reinforces a previous
suggestion that the fundamental variables for quantizing the gravitational
field are the solder form and the connection, and not the metric.


title: CANONICAL QUANTIZATION OF THE BELINSKII-ZAKHAROV ONE-SOLITON SOLUTIONS

abstract:
  We apply the algebraic quantization programme proposed by Ashtekar to the
analysis of the Belinski\v{\i}-Zakharov classical spacetimes, obtained from the
Kasner metrics by means of a generalized soliton transformation. When the
solitonic parameters associated with this transformation are frozen, the
resulting Belinski\v{\i}-Zakharov metrics provide the set of classical
solutions to a gravitational minisuperspace model whose Einstein equations
reduce to the dynamical equations generated by a homogeneous Hamiltonian
constraint and to a couple of second-class constraints. The reduced phase space
of such a model has the symplectic structure of the cotangent bundle over
$I\!\!\!\,R^+\times I\!\!\!\,R^+$. In this reduced phase space, we find a
complete set of real observables which form a Lie algebra under Poisson
brackets. The quantization of the gravitational model is then carried out by
constructing an irreducible unitary representation of that algebra of
observables. Finally, we show that the quantum theory obtained in this way is
unitarily equivalent to that which describes the quantum dynamics of the Kasner
model.


title:
Cosmological Solutions of Higher-Curvature String Effective Theories
  with Dilatons

abstract:
  We study the effect of higher-curvature terms in the string low-energy
effective actions on the cosmological solutions of the theory, up to
corrections quartic in the curvatures, for the bosonic and heterotic strings as
well as the type II superstring. We find that cosmological solutions exist for
all string types but they always disappear when the dilaton field is included,
a conclusion that can be avoided if string-loop effects are taken into account.


title: Radiative energy shifts of accelerated atoms

abstract:
  We consider the influence of acceleration on the radiative energy shifts of
atoms in Minkowski space. We study a two-level atom coupled to a scalar quantum
field. Using a Heisenberg picture approach, we are able to separate the
contributions of vacuum fluctuations and radiation reaction to the Lamb shift
of the two-level atom. The resulting energy shifts for the special case of a
uniformly accelerated atom are then compared with those of an atom at rest.


title:
The space of states of quantum gravity in terms of loops and extended
  loops: some remarks

abstract:
  This article reviews the status of several solutions to all the constraints
of quantum gravity that have been proposed in terms of loops and extended
loops. We discuss pitfalls of several of the results and in particular discuss
the issues of covariance and regularization of the constraints in terms of
extended loops. We also propose a formalism for ``thickened out loops'' which
does not face the covariance problems of extended loops and may allow to
regularize expressions in a consistent manner.


title: Vacuum polarization induced by a uniformly accelerated charge

abstract:
  We consider a point charge fixed in the Rindler coordinates which describe a
uniformly accelerated frame. We determine an integral expression of the induced
charge density due to the vacuum polarization at the first order in the fine
structure constant. In the case where the acceleration is weak, we give
explicitly the induced electrostatic potential.


title: Exact Hypersurface-Homogeneous Solutions in Cosmology and Astrophysics

abstract:
  A framework is introduced which explains the existence and similarities of
most exact solutions of the Einstein equations with a wide range of sources for
the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian
formulation. This class includes the spatially homogeneous cosmological models
and the astrophysically interesting static spherically symmetric models as well
as the stationary cylindrically symmetric models. The framework involves
methods for finding and exploiting hidden symmetries and invariant submanifolds
of the Hamiltonian formulation of the field equations. It unifies, simplifies
and extends most known work on hypersurface-homogeneous exact solutions. It is
shown that the same framework is also relevant to gravitational theories with a
similar structure, like Brans-Dicke or higher-dimensional theories.


title: The Value of Singularities

abstract:
  We point out that spacetime singularities play a useful role in gravitational
theories by eliminating unphysical solutions. In particular, we argue that any
modification of general relativity which is completely nonsingular cannot have
a stable ground state. This argument applies both to classical extensions of
general relativity, and to candidate quantum theories of gravity.


title: Continuous Histories and the History Group in Generalised Quantum Theory

abstract:
  We treat continuous histories within the histories approach to generalised
quantum mechanics. The essential tool is the `history group': the analogue,
within the generalised history scheme, of the canonical group of single-time
quantum mechanics.


title: Non-covariance of the generalized holonomies: Examples

abstract:
  A key aspect of a recent proposal for a {\em generalized loop representation}
of quantum Yang-Mills theory and gravity is considered. Such a representation
of the quantum theory has been expected to arise via consideration of a
particular algebra of observables -- given by the traces of the holonomies of
{\em generalized loops}. We notice, however, a technical subtlety, which
prevents us from reaching the conclusion that the generalized holonomies are
covariant with respect to small gauge transformations. Further analysis is
given which shows that they are {\em not} covariant with respect to small gauge
transformations; their traces are {\em not} observables of the gauge theory.
This result indicates what may be a serious complication to the use of
generalized loops in physics.


title: Apparent Horizons in Vacuum Robinson-Trautman Spacetimes

abstract:
  Vacuum asymptotically flat Robinson-Trautman spacetimes are a well known
class of spacetimes exhibiting outgoing gravitational radiation. In this paper
we describe a method of locating the past apparent horizon in these spacetimes,
and discuss the properties of the horizon. We show that the past apparent
horizon is non-timelike, and that its surface area is a decreasing function of
the retarded time. A numerical simulation of the apparent horizon is also
discussed.


title: MATRIX MODELS FOR SPACETIME TOPODYNAMICS

abstract:
  The machinery is suggested to describe the varying spacetime topology on the
level of its substitutes by finite topological spaces.


title:
OUTLINE OF A GENERALLY COVARIANT QUANTUM FIELD THEORY AND A QUANTUM
  THEORY OF GRAVITY

abstract:
  We study a tentative generally covariant quantum field theory, denoted the
T-Theory, as a tool to investigate the consistency of quantum general
relativity. The theory describes the gravitational field and a minimally
coupled scalar field; it is based on the loop representation, and on a certain
number of quantization choices. Four-dimensional diffeomorphism-invariant
quantum transition probabilities can be computed from the theory. We present
the explicit calculation of the transition probability between two volume
eigenstates as an example. We discuss the choices on which the T-theory relies,
and the possibilities of modifying them.


title: $\La \to 0$ limit of 2+1 Quantum Gravity for arbitrary genus

abstract:
  The abstract quantum algebra of observables for 2+1 gravity is analysed in
the limit of small cosmological constant. The algebra splits into two sets with
an explicit phase space representation;~one set consists of $6g-6$ {\it
commuting} elements which form a basis for an algebraic manifold defined by the
trace and rank identities;~the other set consists of $6g-6$ tangent vectors to
this manifold. The action of the quantum mapping class group leaves the algebra
and algebraic manifold invariant. The previously presented representation for
$g=2$ is analysed in this limit and reduced to a very simple form. The
symplectic form for $g=2$ is computed.


