title: Witten's 2+1 gravity on R x (Klein bottle)

abstract:
  Witten's formulation of 2+1 gravity is investigated on the nonorientable
three-manifold R x (Klein bottle). The gauge group is taken to consist of all
four components of the 2+1 Poincare group. We analyze in detail several
components of the classical solution space, and we show that from four of the
components one can recover nondegenerate spacetime metrics. In particular, from
one component we recover metrics for which the Klein bottles are spacelike. An
action principle is formulated for bundles satisfying a certain orientation
compatibility property, and the corresponding components of the classical
solution space are promoted into a phase space. Avenues towards quantization
are briefly discussed.


title: Zeta-Regularization of the O(N) Non-Linear Sigma Model in D dimensions

abstract:
  The O(N) non-linear sigma model in a $D$-dimensional space of the form ${\bf
R}^{D-M} \times {\bf T}^M$, ${\bf R}^{D-M} \times {\bf S}^M$, or ${\bf T}^M
\times {\bf S}^P$ is studied, where ${\bf R}^M$, ${\bf T}^M$ and ${\bf S}^M$
correspond to flat space, a torus and a sphere, respectively. Using zeta
regularization and the $1/N$ expansion, the corresponding partition functions
and the gap equations are obtained. Numerical solutions of the gap equations at
the critical coupling constants are given, for several values of $D$. The
properties of the partition function and its asymptotic behaviour for large $D$
are discussed. In a similar way, a higher-derivative non-linear sigma model is
investigated too. The physical relevance of our results is discussed.


title:
Linking Topological Quantum Field Theory and Nonperturbative Quantum
  Gravity

abstract:
  Quantum gravity is studied nonperturbatively in the case in which space has a
boundary with finite area. A natural set of boundary conditions is studied in
the Euclidean signature theory, in which the pullback of the curvature to the
boundary is self-dual (with a cosmological constant). A Hilbert space which
describes all the information accessible by measuring the metric and connection
induced in the boundary is constructed and is found to be the direct sum of the
state spaces of all $SU(2)$ Chern-Simon theories defined by all choices of
punctures and representations on the spatial boundary $\cal S$. The integer
level $k$ of Chern-Simons theory is found to be given by $k= 6\pi /G^2 \Lambda
+ \alpha$, where $\Lambda$ is the cosmological constant and $\alpha$ is a $CP$
breaking phase. Using these results, expectation values of observables which
are functions of fields on the boundary may be evaluated in closed form. The
Beckenstein bound and 't Hooft-Susskind holographic hypothesis are confirmed,
(in the limit of large area and small cosmological constant) in the sense that
once the two metric of the boundary has been measured, the subspace of the
physical state space that describes the further information that the observer
on the boundary may obtain about the interior has finite dimension equal to the
exponent of the area of the boundary, in Planck units, times a fixed constant.
Finally,the construction of the state space for quantum gravity in a region
from that of all Chern-Simon theories defined on its boundary confirms the
categorical-theoretic ``ladder of dimensions picture" of Crane.


title:
Mass Formula for a Stationary Axisymmetric Configuration and the
  Physical Realization of the Kerr Metric

abstract:
  We analyse the expression for the mass of a stationary axisymmetric
configuration in general relativity obtained in our previous work [1]. From the
generality of our formula and its incompatibility with the corresponding
expression in Kerr space-time we argue that a stationary equilibrium
distribution of a real matter cannot be a source of the Kerr metric.


title:
Gravitational radiation from a particle in circular orbit around a black
  hole. VI. Accuracy of the post-Newtonian expansion

abstract:
  A particle of mass $\mu$ moves on a circular orbit around a nonrotating black
hole of mass $M$. Under the assumption $\mu \ll M$ the gravitational waves
emitted by such a binary system can be calculated exactly numerically using
black-hole perturbation theory. If, further, the particle is slowly moving,
then the waves can be calculated approximately analytically, and expressed in
the form of a post-Newtonian expansion. We determine the accuracy of this
expansion in a quantitative way by calculating the reduction in signal-to-noise
ratio incurred when matched filtering the exact signal with a nonoptimal,
post-Newtonian filter.


title: Making Predictions in Eternally Inflating Universe

abstract:
  Eternally inflating universes can contain large thermalized regions with
different values of the constants of Nature and with different density
fluctuation spectra. To find the probability for a `typical' observer to detect
a certain set of constants, or a certain fluctuation spectrum, one needs to
compare the volumes occupied by different types of regions. If the volumes are
taken on an equal-time hypersurface, the results of such a comparison are
extremely sensitive to the choice of the time variable t. Here, I propose a
method of comparing the volumes which is rather insensitive to the choice of t.
The method is then applied to evaluate the relative probability of different
minima of the inflaton potential and the probability distribution for the
density fluctuation spectra.


title:
On the conformal equivalence between 2D black holes and Rindler
  spacetime

abstract:
  We study a two-dimensional dilaton gravity model related by a conformal
transformation of the metric to the Callan-Giddings-Harvey-Strominger model. We
find that most of the features and problems of the latter can be simply
understood in terms of the classical and semiclassical dynamics of accelerated
observers in two-dimensional Minkowski space.


title: Euclidean scalar and spinor Green's functions in Rindler space

abstract:
  In Rindler space, we consider the Feynman Green's functions associated with
either the Fulling-Rindler vacuum or the Minkowski vacuum. In Euclidean field
theory, they becomes respectively the Euclidean Green's functions $G_{\infty}$
and $G_{\2\pi}$, whose we give different suitable forms. In the case of the
massive spin-$\frac{1}{2}$ field, we determine also the Euclidean spinor
Green's function $S_{\infty}$ and $S_{\2\pi}$ in different suitable forms. In
both cases for massless fields in four dimensions, we compute the vacuum
expectation value of the energy-momentum tensor relative to the Rindler
observer.


title: Indeterministic Quantum Gravity II: Refinements and Developments

abstract:
  This paper is a continuation of the paper [V.S.Mashkevich, gr-qc/9409010].
Indeterministic quantum gravity is a theory that unifies general relativity and
quantum theory involving indeterministic conception, i.e., quantum jumps. By
the same token the theory claims to describe all the universe.
  Spacetime is the direct product of cosmic time and space. The state of the
universe is given by metric, its derivative with respect to cosmic time, and
the number of an energy level. A quantum jump occurs at the tangency of two
levels. Equations of motion are the restricted Einstein equation (the cosmic
space part thereof) and a probability rule for the quantum jump.
  Keywords: indeterminism, quantum jumps, state vector reduction, cosmology,
cosmic spacetime


title: Quantum field theory in Lorentzian universes-from-nothing

abstract:
  We examine quantum field theory in spacetimes that are time nonorientable but
have no other causal pathology. These are Lorentzian universes-from-nothing,
spacetimes with a single spacelike boundary that nevertheless have a smooth
Lorentzian metric. Classically, such spacetimes are locally indistinguishable
from their globally hyperbolic covering spaces. However, the construction of a
quantum field theory (QFT) is more problematic. One can define a family of
local algebras on an atlas of globally hyperbolic subspacetimes. But one cannot
extend a generic positive linear function from a single algebra to the
collection of all local algebras without violating positivity, while satisfying
the physically appropriate overlap conditions. This difficulty can be overcome
by restricting the size of neighborhoods so that the union of any pair is time-
orientable. The structure of local algebras and states is then locally
indistinguishable from that of QFT on a globally hyperbolic spacetime. But this
size restriction on neighborhoods makes the structure unsatisfactory as a
global field theory. The theory allows less information than QFT in a globally
hyperbolic spacetime, because correlations between field operators at a pair of
points are defined only if a curve joining the points lies in a single neigh-
borhood. Moreover, to extend a local state to a collection of states, we use an
antipodally symmetric state on the covering space, a state that would not yield
a sensible state on the spacetime if all correlations could be measured.


title: Chaos in Static Axisymmetric Spacetimes I : Vacuum Case

abstract:
  We study the motion of test particle in static axisymmetric vacuum spacetimes
and discuss two criteria for strong chaos to occur: (1) a local instability
measured by the Weyl curvature, and (2) a tangle of a homoclinic orbit, which
is closely related to an unstable periodic orbit in general relativity. We
analyze several static axisymmetric spacetimes and find that the first
criterion is a sufficient condition for chaos, at least qualitatively. Although
some test particles which do not satisfy the first criterion show chaotic
behavior in some spacetimes, these can be accounted for the second criterion.


title: Limits on the validity of the semiclassical theory

abstract:
  For want of a more natural proposal, it is generally assumed that the
back-reaction of a quantised matter field on a classical metric is given by the
expectation value of its energy-momentum tensor, evaluated in a specified
state. This proposal can be expected to be quite sound only when the
fluctuations in the energy-momentum tensor of the quantum field are negligible.
Based on this condition, a dimensionless criterion has been suggested earlier
by Kuo and Ford for drawing the limits on the validity of this semiclassical
theory. In this paper, we examine this criterion for the case of a toy model,
constructed with two degrees of freedom and a coupling between them that
exactly mimics the behaviour of a scalar field in a Friedmann universe. To
reproduce the semiclassical regime of the field theory, in the toy model, one
of degrees of freedom is assumed to be classical and the other quantum
mechanical. Also the backreaction is assumed to be given by the expectation
values of the quantum operators involved in the equations of motion for the
classical system. Motivated by the same physical reasoning as Kuo and Ford, we,
here, suggest another criterion, one which will be shown to perform more
reliably as we evaluate these criterions for different states of the quantum
system in the toy model. Finally, from the results obtained we conclude that
the semiclassical theory being considered for the toy model is reliable, during
all stages of its evolution, only if the quantum system is specified to be in
coherent like states. The implications of these investigations on field theory
are discussed.


title: String Theory and Cosmology

abstract:
  We discuss the main cosmological implications of considering string-loop
effects and a potential for the dilaton in the lowest order string effective
action. Our framework is based on the effective model arising from regarding
homogeneous and isotropic dilaton, metric and Yang-Mills field configurations.
The issues of inflation, entropy crisis and the Polonyi problem as well as the
problem of the cosmological constant are discussed.


title: Abelian Higgs Hair for Black Holes

abstract:
  We find evidence for the existence of solutions of the Einstein and Abelian
Higgs field equations describing a black hole pierced by a Nielsen-Olesen
vortex. This situation falls outside the scope of the usual no-hair arguments
due to the non-trivial topology of the vortex configuration and the special
properties of its energy-momentum tensor. By a combination of numerical and
perturbative techniques we conclude that the black hole horizon has no
difficulty in supporting the long range fields of the Nielsen Olesen string.
Moreover, the effect of the vortex can in principle be measured from infinity,
thus justifying its characterization as black hole ``hair".


