title:
Quantization of the Bianchi type-IX model in supergravity with a
  cosmological constant

abstract:
  Diagonal Bianchi type-IX models are studied in the quantum theory of $ N = 1
$ supergravity with a cosmological constant. It is shown, by imposing the
supersymmetry and Lorentz quantum constraints, that there are no physical
quantum states in this model. The $ k = + 1 $ Friedmann model in supergravity
with cosmological constant does admit quantum states. However, the Bianchi
type-IX model provides a better guide to the behaviour of a generic state,
since more gravitino modes are available to be excited. These results indicate
that there may be no physical quantum states in the full theory of $ N = 1 $
supergravity with a non-zero cosmological constant. are available to be
excited. These results indicate that there may be no physical quantum states in
the full theory of $ N = 1 $ supergravity with a non-zero cosmological
constant.


title:
Performance of Newtonian filters in detecting gravitational waves from
  coalescing binaries

abstract:
  Coalescing binary systems are one of the most promising sources of
gravitational waves. The technique of matched filtering used in the detection
of gravitational waves from coalescing binaries relies on the construction of
accurate templates. Until recently filters modelled on the quadrupole or the
Newtonian approximation were deemed sufficient. Recently it was shown that
post-Newtonian effects contribute to a secular growth in the phase difference
between the actual signal and its corresponding Newtonian template. In this
paper we investigate the possibility of compensating for the phase difference
caused by the post-Newtonian terms by allowing for a shift in the Newtonian
filter parameters. We find that Newtonian filters perform adequately for the
purpose of detecting the presence of the signal for both the initial and the
advanced LIGO detectors.


title: Fermions and Topology

abstract:
  The canonical theory of quantum gravity in the loop representation can be
extended to incorporate topology change, in the simple case that this refers to
the creation or annihilation of "minimalist wormholes" in which two points of
the spatial manifold are identified. Furthermore, if the states of the
wormholes threaded by loop states are taken to be antisymmetrized under the
permutation of wormhole mouths, as required by the relation between spin and
statistics, then the quantum theory of pure general relativity, without matter
but with minimalist wormholes, is shown to be equivalent to the quantum theory
of general relativity coupled to a single Weyl fermion field, at both the
kinematical and diffeomorphism invariant levels. The correspondence is also
shown to extend to the action of the dynamics generated by the Hamiltonian
constraint, on a large subspace of the physical state space, and is thus
conjectured to be completely general.


title:
The fate of black hole singularities and the parameters of the standard
  models of particle physics and cosmology

abstract:
  A cosmological scenario which explains the values of the parameters of the
standard models of elementary particle physics and cosmology is discussed. In
this scenario these parameters are set by a process analogous to natural
selection which follows naturally from the assumption that the singularities in
black holes are removed by quantum effects leading to the creation of new
expanding regions of the universe. The suggestion of J. A. Wheeler that the
parameters change randomly at such events leads naturally to the conjecture
that the parameters have been selected for values that extremize the production
of black holes. This leads directly to a prediction, which is that small
changes in any of the parameters should lead to a decrease in the number of
black holes produced by the universe. On plausible astrophysical assumptions it
is found that changes in many of the parameters do lead to a decrease in the
number of black holes produced by spiral galaxies. These include the masses of
the proton,neutron, electron and neutrino and the weak, strong and
electromagnetic coupling constants. Finally,this scenario predicts a natural
time scale for cosmology equal to the time over which spiral galaxies maintain
appreciable rates of star formation, which is compatible with current
observations that $\Omega = .1-.2$.


title: Complementary Relativity

abstract:
  Special theory of relativity has been formulated in a vacuum momentum-energy
representation which is equivalent to Einstein special relativity and predicts
just the same results as it. Although in this sense such a formulation would be
at least classically useless, its consistent extension to noninertial frames
produces a momentum-energy metric which behaves as a new dynamical quantity
that is here interpreted in terms of a cosmological field. This new field would
be complementary to gravity in that its strength varies inversely to as that of
gravity does. Using a strong-field approximation, we suggest that the existence
of this cosmological field would induce a shift of luminous energy which could
justify the existence of all the assumed invisible matter in the universe, so
as the high luminousities found in active galactic nuclei and quasars.


title: Equivalent Sets of Histories and Multiple Quasiclassical Realms

abstract:
  We consider notions of physical equivalence of sets of histories in the
quantum mechanics of a closed system. We show first how the same set of
histories can be relabeled in various ways, including the use of the Heisenberg
equations of motion and of passive transformations of field variables. In the
the usual approximate quantum mechanics of a measured subsystem, two
observables re- presented by different Hermitian operators are physically
distinguished by the different apparatus used to measure them. In the quantum
mechanics of a closed system, however, any apparatus is part of the system and
the notion of physically distinct situations has a different character. We show
that a triple consisting of an initial condition, a Hamiltonian, and a set of
histories is physically equivalent to another triple if the operators
representing these initial conditions, Hamiltonians, and histories are related
by any fixed unitary transformation. We apply this result to the question of
whether the universe might exhibit physically inequivalent quasiclassical
realms (which we earlier called quasiclassical domains), not just the one that
includes familiar experience. We describe how the probabilities of alternative
forms, behaviors, and evolutionary histories of information gathering and
utilizing systems (IGUSes) using the usual quasiclassical realm could in
principle be calculated in quantum cosmology, although it is, of course,
impractical to perform the computations. We discuss how, in principle, the
probabilities of occurence of IGUSes could be calculated in realms distinct
from the usual quasiclassical one. We discuss how IGUSes adapted mainly to two
different realms could draw inferences about each other using a hybrid realm
consisting of alternatives drawn from each.


title: Exotic Black Holes

abstract:
  Black hole solutions can be used to shed light on general issues in General
Relativity and Quantum Physics. Black--hole hair, entropy and naked
singularities are considered here, along with some implications for the
inflationary universe scenario.