title:
TOPOLOGICAL PHASES AND THEIR DUALITY IN ELECTROMAGNETIC AND
  GRAVITATIONAL FIELDS

abstract:
  The duality found by Aharonov and Casher for topological phases in the
electromagnetic field is generalized to an arbitrary linear interaction. This
provides a heuristic principle for obtaining a new solution of the field
equations from a known solution. This is applied to the general relativistic
Sagnac phase shift due to the gravitational field in the interference of mass
or energy around a line source that has angular momentum and the dual phase
shift in the interference of a spin around a line mass. These topological
phases are treated both in the linearized limit of general relativity and the
exact solutions for which the gravitational sources are cosmic strings
containing torsion and curvature, which do not have a Newtonian limit.


title: Are All Static Black Hole Solutions Spherically Symmetric?

abstract:
  The static black hole solutions to the Einstein-Maxwell equations are all
spherically symmetric, as are many of the recently discovered black hole
solutions in theories of gravity coupled to other forms of matter. However,
counterexamples demonstrating that static black holes need not be spherically
symmetric exist in theories, such as the standard electroweak model, with
electrically charged massive vector fields. In such theories, a magnetically
charged Reissner-Nordstrom solution with sufficiently small horizon radius is
unstable against the development of a nonzero vector field outside the horizon.
General arguments show that, for generic values of the magnetic charge, this
field cannot be spherically symmetric. Explicit construction of the solution
shows that it in fact has no rotational symmetry at all.


title: Thermodynamics of Spacetime: The Einstein Equation of State

abstract:
  The Einstein equation is derived from the proportionality of entropy and
horizon area together with the fundamental relation $\delta Q=TdS$ connecting
heat, entropy, and temperature. The key idea is to demand that this relation
hold for all the local Rindler causal horizons through each spacetime point,
with $\delta Q$ and $T$ interpreted as the energy flux and Unruh temperature
seen by an accelerated observer just inside the horizon. This requires that
gravitational lensing by matter energy distorts the causal structure of
spacetime in just such a way that the Einstein equation holds. Viewed in this
way, the Einstein equation is an equation of state. This perspective suggests
that it may be no more appropriate to canonically quantize the Einstein
equation than it would be to quantize the wave equation for sound in air.


title: Cobordism Effects in the Regge Calculus Approach to Quantum Cosmology

abstract:
  We study the ground state wave function for a universe which is topologically
a lens space within the Regge calculus approach. By restricting the four
dimensional simplicial complex to be a cone over the boundary lens space,
described by a single internal edge length, and a single boundary edge length,
one can analyze in detail the analytic properties of the action in the space of
complex edge lengths. The classical extrema and convergent steepest descent
contours of integration yielding the wave function are found. Both the
Hartle-Hawking and Linde-Vilenkin type proposals are examined and, in all
cases, we find wave functions which predict Lorentzian oscillatory behaviour in
the late universe. A factorization property of topology changing amplitudes
within a restricted edge length class of cone type complexes is established.
The behaviour of the results under subdivision of the boundary universe is also
presented.


title: CANONICAL QUANTIZATION OF CYLINDRICALLY SYMMETRIC MODELS

abstract:
  We carry out the canonical quantization of the Levi-Civit\`a family of static
and cylindrical solutions. The reduced phase space of this family of metrics is
proved to coincide with that corresponding to the Kasner model, including the
associated symplectic structures, except for that the respective domains of
definition of one of the phase space variables are not identical. Using this
result, we are able to construct a quantum model that describes spacetimes of
both the Levi-Civit\`a and the Kasner type, and in which the three-dimensional
spatial topology is not uniquely fixed. Finally, we quantize to completion the
subfamily of Levi-Civit\`a solutions which represent the exterior gravitational
field of a straight cosmic string. These solutions are conical geometries,ie,
Minkowski spacetime minus a wedge. The quantum theory obtained provides us with
predictions about the angular size of this wedge.


title: Relativistic Gauge Conditions in Quantum Cosmology

abstract:
  This paper studies the quantization of the electromagnetic field on a flat
Euclidean background with boundaries. One-loop scaling factors are evaluated
for the one-boundary and two-boundary backgrounds. The mode-by-mode analysis of
Faddeev-Popov quantum amplitudes is performed by using zeta-function
regularization, and is compared with the space-time covariant evaluation of the
same amplitudes. It is shown that a particular gauge condition exists for which
the corresponding operator matrix acting on gauge modes is in diagonal form
from the beginning. Moreover, various relativistic gauge conditions are studied
in detail, to investigate the gauge invariance of the perturbative quantum
theory.


title:
Non-Universality of Critical Behaviour in Spherically Symmetric
  Gravitational Collapse

abstract:
  The aim of the present letter is to explain the `critical behaviour' observed
in numerical studies of spherically symmetric gravitational collaps of a
perfect fluid. A simple expression results for the critical index $\gamma$ of
the black hole mass considered as an order parameter. $\gamma$ turns out to
vary strongly with the parameter $k$ of the assumed equation of state
$p=k\rho$.


title: Regularity Theorems in the Nonsymmetric Gravitational Theory

abstract:
  Regularity theorems are presented for cosmology and gravitational collapse in
non-Riemannian gravitational theories. These theorems establish conditions
necessary to allow the existence of timelike and null path complete spacetimes
for matter that satisfies the positive energy condition. Non-Riemannian
theories of gravity can have solutions that have a non-singular beginning of
the universe, and the gravitational collapse of a star does not lead to a black
hole event horizon and a singularity as a final stage of collapse. A
perturbatively consistent version of nonsymmetric gravitational theory is
studied that, in the long-range approximation, has a nonsingular static
spherically symmetric solution which is path complete, does not have black hole
event horizons and has finite curvature invariants. The theory satisfies the
regularity theorems for cosmology and gravitational collapse. The elimination
of black holes resolves the information loss puzzle.


title: Localization of Energy in General Relativity

abstract:
  In the framework of the teleparallel equivalent of general relativity the
energy density of asymptoticaly flat gravitational fields can be naturally and
unambiguously defined. Upon integration of the energy density over the whole
three dimensional space we obtain the ADM energy. We use this energy density to
calculate the energy inside a Schwarzschild black hole.


title: Localization of energy for a Kerr black hole

abstract:
  In the teleparallel equivalent of general relativity the energy density of
asymptoticaly flat gravitational fields can be naturally defined as a scalar
density restricted to a three dimensional spacelike hypersurface. The scalar
density has simple expression in terms of the trace of the torsion tensor. Here
we obtain the formal expression of the localized energy for a Kerr black hole.
The energy inside a surface of constant radius can be explicitly calculated in
the limit of small $a$, the specific angular momentum. Such expression turns
out to be exactly the same as the one obtained by means of the method recently
proposed by Brown and York.


title:
Counterexample to the passive topological censorship of K(pi,1) prime
  factors

abstract:
  A globally hyperbolic asymptotically flat spacetime is presented (having
non-negative energy density and pressures) that shows that not all K(pi,1)
prime factors of the Cauchy surface topology are passively censored according
to asymptotic observers in contradiction to an argument of Friedman, Schleich,
and Witt.