title: Path Integration in Two-Dimensional Toplogical Quantum Field Theory

abstract:
  A positive, diffeomorphism-invariant generalized measure on the space of
metrics of a two-dimensional smooth manifold is constructed. We use the term
generalized measure analogously with the generalized measures of Ashtekar and
Lewandowski and of Baez. A family of actions is presented which, when
integrated against this measure, give the two-dimensional axiomatic topological
quantum field theories, or TQFT's, in terms of which Durhuus and Jonsson
decompose every two-dimensional unitary TQFT as a direct sum.


title: S-Duality at the Black Hole Threshold in Gravitational Collapse

abstract:
  We study gravitational collapse of the axion/dilaton field in classical low
energy string theory, at the threshold for black hole formation. A new critical
solution is derived that is spherically symmetric and continuously
self-similar. The universal scaling and echoing behavior discovered by Choptuik
in gravitational collapse appear in a somewhat different form. In particular,
echoing takes the form of SL(2,R) rotations (cf. S-duality). The collapse
leaves behind an outgoing pulse of axion/dilaton radiation, with nearly but not
exactly flat spacetime within it.


title: Head-on collision of two black holes: comparison of different approaches

abstract:
  A benchmark problem for numerical relativity has been the head-on collision
of two black holes starting from the ``Misner initial data,'' a closed form
momentarily stationary solution to the constraint equations with an adjustable
closeness parameter $\mu_0$. We show here how an eclectic mixture of
approximation methods can provide both an efficient means of determining the
time development of the initial data and a good understanding of the physics of
the problem. When the Misner data is chosen to correspond to holes initially
very close together, a common horizon surrounds both holes and the geometry
exterior to the horizon can be treated as a non-spherical perturbation of a
single Schwarzschild hole. When the holes are initially well separated the
problem can be treated with a different approximation scheme, ``the
particle-membrane method.'' For all initial separations, numerical relativity
is in principle applicable, but is costly and of uncertain accuracy. We present
here a comparison of the different approaches. We compare waveforms, for
$\ell=2$ and $\ell=4$ radiation, for different values of $\mu_0$, from the
three different approaches to the problem.


title:
A definition of the Ponzano-Regge quantum gravity model in terms of
  surfaces

abstract:
  We show that the partition function of the Ponzano-Regge quantum gravity
model can be written as a sum over surfaces in a $(2+1)$ dimensional
space-time. We suggest a geometrical meaning, in terms of surfaces, for the
(regulated) divergences that appear in the partition function.


title: New constraints for canonical general relativity

abstract:
  Ashtekar's canonical theory of classical complex Euclidean GR (no Lorentzian
reality conditions) is found to be invariant under the full algebra of
infinitesimal 4-diffeomorphisms, but non-invariant under some finite proper
4-diffeos when the densitized dreibein, $\tilE^a_i$, is degenerate. The
breakdown of 4-diffeo invariance appears to be due to the inability of the
Ashtekar Hamiltonian to generate births and deaths of $\tilE$ flux loops
(leaving open the possibility that a new `causality condition' forbidding the
birth of flux loops might justify the non-invariance of the theory).
  A fully 4-diffeo invariant canonical theory in Ashtekar's variables, derived
from Plebanski's action, is found to have constraints that are stronger than
Ashtekar's for $rank\tilE < 2$. The corresponding Hamiltonian generates births
and deaths of $\tilE$ flux loops.
  It is argued that this implies a finite amplitude for births and deaths of
loops in the physical states of quantum GR in the loop representation, thus
modifying this (partly defined) theory substantially.
  Some of the new constraints are second class, leading to difficulties in
quantization in the connection representation. This problem might be overcome
in a very nice way by transforming to the classical loop variables, or the
`Faraday line' variables of Newman and Rovelli, and then solving the offending
constraints.
  Note that, though motivated by quantum considerations, the present paper is
classical in substance.


title: TEMPERATURE AND RELATIVITY

abstract:
  We investigate whether inertial thermometers moving in a thermal bath behave
as being hotter or colder. This question is directly related to the classical
controversy concerning how temperature transforms under Lorentz
transformations. Rather than basing our arguments on thermodynamical
hypotheses, we perform straightforward calculations in the context of
relativistic quantum field theory. For this purpose we use Unruh-DeWitt
detectors, since they have been shown to be reliable thermometers in
semi-classical gravity. We believe that our discussion helps in definitely
clarifying this issue.


title:
Quantum Fluctuations, Decoherence of the Mean Field, and Structure
  Formation in the Early Universe

abstract:
  We examine from first principles one of the basic assumptions of modern
quantum theories of structure formation in the early universe, i.e., the
conditions upon which fluctuations of a quantum field may transmute into
classical stochastic perturbations, which grew into galaxies. Our earlier works
have discussed the quantum origin of noise in stochastic inflation and quantum
fluctuations as measured by particle creation in semiclassical gravity. Here we
focus on decoherence and the relation of quantum and classical fluctuations.
Instead of using the rather ad hoc splitting of a quantum field into long and
short wavelength parts, the latter providing the noise which decoheres the
former, we treat a nonlinear theory and examine the decoherence of a quantum
mean field by its own quantum fluctuations, or that of other fields it
interacts with. This is an example of `dynamical decoherence' where an
effective open quantum system decoheres through its own dynamics. The model we
use to discuss fluctuation generation has the inflation field coupled to the
graviton field. We show that when the quantum to classical transition is
properly treated, with due consideration of the relation of decoherence, noise,
fluctuation and dissipation, the amplitude of density contrast predicted falls
in the acceptable range without requiring a fine tuning of the coupling
constant of the inflation field ($\lambda$). The conventional treatment which
requires an unnaturally small $\lambda \approx 10^{-12}$ stems from a basic
flaw in naively identifying classical perturbations with quantum fluctuations.


title:
The conformal anomaly in N-dimensional space having a hyperbolic spatial
  section

abstract:
  The conformal anomaly for spinors and scalars on a N-dimensional hyperbolic
space is calculated explicitly, by using zeta-function regularization
techniques and the Selberg trace formula. In the case of conformally invariant
spinors and scalars the results are very much related with those corresponding
to a N-dimensional sphere.


title:
Quantization of the Bianchi type-IX model in N=1 Supergravity in the
  Presence of Supermatter

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 K\"ahler geometry
is chosen to be a two-dimensional flat one. The Lorentz invariant Ansatz for
the wave function of the universe is taken to be as simple as possible in order
to obtain {\it new} solutions. The set of differential equations derived from
the quantum constraints are analysed in two different cases: if the supermatter
terms include an analytical potential or not. In the latter the wave function
is found to have a simple form.


title: Poincare gauge invariance and gravitation in Minkowski spacetime

abstract:
  A formulation of Poincare symmetry as an inner symmetry of field theories
defined on a fixed Minkowski spacetime is given. Local P gauge transformations
and the corresponding covariant derivative with P gauge fields are introduced.
The renormalization properties of scalar, spinor and vector fields in P gauge
field backgrounds are determined. A minimal gauge field dynamics consistent
with the renormalization constraints is given.


title: Testing Single-Parameter Classical Standpoint Cosmology

abstract:
  Experimental tests of homogeneous-universe classical standpoint cosmology are
proposed after presentation of conceptual considerations that encourage this
radical departure from the standard model. Among predictions of the new model
are standpoint age equal to Hubble time, energy-density parameter $\Omega_0 = 2
- \sqrt{2} =.586$, and relations between redshift, Hubble-scale distribution of
matter and galaxy luminosity and angular diameter. These latter relations
coincide with those of the standard model for zero deceleration. With eye to
further tests, geodesics of the non-Riemannian standpoint metric are explicitly
given. Although a detailed thermodynamic ``youthful-standpoint'' approximation
remains to be developed (for particle mean free path small on standpoint
scale), standpoint temperature depending only on standpoint age is a natural
concept, paralleling energy density and redshift that perpetuates thermal
spectrum for cosmic background radiation. Prospects for primordial
nucleosynthesis are promising.


title: Coarse-Graining and Renormalization Group in the Einstein Universe

abstract:
  The Kadanoff-Wilson renormalization group approach for a scalar
self-interacting field theor generally coupled with gravity is presented. An
average potential that monitors the fluctuations of the blocked field in
different scaling regimes is constructed in a nonflat background and explicitly
computed within the loop-expansion approximation for an Einstein universe. The
curvature turns out to be dominant in setting the crossover scale from a
double-peak and a symmetric distribution of the block variables. The evolution
of all the coupling constants generated by the blocking procedure is examined:
the renormalized trajectories agree with the standard perturbative results for
the relevant vertices near the ultraviolet fixed point, but new effective
interactions between gravity and matter are present. The flow of the conformal
coupling constant is therefore analyzed in the improved scheme and the infrared
fixed point is reached for arbitrary values of the renormalized parameters.


title: THERMODYNAMIC PROPERTIES OF $\gamma$--FLUIDS AND THE QUANTUM VACCUM

abstract:
  The thermodynamic behaviour of a relativistic perfect simple fluid obeying
the equation of state $p=(\gamma-1)\rho $, where $0 \le \gamma \le 2$ is a
constant, has been investigated. Particular cases include: vacuum($p=-\rho $,
$\gamma=0$), a randomly oriented distribution of cosmic strings ($p=-{1 \over
3} \rho $, $\gamma =2/3$), blackbody radiation ($p={1\over 3} \rho$, $\gamma
=4/3$) and stiff matter ($p=\rho$, $\gamma=2$). Fluids with $\gamma <1$ become
hotter when they expand adiabatically ($T\propto V^{1- \gamma}$). By assuming
that such fluids may be regarded as a kind of generalized radiation, the
general Planck's type form of the spectrum is deduced. As a limiting case, a
new Lorentz invariant spectrum of the vacuum which is compatible with the
equation of state and other thermodynamic constraints is proposed. Some
possible consequences to the early universe physics are also discussed.


title: The Quest for Quantum Gravity

abstract:
  One of the greatest challenges facing theoretical physics lies in reconciling
Einstein's classical theory of gravity - general relativity - with quantum
field theory. Although both theories have been experimentally supported in
their respective regimes, they seem mutually incompatible. This article
summarises the current status of the superstring approach to the problem, the
status of the Ashtekar program, and addresses the problem of time in quantum
gravity. It contains interviews with Abhay Ashtekar, Chris Isham, and Edward
Witten.