title: Stability of the Cauchy horizon in Kerr--de Sitter spacetimes

abstract:
  We begin a program of work aimed at examining the interior of a rotating
black hole with a non--zero cosmological constant. The generalisation of
Teukolsky's equation for the radial mode functions is presented. It is shown
that the energy fluxes of scalar, electromagnetic and gravity waves are regular
at the Cauchy horizon whenever the surface gravity there is less than the
surface gravity at the cosmological horizon. This condition is narrowly
allowed, even when the cosmological constant is very small, thus permitting an
observer to pass through the hole, viewing the naked singularity along the way.


title: Generating new magnetic universe solutions from old

abstract:
  In this paper we apply the techniques which have been developed over the last
few decades for generating nontrivially new solutions of the Einstein-Maxwell
equations from seed solutions for simple spacetimes. The simple seed spacetime
which we choose is the "magnetic universe" to which we apply the Ehlers
transformation. Three interesting non-singular metrics are generated. Two of
these may be described as "rotating magnetic universes" and the third as an
"evolving magnetic universe." Each is causally complete - in that all timelike
and lightlike geodesics do not end in a finite time or affine parameter. We
also give the electromagnetic field in each case. For the two rotating
stationary cases we give the projection with respect to a stationary observer
of the electromagnetic field into electric and magnetic components.


title: Quasiclassical Realms in a Quantum Universe

abstract:
  In this universe, governed fundamentally by quantum mechanical laws,
characterized by indeterminism and distributed probabilities, classical
deterministic laws are applicable over a wide range of time, place, and scale.
We review the origin of these laws in the context of the quantum mechanics of
closed systems, most generally, the universe as a whole. There probabilities
are predicted for members of decoherent sets of alternative histories of the
universe, ie ones for which the interference between pairs in the set is
negligible as measured by a decoherence functional. An expansion of the
decoherence functional in the separation between histories allows the form of
the deterministic equations of motion to be derived for suitable coarse
grainings of a class of non-relativistic systems, including ones with general
non-linear interactions. More coarse graining is needed to achieve classical
predictability than naive arguments based on the uncertainty principle would
suggest. Coarse graining is needed for decoherence, and coarse graining beyond
that for the inertia necessary to resist the noise that mechanisms of
decoherence produce. Sets of histories governed largely by deterministic laws
constitute the quasiclassical realm of everyday experience which is an emergent
feature of the closed system's initial condition and Hamiltonian. We analyse
the sensitivity of the existence of a quasiclassical realm to the particular
form of the initial condition. We find that almost any initial condition will
exhibit a quasiclassical realm of some sort, but only a small fraction of the
total number of possible initial states could reproduce the everyday
quasiclassical realm of our universe. (Talk given at the Lanczos Centenary
Conference, North Carolina State University, December 15, 1993.)


title: Fermion Helicity Flip in Weak Gravitational Fields

abstract:
  The helicity flip of a spin-${\textstyle \frac{1}{2}}$ Dirac particle
interacting gravitationally with a scalar field is analyzed in the context of
linearized quantum gravity. It is shown that massive fermions may have their
helicity flipped by gravity, in opposition to massless fermions which preserve
their helicity.


title: The Positivity of Energy for Asymptotically Anti-de Sitter Spacetimes

abstract:
  We use the formulation of asymptotically anti-de Sitter boundary conditions
given by Ashtekar and Magnon to obtain a coordinate expression for the general
asymptotically AdeS metric in a neighbourhood of infinity. From this, we are
able to compute the time delay of null curves propagating near infinity. If the
gravitational mass is negative, so will be the time delay (relative to null
geodesics at infinity) for certain null geodesics in the spacetime. Following
closely an argument given by Penrose, Sorkin, and Woolgar, who treated the
asymptotically flat case, we are then able to argue that a negative time delay
is inconsistent with non-negative matter-energies in spacetimes having good
causal properties. We thereby obtain a new positive mass theorem for these
spacetimes. The theorem may be applied even when the matter flux near the
boundary-at-infinity falls off so slowly that the mass changes, provided the
theorem is applied in a time-averaged sense. The theorem also applies in
certain spacetimes having local matter-energy that is sometimes negative, as
can be the case in semi-classical gravity.


title:
Positive Energy for Asymptotically Anti-de Sitter Schwarzschild
  Spacetimes

abstract:
  Within the general class of Asymptotically Anti-de Sitter spacetimes that are
asymptotic to the A-de-S Schwarzschild metric, we give a simple positive mass
theorem based on arguments from causal structure. A general result for all
asymptotically A-de-S spacetimes will be given elsewhere.


title: The Decoherence of Phase Space Histories

abstract:
  In choosing a family of histories for a system, it is often convenient to
choose a succession of locations in phase space, rather than configuration
space, for comparison to classical histories. Although there are no good
projections onto phase space, several approximate projections have been used in
the past; three of these are examined in this paper. Expressions are derived
for the probabilities of histories containing arbitrary numbers of projections
onto phase space, and the conditions for the decoherence of these histories are
studied.


title: The Role of the Future in Quantum Theory

abstract:
  Interpretation problems are eliminated from quantum theory by picturing a
quantum history as having been sampled from a probability distribution over the
set of histories which are permitted by all relevant boundary conditions. In
laboratory physics, the final measurement plays a crucial role in defining the
set of allowed histories by constraining the final state to be an eigenstate of
the measurement operator. For the universe itself, a final boundary condition
can play a similar role. Together with the special big bang initial state, the
final constraint may ensure that the universe admits a classical description in
the asymptotic future. Acknowledging the role of a future constraint dispels
the mysteries of quantum theory without any amendment to the theory itself.