title: Rarita-Schwinger Potentials in Quantum Cosmology

abstract:
  This paper studies the two-spinor form of the Rarita-Schwinger potentials
subject to local boundary conditions compatible with local supersymmetry. The
massless Rarita-Schwinger field equations are studied in four-real-dimensional
Riemannian backgrounds with boundary. Gauge transformations on the potentials
are shown to be compatible with the field equations providing the background is
Ricci-flat, in agreement with previous results in the literature. However, the
preservation of boundary conditions under such gauge transformations leads to a
restriction of the gauge freedom. The recent construction by Penrose of
secondary potentials which supplement the Rarita-Schwinger potentials is then
applied. The equations for the secondary potentials, jointly with the boundary
conditions, imply that the background four-geometry is further restricted to be
totally flat.


title:
A Modular Invariant Quantum Theory From the Connection Formulation of
  (2+1)-Gravity on the Torus

abstract:
  By choosing an unconventional polarization of the connection phase space in
(2+1)-gravity on the torus, a modular invariant quantum theory is constructed.
Unitary equivalence to the ADM-quantization is shown.


title: Cosmological production of charged black hole pairs

abstract:
  We investigate the pair creation of charged black holes in a background with
a positive cosmological constant. We consider $C$ metrics with a cosmological
constant, and show that the conical singularities in the metric only disappear
when it reduces to the Reissner-Nordstr\"om de Sitter metric. We construct an
instanton describing the pair production of extreme black holes and an
instanton describing the pair production of non-extreme black holes from the
Reissner-Nordstr\"om de Sitter metric, and calculate their actions. There are a
number of striking similarities between these instantons and the Ernst
instantons, which describe pair production in a background electromagnetic
field. We also observe that the type I instanton in the ordinary $C$ metric
with zero cosmological constant is actually the Reissner-Nordstr\"om solution.


title: One-Loop Amplitudes in Euclidean Quantum Gravity

abstract:
  This paper studies the linearized gravitational field in the presence of
boundaries. For this purpose, $\zeta$-function regularization is used to
perform the mode-by-mode evaluation of BRST-invariant Faddeev-Popov amplitudes
in the case of flat Euclidean four-space bounded by a three-sphere. On choosing
the de Donder gauge-averaging term, the resulting $\zeta(0)$ value is found to
agree with the space-time covariant calculation of the same amplitudes, which
relies on the recently corrected geometric formulas for the asymptotic heat
kernel in the case of mixed boundary conditions. Two sets of mixed boundary
conditions for Euclidean quantum gravity are then compared in detail. The
analysis proves that one cannot restrict the path-integral measure to
transverse-traceless perturbations. By contrast, gauge-invariant amplitudes are
only obtained on considering from the beginning all perturbative modes of the
gravitational field, jointly with ghost modes.


title: STABLE CLOCKS AND GENERAL RELATIVITY

abstract:
  We survey the role of stable clocks in general relativity. Clock comparisons
have provided important tests of the Einstein Equivalence Principle, which
underlies metric gravity. These include tests of the isotropy of clock
comparisons (verification of local Lorentz invariance) and tests of the
homogeneity of clock comparisons (verification of local position invariance).
Comparisons of atomic clocks with gravitational clocks test the Strong
Equivalence Principle by bounding cosmological variations in Newton's constant.
Stable clocks also play a role in the search for gravitational radiation:
comparision of atomic clocks with the binary pulsar's orbital clock has
verified gravitational-wave damping, and phase-sensitive detection of waves
from inspiralling compact binaries using laser interferometric gravitational
observatories will facilitate extraction of useful source information from the
data. Stable clocks together with general relativity have found important
practical applications in navigational systems such as GPS.


title:
Quantization of diffeomorphism invariant theories of connections with
  local degrees of freedom

abstract:
  Quantization of diffeomorphism invariant theories of connections is studied.
A solutions of the diffeomorphism constraints is found. The space of solutions
is equipped with an inner product that is shown to satisfy the physical reality
conditions. This provides, in particular, a quantization of the
Husain-Kucha\v{r} model. The main results also pave way to quantization of
other diffeomorphism invariant theories such as general relativity. In the
Riemannian case (i.e., signature ++++), the approach appears to contain all the
necessary ingredients already. In the Lorentzian case, it will have to combined
in an appropriate fashion with a coherent state transform to incorporate
complex connections.


title: Semiclassical Stability of the Extreme Reissner-Nordstrom Black Hole

abstract:
  The stress-energy tensor of a free quantized scalar field is calculated in
the extreme Reissner-Nordstr\"{o}m black hole spacetime in the zero temperature
vacuum state. The stress-energy appears to be regular on the event horizon,
contrary to the suggestion provided by two-dimensional calculations. An
analytic calculation on the event horizon for a thermal state shows that if the
temperature is nonzero then the stress-energy diverges strongly there.


title: Effective Lagrangian for Quantum Black Holes

abstract:
  We discuss the most general effective Lagrangian obtained from the assumption
that the degrees of freedom to be quantized, in a black hole, are on the
horizon. The effective Lagrangian depends only on the induced metric and the
extrinsic curvature of the (fluctuating) horizon, and the possible operators
can be arranged in an expansion in powers of $\mpl/M$, where $\mpl$ is the
Planck mass and $M$ the black hole mass. We perform a semiclassical expansion
of the action with a formalism which preserves general covariance explicitly.
Quantum fluctuations over the classical solutions are described by a single
scalar field living in the 2+1 dimensional world-volume swept by the horizon,
with a given coupling to the background geometry. We discuss the resulting
field theory and we compute the black hole entropy with our formalism.


title: Massive scalar field in multiply connected flat spacetimes

abstract:
  The vacuum expectation value of the stress-energy tensor $\left\langle
0\left| T_{\mu\nu} \right|0\right\rangle$ is calculated in several multiply
connected flat spacetimes for a massive scalar field with arbitrary curvature
coupling. We find that a nonzero field mass always decreases the magnitude of
the energy density in chronology-respecting manifolds such as $R^3 \times S^1$,
$R^2 \times T^2$, $R^1 \times T^3$, the M\"{o}bius strip, and the Klein bottle.
In Grant space, which contains nonchronal regions, whether $\left\langle
0\left| T_{\mu\nu} \right|0\right\rangle$ diverges on a chronology horizon or
not depends on the field mass. For a sufficiently large mass $\left\langle
0\left| T_{\mu\nu} \right|0\right\rangle$ remains finite, and the metric
backreaction caused by a massive quantized field may not be large enough to
significantly change the Grant space geometry.


title: STATIONARY SOLUTIONS IN BRANS-DICKE STOCHASTIC INFLATIONARY COSMOLOGY

abstract:
  In Brans-Dicke theory the Universe becomes divided after inflation into many
exponentially large domains with different values of the effective
gravitational constant. Such a process can be described by diffusion equations
for the probability of finding a certain value of the inflaton and dilaton
fields in a physical volume of the Universe. For a typical chaotic inflation
potential, the solutions for the probability distribution never become
stationary but grow forever towards larger values of the fields. We show here
that a non-minimal conformal coupling of the inflaton to the curvature scalar,
as well as radiative corrections to the effective potential, may provide a
dynamical cutoff and generate stationary solutions. We also analyze the
possibility of large nonperturbative jumps of the fluctuating inflaton scalar
field, which was recently revealed in the context of the Einstein theory. We
find that in the Brans--Dicke theory the amplitude of such jumps is strongly
suppressed.