title:
Quantum states on supersymmetric minisuperspace with a cosmological
  constant

abstract:
  Spatially homogeneous models in quantum supergravity with a nonvanishing
cosmological constant are studied. A class of exact nontrivial solutions of the
supersymmetry and Lorentz constraints is obtained in terms of the Chern-Simons
action on the spatially homogeneous 3-manifold, both in Ashketar variables
where the solution is explicit up to reality conditions, and, more concretely,
in the tetrad-representation, where the solutions are given as integral
representations differing only by the contours of integration. In the limit of
a vanishing cosmological constant earlier exact solutions for Bianchi type IX
models in the tetrad-representation are recovered and additional asymmetric
solutions are found.


title: Dynamic wormholes and Energy Conditions

abstract:
  A class of exact solutions of the Einstein field equations representing
non-static wormholes that obey the {\em weak and dominant energy conditions }
is presented. Hence, in principle, these wormholes can be built with less
exotic matter than the static ones.


title: Bubbles and Wormholes: Analytic Models

abstract:
  The first junction conditions of spherically symmetric bubbles are solved for
some cases, and whereby analytic models to the Einstein field equations are
constructed. The effects of bubbles on the spacetime structure are studied and
it is found that in some cases bubbles can close the spatial sector of the
spacetime and turn it into a compact one, while in other cases they can give
rise to wormholes. One of the most remarkable features of these wormholes is
that they do not necessarily violate the weak and dominant energy condition
even at the classical level.


title:
Global solutions of a free boundary problem for selfgravitating scalar
  fields

abstract:
  The weak cosmic censorship hypothesis can be understood as a statement that
there exists a global Cauchy evolution of a selfgravitating system outside an
event horizon. The resulting Cauchy problem has a free null-like inner
boundary. We study a selfgravitating spherically symmetric nonlinear scalar
field. We show the global existence of a spacetime with a null inner boundary
that initially is located outside the Schwarzschild radius or, more generally,
outside an apparent horizon. The global existence of a patch of a spacetime
that is exterior to an event horizon is obtained as a limiting case.


title: Edge States in Canonical Gravity

abstract:
  It is well-known that gauge fields defined on manifolds with spatial
boundaries support states localized at the boundary. In this talk, we show how
similar states arise in canonical gravity abd discuss their physical relevance
using their analogy to quantum Hall effect.


title: Neighbours of Einstein's Equations: Connections and Curvatures

abstract:
  Once the action for Einstein's equations is rewritten as a functional of an
SO(3,C) connection and a conformal factor of the metric, it admits a family of
``neighbours'' having the same number of degrees of freedom and a precisely
defined metric tensor. This paper analyzes the relation between the Riemann
tensor of that metric and the curvature tensor of the SO(3) connection. The
relation is in general very complicated. The Einstein case is distinguished by
the fact that two natural SO(3) metrics on the GL(3) fibers coincide. In the
general case the theory is bimetric on the fibers.


title: Spacetime Covariant Form of Ashtekar's Constraints

abstract:
  The Lagrangian formulation of classical field theories and in particular
general relativity leads to a coordinate-free, fully covariant analysis of
these constrained systems. This paper applies multisymplectic techniques to
obtain the analysis of Palatini and self-dual gravity theories as constrained
systems, which have been studied so far in the Hamiltonian formalism. The
constraint equations are derived while paying attention to boundary terms, and
the Hamiltonian constraint turns out to be linear in the multimomenta. The
equivalence with Ashtekar's formalism is also established. The whole constraint
analysis, however, remains covariant in that the multimomentum map is evaluated
on {\it any} spacelike hypersurface. This study is motivated by the
non-perturbative quantization program of general relativity.


title: Degrees of Freedom of Arbitrarily Higher-Derivative Field Theories

abstract:
  As an example of what happens with physically relevant theories like
effective gravity, we consider the covariant relativistic theory of a scalar
field of arbitrarily higher differential order. A procedure based on the
Legendre transformation and suitable field redefinitions allows to recast it as
a theory of second order with one explicit independent field for each degree of
freedom. The physical and ghost fields are then apparent. The full (classical)
equivalence of both Higher and Lower Derivative versions is shown. An artifact
of the method is the appearance of irrelevant spurious fields which are devoid
of any dynamical content.


title:
Comment on the paper of Leonard Parker and Yang Zhang ``Cosmological
  perturbations of a relativistic condensate''

abstract:
  In a recent paper, Parker and Zhang [1] consider cosmological perturbations
that can be possibly produced in the early Universe. This is an interesting
problem having important observational implications. The paper of Parker and
Zhang is transparent and honest, in the sense that the authors clearly identify
what they derive and what they use from the previous literature. The final
numerical estimates of the paper~[1] rely entirely on a formula which the
authors take from the inflationary literature. This formula, see Eqs.~(22),
(43), relates the amplitude of perturbations today with the amplitude of
perturbations during the inflationary stage. The formula suggests an enormous
increase of the amplitude, if the equation of state at the inflationary phase
has happened to be sufficiently close to the de Sitter one. The point of my
comment is that this formula is incorrect, as we will see below, and the
results based on this formula cannot be trusted.


title:
Euclidean thermal spinor Green's function in the spacetime of a straight
  cosmic string

abstract:
  Within the framework of the quantum field theory at finite temperature on a
conical space, we determine the Euclidean thermal spinor Green's function for a
massless spinor field. We then calculate the thermal average of the
energy-momentum tensor of a thermal bath of massless fermions. In the
high-temperature limit, we find that the straight cosmic string does not
perturb the thermal bath


title: Boundary Terms in Complex General Relativity

abstract:
  A recent analysis of real general relativity based on multisymplectic
techniques has shown that boundary terms may occur in the constraint equations,
unless some boundary conditions are imposed. This paper studies the
corresponding form of such boundary terms in complex general relativity, where
space-time is a four-complex-dimensional complex-Riemannian manifold. A complex
Ricci-flat space-time is recovered providing some boundary conditions are
imposed on two-complex-dimensional surfaces. One then finds that the
holomorphic multimomenta should vanish on an arbitrary
three-complex-dimensional surface, to avoid having restrictions at this surface
on the spinor fields which express the invariance of the theory under
holomorphic coordinate transformations. The Hamiltonian constraint of real
general relativity is then replaced by a geometric structure linear in the
holomorphic multimomenta, and a link with twistor theory is found. Moreover, a
deep relation emerges between complex space-times which are not anti-self-dual
and two-complex-dimensional surfaces which are not totally null.


title: New Perspectives in Complex General Relativity

abstract:
  In complex general relativity, Lorentzian space-time is replaced by a
four-complex-dimensional complex-Riemannian manifold, with holomorphic
connection and holomorphic curvature tensor. A multisymplectic analysis shows
that the Hamiltonian constraint is replaced by a geometric structure linear in
the holomorphic multimomenta, providing some boundary conditions are imposed on
two-complex-dimensional surfaces. On studying such boundary conditions, a link
with the Penrose twistor programme is found. Moreover, in the case of real
Riemannian four-manifolds, the local theory of primary and secondary potentials
for gravitino fields, recently proposed by Penrose, has been applied to
Ricci-flat backgrounds with boundary. The geometric interpretation of the
differential equations obeyed by such secondary potentials is related to the
analysis of integrability conditions in the theory of massless fields, and
might lead to a better understanding of twistor geometry. Thus, new tools are
available in complex general relativity and in classical field theory in real
Riemannian backgrounds.


title: THE VOLUME OPERATOR IN DISCRETIZED QUANTUM GRAVITY

abstract:
  We investigate the spectral properties of the volume operator in quantum
gravity in the framework of a previously introduced lattice discretization. The
presence of a well-defined scalar product in this approach permits us to make
definite statements about the hermiticity of quantum operators. We find that
the spectrum of the volume operator is discrete, but that the nature of its
eigenstates differs from that found in an earlier continuum treatment.


title: SCALAR FIELD COSMOLOGIES WITH PERFECT FLUID IN ROBERTSON-WALKER METRIC

abstract:
  Several isotropic, homogeneous cosmological models containing a
self-interacting minimally coupled scalar field, a perfect fluid source and
cosmological constant are solved. New exact, asymptotically stable solutions
with an inflationary regime or a final Friedmann stage are found for some
simple, interesting potentials. It is shown that the fluid and the curvature
may determine how these models evolve for large times.


title: The Robinson-Trautman Type III Prolongation Structure Contains K$_2$

abstract:
  The minimal prolongation structure for the Robinson-Trautman equations of
Petrov type III is shown to always include the infinite-dimensional,
contragredient algebra, K$_2$, which is of infinite growth. Knowledge of
faithful representations of this algebra would allow the determination of
B\"acklund transformations to evolve new solutions.


title: Gravity Driven Inflation

abstract:
  The union of high-energy particle theories and gravitation often gives rise
to an evolving strength of gravity. The standard picture of the earliest
universe would certainly deserve revision if the Planck mass, which defines the
strength of gravity, varied. A notable consequence is a gravity-driven, kinetic
inflation. Unlike standard inflation, there is no potential or cosmological
constant. The unique elasticity in the kinetic energy of the Planck mass
provides a negative pressure able to drive inflation. As the kinetic energy
grows, the spacetime expands more quickly. The phenomenon of kinetic inflation
has been uncovered in both string theory and Kaluza-Klein theories. The
difficulty in exiting inflation in these cases is reviewed. General forms of
the Planck field coupling are shown to avoid the severity of the graceful exit
problem found in string and Kaluza-Klein theories. The completion of the model
is foreshadowed with a suggestion for a heating mechanism to generate the hot
soup of the big bang.


title: Cosmic Colored Black Holes

abstract:
  We present spherically symmetric static solutions (a particle-like solution
and a black hole solution) in the Einstein-Yang-Mills system with a
cosmological constant.Although their gravitational structures are locally
similar to those of the Bartnik-McKinnon particles or the colored black holes,
the asymptotic behavior becomes quite different because of the existence of a
cosmological horizon. We also discuss their stability by means of a catastrophe
theory as well as a linear perturbation analysis and find the number of
unstable modes.


title:
The asymptotic dynamics of three-dimensional Einstein gravity with a
  negative cosmological constant

abstract:
  Liouville theory is shown to describe the asymptotic dynamics of
three-dimensional Einstein gravity with a negative cosmological constant. This
is because (i) Chern-Simons theory with a gauge group $SL(2,R) \times SL(2,R)$
on a space-time with a cylindrical boundary is equivalent to the non-chiral
$SL(2,R)$ WZW model; and (ii) the anti-de Sitter boundary conditions implement
the constraints that reduce the WZW model to the Liouville theory.