title:
Higher order gravity, gauge invariant variables, and quantum behavior in
  Weyl-like geometries

abstract:
  This paper presents the detailed, standard treatment of a simple, gauge
invariant action for Weyl and Weyl-like Cartan geometries outlined in a
previous paper. In addition to the familiar scalar curvature squared and
Maxwell terms, the action chosen contains the logarithmic derivative of the
scalar curvature combined with the intrinsic four vector (Weyl vector) in a
gauge invariant fashion. This introduces higher order derivative terms directly
into the action. No separate, "matter" fields are introduced. As the usual Weyl
metric and four vector are varied, certain gauge invariant combinations of
quantities arise naturally as the results are collected, provided the scalar
curvature is nonzero. This paper demonstrates the general validity of these
results for any gauge choice. Additionally, "matter" terms appear in the field
equations. Furthermore, the resulting forms isolate the familiar mathematical
structure of a coupled Einstein-Maxwell-Schroedinger (relativistic) system of
classical fields, with the exception of additional, second derivative terms in
the stress tensor for the Schroedinger field, and the algebraic independence of
the conjugate wavefunction. This independence is found to be equivalent to the
presence of a second, negative energy, Schroedinger field. A detailed
comparison is made between this model, and the standard
Einstein-Maxwell-Schroedinger field theory. The possible use of such continuum
models as a basis for quantum phenomena, and some generalizations of the model
are discussed.


title: Gravitation Singularities of the Caustic Type

abstract:
  In view of the well-known correspondence between gravitational fields and
space-time distributions on a world manifold X, the criterion of gravitation
singularities as singularities of these distributions is suggested. In the germ
terms, singularities of a (3+1) distribution look locally like singularities of
a foliation whose leaves are level surfaces of a real function f on X. If f is
a single-valued function, changes of leave topology at critical points of f
take place. In case of a multi-valued function f, one can lift the foliation to
the total space of the cotangent bundle over X, then extend it over branch
points of f and project this extension onto X. Singular points of this
projection constitute a Lagrange map caustic by Arnol'd.


title: Entropy Generation in Quantum Gravity and Black Hole Remnants

abstract:
  The area entropy $A/4$ and the related Hawking temperature in the presence of
event horizons are rederived, for de Sitter and black hole topologies, as a
consequence of a tunneling of the wave functional associated to the classical
coupled matter and gravitational fields. The extension of the wave functional
outside the barrier provides a reservoir of quantum states which allows for an
additive constant to $A/4$. While, in a semi-classical analysis, this gives no
new information in the de Sitter case, it yields an infinite constant in the
black hole case. Evaporating black holes would then leave residual ``planckons"
- Planckian remnants with infinite degeneracy. Generic planckons can neither
decay into, nor be directly formed from, ordinary matter in a finite time. Such
opening at the Planck scale of an infinite Hilbert space is expected to provide
the ultraviolet cutoff required to render the theory finite in the sector of
large scale physics.


title: Source Vacuum Fluctuations of Black Hole Radiance

abstract:
  The emergence of Hawking radiation from vacuum fluctuations is analyzed in
conventional field theories and their energy content is defined through the
Aharonov weak value concept. These fluctuations travel in flat space-time and
carry transplanckian energies sharply localized on cisplanckian distances. We
argue that these features cannot accommodate gravitational nonlinearities. We
suggest that the very emission of Hawking photons from tamed vacuum
fluctuations requires the existence of an exploding set of massive fields.
These considerations corroborate some conjectures of Susskind and may prove
relevant for the back-reaction problem and for the unitarity issue.


title: Gravitational Shock Waves for Schwarzschild and Kerr Black Holes

abstract:
  The metrics of gravitational shock waves for a Schwarzschild black hole in
ordinary coordinates and for a Kerr black hole in Boyer-Lindquist coordinates
are derived. The Kerr metric is discussed for two cases: the case of a Kerr
black hole moving parallel to the rotational axis, and moving perpendicular to
the rotational axis. Then, two properties from the derived metrics are
investigated: the shift of a null coordinate and the refraction angle crossing
the gravitational shock wave. Astrophysical applications for these metrics are
discussed in short.


title:
Decoherence, Correlation, and Unstable Quantum States in Semiclassical
  Cosmology

abstract:
  It is demonstrated that almost any S-matrix of quantum field theory in curved
spaces posses an infinite set of complex poles (or branch cuts). These poles
can be transformed into complex eigenvalues, the corresponding eigenvectors
being Gamow vectors. All this formalism, which is heuristic in ordinary Hilbert
space, becomes a rigorous one within the framework of a properly chosen rigged
Hilbert space. Then complex eigenvalues produce damping or growing factors. It
is known that the growth of entropy, decoherence, and the appearance of
correlations, occur in the universe evolution, but only under a restricted set
of initial conditions. It is proved that the damping factors allow to enlarge
this set up to almost any initial conditions.


title: The Problems of Time and Observables: Some Recent Mathematical Results

abstract:
  We present 2 recent results on the problems of time and observables in
canonical gravity. (1) We cannot use parametrized field theory to solve the
problem of time because, strictly speaking, general relativity is not a
parametrized field theory. (2) We show that there are essentially no local
observables for vacuum spacetimes.


title:
Classification of Generalized Symmetries for the Vacuum Einstein
  Equations

abstract:
  A generalized symmetry of a system of differential equations is an
infinitesimal transformation depending locally upon the fields and their
derivatives which carries solutions to solutions. We classify all generalized
symmetries of the vacuum Einstein equations in four spacetime dimensions. To
begin, we analyze symmetries that can be built from the metric, curvature, and
covariant derivatives of the curvature to any order; these are called natural
symmetries and are globally defined on any spacetime manifold. We next classify
first-order generalized symmetries, that is, symmetries that depend on the
metric and its first derivatives. Finally, using results from the
classification of natural symmetries, we reduce the classification of all
higher-order generalized symmetries to the first-order case. In each case we
find that the generalized symmetries are infinitesimal generalized
diffeomorphisms and constant metric scalings. There are no non-trivial
conservation laws associated with these symmetries. A novel feature of our
analysis is the use of a fundamental set of spinorial coordinates on the
infinite jet space of Ricci-flat metrics, which are derived from Penrose's
``exact set of fields'' for the vacuum equations.


title: Optical scalars in spherical spacetimes

abstract:
  Consider a spherically symmetric spacelike slice through a spherically
symmetric spacetime. One can derive a universal bound for the optical scalars
on any such slice. The only requirement is that the matter sources satisfy the
dominant energy condition and that the slice be asymptotically flat and regular
at the origin. This bound can be used to derive new conditions for the
formation of apparent horizons. The bounds hold even when the matter has a
distribution on a shell or blows up at the origin so as to give a conical
singularity.