title:
Selfdual 2-form formulation of gravity and classification of
  energy-momentum tensors

abstract:
  It is shown how the different irreducibility classes of the energy-momentum
tensor allow for a Lagrangian formulation of the gravity-matter system using a
selfdual 2-form as a basic variable. It is pointed out what kind of
difficulties arise when attempting to construct a pure spin-connection
formulation of the gravity-matter system. Ambiguities in the formulation
especially concerning the need for constraints are clarified.


title: Interacting scalar fields in de Sitter space

abstract:
  We investigate the massless $\lambda \phi^4$ theory in de~Sitter space. It is
unnatural to assume a minimally coupled interacting scalar field, since $\xi=0$
is not a fixed point of the renormalization group once interactions are
included. In fact, the only case where perturbation theory can be trusted is
when the field is non-minimally coupled at the minimum of the effective
potential. Thus, in perturbation theory, there is no infrared divergence
associated with this scalar field.


title: Quantum Tunneling Effect in Oscillating Friedmann Cosmology

abstract:
  It is shown that the tunneling effect in quantum cosmology is possible not
only at the very beginning or the very end of the evolution, but also at the
moment of maximum expansion of the universe. A positive curvature expanding
Friedmann universe changes its state of evolution spontaneously and completely,
{\it without} any changes in the matter content, avoiding recollapse, and
falling into oscillations between the nonzero values of the scale factor. On
the other hand, an oscillating nonsingular universe can tunnel spontaneously to
a recollapsing regime. The probability of such kind of tunneling is given
explicitly. It is inversely related to the amount of nonrelativistic matter
(dust), and grows from a certain fixed value to unity if the negative
cosmological constant approaches zero.


title:
New variables, the gravitational action, and boosted quasilocal
  stress-energy-momentum

abstract:
  This paper presents a complete set of quasilocal densities which describe the
stress-energy-momentum content of the gravitational field and which are built
with Ashtekar variables. The densities are defined on a two-surface $B$ which
bounds a generic spacelike hypersurface $\Sigma$ of spacetime. The method used
to derive the set of quasilocal densities is a Hamilton-Jacobi analysis of a
suitable covariant action principle for the Ashtekar variables. As such, the
theory presented here is an Ashtekar-variable reformulation of the metric
theory of quasilocal stress-energy-momentum originally due to Brown and York.
This work also investigates how the quasilocal densities behave under
generalized boosts, i. e. switches of the $\Sigma$ slice spanning $B$. It is
shown that under such boosts the densities behave in a manner which is similar
to the simple boost law for energy-momentum four-vectors in special relativity.
The developed formalism is used to obtain a collection of two-surface or boost
invariants. With these invariants, one may ``build" several different mass
definitions in general relativity, such as the Hawking expression. Also
discussed in detail in this paper is the canonical action principle as applied
to bounded spacetime regions with ``sharp corners."


title: Rotating Dilaton Black Holes

abstract:
  We consider the axially symmetric coupled system of gravitation,
electromagnetism and a dilaton field. Reducing from four to three dimensions,
the system is described by gravity coupled to a non-linear $\sigma$-model. We
find the target space isometries and use them to generate new solutions. It
seems that it is only possible to generate rotating solutions from non-rotating
ones for the special cases when the dilaton coupling parameter $a=0, \pm
\sqrt{3}$. For those particular values, the target space symmetry is enlarged.


title: Quantum Probes of Spacetime Singularities

abstract:
  It is shown that there are static spacetimes with timelike curvature
singularities which appear completely nonsingular when probed with quantum test
particles. Examples include extreme dilatonic black holes and the fundamental
string solution. In these spacetimes, the dynamics of quantum particles is well
defined and uniquely determined.


title: Dynamics of Yang-Mills Cosmology Bubbles in Bartnik-McKinnon Spacetimes

abstract:
  We investigate the dynamics of a Yang-Mills cosmology (YMC, the FRW type
spacetime) bubble in the Bartnik-McKinnon (BK) spacetimes. Because a BK
spacetime can be identified to a YMC spacetime with a finite scale factor in
the neighborhood of the origin, we can give a natural initial condition for the
YMC bubble. The YMC bubble can smoothly emerge from the origin without an
initial singularity. Under a certain condition, the bubble develops
continuously and finally replaces the entire BK spacetime, the metric of which
is the same as the one of the radiation dominated universe. We also discuss why
an initial singularity can be avoided in the present case in spite of the
singularity theorems by Hawking and Penrose.


title: Semiclassicality and Decoherence of Cosmological Perturbations

abstract:
  Transition to the semiclassical behaviour and the decoherence process for
inhomogeneous perturbations generated from the vacuum state during an
inflationary stage in the early Universe are considered both in the Heisenberg
and the Schr\"odinger representations to show explicitly that both approaches
lead to the same prediction: the equivalence of these quantum perturbations to
classical perturbations having stochastic Gaussian amplitudes and belonging to
the quasi-isotropic mode. This equivalence and the decoherence are achieved
once the exponentially small (in terms of the squeezing parameter $r_k$)
decaying mode is neglected. In the quasi-classical limit $|r_k|\to \infty$, the
perturbation mode functions can be made real by a time-independent phase
rotation, this is shown to be equivalent to a fixed relation between squeezing
angle and phase for all modes in the squeezed-state formalism. Though the
present state of the gravitational wave background is not a squeezed quantum
state in the rigid sense and the squeezing parameters loose their direct
meaning due to interaction with the environment and other processes, the
standard predictions for the rms values of the perturbations generated during
inflation are not affected by these mechanisms (at least, for scales of
interest in cosmological applications). This stochastic background still
occupies a small part of phase space.


title:
Just how long can you live in a black hole and what can be done about
  it?

abstract:
  We study the problem of how long a journey within a black hole can last.
Based on our observations, we make two conjectures. First, for observers that
have entered a black hole from an asymptotic region, we conjecture that the
length of their journey within is bounded by a multiple of the future
asymptotic ``size'' of the black hole, provided the spacetime is globally
hyperbolic and satisfies the dominant-energy and non-negative-pressures
conditions. Second, for spacetimes with ${\Bbb R}^3$ Cauchy surfaces (or an
appropriate generalization thereof) and satisfying the dominant energy and
non-negative-pressures conditions, we conjecture that the length of a journey
anywhere within a black hole is again bounded, although here the bound requires
a knowledge of the initial data for the gravitational field on a Cauchy
surface. We prove these conjectures in the spherically symmetric case. We also
prove that there is an upper bound on the lifetimes of observers lying ``deep
within'' a black hole, provided the spacetime satisfies the
timelike-convergence condition and possesses a maximal Cauchy surface. Further,
we investigate whether one can increase the lifetime of an observer that has
entered a black hole, e.g., by throwing additional matter into the hole.
Lastly, in an appendix, we prove that the surface area $A$ of the event horizon
of a black hole in a spherically symmetric spacetime with ADM mass
$M_{\text{ADM}}$ is always bounded by $A \le 16\pi M_{\text{ADM}}^2$, provided
that future null infinity is complete and the spacetime is globally hyperbolic
and satisfies the dominant-energy condition.