title: Pair production of black holes on cosmic strings

abstract:
  We discuss the pair creation of black holes by the breaking of a cosmic
string. We obtain an instanton describing this process from the $C$ metric, and
calculate its probability. This is very low for the strings that have been
suggested for galaxy formation.


title:
$\rm \Psi= W e^{\pm \Phi}$ quantum cosmological solutions for Class A
  Bianchi Models

abstract:
  We find solutions for quantum Class A Bianchi models of the form $\rm \Psi=W
e^{\pm \Phi}$ generalizing the results obtained by Moncrief and Ryan in
standard quantum cosmology. For the II and IX Bianchi models there are other
solutions $\rm \tilde\Phi_2$, $\rm \tilde\Phi_9$ to the Hamilton-Jacobi
equation for which $\rm \Psi$ is necessarely zero, in contrast with solutions
found in supersymmetric quantum cosmology.


title:
Coalescing binary systems of compact objects to (post)$^{5/2}-Newtonian
  order. V. Spin Effects

abstract:
  We examine the effects of spin-orbit and spin-spin coupling on the inspiral
of a coalescing binary system of spinning compact objects and on the
gravitational radiation emitted therefrom. Using a formalism developed by
Blanchet, Damour, and Iyer, we calculate the contributions due to the spins of
the bodies to the symmetric trace-free radiative multipole moments which are
used to calculate the waveform, energy loss, and angular momentum loss from the
inspiralling binary. Using equations of motion which include terms due to
spin-orbit and spin-spin coupling, we evolve the orbit of a coalescing binary
and use the orbit to calculate the emitted gravitational waveform. We find the
spins of the bodies affect the waveform in several ways: 1) The spin terms
contribute to the orbital decay of the binary, and thus to the accumulated
phase of the gravitational waveform. 2) The spins cause the orbital plane to
precess, which changes the orientation of the orbital plane with respect to an
observer, thus causing the shape of the waveform to be modulated. 3) The spins
contribute directly to the amplitude of the waveform. We discuss the size and
importance of spin effects for the case of two coalescing neutron stars, and
for the case of a neutron star orbiting a rapidly rotating $10M_\odot$ black
hole.


title:
Effect of gravitational radiation reaction on circular orbits around a
  spinning black hole

abstract:
  The effect of gravitational radiation reaction on circular orbits around a
spinning (Kerr) black hole is computed to leading order in $S$ (the magnitude
of the spin angular momentum of the hole) and in the strength of gravity $M/r$
(where $M$ is the mass of the black hole, $r$ is the orbital radius, and
$G=c=1$). The radiation reaction makes the orbit shrink but leaves it circular,
and drives the orbital plane very slowly toward antialignment with the spin of
the hole: $\tan (\iota /2) = \tan (\iota_0 /2) [1+(61/72)(S/M^2) (M/r)^{3/2}]$,
where $\iota$ is the angle between the normal to the orbital plane and the spin
direction, and $\iota_0$ is the initial value of $\iota$, when $r$ is very
large.


title: Gravitational-Wave Detector for a Space Laboratory

abstract:
  A new method of gravitational- waves detection in the $10^{-2}\div 10^{-1}
Hz$ band for a space laboratory is proposed based on the use of the Kozorez
effect in the magnetic interaction of superconducting solenoids.


title: Pair creation of black holes joined by cosmic strings

abstract:
  We argue that production of charged black hole pairs joined by a cosmic
string in the presence of a magnetic field can be analyzed using the Ernst
metric. The effect of the cosmic string is to pull the black holes towards each
other, opposing to the background field. An estimation of the production rate
using the Euclidean action shows that the process is suppressed as compared to
the formation of black holes without strings.


title: Wavefunctions for Highly Anisotropic Homogeneous Cosmologies

abstract:
  The canonical quantization of homogeneous cosmologies is considered in the
high anisotropic limit. Exact wavefunctions are found in this limit when the
momentum constraints are reduced at the classical level. Lorentzian solutions
that represent tunnelling from classically forbidden regimes are identified.
Solutions to the modified Wheeler-DeWitt equation are also found for the vacuum
Bianchi IX model when a quantum reduction of the momentum constraints is
considered.


title: Pulsation of Spherically Symmetric Systems in General Relativity

abstract:
  The pulsation equations for spherically symmetric black hole and soliton
solutions are brought into a standard form. The formulae apply to a large class
of field theoretical matter models and can easily be worked out for specific
examples. The close relation to the energy principle in terms of the second
variation of the Schwarzschild mass is also established. The use of the general
expressions is illustrated for the Einstein-Yang-Mills and the Einstein-Skyrme
system.


title: Woven Geometries: Black Holes

abstract:
  Tangles of loops which approximate an aspect of the Kerr-Newman black hole
metrics at large scales compared to the Planck length are constructed. The
physical aspect the tangles approximate is discussed. This construction may be
useful in the loop representation of canonical quantum gravity. Implications
and applications of the tangles are remarked.


title:
Quantum Loop Representation for Fermions coupled to Einstein-Maxwell
  field

abstract:
  Quantization of the system comprising gravitational, fermionic and
electromagnetic fields is developed in the loop representation. As a result we
obtain a natural unified quantum theory. Gravitational field is treated in the
framework of Ashtekar formalism; fermions are described by two Grassmann-valued
fields. We define a $C^{*}$-algebra of configurational variables whose
generators are associated with oriented loops and curves; ``open'' states --
curves -- are necessary to embrace the fermionic degrees of freedom. Quantum
representation space is constructed as a space of cylindrical functionals on
the spectrum of this $C^{*}$-algebra. Choosing the basis of ``loop'' states we
describe the representation space as the space of oriented loops and curves;
then configurational and momentum loop variables become in this basis the
operators of creation and annihilation of loops and curves. The important
difference of the representation constructed from the loop representation of
pure gravity is that the momentum loop operators act in our case simply by
joining loops in the only compatible with their orientaiton way, while in the
case of pure gravity this action is more complicated.


title: Quantum Cosmology of Generalized Two--Dimensional Dilaton Gravity Models

abstract:
  The quantum cosmology of two-dimensional dilaton-gravity models is
investigated. A class of models is mapped onto the constrained
oscillator-ghost-oscillator model. A number of exact and approximate solutions
to the corresponding Wheeler-DeWitt equation are presented. A wider class of
minisuperspace models that can be solved in this fashion is identified.
Supersymmetric extensions to the induced gravity theory and the bosonic string
theory are then considered and closed-form solutions to the associated quantum
constraints are derived. The possibility of applying the third-quantization
procedure to two-dimensional dilaton-gravity is briefly discussed.


title:
Classification of Second Order Symmetric Tensors in 5-Dimensional
  Kaluza-Klein-Type Theories

abstract:
  An algebraic classification of second order symmetric tensors in
5-dimensional Kaluza-Klein-type Lorentzian spaces is presented by using Jordan
matrices. We show that the possible Segre types are $[1,1111]$, [2111], [311],
[z,\bar{z},111], and the degeneracies thereof. A set of canonical forms for
each Segre type is found. The possible continuous groups of symmetry for each
canonical form are also studied.


title:
Quantum Formation of Black Hole and Wormhole in Gravitational Collapse
  of a Dust Shell

abstract:
  Quantum-mechanical model of self-gravitating dust shell is considered. To
clarify the relation between classical and quantum spacetime which the shell
collapse form, we consider various time slicing on which quantum mechanics is
developed. By considering the static time slicing which corresponds to an
observer at a constant circumference radius, we obtain the wave functions of
the shell motion and the discrete mass spectra which specify the global
structures of spherically symmetric spacetime formed by the shell collapse. It
is found that wormhole states are forbidden when the rest mass is comparable
with Plank mass scale due to the zero-point quantum fluctuations.


title: On the formation of black holes in non-symmetric gravity

abstract:
  It has been recently suggested that the Non-symmetric Gravitational Theory
(NGT) is free of black holes. Here, we study the linear version of NGT. We find
that even with spherical symmetry the skew part of the metric is generally
non-static. In addition, if the skew field is initially regular, it will remain
regular everywhere and, in particular, at the horizon. Therefore, in the
fully-nonlinear theory, if the initial skew-field is sufficiently small, the
formation of a black hole is to be anticipated.


title: Quantum Corrections to the Two-dimensional Gravity with External Field

abstract:
  We introduce an external field to calculate the quantum corrections of the 2d
gravity, via trace anomaly. We show that there are black hole type solution
even in the absence of matter field and cosmological constant. We also see that
these solutions are similar to the ones obtained from dilaton two-dimensional
gravity.


title:
Quantization of the Reduced Phase Space of Two-Dimensional Dilaton
  Gravity

abstract:
  We study some two-dimensional dilaton gravity models using the formal theory
of partial differential equations. This allows us to prove that the reduced
phase space is two-dimensional without an explicit construction. By using a
convenient (static) gauge we reduce the theory to coupled \ode s and we are
able to derive for some potentials of interest closed-form solutions. We use an
effective (particle) Lagrangian for the reduced field equations in order to
quantize the system in a finite-dimensional setting leading to an exact partial
differential Wheeler-DeWitt equation instead of a functional one. A WKB
approximation for some quantum states is computed and compared with the
classical Hamilton-Jacobi theory. The effect of minimally coupled matter is
examined.


title: Spacetime Defects: Torsion Loops

abstract:
  Spacetimes with everywhere vanishing curvature tensor, but with torsion
different from zero only on world sheets that represent closed loops in
ordinary space are presented, also defects along open curves with end points at
infinity are studied. The case of defects along timelike loops is also
considered and the geodesics in these spaces are briefly discussed.


title: Quantal Modifications to the Wheeler DeWitt Equation

abstract:
  Commutator anomalies obstruct solving the Wheeler-DeWitt constraint equation
in Dirac quantization of quantum gravity-matter theory. When the obstruction is
removed, there result quantal modifications to the constraints. The same
classical theory gives rise to different quantum theories when different
procedures for overcoming anomalies are implemented.


title:
Involutions on the Algebra of Physical Observables From Reality
  Conditions

abstract:
  Some aspects of the algebraic quantization programme proposed by Ashtekar are
revisited in this article. It is proved that, for systems with first-class
constraints, the involution introduced on the algebra of quantum operators via
reality conditions can never be projected unambiguously to the algebra of
physical observables, ie, of quantum observables modulo constraints. It is
nevertheless shown that, under sufficiently general assumptions, one can still
induce an involution on the algebra of physical observables from reality
conditions, though the involution obtained depends on the choice of particular
representatives for the equivalence classes of quantum observables and this
implies an additional ambiguity in the quantization procedure suggested by
Ashtekar.