title:
Resolution of simple singularities yielding particle symmetries in a
  space-time

abstract:
  A finite subgroup of the conformal group SL(2,C) can be related to invariant
polynomials on a hypersurface in C^3. The latter then carries a simple
singularity, which resolves by a finite iteration of basic cycles of
deprojections. The homological intersection graph of this cycles is the Dynkin
graph of an ADE Lie group. The deformation of the simple singularity
corresponds to ADE symmetry breaking. A 3+1-dimensional topological model of
observation is constructed, transforming consistently under SL(2,C), as an
evolving 3-dimensional system of world tubes, which connect ``possible points
of observation". The existence of an initial singularity for the 4-dimensional
space-time is related to its global topological structure. Associating the
geometry of ADE singularities to the vertex structure of the topological model
puts forward the conjecture on a likewise relation of inner symmetries of
elementary particles to local space-time structure.


title: Conformal Coupling and Invariance in Different Dimensions

abstract:
  Conformal transformations of the following kinds are compared: (1) conformal
coordinate transformations, (2) conformal transformations of Lagrangian models
for a D-dimensional geometry, given by a Riemannian manifold M with metric g of
arbitrary signature, and (3) conformal transformations of (mini-)superspace
geometry. For conformal invariance under this transformations the following
applications are given respectively: (1) Natural time gauges for
multidimensional geometry, (2) conformally equivalent Lagrangian models for
geometry coupled to a spacially homogeneous scalar field, and (3) the conformal
Laplace operator on the $n$-dimensional manifold $M of minisuperspace for
multidimensional geometry and the Wheeler de Witt equation. The conformal
coupling constant xi_c is critically distinguished among arbitrary couplings
xi, for both, the equivalence of Lagrangian models with D-dimensional geometry
and the conformal geometry on n-dimensional minisuperspace. For dimension
D=3,4,6 or 10, the critical number xi_c={D-2}/{4(D-1)} is especially simple as
a rational fraction.


title: Static axisymmetric spacetimes with non-generic world-line SUSY

abstract:
  The conditions for the existence of Killing-Yano tensors, which are closely
related to the appearance of non-generic world-line SUSY, are presented for
static axisymmetric spacetimes. Imposing the vacuum Einstein equation, the set
of solutions admitting Killing-Yano tensors is considered. In particular, it is
shown that static, axisymmetric and asymptotically flat vacuum solutions
admitting Killing-Yano tensors are only the Schwarzschild solution.


title:
Universal Approach to Cosmological Singularities in Two Dimensional
  Dilaton Gravity

abstract:
  We show that in a large class of two dimensional models with conformal matter
fields, the semiclassical cosmological solutions have a weak coupling
singularity if the classical matter content is below a certain threshold. This
threshold and the approach to the singularity are model-independent. When the
matter fields are not conformally invariant, the singularity persists if the
quantum state is the vacuum near the singularity, and could dissappear for
other quantum states.


title: Wavefunction of a Black Hole and the Dynamical Origin of Entropy

abstract:
  Recently it was proposed to explain the dynamical origin of the entropy of a
black hole by identifying its dynamical degrees of freedom with states of
quantum fields propagating in the black-hole's interior. The present paper
contains the further development of this approach. The no-boundary proposal
(analogous to the Hartle-Hawking no-boundary proposal in quantum cosmology) is
put forward for defining the wave function of a black hole. This wave function
is a functional on the configuration space of physical fields (including the
gravitational one) on the three-dimensional space with the Einstein-Rosen
bridge topology.It is shown that in the limit of small perturbations on the
Kruskal background geometry the no-boundary wave function coincides with the
Hartle-Hawking vacuum state. The invariant definition of inside and outside
modes is proposed. The density matrix describing the internal state of a black
hole is obtained by averaging over the outside modes. This density matrix is
used to define the entropy of a black hole, which is to be divergent. It is
argued that the quantum fluctuations of the horizon which are internally
present in the proposed formalism may give the necessary cut-off and provide a
black hole with the finite entropy.


title: Why do all the curvature invariants of a gravitational wave vanish ?

abstract:
  We prove the theorem valid for (Pseudo)-Riemannian manifolds $V_n$: "Let $x
\in V_n$ be a fixed point of a homothetic motion which is not an isometry then
all curvature invariants vanish at $x$." and get the Corollary: "All curvature
invariants of the plane wave metric $$ds \sp 2 \quad = \quad 2 \, du \, dv \, +
\, a\sp 2 (u) \, dw \sp 2 \, + \, b\sp 2 (u) \, dz \sp 2 $$ identically
vanish." Analysing the proof we see: The fact that for definite signature
flatness can be characterized by the vanishing of a curvature invariant,
essentially rests on the compactness of the rotation group $SO(n)$. For Lorentz
signature, however, one has the non-compact Lorentz group $SO(3,1)$ instead of
it. A further and independent proof of the corollary uses the fact, that the
Geroch limit does not lead to a Hausdorff topology, so a sequence of
gravitational waves can converge to the flat space-time, even if each element
of the sequence is the same pp-wave.


title: Stability and Hamiltonian formulation of higher derivative theories

abstract:
  We analyze the presumptions which lead to instabilities in theories of order
higher than second. That type of fourth order gravity which leads to an
inflationary (quasi de Sitter) period of cosmic evolution by inclusion of one
curvature squared term (i.e. the Starobinsky model) is used as an example. The
corresponding Hamiltonian formulation (which is necessary for deducing the
Wheeler de Witt equation) is found both in the Ostrogradski approach and in
another form. As an example, a closed form solution of the Wheeler de Witt
equation for a spatially flat Friedmann model and L=R\sp 2 is found. The method
proposed by Simon to bring fourth order gravity to second order can be (if
suitably generalized) applied to bring sixth order gravity to second order. In
the Erratum we show that a spatially flat Friedmann model need not be
geodesically complete even if the scale factor a(t) is positive and smooth for
all real values of the synchronized time t.