title:
A New Test of the Einstein Equivalence Principle and the Isotropy of
  Space

abstract:
  Recent research has established that nonsymmetric gravitation theories like
Moffat's NGT predict that a gravitational field singles out an orthogonal pair
of polarization states of light that propagate with different phase velocities.
We show that a much wider class of nonmetric theories encompassed by the $\chi
g$ formalism predict such violations of the Einstein equivalence principle.
This gravity-induced birefringence of space implies that propagation through a
gravitational field can alter the polarization of light. We use data from
polarization measurements of extragalactic sources to constrain birefringence
induced by the field of the Galaxy. Our new constraint is $10^8$ times sharper
than previous ones.


title: A Phase Space Path Integral for (2+1)-Dimensional Gravity

abstract:
  I investigate the relationship between the phase space path integral in
(2+1)-dimensional gravity and the canonical quantization of the corresponding
reduced phase space in the York time slicing. I demonstrate the equivalence of
these two approaches, and discuss some subtleties in the definition of the path
integral necessary to prove this equivalence.


title:
The Mixmaster Cosmological Model as a Pseudo-Euclidean Generalized Toda
  Chain

abstract:
  The question of the integrability of the mixmaster model of the Universe,
presented as a dynamical system with finite degrees of freedom, is investigated
in present paper. As far as the model belongs to the class of pseudo-Euclidean
generalized Toda chains, the method of getting Kovalevskaya exponents developed
for chains of Euclidean type, is used. The generalized formula of Adler and van
Moerbeke for systems of an indefinite metric is obtained. There was shown that
although by the formula we got integer values of Kovalevskaya exponents there
were multivalued solutions, branched at particular points on a plain of complex
time t. This class of solutions differs from known ones. Apparently, the system
does not possess additional algebraic and one-valued first integrals because of
complex and transcendental values of the exponents. In addition, a
ten-dimensional mixmaster model was studied. There were not integer exponents
for this case.


title:
Diffeomorphism invariant subspaces in Witten's 2+1 quantum gravity on
  ${\bf R} \times T^2$

abstract:
  We address the role of large diffeomorphisms in Witten's 2+1 gravity on the
manifold ${\bf R} \times T^2$. In a ``spacelike sector" quantum theory that
treats the large diffeomorphisms as a symmetry, rather than as gauge, the
Hilbert space is shown to contain no nontrivial finite dimensional subspaces
that are invariant under the large diffeomorphisms. Infinite dimensional closed
invariant subspaces are explicitly constructed, and the representation of the
large diffeomorphisms is thus shown to be reducible. Comparison is made to
Witten's theory on ${\bf R} \times \Sigma$, where $\Sigma$ is a higher genus
surface.


title: Spin Networks in Nonperturbative Quantum Gravity

abstract:
  A spin network is a generalization of a knot or link: a graph embedded in
space, with edges labelled by representations of a Lie group, and vertices
labelled by intertwining operators. Such objects play an important role in
3-dimensional topological quantum field theory, functional integration on the
space A/G of connections modulo gauge transformations, and the loop
representation of quantum gravity. Here, after an introduction to the basic
ideas of nonperturbative canonical quantum gravity, we review a rigorous
approach to functional integration on A/G in which L^2(A/G) is spanned by
states labelled by spin networks. Then we explain the `new variables' for
general relativity in 4-dimensional spacetime and describe how canonical
quantization of gravity in this formalism leads to interesting applications of
these spin network states.


title: Soliton Induced Singularities in 2 d Gravity and their Evaporation

abstract:
  Positive energy singularities induced by Sine-Gordon solitons in 1+1
dimensional dilaton gravity with positive and negative cosmological constant
are considered. When the cosmological constant is positive, the singularities
combine a white hole, a timelike singularity and a black hole joined smoothly
near the soliton center. When the cosmological constant is negative, the
solutions describe two timelike singularities joined smoothly near the soliton
center. We describe these spacetimes and examine their evaporation in the one
loop approximation.


title: Clock and Category; IS QUANTUM GRAVITY ALGEBRAIC

abstract:
  We investigate the possibility that the quantum theory of gravity could be
constructed discretely using algebraic methods. The algebraic tools are similar
to ones used in constructing topological quantum field theories.The algebraic
tools are related to ideas about the reinterpretation of quantum mechanics in a
general relativistic context.


title:
The Constraints in Spherically Symmetric General Relativity III ---
  Identifying the Configuration Space: $J\ne 0$

abstract:
  We continue our examination of the constraints in spherically symmetric
general relativity begun in I (gr-qc/9411009) and II (gr-qc/9411010). We extend
to general configurations with $J\ne 0$ the analysis of II which treated a
moment of time symmetry. We exploit the one parameter family of foliations
introduced in I which are linear and homogeneous in the extrinsic curvature to
characterize apparent horizons and spatial singularities in the initial data.
In particular, we demonstrate that these characterizations do not depend
sensitively on the foliation.


title:
Dimensionality, topology, energy, the cosmological constant, and
  signature change

abstract:
  Using the concept of real tunneling configurations (classical signature
change) and nucleation energy, we explore the consequences of an alternative
minimization procedure for the Euclidean action in multiple-dimensional quantum
cosmology. In both standard Hartle-Hawking type as well as Coleman type
wormhole-based approaches, it is suggested that the action should be minimized
among configurations of equal energy. In a simplified model, allowing for
arbitrary products of spheres as Euclidean solutions, the favoured space-time
dimension is 4, the global topology of spacelike slices being ${\bf S}^1 \times
{\bf S}^2$ (hence predicting a universe of Kantowski-Sachs type). There is,
however, some freedom for a Kaluza-Klein scenario, in which case the observed
spacelike slices are ${\bf S}^3$. In this case, the internal space is a product
of two-spheres, and the total space-time dimension is 6, 8, 10 or 12.


title:
``Faster than Light'' Photons in Gravitational Fields -- Causality,
  Anomalies and Horizons

abstract:
  A number of general issues relating to superluminal photon propagation in
gravitational fields are explored. The possibility of superluminal, yet causal,
photon propagation arises because of Equivalence Principle violating
interactions induced by vacuum polarisation in QED in curved spacetime. Two
general theorems are presented: first, a polarisation sum rule which relates
the polarisation averaged velocity shift to the matter energy-momentum tensor
and second, a `horizon theorem' which ensures that the geometric event horizon
for black hole spacetimes remains a true horizon for real photon propagation in
QED. A comparision is made with the equivalent results for electromagnetic
birefringence and possible connections between superluminal photon propagation,
causality and the conformal anomaly are exposed.


title:
Self-dual variables, positive semi-definite action, and discrete
  transformations in four-dimensional quantum gravity

abstract:
  A positive semi-definite Euclidean action for arbitrary four-topologies can
be constructed by adding appropriate Yang-Mills and topological terms to the
Samuel-Jacobson-Smolin action of gravity with (anti)self-dual variables.
Moreover, on-shell, the (anti)self-dual sector of the new theory corresponds
precisely to all Einstein manifolds in four dimensions. The Lorentzian
signature action, and its analytic continuations are also considered. A
self-contained discussion is given on the effects of discrete transformations
C, P and T on the Samuel-Jacobson-Smolin action, and other proposed actions
which utilize self- or anti-self-dual variables as fundamental variables in the
description of four-dimensional gravity.