title: On quantum and parallel transport in a Hilbert bundle over spacetime

abstract:
  We study the Hilbert bundle description of stochastic quantum mechanics in
curved spacetime developed by Prugove\v{c}ki, which gives a powerful new
framework for exploring the quantum mechanical propagation of states in curved
spacetime. We concentrate on the quantum transport law in the bundle,
specifically on the information which can be obtained from the flat space
limit. We give a detailed proof that quantum transport coincides with parallel
transport in the bundle in this limit, confirming statements of Prugove\v{c}ki.
We furthermore show that the quantum-geometric propagator in curved spacetime
proposed by Prugove\v{c}ki, yielding a Feynman path integral-like formula
involving integrations over intermediate phase space variables, is Poincar\'e
gauge covariant (i.e.$\!$ is gauge invariant except for transformations at the
endpoints of the path) provided the integration measure is interpreted as a
``contact point measure'' in the soldered stochastic phase space bundle raised
over curved spacetime.


title: Loop Variables for a Class of Conical Spacetimes

abstract:
  Loop variables are used to describe the presence of topological defects in
spacetime. In particular we study the dependence of the holonomy transformation
on angular momentum and torsion for a multi-chiral cone. We also compute the
holonomies for multiple moving crossed cosmic strings and two plane topological
defects-crossed by a cosmic string.


title: Breaking Cosmic Strings without Monopoles

abstract:
  It is shown that topologically stable cosmic strings can, in fact, appear to
end or to break, even in theories without monopoles. This can occur whenever
the spatial topology of the universe is nontrivial. For the case of
Abelian-Higgs strings, we describe the gauge and scalar field configurations
necessary for a string to end on a black hole. We give a lower bound for the
rate at which a cosmic string will break via black hole pair production, using
an instanton calculation based on the Euclidean C-metric.


title: The Case of the Missing Wormhole State

abstract:
  The issue concerning the existence of wormhole states in locally
supersymmetric minisuperspace models with matter is addressed. Wormhole states
are apparently absent in models obtained from the more general theory of N=1
supergravity with supermatter. A Hartle-Hawking type solution can be found,
even though some terms (which are scalar field dependent) cannot be determined
in a satisfactory way. A possible cause is investigated here. As far as the
wormhole situation is concerned, we argue here that the type of Lagrange
multipliers and fermionic derivative ordering one uses may make a difference. A
proposal is made for supersymmetric quantum wormholes to also be invested with
a Hilbert space structure, associated with a maximal analytical extension of
the corresponding minisuperspace.


title:
Combinatorial solutions to the Hamiltonian constraint in
  (2+1)-dimensional Ashtekar gravity

abstract:
  Dirac's quantization of the (2+1)-dimensional analog of Ashtekar's approach
to quantum gravity is investigated. After providing a diffeomorphism-invariant
regularization of the Hamiltonian constraint, we find a set of solutions to
this Hamiltonian constraint which is a generalization of the solution
discovered by Jacobson and Smolin. These solutions are given by particular
linear combinations of the spin network states. While the classical
counterparts of these solutions have degenerate metric, due to a \lq quantum
effect' the area operator has nonvanishing action on these states. We also
discuss how to extend our results to (3+1)-dimensions.


title: The spherically symmetric collapse of a massless scalar field

abstract:
  We report on a numerical study of the spherically symmetric collapse of a
self-gravitating massless scalar field. Earlier results of Choptuik(1992, 1994)
are confirmed. The field either disperses to infinity or collapses to a black
hole, depending on the strength of the initial data. For evolutions where the
strength is close to but below the strength required to form a black hole, we
argue that there will be a region close to the axis where the scalar curvature
and field energy density can reach arbitrarily large levels, and which is
visible to distant observers


title:
Comment on ``Perturbative Method to solve fourth-order Gravity Field
  Equations"

abstract:
  We reconsider the cosmic string perturbative solution to the classical
fourth-order gravity field equations, obtained in Ref.\cite{CLA94}, and we
obtain that static, cylindricaly symmetric gauge cosmic strings, with constant
energy density, can contain only $\beta$-terms in the first order corrections
to the interior gravitational field, while the exact exterior solution is a
conical spacetime with deficit angle $D=8\pi\mu$.


title: The Impact of Quantum Cosmology on Quantum Field Theory

abstract:
  The basic problem of quantum cosmology is the definition of the quantum state
of the universe, with appropriate boundary conditions on Riemannian
three-geometries. This paper describes recent progress in the corresponding
analysis of quantum amplitudes for Euclidean Maxwell theory and linearized
gravity. Within the framework of Faddeev-Popov formalism and zeta-function
regularization, various choices of mixed boundary conditions lead to a deeper
understanding of quantized gauge fields and quantum gravity in the presence of
boundaries.


title: The Probability for Primordial Black Holes

abstract:
  We consider two quantum cosmological models with a massive scalar field: an
ordinary Friedmann universe and a universe containing primordial black holes.
For both models we discuss the complex solutions to the Euclidean Einstein
equations. Using the probability measure obtained from the Hartle-Hawking
no-boundary proposal, we find that the only unsuppressed black holes start at
the Planck size but can grow with the horizon scale during the roll down of the
scalar field to the minimum.


title: Asymptotic Heat Kernels in Quantum Field Theory

abstract:
  Asymptotic expansions were first introduced by Henri Poincare in 1886. This
paper describes their application to the semi-classical evaluation of
amplitudes in quantum field theory with boundaries. By using zeta-function
regularization, the conformal anomaly for a massless spin-${1\over 2}$ field in
flat Euclidean backgrounds with boundary is obtained on imposing locally
supersymmetric boundary conditions. The quantization program for gauge fields
and gravitation in the presence of boundaries is then introduced by focusing on
conformal anomalies for higher-spin fields. The conditions under which the
covariant Schwinger-DeWitt and the non-covariant, mode-by-mode analysis of
quantum amplitudes agree are described.


title: Quantization of Field Theories in the Presence of Boundaries

abstract:
  This paper reviews the progress made over the last five years in studying
boundary conditions and semiclassical properties of quantum fields about
4-real-dimensional Riemannian backgrounds. For massless spin-${1\over 2}$
fields one has a choice of spectral or supersymmetric boundary conditions, and
the corresponding conformal anomalies have been evaluated by using
zeta-function regularization. For Euclidean Maxwell theory in vacuum, the
mode-by-mode analysis of BRST-covariant Faddeev-Popov amplitudes has been
performed for relativistic and non-relativistic gauge conditions. For massless
spin-${3\over 2}$ fields, the contribution of physical degrees of freedom to
one-loop amplitudes, and the 2-spinor analysis of Dirac and Rarita-Schwinger
potentials, have been obtained. In linearized gravity, gauge modes and ghost
modes in the de Donder gauge have been studied in detail. This program may lead
to a deeper understanding of different quantization techniques for gauge fields
and gravitation, to a new vision of gauge invariance, and to new points of view
in twistor theory.


title: Constraints from Inflation on Scalar-Tensor Gravity Theories

abstract:
  We show how observations of the perturbation spectra produced during
inflation may be used to constrain the parameters of general scalar-tensor
theories of gravity, which include both an inflaton and dilaton field. An
interesting feature of these models is the possibility that the curvature
perturbations on super-horizon scales may not be constant due to non-adiabatic
perturbations of the two fields. Within a given model, the tilt and relative
amplitude of the scalar and tensor perturbation spectra gives constraints on
the parameters of the gravity theory, which may be comparable with those from
primordial nucleosynthesis and post-Newtonian experiments.


title:
A Toy Model Approach to the Canonical Non-perturbative Quantization of
  the Spatially Flat Robertson-Walker Spacetimes with Cosmological Constant

abstract:
  We present a toy model approach to the canonical non-perturbative
quantization of the spatially-flat Robertson-Walker Universes with cosmological
constant, based on the fact that such models are exactly solvable within the
framework of a simple Lagrangian formulation. The essential quantum dynamical
metric-field and the corresponding Hamiltonian, explicitly derived in terms of
annihilation and creation operators, point out that the Wheeler - DeWitt
equation is a natural (quantum) generalization of the $G_{44}$ - Einstein
equation for the classical De Sitter spacetime and selects the physical states
of the quantum De Sitter Universe. As a result of the exponential universal
expansion, the usual Fock states (defined as the eigenstates of the
number-operator) are no longer invariant under the derived Hamiltonian. They
exhibit quantum fluctuation of the energy and of the metric field which lead to
a (geometrical) volume quantization.


title: Averaged Energy Conditions and Evaporating Black Holes

abstract:
  In this paper the averaged weak (AWEC) and averaged null (ANEC) energy
conditions, together with uncertainty principle-type restrictions on negative
energy (``quantum inequalities''), are examined in the context of evaporating
black hole backgrounds in both two and four dimensions. In particular,
integrals over only half-geodesics are studied. We determine the regions of the
spacetime in which the averaged energy conditions are violated. In all cases
where these conditions fail, there appear to be quantum inequalities which
bound the magnitude and extent of the negative energy, and hence the degree of
the violation. The possible relevance of these results for the validity of
singularity theorems in evaporating black hole spacetimes is discussed.


title: Euclidean Maxwell Theory in the Presence of Boundaries

abstract:
  This paper describes recent progress in the analysis of relativistic gauge
conditions for Euclidean Maxwell theory in the presence of boundaries. The
corresponding quantum amplitudes are studied by using Faddeev-Popov formalism
and zeta-function regularization, after expanding the electromagnetic potential
in harmonics on the boundary 3-geometry. This leads to a semiclassical analysis
of quantum amplitudes, involving transverse modes, ghost modes, coupled normal
and longitudinal modes, and the decoupled normal mode of Maxwell theory. On
imposing magnetic or electric boundary conditions, flat Euclidean space bounded
by two concentric 3-spheres is found to give rise to gauge-invariant one-loop
amplitudes, at least in the cases considered so far. However, when flat
Euclidean 4-space is bounded by only one 3-sphere, one-loop amplitudes are
gauge-dependent, and the agreement with the covariant formalism is only
achieved on studying the Lorentz gauge. Moreover, the effects of gauge modes
and ghost modes do not cancel each other exactly for problems with boundaries.
Remarkably, when combined with the contribution of physical (i.e. transverse)
degrees of freedom, this lack of cancellation is exactly what one needs to
achieve agreement with the results of the Schwinger-DeWitt technique. The most
general form of coupled eigenvalue equations resulting from arbitrary
gauge-averaging functions is now under investigation.