title: Black Hole Entropy and Induced Gravity

abstract:
  In this short essay we review the arguments showing that black hole entropy
is, at least in part, ``entanglement entropy", i.e., missing information
contained in correlations between quantum field fluctuations inside and outside
the event horizon. Although the entanglement entropy depends upon the matter
field content of the theory, it turns out that so does the Bekenstein-Hawking
entropy $A/4\hbar G_{ren}$, in precisely the same way, because the effective
gravitational constant $G_{ren}$ is renormalized by the very same quantum
fluctuations. It appears most satisfactory if the entire gravitational action
is ``induced", in the manner suggested by Sakharov, since then the black hole
entropy is purebred entanglement entropy, rather than being hybrid with bare
gravitational entropy (whatever that might be.)


title: Static Charged Black Holes in $(2+1)$ Dimensional Dilaton Gravity

abstract:
  A one parameter family of static charged black hole solutions in
$(2+1)$-dimensional general relativity minimally coupled to a dilaton
$\phi\propto ln({r\over\beta})$ with a potential term $e^{b\phi}\Lambda$ is
obtained. Their causal strutures are investigated, and thermodynamical
temperature and entropy are computed. One particular black hole in the family
has the same thermodynamical properties as the Schwarzschild black hole in
$3+1$ dimensions. Solutions with cosmological horizons are also discussed.
Finally, a class of black holes arising from the dilaton with a negative
kinetic term (tachyon) is briefly discussed.


title: Cylindrical Black Hole in General Relativity

abstract:
  A black hole solution of Einstein's field equations with cylindrical symmetry
is found. Using the Hamiltonian formulation one is able to define mass and
angular momentum for the cylindrical black hole through the corresponding and
equivalent three dimensional theory. The causal structure is analyzed.
Comments: revised version.


title: Bases of Wormholes in Quantum Cosmology

abstract:
  We show that if the space of physical states spanned by the wormhole wave
functions can be equipped with a Hilbert structure, such a Hilbert space must
coincide with that of the Lorentzian gravitational system under consideration.
The physical inner product can then be determined by imposing a set of
Lorentzian reality conditions. The Hilbert space of the gravitational model
admits in this case a basis of wormhole solutions, and every proper quantum
state can be interpreted as a superposition of wormholes. We also argue that
the wave functions that form the basis of wormholes must be eigenfunctions of a
complete set of compatible observables. The associated eigenvalues provide a
set of well-defined wormhole parameters, in the sense that they can be employed
to designate the different elements of the basis of wormholes. We analyse in
detail the case of a Friedmann-Robertson-Walker spacetime minimally coupled to
a massless scalar field. For this minisuperspace, we prove the validity of all
the above statements and discuss various admissible choices of bases of
wormhole wave functions.


title:
Three-dimensional initial data for the collision of two black holes II:
  Quasi-circular orbits for equal-mass black holes

abstract:
  The construction of initial-data sets representing binary black-hole
configurations in quasi-circular orbits is studied in the context of the
conformal-imaging formalism. An effective-potential approach for locating
quasi-circular orbits is outlined for the general case of two holes of
arbitrary size and with arbitrary spins. Such orbits are explicitly determined
for the case of two equal-sized nonrotating holes, and the innermost stable
quasi-circular orbit is located. The characteristics of this innermost orbit
are compared to previous estimates for it, and the entire sequence of
quasi-circular orbits is compared to results from the post-Newtonian
approximation. Some aspects of the numerical evolution of such data sets are
explored.


title: Quantum Cosmology and Higher-Order Lagrangian Theories

abstract:
  In this paper the quantum cosmological consequences of introducing a term
cubic in the Ricci curvature scalar $R$ into the Einstein--Hilbert action are
investigated. It is argued that this term represents a more generic
perturbation to the action than the quadratic correction usually considered. A
qualitative argument suggests that there exists a region of parameter space in
which neither the tunneling nor the no-boundary boundary conditions predict an
epoch of inflation that can solve the horizon and flatness problems of the big
bang model. This is in contrast to the $R^2$--theory.


title: Classical and Quantum Properties of Liouville Black Holes

abstract:
  Black hole spacetimes can arise when a Liouville field is coupled to two-
dimensional gravity. Exact solutions are obtained both classically and when
quantum corrections due to back reaction effects are included. The black hole
temperature depends upon the mass and the thermodynamic limit breaks down
before evaporation of the black hole is complete, indicating that higher-loop
effects must be included for a full description of the process.


title:
Traversable Wormholes in (2+1) and (3+1) Dimensions with a Cosmological
  Constant

abstract:
  Macroscopic traversable wormhole solutions to Einstein's field equations in
$(2+1)$ and $(3+1)$ dimensions with a cosmological constant are investigated.
Ensuring traversability severely constrains the material used to generate the
wormhole's spacetime curvature. Although the presence of a cosmological
constant modifies to some extent the type of matter permitted (for example it
is possible to have a positive energy density for the material threading the
throat of the wormhole in $(2+1)$ dimensions), the material must still be
``exotic'', that is matter with a larger radial tension than total mass-energy
density multiplied by $c^2$. Two specific solutions are applied to the general
cases and a partial stability analysis of a $(2+1)$ dimensional solution is
explored.


title: Radiation collapse and gravitational waves in three dimensions

abstract:
  Two non-static solutions for three dimensional gravity coupled to matter
fields are given. One describes the collapse of radiation that results in a
black hole. This is the three dimensional analog of the Vaidya metric, and is
used to construct a model for mass inflation. The other describes plane
gravitational waves for coupling to a massless scalar field.


title:
Semiclassical Gravitational Effects in de Sitter Space at Finite
  Temperature

abstract:
  In the framework of finite temperature conformal scalar field theory on de
Sitter space-time the linearized Einstein equations for the renormalized stress
tensor are exactly solved. In this theory quantum field fluctuations are
concentrated near two spheres of the de Sitter radius, propagating as light
wave fronts. Related cosmological aspects are shortly discussed. The analysis,
performed for flat expanding universe, shows exponential damping of the
back-reaction effects far from these spherical objects. The obtained solutions
for the semiclassical Einstein equations in de Sitter background can be
straightforwardly extended also to the anti-de Sitter geometry.