title:
Canonical General Relativity on a Null Surface with Coordinate and Gauge
  Fixing

abstract:
  We use the canonical formalism developed together with David Robinson to st=
udy the Einstein equations on a null surface. Coordinate and gauge conditions =
are introduced to fix the triad and the coordinates on the null surface. Toget=
her with the previously found constraints, these form a sufficient number of
second class constraints so that the phase space is reduced to one pair of
canonically conjugate variables: $\Ac_2\and\Sc^2$. The formalism is related to
both the Bondi-Sachs and the Newman-Penrose methods of studying the
gravitational field at null infinity. Asymptotic solutions in the vicinity of
null infinity which exclude logarithmic behavior require the connection to fall
off like $1/r^3$ after the Minkowski limit. This, of course, gives the previous
results of Bondi-Sachs and Newman-Penrose. Introducing terms which fall off
more slowly leads to logarithmic behavior which leaves null infinity intact,
allows for meaningful gravitational radiation, but the peeling theorem does not
extend to $\Psi_1$ in the terminology of Newman-Penrose. The conclusions are in
agreement with those of Chrusciel, MacCallum, and Singleton. This work was
begun as a preliminary study of a reduced phase space for quantization of
general relativity.


title: Thermal divergences on the event horizons of two-dimensional black holes

abstract:
  The expectation value of the stress-energy tensor $\langleT_{\mu\nu}\rangle$
of a free conformally invariant scalar field is computed in a general static
two-dimensional black hole spacetime when the field is in either a zero
temperature vacuum state or a thermal state at a nonzero temperature. It is
found that for every static two-dimensional black hole the stress-energy
diverges strongly on the event horizon unless the field is in a state at the
natural black hole temperature which is defined by the surface gravity of the
event horizon. This implies that both extreme and nonextreme two-dimensional
black holes can only be in equilibrium with radiation at the natural black hole
temperature.


title:
Statistics of the Microwave Background Anisotropies Caused by the
  Squeezed Cosmological Perturbations

abstract:
  It is likely that the observed large-angular-scale anisotropies in the
microwave background radiation are induced by the cosmological perturbations of
quantum-mechanical origin. Such perturbations are now placed in squeezed vacuum
quantum states and, hence, are characterized by large variances of their
amplitude. The statistical properties of the anisotropies should reflect the
underlying statistics of the squeezed vacuum quantum states. The theoretical
variances for the temperature angular correlation function are derived and
described quantitatively. It is shown that they are indeed large.
Unfortunately, these large theoretical statistical uncertainties will make the
extraction of cosmological information from the measured anisotropies a much
more difficult problem than we wanted it to be.


title: Gravitational Waves in Bianchi Type-I Universes I: The Classical Theory

abstract:
  The propagation of classical gravitational waves in Bianchi Type-I universes
is studied. We find that gravitational waves in Bianchi Type-I universes are
not equivalent to two minimally coupled massless scalar fields as it is for the
Robertson-Walker universe. Due to its tensorial nature, the gravitational wave
is much more sensitive to the anisotropy of the spacetime than the scalar field
is and it gains an effective mass term. Moreover, we find a coupling between
the two polarization states of the gravitational wave which is also not present
in the Robertson-Walker universe.


title:
Physical Consequences of the Interpretation of the Skew Part of
  $g_{\mu\nu}$ in Einstein's Nonsymmetric Unified Field Theory

abstract:
  The electromagnetic interaction in the Einstein-Infeld-Hoffmann (EIH)
equations of motion for charged particles in Einstein's Unified Field Theory is
found to be {\em automatically\/} precluded by the conventional identification
of the skew part of the fundamental tensor with the Faraday tensor. It is shown
that an alternative identification, suggested by observations of Einstein,
Bergmann and Papapetrou, would lead to the expected electromagnetic
interaction, were it not for the intervention of an infelicitous (radiation)
gauge. Therefore, an EIH analysis of EUFT is {\em inconclusive\/} as a test of
the physical viability of the theory, and it follows that EUFT cannot be
considered necessarily unphysical on the basis of such an analysis. Thus,
historically, Einstein's Unified Field Theory was rejected for the wrong
reason.


title: A Judgement on Sinors

abstract:
  This note contains some comments on a recent paper by Friedman on
two-component spinors in spacetimes which do not admit a time-orientation, and
is intended to clarify the relation of the work reported in that paper to
previous literature.


title: Entanglement entropy in curved spacetimes with event horizons

abstract:
  We consider the computation of the entanglement entropy in curved backgrounds
with event horizons. We use a Hamiltonian approach to the problem and perform
numerical computations on a spherical lattice of spacing $a$. We study the
cosmological case and make explicit computations for the
Friedmann-Robertson-Walker universe. Our results for a massless, minimally
coupled scalar field can be summarized by $S_{ent}=0.30 r_H^2/a^2$,which
resembles the flat space formula, although here the horizon radius, $r_H$, is
time-dependent.


title: Yilmaz Cancels Newton

abstract:
  A central tenet of the new theory of gravity proposed by H. Yilmaz is the
inclusion of a gravitational stress-energy tensor $-{t_\mu}^\nu$ along with the
matter stress-energy tensor ${T_\mu}^\nu$ on the right hand side of the
Einstein field equations. This change does not effect the Newtonian limit of
the field equations since these terms are quadratic in potential gradients.
{}From the Bianchi identities, however, important changes appear in any
equations of motion consistent with these field equations. For matter described
as a perfect fluid, and with Yilmaz's choice of signs when introducing these
quadratic terms, we find that the Euler hydrodynamic equation in the Newtonian
limit is modified to remove all gravitational forces. This allows, e.g., a
solar system in which the Sun and the planets are permanently at rest, but does
not explain how fluid bodies such as the Sun or Jupiter could form or be
prevented from dispersing.


title: The Generalised Raychaudhuri Equations : Examples

abstract:
  Specific examples of the generalized Raychaudhuri Equations for the evolution
of deformations along families of $D$ dimensional surfaces embedded in a
background $N$ dimensional spacetime are discussed. These include string
worldsheets embedded in four dimensional spacetimes and two dimensional
timelike hypersurfaces in a three dimensional curved background. The issue of
focussing of families of surfaces is introduced and analysed in some detail.


title:
Back to Basics?... or How can supersymmetry be used in simple quantum
  cosmological model

abstract:
  The general theory of N=1 supergravity with supermatter is applied to a
Bianchi type IX diagonal model. The supermatter is constituted by a complex
scalar field and its spin-$1\over 2$ fermionic partners. The Lorentz invariant
Ansatz for the wave function of the universe, $\Psi$, is taken to be as simple
as possible in order to obtain {\it new} solutions. The wave function has a
simple form when the potential energy term is set to zero. However, neither the
wormhole or the Hartle-Hawking state could be found. The Ansatz for $\Psi$ used
in this paper is constrasted with the more general framework of R. Graham and
A. Csord\'as.


title: Back reaction in the formation of a straight cosmic string

abstract:
  A simple model for the formation of a straight cosmic string, wiggly or
unperturbed is considered. The gravitational field of such string is computed
in the linear approximation. The vacuum expectation value of the stress tensor
of a massless scalar quantum field coupled to the string gravitational field is
computed to the one loop order. Finally, the back-reaction effect on the
gravitational field of the string is obtained by solving perturbatively the
semiclassical Einstein's equations.