title: Smooth metrics for snapping strings

abstract:
  We construct two possible metrics for abelian Higgs vortices with ends on
black holes. We show how the detail of the vortex fields smooths out the nodal
singularities which exist in the idealized metrics. A corollary is that
apparently topologically stable strings might be able to split by black hole
pair production. We estimate the rate per unit length by reference to related
Ernst and C-metric instantons, concluding that it is completely negligible for
GUT-scale strings. The estimated rate for macroscopic superstrings is much
higher, although still extremely small, unless there is an early phase of
strong coupling.


title: Comment on the formation of black holes in nonsymmetric gravity

abstract:
  We critically examine the claim made by Burko and Ori that black holes are
expected to form in nonsymmetric gravity and find their analysis to be
inconclusive. Their conclusion is a result of the approximations they make, and
not a consequence of the true dynamics of the theory. The approximation they
use fails to capture the crucial equivalence principle violations which enable
the full nonsymmetric field equations to detect and tame would-be horizons. An
examination of the dynamics of the full theory reveals no indication that black
holes should form. For these reasons, one cannot conclude from their analysis
that nonsymmetric gravity has black holes. A definitive answers awaits a
comprehensive study of gravitational collapse, using the full field equations.


title: Spin-Raising Operators and Spin-3/2 Potentials in Quantum Cosmology

abstract:
  Local boundary conditions involving field strengths and the normal to the
boundary, originally studied in anti-de Sitter space-time, have been recently
considered in one-loop quantum cosmology. This paper derives the conditions
under which spin-raising operators preserve these local boundary conditions on
a 3-sphere for fields of spin 0,1/2,1,3/2 and 2. Moreover, the two-component
spinor analysis of the four potentials of the totally symmetric and independent
field strengths for spin 3/2 is applied to the case of a 3-sphere boundary. It
is shown that such boundary conditions can only be imposed in a flat Euclidean
background, for which the gauge freedom in the choice of the potentials
remains.


title:
On the Resolution of Time Problem in Quantum Gravity Induced from
  Unconstrained Membranes

abstract:
  The relativistic theory of unconstrained $p$-dimensional membranes
($p$-branes) is further developed and then applied to the embedding model of
induced gravity. Space-time is considered as a 4-dimensional unconstrained
membrane evolving in an $N$-dimensional embedding space. The parameter of
evolution or the evolution time $\tau$ is a distinct concept from the
coordinate time $t = x^0$. Quantization of the theory is also discussed. A
covariant functional Schr\" odinger equations has a solution for the wave
functional such that it is sharply localized in a certain subspace $P$ of
space-time, and much less sharply localized (though still localized) outside
$P$. With the passage of evolution the region $P$ moves forward in space-time.
Such a solution we interpret as incorporating two seemingly contradictory
observations: (i) experiments clearly indicate that space-time is a continuum
in which events are existing; (ii) not the whole 4-dimensional space-time, but
only a 3-dimensional section which moves forward in time is accessible to our
immediate experience. The notorious problem of time is thus resolved in our
approach to quantum gravity. Finally we include sources into our unconstrained
embedding model. Possible sources are unconstrained worldlines which are free
from the well known problem concerning the Maxwell fields generated by charged
unconstrained point particles.


title: Twistors and Spin 3/2 Potentials in Quantum Gravity

abstract:
  Local boundary conditions involving field strengths and the normal to the
boundary, originally studied in anti-de Sitter space-time, have been recently
considered in one-loop quantum cosmology. This paper derives the conditions
under which spin-lowering and spin-raising operators preserve these local
boundary conditions on a 3-sphere for fields of spin 0,1/2,1,3/2 and 2.
Moreover, the two-component spinor analysis of the four potentials of the
totally symmetric and independent field strengths for spin 3/2 is applied to
the case of a 3-sphere boundary. It is shown that such boundary conditions can
only be imposed in a flat Euclidean background, for which the gauge freedom in
the choice of the potentials remains. Alternative boundary conditions for
supergravity involving the spinor-valued 1-forms for gravitinos and the normal
to the boundary are also studied.


title: Concerning the vacuum velocity of gravitational waves

abstract:
  It is pointed out that if gravitational interactions among ordinary bodies
propagate in extra space-time dimensions the velocity of gravitational waves in
vacuum could be different from the speed of light $c$.


title:
Gauge-Averaging Functionals for Euclidean Maxwell Theory in the Presence
  of Boundaries

abstract:
  This paper studies the one-loop expansion of the amplitudes of
electromagnetism about flat Euclidean backgrounds bounded by a 3-sphere,
recently considered in perturbative quantum cosmology, by using zeta-function
regularization. For a specific choice of gauge-averaging functional, the
contributions to the full zeta value owed to physical degrees of freedom,
decoupled gauge mode, coupled gauge modes and Faddeev-Popov ghost field are
derived in detail, and alternative choices for such a functional are also
studied. This analysis enables one to get a better understanding of different
quantization techniques for gauge fields and gravitation in the presence of
boundaries.


title: Euclidean Maxwell Theory in the Presence of Boundaries. II

abstract:
  Zeta-function regularization is applied to complete a recent analysis of the
quantized electromagnetic field in the presence of boundaries. The quantum
theory is studied by setting to zero on the boundary the magnetic field, the
gauge-averaging functional and hence the Faddeev-Popov ghost field. Electric
boundary conditions are also studied. On considering two gauge functionals
which involve covariant derivatives of the 4-vector potential, a series of
detailed calculations shows that, in the case of flat Euclidean 4-space bounded
by two concentric 3-spheres, one-loop quantum amplitudes are gauge independent
and their mode-by-mode evaluation agrees with the covariant formulae for such
amplitudes and coincides for magnetic or electric boundary conditions. By
contrast, if a single 3-sphere boundary is studied, one finds some
inconsistencies, i.e. gauge dependence of the amplitudes.


title: Coulomb Gauge in One-Loop Quantum Cosmology

abstract:
  The well-known discrepancies between covariant and non-covariant formalisms
in quantum field theory and quantum cosmology are analyzed by focusing on the
Coulomb gauge for vacuum Maxwell theory. On studying a flat Euclidean
background with boundaries, the corresponding mode-by-mode analysis of one-loop
quantum amplitudes agrees with the results of the Schwinger-DeWitt technique
and of mode-by-mode calculations in relativistic gauges.


title: Testing gravity to second post-Newtonian order: a field-theory approach

abstract:
  A new, field-theory-based framework for discussing and interpreting tests of
gravity, notably at the second post-Newtonian (2PN) level, is introduced.
Contrary to previous frameworks which attempted at parametrizing any
conceivable deviation from general relativity, we focus on the best motivated
class of models, in which gravity is mediated by a tensor field together with
one or several scalar fields. The 2PN approximation of these
"tensor-multi-scalar" theories is obtained thanks to a diagrammatic expansion
which allows us to compute the Lagrangian describing the motion of N bodies. In
contrast with previous studies which had to introduce many phenomenological
parameters, we find that the 2PN deviations from general relativity can be
fully described by only two new 2PN parameters, epsilon and zeta, beyond the
usual (Eddington) 1PN parameters beta and gamma. It follows from the basic
tenets of field theory, notably the absence of negative-energy excitations,
that (beta-1), epsilon and zeta (as well as any new parameter entering higher
post-Newtonian orders) must tend to zero with (gamma-1). It is also found that
epsilon and zeta do not enter the 2PN equations of motion of light. Therefore,
light-deflection or time-delay experiments cannot probe any theoretically
motivated 2PN deviation from general relativity, but they can give a clean
access to (gamma-1), which is of greatest significance as it measures the basic
coupling strength of matter to the scalar fields. Because of the importance of
self-gravity effects in neutron stars, binary-pulsar experiments are found to
constitute a unique testing ground for the 2PN structure of gravity. A
simplified analysis of four binary pulsars already leads to significant
constraints: |epsilon| < 7x10^-2, |zeta| < 6x10^-3.


title:
Hawking Radiation and Evaporation of the Black Hole Induced by a
  Klein-Gordon Soliton

abstract:
  A two-dimensional dilatonic black hole induced by a topological soliton is
exactly solvable in the scalar field theory coupled to dilaton gravity. The
Hawking radiation of the black hole is studied in the one-loop approximation
with the help of the trace anomaly of energy-momentum tensors which is a
geometrical invariant. The quantum theory can be also soluble in the RST scheme
in order to consider the back reaction of the metric. The energy of the black
hole system is calculated and the classical thunderpop energy corresponding to
the soliton energy is needed to describe the final state of the black hole.
Finally we discuss the possibility of conservation of the topological charge.


title: Local Supersymmetry in One-Loop Quantum Cosmology

abstract:
  The contribution of physical degrees of freedom to the one-loop amplitudes of
Euclidean supergravity is here evaluated in the case of flat Euclidean
backgrounds bounded by a three-sphere, recently considered in perturbative
quantum cosmology. The physical degrees of freedom (denoted by PDF) are picked
out by imposing the supersymmetry constraints and choosing a gauge condition.
Remarkably, for the massless gravitino field the PDF method and local boundary
conditions lead to a result for the trace anomaly which is equal to the PDF
value one obtains using spectral boundary conditions on a 3-sphere.


title:
Gravitons in One-Loop Quantum Cosmology: Correspondence Between
  Covariant and Non-Covariant Formalisms

abstract:
  The discrepancy between the results of covariant and non-covariant one-loop
calculations for higher-spin fields in quantum cosmology is analyzed. A
detailed mode-by-mode study of perturbative quantum gravity about a flat
Euclidean background bounded by two concentric 3-spheres, including
non-physical degrees of freedom and ghost modes, leads to one-loop amplitudes
in agreement with the covariant Schwinger-DeWitt method. This calculation
provides the generalization of a previous analysis of fermionic fields and
electromagnetic fields at one-loop about flat Euclidean backgrounds admitting a
well-defined 3+1 decomposition.


title: Black hole singularities: a numerical approach

abstract:
  The singularity structure of charged spherical collapse is studied by
considering the evolution of the gravity-scalar field system. A detailed
examination of the geometry at late times strongly suggests the validity of the
mass-inflation scenario~\cite{PI:90}. Although the area of the two-spheres
remains finite at the Cauchy horizon, its generators are eventually focused to
zero radius. Thus the null, mass-inflation singularity {\em generally}\/
precedes a crushing $r=0$ singularity deep inside the black hole core. This
central singularity is spacelike.