title:
Closed spherically symmetric massless scalar field spacetimes have
  finite lifetimes

abstract:
  The closed-universe recollapse conjecture is studied for a class of closed
spherically symmetric spacetimes which includes those having as a matter
source: (1) a massless scalar field; (2) a perfect fluid obeying the equation
of state $\rho = P$; and (3) null dust. It is proven that all timelike curves
in any such spacetime must have length less than $6 \max_\Sigma(2m)$, where $m$
is the mass associated with the spheres of symmetry and $\Sigma$ is any Cauchy
surface for the spacetime. The simplicity of this result leads us to conjecture
that a similar bound can be established for the more general spherically
symmetric spacetimes.


title: Stringy Quantum Cosmology of the Bianchi Class a

abstract:
  The quantum cosmology of the string effective action is considered within the
context of the Bianchi class A minisuperspace. An exact unified solution is
found for all Bianchi types and interpreted physically as a quantum wormhole.
The solution is generalized for types ${\rm VI_0}$ and ${\rm VII_0}$. The
Bianchi type IX wavefunction becomes increasingly localized around the
isotropic Universe at large three-geometries.


title: Comment on ``Meaning of the Wave Function''

abstract:
  We draw attention to an elementary flaw in a recently proposed experiment to
measure the wave function of a single quantum system.


title: Vector Fields on a Disk with Mixed Boundary Conditions

abstract:
  We study vector fields on a disk satisfying two types of mixed boundary
conditions. These boundary conditions are selected by BRST-invariance in
electrodynamics. They also appear in the de Rham complex. The manifest
construction of the harmonic expansion is presented. The eigenfunctions of the
vector Laplace operator are expressed in terms of fields satisfying pure
Dirichlet or Robin boundary conditions. For the case of four-dimensional disk
several first coefficients of the heat kernel expansion are computed. An error
in the analitical expression by Branson and Gilkey is corrected.


title: Quantum Observables and Recollapsing Dynamics

abstract:
  Within a simple quantization scheme, observables for a large class of finite
dimensional time reparametrization invariant systems may be constructed by
integration over the manifold of time labels. This procedure is shown to
produce a complete set of densely defined operators on a physical Hilbert space
for which an inner product is identified and to provide reasonable results for
simple test cases. Furthermore, many of these observables have a clear
interpretation in the classical limit and we use this to demonstrate that, for
a class of minisuperspace models including LRS Bianchi IX and the
Kantowski-Sachs model this quantization agrees with classical physics in
predicting that such spacetimes recollapse.


title:
Linear stochastic wave-equations for continuously measured quantum
  systems

abstract:
  While the linearity of the Schr\"odinger equation and the superposition
principle are fundamental to quantum mechanics, so are the backaction of
measurements and the resulting nonlinearity. It is remarkable, therefore, that
the wave-equation of systems in continuous interaction with some reservoir,
which may be a measuring device, can be cast into a linear form, even after the
degrees of freedom of the reservoir have been eliminated. The superposition
principle still holds for the stochastic wave-function of the observed system,
and exact analytical solutions are possible in sufficiently simple cases. We
discuss here the coupling to Markovian reservoirs appropriate for homodyne,
heterodyne, and photon counting measurements. For these we present a derivation
of the linear stochastic wave-equation from first principles and analyze its
physical content.


title: The Sources of the a and B Degenerate Static Vacuum Fields

abstract:
  We attempt to a physical interpretation of some known static vacuum solutions
of Einstein's equations, namely, the A and B metrics of Ehlers and Kundt. All
of them have axial symmetry, so they can be transformed to the Weyl form. In
Weyl coordinates $\ln\sqrt{-g_{44}}$ obeys a Laplace equation, and from this a
source, called The Newtonian image source can be identified. We use the image
sources to interpret the metrics. The procedure is sucessful in some cases. In
others it fails because the Weyl transform does not have reasonable properties
at infinity.


title: Velocity Dominance Near a Crushing Singularity

abstract:
  The asymptotic behavior of geometry near the boundary of maximal Cauchy
development is studied using a perturbative method, which at the zeroth order
reduces Einstein's equations to an exactly solvable set of
equations---Einstein's equations with all ``space" derivatives dropped. The
perturbative equations are solved to an {\em arbitrarily-high order} for the
cosmological spacetimes admitting constant-mean-curvature foliation that ends
in a crushing singularity, i..e., whose mean curvature blows up somewhere.
Using a ``new" set of dynamical variables (generalized Kasner variables)
restrictions on the initial data are found that make the zeroth-order term in
the expansion asymptotically dominant when approaching the crushing
singularity. The results obtained are in agreement with the first order results
of Belinskii, Lifshitz and Khalatnikov on general velocity-dominated
cosmological singularities, and, in addition, provide clearer geometrical
formulation.


title:
From Vacuum Fluctuations to Radiation: Accelerated Detectors and Black
  Holes

abstract:
  The vacuum fluctuations that induce the transitions and the thermalisation of
a uniformly accelerated two level atom are studied in detail. Their energy
content is revealed through the weak measurement formalism of Aharonov et al.
It is shown that each time the detector makes a transition it radiates a
Minkowski photon. The same analysis is then applied to the conversion of vacuum
fluctuations into real quanta in the context of black hole radiation. Initially
these fluctuations are located around the light like geodesic that shall
generate the horizon and carry zero total energy. However upon exiting from the
star they break up into two pieces one of which gradually acquires positive
energy and becomes a Hawking quantum, the other, its ''partner", ends up in the
singularity. As time goes by the vacuum fluctuations generating Hawking quanta
have exponentially large energy densities. This implies that back reaction
effects are large.


title: Aspects of the Thermo-Dynamics of a Black Hole with a Topological Defect

abstract:
  Aspects of the thermo-dynamics of a black hole which is either pierced by a
cosmic gauge string or contains a global monopole are investigated. We also
make some comments on the physical significance of the fact that the
gravitational mass carried by a global monopole is negative. We note in
particular that the negative monopole mass implies a gravitational
super-radiance effect.