title: Obstructions to Pin Structures on Kleinian Manifolds

abstract:
  We develop various topological notions on four-manifolds of Kleinian
signature $(- - + +)$. In particular, we extend the concept of `Kleinian metric
homotopy' to non-orientable manifolds. We then derive the topological
obstructions to pin-Klein cobordism, for all of the pin groups. Finally, we
discuss various examples and applications which arise from this work.


title: Massive NGT and Spherically Symmetric Systems

abstract:
  The arguments leading to the introduction of the massive Nonsymmetric
Gravitational action are reviewed \cite{Moffat:1994,Moffat:1995b}, leading to
an action that gives asymptotically well-behaved perturbations on GR
backgrounds. Through the analysis of spherically symmetric perturbations about
GR (Schwarzschild) and NGT (Wyman-type) static backgrounds, it is shown that
spherically symmetric systems are not guaranteed to be static, and hence
Birkhoff's theorem is not valid in NGT. This implies that in general one must
consider time dependent exteriors when looking at spherically symmetric systems
in NGT. For the surviving monopole mode considered here there is no energy flux
as it is short ranged by construction. Further work on the spherically
symmetric case will be motivated through a discussion of the possibility that
there remain additional modes that do not show up in weak field situations, but
nonetheless exist in the full theory and may again result in bad global
asymptotics. A presentation of the action and field equations in a general
frame is given in the course of the paper, providing an alternative approach to
dealing with the algebraic complications inherent in NGT, as well as offering a
more general framework for discussing the physics of the antisymmetric sector.


title: Spin Networks and Quantum Gravity

abstract:
  We introduce a new basis on the state space of non-perturbative quantum
gravity. The states of this basis are linearly independent, are well defined in
both the loop representation and the connection representation, and are labeled
by a generalization of Penrose's spin netoworks. The new basis fully reduces
the spinor identities (SU(2) Mandelstam identities) and simplifies calculations
in non-perturbative quantum gravity. In particular, it allows a simple
expression for the exact solutions of the Hamiltonian constraint
(Wheeler-DeWitt equation) that have been discovered in the loop representation.
Since the states in this basis diagnolize operators that represent the three
geometry of space, such as the area and volumes of arbitrary surfaces and
regions, these states provide a discrete picture of quantum geometry at the
Planck scale.


title: Quasilocal Thermodynamics of Dilaton Gravity coupled to Gauge Fields

abstract:
  We consider an Einstein-Hilbert-Dilaton action for gravity coupled to various
types of Abelian and non-Abelian gauge fields in a spatially finite system.
These include Yang-Mills fields and Abelian gauge fields with three and
four-form field strengths. We obtain various quasilocal quantities associated
with these fields, including their energy and angular momentum, and develop
methods for calculating conserved charges when a solution possesses sufficient
symmetry. For stationary black holes, we find an expression for the entropy
from the micro-canonical form of the action. We also find a form of the first
law of black hole thermodynamics for black holes with the gauge fields of the
type considered here.


title: Gravitational energy of conical defects

abstract:
  The energy density of asymptotically flat gravitational fields can be
calculated from a simple expression involving the trace of the torsion tensor.
Integration of this energy density over the whole space yields the ADM energy.
Such expression can be justified within the framework of the teleparallel
equivalent of general relativity, which is an alternative geometrical
formulation of Einstein's general relativity. In this paper we apply this
energy density to the evaluation of the energy per unit length of a class of
conical defects of topological nature, which include disclinations and
dislocations (in the terminology of crystallography). Disclinations correspond
to cosmic strings, and for a spacetime endowed with only such a defect we
obtain precisely the well known expression of energy per unit length. However
for a pure spacetime dislocation the total gravitational energy is zero.


title:
On the eigenfunctions of the Dirac operator on spheres and real
  hyperbolic spaces

abstract:
  The eigenfunctions of the Dirac operator on spheres and real hyperbolic
spaces of arbitrary dimension are computed by separating variables in geodesic
polar coordinates. These eigenfunctions are used to derive the heat kernel of
the iterated Dirac operator on these spaces. They are then studied as cross
sections of homogeneous vector bundles, and a group-theoretic derivation of the
spinor spherical functions and heat kernel is given based on Harish-Chandra's
formula for the radial part of the Casimir operator.


title:
SHORTCUT METHOD OF SOLUTION OF GEODESIC EQUATIONS FOR SCHWARZSCHILD
  BLACK HOLE

abstract:
  It is shown how the use of the Kerr-Schild coordinate system can greatly
simplify the formulation of the geodesic equation of the Schwarzschild
solution. An application of this formulation to the numerical computation of
the aspect of a non-rotating black hole is presented. The generalization to the
case of the Kerr solution is presented too.


title: REALITY AND GEOMETRY OF STATES AND OBSERVABLES IN QUANTUM THEORY

abstract:
  The determination of the quantum state of a single system by protective
observation is used to justify operationally a formulation of quantum theory on
the quantum state space (projective Hilbert space) $\cal P$. Protective
observation is extended to a more general quantum theory in which the
Schrodinger evolution is generalized so that it preserves the symplectic
structure but not necessarily the metric in $\cal P$. The relevance of this
more general evolution to the apparant collapse of the state vector during the
usual measurement, and its possible connection to gravity is suggested. Some
criticisms of protective observation are answered. A comparison is made between
the determination of quantum states using the geometry of $\cal P$ by
protective measurements, via a reconstruction theorem, and the determination of
space-time points by means of the space-time geometry, via Einstein's hole
argument. It is argued that a protective measurement may not determine a time
average.


title: Spectroscopy of the quantum black hole

abstract:
  We develop the idea that, in quantum gravity where the horizon fluctuates, a
black hole should have a discrete mass spectrum with concomitant line emission.
Simple arguments fix the spacing of the lines, which should be broad but
unblended. Assuming uniformity of the matrix elements for quantum transitions
between near levels, we work out the probabilities for the emission of a
specified series of quanta and the intensities of the spectral lines. The
thermal character of the radiation is entirely due to the degeneracy of the
levels, the same degeneracy that becomes manifest as black hole entropy. One
prediction is that there should be no lines with wavelength of order the black
hole size or larger. This makes it possible to test quantum gravity with black
holes well above Planck scale.


title: Toda Lattice and Tomimatsu-Sato Solutions

abstract:
  We discuss an analytic proof of a conjecture (Nakamura) that solutions of
Toda molecule equation give those of Ernst equation giving Tomimatsu-Sato
solutions of Einstein equation. Using Pfaffian identities it is shown for Weyl
solutions completely and for generic cases partially.


title:
The stress energy tensor of a locally supersymmetric quantum field on a
  curved spacetime

abstract:
  For an analogon of the free Wess-Zumino model on Ricci flat spacetimes, the
relation between a conserved `supercurrent' and the point-separated improved
energy momentum tensor is investigated and a similar relation as on Minkowski
space is established. The expectation value of the latter in any globally
Hadamard product state is found to be a priori finite in the coincidence limit
if the theory is massive. On arbitrary globally hyperbolic spacetimes the
`supercurrent' is shown to be a well defined operator valued distribution on
the GNS Hilbertspace of any globally Hadamard product state. Viewed as a new
field, all n-point distributions exist, giving a new example for a Wightman
field on that manifold. Moreover, it is shown that this field satisfies a new
wave front set spectrum condition in a non trivial way.