title: Dynamics of Topological Defects and Inflation

abstract:
  We study the dynamics of topological defects in the context of ``topological
inflation" proposed by Vilenkin and Linde independently. Analysing the time
evolution of planar domain walls and of global monopoles, we find that the
defects undergo inflationary expansion if $\eta\stackrel{>}{\sim}0.33m_{Pl}$,
where $\eta$ is the vacuum expectation value of the Higgs field and $m_{Pl}$ is
the Planck mass. This result confirms the estimates by Vilenkin and Linde. The
critical value of $\eta$ is independent of the coupling constant $\lambda$ and
the initial size of the defect. Even for defects with an initial size much
greater than the horizon scale, inflation does not occur at all if $\eta$ is
smaller than the critical value. We also examine the effect of gauge fields for
static monopole solutions and find that the spacetime with a gauge monopole has
an attractive nature, contrary to the spacetime with a global monopole. It
suggests that gauge fields affect the onset of inflation.


title: Three Dimensional Canonical Quantum Gravity

abstract:
  General aspects of vielbein representation, ADM formulation and canonical
quantization of gravity are reviewed using pure gravity in three dimensions as
a toy model. The classical part focusses on the role of observers in general
relativity, which will later be identified with quantum observers. A precise
definition of gauge symmetries and a classification of inequivalent solutions
of Einstein's equations in dreibein formalism is given as well. In the quantum
part the construction of the physical Hilbert space is carried out explicitly
for a torus and cylinder type space manifold, which has not been done so far.
Some conceptual problems of quantum gravity are discussed from the point of
view of an observer sitting inside the universe.


title: Quantum Gravity as Topological Quantum Field Theory

abstract:
  The physics of quantum gravity is discussed within the framework of
topological quantum field theory. Some of the principles are illustrated with
examples taken from theories in which space-time is three dimensional.


title: Geometrical Well Posed Systems for the Einstein Equations

abstract:
  We show that, given an arbitrary shift, the lapse $N$ can be chosen so that
the extrinsic curvature $K$ of the space slices with metric $\overline g$ in
arbitrary coordinates of a solution of Einstein's equations satisfies a
quasi-linear wave equation. We give a geometric first order symmetric
hyperbolic system verified in vacuum by $\overline g$, $K$ and $N$. We show
that one can also obtain a quasi-linear wave equation for $K$ by requiring $N$
to satisfy at each time an elliptic equation which fixes the value of the mean
extrinsic curvature of the space slices.


title: Einstein and Yang-Mills theories in hyperbolic form without gauge-fixing

abstract:
  The evolution of physical and gauge degrees of freedom in the Einstein and
Yang-Mills theories are separated in a gauge-invariant manner. We show that the
equations of motion of these theories can always be written in
flux-conservative first-order symmetric hyperbolic form. This dynamical form is
ideal for global analysis, analytic approximation methods such as
gauge-invariant perturbation theory, and numerical solution.


title: Self-Dual Action for Fermionic Fields and Gravitation

abstract:
  This paper studies the self-dual Einstein-Dirac theory. A generalization is
obtained of the Jacobson-Smolin proof of the equivalence between the self-dual
and Palatini purely gravitational actions. Hence one proves equivalence of
self-dual Einstein-Dirac theory to the Einstein-Cartan-Sciama-Kibble-Dirac
theory. The Bianchi symmetry of the curvature, core of the proof, now contains
a non-vanishing torsion. Thus, in the self-dual framework, the extra terms
entering the equations of motion with respect to the standard Einstein-Dirac
field equations, are neatly associated with torsion.


title: Hartle-Hawking state in supersymmetric minisuperspace

abstract:
  The Hartle-Hawking `no-boundary' state is constructed explicitly for the
recently developed supersymmetric minisuperspace model with non-vanishing
fermion number.


title: Lagrangian Theory of Constrained Systems: Cosmological Application

abstract:
  Previous work in the literature has studied the Hamiltonian structure of an
R-squared model of gravity with torsion in a closed Friedmann-Robertson-Walker
universe. Within the framework of Dirac's theory, torsion is found to lead to a
second-class primary constraint linear in the momenta and a second-class
secondary constraint quadratic in the momenta. This paper studies in detail the
same problem at a Lagrangian level, i.e. working on the tangent bundle rather
than on phase space. The corresponding analysis is motivated by a more general
program, aiming to obtain a manifestly covariant, multisymplectic framework for
the analysis of relativistic theories of gravitation regarded as constrained
systems. After an application of the Gotay-Nester Lagrangian analysis, the
paper deals with the generalized method, which has the advantage of being
applicable to any system of differential equations in implicit form.
Multiplication of the second-order Lagrange equations by a vector with zero
eigenvalue for the Hessian matrix yields the so-called first-generation
constraints. Remarkably, in the cosmological model here considered, if Lagrange
equations are studied using second-order formalism, a second-generation
constraint is found which is absent in first-order formalism. This happens
since first- and second-order formalisms are inequivalent. There are, however,
no {\it a priori} reasons for arguing that one of the two is incorrect. First-
and second-generation constraints are used to derive physical predictions for
the cosmological model.


title: Boundary Terms for Massless Fermionic Fields

abstract:
  Local supersymmetry leads to boundary conditions for fermionic fields in
one-loop quantum cosmology involving the Euclidean normal to the boundary and a
pair of independent spinor fields. This paper studies the corresponding
classical properties, i.e. the classical boundary-value problem and boundary
terms in the variational problem. Interestingly, a link is found with the
classical boundary-value problem when spectral boundary conditions are imposed
on a 3-sphere in the massless case. Moreover, the boundary term in the action
functional is derived.


title: On the Newtonian Limit of General Relativity

abstract:
  We find a choice of variables for the 3+1 formulation of general relativity
which casts the evolution equations into (flux-conservative)
symmetric-hyperbolic first order form for arbitrary lapse and shift, for the
first time. We redefine the lapse function in terms of the determinant of the
3-metric and a free function U which embodies the lapse freedom. By rescaling
the variables with appropriate factors of 1/c, the system is shown to have a
smooth Newtonian limit when the redefined lapse U and the shift are fixed by
means of elliptic equations to be satisfied on each time slice. We give a
prescription for the choice of appropriate initial data with controlled
extra-radiation content, based on the theory of problems with different
time-scales. Our results are local, in the sense that we are not concerned with
the treatment of asymptotic regions. On the other hand, this local theory is
all what is needed for most problems of practical numerical computation.


title:
Critical Exponents and Stability at the Black Hole Threshold for a
  Complex Scalar Field

abstract:
  This paper continues a study on Choptuik scaling in gravitational collapse of
a complex scalar field at the threshold for black hole formation. We perform a
linear perturbation analysis of the previously derived complex critical
solution, and calculate the critical exponent for black hole mass, $\gamma
\approx 0.387106$. We also show that this critical solution is unstable via a
growing oscillatory mode.


title: The (2+1)-Dimensional Black Hole

abstract:
  I review the classical and quantum properties of the (2+1)-dimensional black
hole of Ba{\~n}ados, Teitelboim, and Zanelli. This solution of the Einstein
field equations in three spacetime dimensions shares many of the
characteristics of the Kerr black hole: it has an event horizon, an inner
horizon, and an ergosphere; it occurs as an endpoint of gravitational collapse;
it exhibits mass inflation; and it has a nonvanishing Hawking temperature and
interesting thermodynamic properties. At the same time, its structure is simple
enough to allow a number of exact computations, particularly in the quantum
realm, that are impractical in 3+1 dimensions.


title:
Head-on collision of compact objects in general relativity: Comparison
  of post-Newtonian and perturbation approaches

abstract:
  The gravitational-wave energy flux produced during the head-on infall and
collision of two compact objects is calculated using two approaches: (i) a
post-Newtonian method, carried to second post-Newtonian order beyond the
quadrupole formula, valid for systems of arbitrary masses; and (ii) a
black-hole perturbation method, valid for a test-body falling radially toward a
black hole. In the test-body case, the methods are compared. The post-Newtonian
method is shown to converge to the ``exact'' perturbation result more slowly
than expected {\it a priori\/}. A surprisingly good approximation to the energy
radiated during the infall phase, as calculated by perturbation theory, is
found to be given by a Newtonian, or quadrupole, approximation combined with
the exact test-body equations of motion in the Schwarzschild spacetime.


title: Quantum Potential Approach to Quantum Cosmology

abstract:
  In this paper we discuss the quantum potential approach of Bohm in the
context of quantum cosmological model. This approach makes it possible to
convert the wavefunction of the universe to a set of equations describing the
time evolution of the universe. Following Ashtekar et.\ al., we make use of
quantum canonical transformation to cast a class of quantum cosmological models
to a simple form in which they can be solved explicitly, and then we use the
solutions to recover the time evolution.


title:
Refutation of C. W. Misner's claims in his article "Yilmaz Cancels
  Newton''

abstract:
  It is shown that an article by C. W. Misner contains serious errors. In
particular, the claim that the Yilmaz theory of gravitation cancels the
Newtonian gravitational interaction is based on a false premise. With the
correct premise the conclusion of the article regarding the absence of
gravitational interactions applies to general relativity and not to the Yilmaz
theory.


title: Thin-shell wormholes: Linearization stability

abstract:
  The class of spherically-symmetric thin-shell wormholes provides a
particularly elegant collection of exemplars for the study of traversable
Lorentzian wormholes. In the present paper we consider linearized (spherically
symmetric) perturbations around some assumed static solution of the Einstein
field equations. This permits us to relate stability issues to the (linearized)
equation of state of the exotic matter which is located at the wormhole throat.


title: Gravitational Waves from Compact Bodies

abstract:
  A review is given of recent research on gravitational waves from compact
bodies and its relevance to the LIGO/VIRGO international network of
high-frequency (10 to 10,000 Hz) gravitational-wave detectors, and to the
proposed LISA system of low-frequency (0.1 to 0.0001 Hz) detectors. The sources
that are reviewed are ordinary binary star systems, binaries made from compact
bodies (black holes and neutron stars), the final inspiral and coalescence of
compact-body binaries, the inspiral of stars and small black holes into massive
black holes, the stellar core collapse that triggers supernovae, and the spin
of neutron stars. This paper is adapted from a longer review article entitled
``Gravitational Waves'' (GRP-411) that the author has written for the
Proceedings of the Snowmass '94 Summer Study on Particle and Nuclear
Astrophysics and Cosmology.