title: The constraint algebra of quantum gravity in the loop representation

abstract:
  We study the algebra of constraints of quantum gravity in the loop
representation based on Ashtekar's new variables. We show by direct computation
that the quantum commutator algebra reproduces the classical Poisson bracket
one, in the limit in which regulators are removed. The calculation illustrates
the use of several computational techniques for the loop representation.


title: Generalized coordinates on the phase space of Yang-Mills theory

abstract:
  We study the suitability of complex Wilson loop variables as (generalized)
coordinates on the physical phase space of $SU(2)$-Yang-Mills theory. To this
end, we construct a natural one-to-one map from the physical phase space of the
Yang-Mills theory with compact gauge group $G$ to a subspace of the physical
configuration space of the complex $G^\C$-Yang-Mills theory. Together with a
recent result by Ashtekar and Lewandowski this implies that the complex Wilson
loop variables form a complete set of generalized coordinates on the physical
phase space of $SU(2)$-Yang-Mills theory. They also form a generalized
canonical loop algebra. Implications for both general relativity and gauge
theory are discussed.


title: The basis of nonlocal curvature invariants in quantum gravity theory

abstract:
  A complete basis of nonlocal invariants in quantum gravity theory is built to
third order in spacetime curvature and matter-field strengths. The nonlocal
identities are obtained which reduce this basis for manifolds with
dimensionality $2\omega<6$. The present results are used in heat-kernel theory,
theory of gauge fields and serve as a basis for the model-independent approach
to quantum gravity and, in particular, for the study of nonlocal vacuum effects
in the gravitational collapse problem.


title: Quantum scale of inflation and particle physics of the early universe

abstract:
  The quantum gravitational scale of inflation is calculated by finding a sharp
probability peak in the distribution function of chaotic inflationary
cosmologies driven by a scalar field with large negative constant $\xi$ of
nonminimal interaction. In the case of the no-boundary state of the universe
this peak corresponds to the eternal inflation, while for the tunnelling
quantum state it generates a standard inflationary scenario. The sub-Planckian
parameters of this peak (the mean value of the corresponding Hubble constant
${\mbox{\boldmath $H$}}\simeq 10^{-5}m_P$, its quantum width
$\Delta{\mbox{\boldmath $H$}}/{\mbox{\boldmath $H$}}\simeq 10^{-5}$ and the
number of inflationary e-foldings ${\mbox{\boldmath $N$}}\simeq 60$) are found
to be in good correspondence with the observational status of inflation theory,
provided the coupling constants of the theory are constrained by a condition
which is likely to be enforced by the (quasi) supersymmetric nature of the
sub-Planckian particle physics model.


title:
Asymptotic behaviours of the heat kernel in covariant perturbation
  theory

abstract:
  The trace of the heat kernel is expanded in a basis of nonlocal curvature
invariants of $N$th order. The coefficients of this expansion (the nonlocal
form factors) are calculated to third order in the curvature inclusive. The
early-time and late-time asymptotic behaviours of the trace of the heat kernel
are presented with this accuracy. The late-time behaviour gives the criterion
of analyticity of the effective action in quantum field theory. The latter
point is exemplified by deriving the effective action in two dimensions.


title: Comments on Omn\`es' Model for Uniqueness of Data

abstract:
  Standard methods of the theory of permanent state reduction are shown to
offer an alternative realization of Omn\`es' project. Our proposal, as simple
as Omn\`es' one, possesses closed master equation for the ensemble density
operator, assuring causality.


title: Energy-Momentum Restrictions on the Creation of Gott Time Machines

abstract:
  The discovery by Gott of a remarkably simple spacetime with closed timelike
curves (CTC's) provides a tool for investigating how the creation of time
machines is prevented in classical general relativity. The Gott spacetime
contains two infinitely long, parallel cosmic strings, which can equivalently
be viewed as point masses in (2+1)-dimensional gravity. We examine the
possibility of building such a time machine in an open universe. Specifically,
we consider initial data specified on an edgeless, noncompact, spacelike
hypersurface, for which the total momentum is timelike (i.e., not the momentum
of a Gott spacetime). In contrast to the case of a closed universe (in which
Gott pairs, although not CTC's, can be produced from the decay of stationary
particles), we find that there is never enough energy for a Gott-like time
machine to evolve from the specified data; it is impossible to accelerate two
particles to sufficiently high velocity. Thus, the no-CTC theorems of Tipler
and Hawking are enforced in an open (2+1)-dimensional universe by a mechanism
different from that which operates in a closed universe. In proving our result,
we develop a simple method to understand the inequalities that restrict the
result of combining momenta in (2+1)-dimensional gravity.


title: Kinks and Time Machines

abstract:
  We show that it is not possible to smooth out the metric on the
Deutsch-Politzer time machine to obtain an everywhere non-singular
asymptotically flat Lorentzian metric.


title:
Real Formulations of Complex Gravity and a Complex Formulation of Real
  Gravity

abstract:
  Two gauge and diffeomorphism invariant theories on the Yang-Mills phase space
are studied. They are based on the Lie-algebras $so(1,3)$ and
$\widetilde{so(3)}$ -- the loop-algebra of $so(3)$. Although the theories are
manifestly real, they can both be reformulated to show that they describe
complex gravity and an infinite number of copies of complex gravity,
respectively. The connection to real gravity is given. For these theories, the
reality conditions in the conventional Ashtekar formulation are represented by
normal constraint-like terms.


title: Limiting Behavior of Solutions to the Einstein-Yang/Mills Equations

abstract:
  The ADM masses of particle-like solutions to the Einstein-Yang/Mills
Equations tend to 2 as the number of nodes of the solutions increases. The same
result is true for black hole solutions with event horizon less than 1. For
event horizon $\rho > 1$ the ADM masses converge to $\rho + \rho^{-1} .$ These
statements extend and correct ``An Investigation at the Limiting Behavior of
Particle-Like Solutions to the Einstein-Yang/Mills Equations and a New black
Hole Solutions'', by J. A. Smoller and A. G. Wasserman, in Comm. Math. Phys.,
161, 365-389, (1994).