title: On the Geometry of Planar Domain Walls

abstract:
  The Geometry of planar domain walls is studied. It is argued that the planar
walls indeed have plane symmetry. In the Minkowski coordinates the walls are
mapped into revolution paraboloids.


title: Semiclassical Gravity and Large Scale Structure

abstract:
  The possible cosmological effects of primordial fluctuation corrections to
the evolution equation of matter obtained from the Wheeler--De Witt equation
are explored. In particular, both the metric and a scalar matter field are
expanded around their homogeneous values and the corrections induced on the
scalar field fluctuation spectrum are perturbatively estimated. Finally,
results of a preliminary numerical simulation to investigate the effects on
large--scale structure formation are presented.


title:
The initial singularity in solutions of the Einstein-Vlasov system of
  Bianchi type I

abstract:
  The dynamics of solutions of the Einstein-Vlasov system with Bianchi I
symmetry is discussed in the case of massive or massless particles. It is shown
that in the case of massive particles the solutions are asymptotic to isotropic
dust solutions at late times. The initial singularity is more difficult to
analyse. It is shown that the asymptotic behaviour there must be one of a small
set of possibilities but it is not clear whether all of these possibilities are
realized. One solution is exhibited in the case of massless particles which
behaves quite differently near the singularity from any Bianchi I solution with
perfect fluid as matter model. In particular the matter is not dynamically
negligeable near the singularity for this solution.


title: GRAVITATIONAL RADIATION FROM REALISTIC COSMIC STRING LOOPS

abstract:
  We examine the rates at which energy and momentum are radiated into
gravitational waves by a large set of realistic cosmic string loops. The string
loops are generated by numerically evolving parent loops with different initial
conditions forward in time until they self-intersect, fragmenting into two
child loops. The fragmentation of the child loops is followed recursively until
only non-self-intersecting loops remain. The properties of the final
non-self-intersecting loops are found to be independent of the initial
conditions of the parent loops. We have calculated the radiated energy and
momentum for a total of 11,625 stable child loops. We find that the majority of
the final loops do not radiate significant amounts of spatial momentum. The
velocity gained due to the rocket effect is typically small compared to the
center-of-mass velocity of the fragmented loops. The distribution of
gravitational radiation rates in the center of mass frame of the loops,
$\gamma^0 \equiv (G\mu^2)^{-1} \Delta E/\Delta \tau$, is strongly peaked in the
range $\gamma^0=45-55$, however there are no loops found with $\gamma^0 < 40$.
Because the radiated spatial momentum is small, the distribution of
gravitational radiation rates appears roughly the same in any reference frame.
We conjecture that in the center-of-mass frame there is a lower bound
$\gamma^0_{\rm min}>0$ for the radiation rate from cosmic string loops. In a
second conjecture, we identify a candidate for the loop with the minimal
radiation rate and suggest that $\gamma^0_{\rm min}\cong 39.003$.


title: General considerations of matter coupling with the self-dual connection

abstract:
  It has been shown for low-spin fields that the use of only the self-dual part
of the connection as basic variable does not lead to extra conditions or
inconsistencies. We study whether this is true for more general chiral action.
We generalize the chiral gravitational action, and assume that half-integer
spin fields are coupled with torsion linearly. The equation for torsion is
solved and substituted back into the generalized chiral action, giving
four-fermion contact terms. If these contact terms are complex, the imaginary
part will give rise to extra conditions for the gravitational and matter field
equations. We study the four-fermion contact terms taking spin-1/2 and spin-3/2
fields as examples.


title: ON SPHERICALLY SYMMETRIC SOLUTIONS IN D-DIMENSIONAL DILATON GRAVITY

abstract:
  Exact static, spherically symmetric solutions to the Einstein-Abelian
gauge-dilaton equations, in $D$-dimensional gravity with a chain of $n$
Ricci-flat internal spaces are considered, with the gauge field potential
having three nonzero components: the temporal, Coulomb-like one, the one
pointing to one of the extra dimensions, and the one responsible for a radial
magnetic field. For dilaton coupling implied by string theory an
$(n+5)$-parametric family of exact solutions is obtained, while for other
dilaton couplings only $(n+3)$-parametric ones. The geometric properties and
special cases of the solutions are discussed, in particular, those when there
are horizons in the space-time. Two types of horizons are distinguished: the
conventional black-hole (BH) ones and those at which the physical section of
the space-time changes its signature ({\it T-horizons}). Two theorems are
proved, one fixing the BH and T-horizon existence conditions, the other
discarding the possibility of a regular center. Different conformal gauges are
used to characterize the system from the $D$-dimensional and 4-dimensional
viewpoints.


title: VACUUM STATIC, AXIALLY SYMMETRIC FIELDS IN D-DIMENSIONAL GRAVITY

abstract:
  Vacuum static, axially symmetric space-times in $D$-dimensional general
relativity with a Ricci-flat internal space are discussed. It is shown, in
particular, that some of the monopole-type solutions are free of curvature
singularities and their source can be a disk membrane bounded by a ring with a
string or branching type singularity. Another possibility is a wormhole
configuration where a particle can penetrate to another spatial infinity by
passing through a ring with a string or branching type singularity. The results
apply, in particular, to vacuum and scalar-vacuum configurations in
conventional general relativity.


title: Cosmology as a Problem in Critical Phenomena

abstract:
  Several problems in cosmology and astrophysics are described in which
critical phenomena of various types may play a role. These include the
organization of the disks of spiral galaxies, various aspects of the problem of
structure formation in icosmology, the problem of the selection of initial
conditions and parameters in particle physics and cosmology and the problem of
recovering the classical limit from non-perturbative formulations of quantum
gravity.


title: NONLINEAR WAVE EQUATIONS FOR RELATIVITY

abstract:
  Graviational radiation is described by canonical Yang-Mills wave equations on
the curved space-time manifold, together with evolution equations for the
metric in the tangent bundle. The initial data problem is described in
Yang-Mills scalar and vector potentials, resulting in Lie-constraints in
addition to the familiar Gauss-Codacci relations.


title: On critical behaviour in gravitational collapse

abstract:
  We give an approach to studying the critical behaviour that has been observed
in numerical studies of gravitational collapse. These studies suggest, among
other things, that black holes initially form with infinitesimal mass. We show
generally how a black hole mass formula can be extracted from a transcendental
equation.
  Using our approach, we give an explicit one parameter set of metrics that are
asymptotically flat and describe the collapse of apriori unspecified but
physical matter fields. The black hole mass formula obtained from this metric
exhibits a mass gap - that is, at the onset of black hole formation, the mass
is finite and non-zero.


title: Orbits, forces and accretion dynamics near spinning black holes

abstract:
  We analyze the relativistic dynamical properties of Keplerian and
non-Keplerian circular orbits in a general axisymmetric and stationary
gravitational field, and discuss the implications for the stability of co- and
counter-rotating accretion disks and tori surrounding a spinning black hole.
Close to the horizon there are orbital peculiarities which can seem
counterintuitive, but are elucidated by formulating the dynamics in terms of
the orbital velocity actually measured by a local, zero-angular-momentum
observer.