title:
Black Hole Entropy and the Hamiltonian Formulation of Diffeomorphism
  Invariant Theories

abstract:
  Path integral methods are used to derive a general expression for the entropy
of a black hole in a diffeomorphism invariant theory. The result, which depends
on the variational derivative of the Lagrangian with respect to the Riemann
tensor, agrees with the result obtained from Noether charge methods by Iyer and
Wald. The method used here is based on the direct expression of the density of
states as a path integral (the microcanonical functional integral). The
analysis makes crucial use of the Hamiltonian form of the action. An algorithm
for placing the action of a diffeomorphism invariant theory in Hamiltonian form
is presented. Other path integral approaches to the derivation of black hole
entropy include the Hilbert action surface term method and the conical deficit
angle method. The relationships between these path integral methods are
presented.


title: Gravitational Waves

abstract:
  This article reviews current efforts and plans for gravitational-wave
detection, the gravitational-wave sources that might be detected, and the
information that the detectors might extract from the observed waves. Special
attention is paid to (i) the LIGO/VIRGO network of earth-based, kilometer-scale
laser interferometers, which is now under construction and will operate in the
high-frequency band ($1$ to $10^4$ Hz), and (ii) a proposed
5-million-kilometer-long Laser Interferometer Space Antenna (LISA), which would
fly in heliocentric orbit and operate in the low-frequency band ($10^{-4}$ to
$1$ Hz). LISA would extend the LIGO/VIRGO studies of stellar-mass ($M\sim2$ to
$300 M_\odot$) black holes into the domain of the massive black holes
($M\sim1000$ to $10^8M_\odot$) that inhabit galactic nuclei and quasars.


title:
Time machines: the Principle of Self-Consistency as a consequence of the
  Principle of Minimal Action

abstract:
  We consider the action principle to derive the classical, non-relativistic
motion of a self-interacting particle in a 4-D Lorentzian spacetime containing
a wormhole and which allows the existence of closed time-like curves. For the
case of a `hard-sphere' self-interaction potential we show that the only
possible trajectories (for a particle with fixed initial and final positions
and which traverses the wormhole once) minimizing the classical action are
those which are globally self-consistent, and that the `Principle of
self-consistency' (originally introduced by Novikov) is thus a natural
consequence of the `Principle of minimal action.'


title: Mathematical Structures of Space-Time

abstract:
  At first we introduce the space-time manifold and we compare some aspects of
Riemannian and Lorentzian geometry such as the distance function and the
relations between topology and curvature. We then define spinor structures in
general relativity, and the conditions for their existence are discussed. The
causality conditions are studied through an analysis of strong causality,
stable causality and global hyperbolicity. In looking at the asymptotic
structure of space-time, we focus on the asymptotic symmetry group of Bondi,
Metzner and Sachs, and the b-boundary construction of Schmidt. The Hamiltonian
structure of space-time is also analyzed, with emphasis on Ashtekar's spinorial
variables. Finally, the question of a rigorous theory of singularities in
space-times with torsion is addressed, describing in detail recent work by the
author. We define geodesics as curves whose tangent vector moves by parallel
transport. This is different from what other authors do, because their
definition of geodesics only involves the Christoffel symbols, though studying
theories with torsion. We then prove how to extend Hawking's singularity
theorem without causality assumptions to the space-time of the ECSK theory.
This is achieved studying the generalized Raychaudhuri equation in the ECSK
theory, the conditions for the existence of conjugate points and properties of
maximal timelike geodesics. Our result can also be interpreted as a
no-singularity theorem if the torsion tensor does not obey some additional
conditions. Thus, it seems that the occurrence of singularities in closed
cosmological models based on the ECSK theory is less generic than in general
relativity. Our work should be compared with important previous papers. There
are some relevant differences, because we rely on a different definition of


title: Singularity Theory in Classical Cosmology

abstract:
  This paper compares recent approaches appearing in the literature on the
singularity problem for space-times with nonvanishing torsion.


title: Alpha Surfaces for Complex Space-Times with Torsion

abstract:
  This paper studies necessary conditions for the existence of alpha-surfaces
in complex space-time manifolds with nonvanishing torsion. For these manifolds,
Lie brackets of vector fields and spinor Ricci identities contain explicitly
the effects of torsion. This leads to an integrability condition for
alpha-surfaces which does not involve just the self-dual Weyl spinor, as in
complex general relativity, but also the torsion spinor, in a nonlinear way,
and its covariant derivative. Interestingly, a particular solution of the
integrability condition is given by conformally right-flat and
right-torsion-free space-times.


title:
Spontaneously Broken SU(5) Symmetries and One-Loop Effects in the Early
  Universe

abstract:
  This paper studies one-loop effective potential and
spontaneous-symmetry-breaking pattern for SU(5) gauge theory in de Sitter
space-time. Curvature effects modify the flat-space effective potential by
means of a very complicated special function previously derived in the
literature. An algebraic technique already developed by the first author to
study spontaneous symmetry breaking of SU(n) for renormalizable polynomial
potentials is here generalized, for SU(5), to the much harder case of a de
Sitter background. A detailed algebraic and numerical analysis provides a
better derivation of the stability of the extrema in the maximal subgroups
SU(4) x U(1), SU(3) x SU(2) x U(1), SU(3) x U(1) x U(1) x R(311), SU(2) x SU(2)
x U(1) x U(1) x R(2211), where R(311) and R(2211) discrete symmetries select
particular directions in the corresponding two-dimensional strata. One thus
obtains a deeper understanding of the result, previously found with a different
numerical analysis, predicting the slide of the inflationary universe into
either the SU(3) x SU(2) x U(1) or SU(4) x U(1) extremum. Interestingly, using
this approach, one can easily generalize all previous results to a more
complete SU(5) tree-level potential also containing cubic terms.


title: Mixed Boundary Conditions in Euclidean Quantum Gravity

abstract:
  This paper studies a new set of mixed boundary conditions in Euclidean
quantum gravity. These involve, in particular, Robin boundary conditions on the
perturbed 3-metric and hence lead, by gauge invariance, to Robin conditions on
the whole ghost 1-form. The corresponding trace anomaly is evaluated in the
case of flat Euclidean 4-space bounded by a 3-sphere. In general, this anomaly
differs from the ones resulting from other local or non-local boundary
conditions studied in the recent literature.


title: Cosmological Restrictions on Conformally Invariant SU(5) GUT Models

abstract:
  Dirac's theory of constrained Hamiltonian systems is applied to the minimal
conformally invariant SU(5) grand-unified model studied at 1-loop level in a de
Sitter universe. For this model, which represents a simple and interesting
example of GUT theory and at the same time is a step towards theories with
larger gauge group like SO(10), second-class constraints in the Euclidean-time
regime exist. In particular, they enable one to prove that, to be consistent
with the experimentally established electroweak standard model and with
inflationary cosmology, the residual gauge-symmetry group of the early
universe, during the whole de Sitter era, is bound to be SU(3) x SU(2) x U(1).
Moreover, the numerical solution of the field equations subject to second-class
constraints is obtained. This confirms the existence of a sufficiently long de
Sitter phase of the early universe, in agreement with the initial assumptions.


title: Evolving Lorentzian Wormholes

abstract:
  Evolving Lorentzian wormholes with the required matter satisfying the Energy
conditions are discussed. Several different scale factors are used and the
corresponding consequences derived. The effect of extra, decaying (in time)
compact dimensions present in the wormhole metric is also explored and certain
interesting conclusions are derived for the cases of exponential and
Kaluza--Klein inflation.


title: Quantum Mechanical Lorentzian Wormholes in Cosmological Backgrounds

abstract:
  We present a minisuperspace analysis of a class of Lorentzian wormholes that
evolves quantum mechanically in a background Friedman Robertson Walker
spacetime. The quantum mechanical wavefunction for these wormholes is obtained
by solving the Wheeler-DeWitt equation for Einstein gravity on this
minisuperspace. The time-dependent expectation value of the wormhole throat
radius is calculated to lowest order in an adiabatic expansion of the
Wheeler-DeWitt hamiltonian. For a radiation dominated expansion, the radius is
shown to relax asymptotically to obtain a value of order the Planck length
while for a deSitter background, the radius is stationary but always larger
than the Planck length. These two cases are of particular relevance when
considering wormholes in the early universe.


title: Correlations between black holes formed in cosmic string breaking

abstract:
  An analysis of cosmic string breaking with the formation of black holes
attached to the ends reveals a remarkable feature: the black holes can be
correlated or uncorrelated. We find that, as a consequence, the
number-of-states enhancement factor in the action governing the formation of
uncorrelated black holes is twice the one for a correlated pair. We argue that
when an uncorrelated pair forms at the ends of the string, the physics involved
is more analogous to thermal nucleation than to particle-antiparticle creation.
Also, we analyze the process of intercommuting strings induced by black hole
annihilation and merging. Finally, we discuss the consequences for grand
unified strings. The process whereby uncorrelated black holes are formed yields
a rate which significantly improves over those previously considered, but still
not enough to modify string cosmology.


title: A Normal Coordinate Expansion for the Gauge Potential

abstract:
  In this pedagogical note, I present a method for constructing a fully
covariant normal coordinate expansion of the gauge potential on a curved
space-time manifold. Although the content of this paper is elementary, the
results may prove useful in some applications and have not, to the best of my
knowledge, been discussed explicitly in the literature.


title:
Local Boundary Conditions for the Dirac Operator and One-Loop Quantum
  Cosmology

abstract:
  This paper studies local boundary conditions for fermionic fields in quantum
cosmology, originally introduced by Breitenlohner, Freedman and Hawking for
gauged supergravity theories in anti-de Sitter space. For a spin-1/2 field the
conditions involve the normal to the boundary and the undifferentiated field. A
first-order differential operator for this Euclidean boundary-value problem
exists which is symmetric and has self-adjoint extensions. The resulting
eigenvalue equation in the case of a flat Euclidean background with a
three-sphere boundary of radius a is found to be:
$F(E)=[J_{n+1}(Ea)]^{2}-[J_{n+2}(Ea)]^{2}=0 , \forall n \geq 0$. Using the
theory of canonical products, this function F may be expanded in terms of
squared eigenvalues, in a way which has been used in other recent one-loop
calculations involving eigenvalues of second-order operators. One can then
study the generalized Riemann zeta-function formed from these squared
eigenvalues. The value of zeta(0) determines the scaling of the one-loop
prefactor in the Hartle-Hawking amplitude in quantum cosmology. Suitable
contour formulae, and the uniform asymptotic expansions of the Bessel functions
and their first derivatives, yield for a massless Majorana field:
zeta(0)=11/360. Combining this with zeta(0) values for other spins, one can
then check whether the one-loop divergences in quantum cosmology cancel in a
supersymmetric theory.