title: Singularity-Free Two Dimensional Cosmologies

abstract:
  We present a class of theories of two dimensional gravity which admits
homogeneous and isotropic solutions that are nonsingular and asymptotically
approach a FRW matter dominated universe at late times. These models are
generalizations of two dimensional dilaton gravity and both vacuum solutions
and those including conformally coupled matter are investigated. In each case
our construction leads to an inflationary stage driven by the gravitational
sector. Our work comprises a simple example of the `Nonsingular Universe'
constructions of ref. [1].


title:
A Closed-Form Expression for the Gravitational Radiation Rate from
  Cosmic Strings

abstract:
  We present a new formula for the rate at which cosmic strings lose energy
into gravitational radiation, valid for all piecewise-linear cosmic string
loops. At any time, such a loop is composed of $N$ straight segments, each of
which has constant velocity. Any cosmic string loop can be arbitrarily-well
approximated by a piecewise-linear loop with $N$ sufficiently large. The
formula is a sum of $O(N^4)$ polynomial and log terms, and is exact when the
effects of gravitational back-reaction are neglected. For a given loop, the
large number of terms makes evaluation ``by hand" impractical, but a computer
or symbolic manipulator yields accurate results. The formula is more accurate
and convenient than previous methods for finding the gravitational radiation
rate, which require numerical evaluation of a four-dimensional integral for
each term in an infinite sum. It also avoids the need to estimate the
contribution from the tail of the infinite sum. The formula has been tested
against all previously published radiation rates for different loop
configurations. In the cases where discrepancies were found, they were due to
errors in the published work. We have isolated and corrected both the analytic
and numerical errors in these cases. To assist future work in this area, a
small catalog of results for some simple loop shapes is provided.


title: Shrinking and the True Power Spectrum at Decoupling

abstract:
  In this paper we examine the change in the estimated spatial power spectra at
decoupling due to the effects of our clumpy universe which modify observational
distances. We find that scales at decoupling can be significantly underestmated
in our approximation of neglecting the shear of the ray bundle. We compare our
results with other work on lensing and speculate on the implications for
structure formation. In particular we examine a proposal to use the position of
the first Doppler peak to determine $\Omega$, and find that shrinking will
modify the esimated curvature, so that it must be included to obtain an
accurate estimate of $\Omega$. Finally we consider future applications and
improvements of our results.


title:
Temperature, Energy, and Heat Capacity of Asymptotically Anti-De Sitter
  Black Holes

abstract:
  We investigate the thermodynamical properties of black holes in (3+1) and
(2+1) dimensional Einstein gravity with a negative cosmological constant. In
each case, the thermodynamic internal energy is computed for a finite spatial
region that contains the black hole. The temperature at the boundary of this
region is defined by differentiating the energy with respect to entropy, and is
equal to the product of the surface gravity (divided by~$2\pi$) and the Tolman
redshift factor for temperature in a stationary gravitational field. We also
compute the thermodynamic surface pressure and, in the case of the (2+1) black
hole, show that the chemical potential conjugate to angular momentum is equal
to the proper angular velocity of the black hole with respect to observers who
are at rest in the stationary time slices. In (3+1) dimensions, a calculation
of the heat capacity reveals the existence of a thermodynamically stable black
hole solution and a negative heat capacity instanton. This result holds in the
limit that the spatial boundary tends to infinity only if the comological
constant is negative; if the cosmological constant vanishes, the stable black
hole solution is lost. In (2+1) dimensions, a calculation of the heat capacity
reveals the existence of a thermodynamically stable black hole solution, but no
negative heat capacity instanton.


title: Conserved Quantities in Perturbed Inflationary Universes

abstract:
  Given that observations seem to favour a \index{density parameter}
$\Omega_0<1$, corresponding to an open universe, we consider gauge\hs invariant
perturbations of non\hs flat Robertson\hs Walker universes filled with a
general imperfect fluid which can also be taken to represent a scalar field.
Our aim is to set up the equations that govern the evolution of the density
perturbations $\Delta$ so that it can be determined through a {\it first order
differential equation} with a quantity $\kk$ which is conserved at any length
scale, even in non\hs flat universe models, acting as a source term. The
quantity $\kk$ generalizes other variables that are conserved in specific cases
(for example at large scales in a flat universe) and is useful to connect
different epochs in the evolution of density perturbations via a transfer
function. We show that the problem of finding a conserved $\kk$ can be reduced
to determining two auxiliary variables $X$ and $Y$, and illustrate the method
with two simple examples.


title:
Constraints on Inflationary Solutions in the Presence of Shear and Bulk
  Viscosity

abstract:
  Inflationary models and their claim to solve many of the outstanding problems
in cosmology have been the subject of a great deal of debate over the last few
years. A major sticking point has been the lack of both good observational and
theoretical arguments to single out one particular model out of the many that
solve these problems. Here we examine the degree of restrictiveness on the
dynamical relationship between the cosmological scale factor and the inflation
driving self-interaction potential of a minimally coupled scalar field, imposed
by the condition that the scalar field is required to be real during a
classical regime (the reality condition). We systema\-tically look at the
effects of this constraint on many of the inflationary models found in the
literature within the FLRW framework, and also look at what happens when
physically motivated perturbations such as shear and bulk viscosity are
introduced. We find that in many cases, either the models are totally excluded
or the reality condition gives rise to constraints on the scale factor and on
the various parameters of the model.


title: Exotic Smoothness and Physics

abstract:
  The essential role played by differentiable structures in physics is reviewed
in light of recent mathematical discoveries that topologically trivial
space-time models, especially the simplest one, ${\bf R^4}$, possess a rich
multiplicity of such structures, no two of which are diffeomorphic to each
other and thus to the standard one. This means that physics has available to it
a new panoply of structures available for space-time models. These can be
thought of as source of new global, but not properly topological, features.
This paper reviews some background differential topology together with a
discussion of the role which a differentiable structure necessarily plays in
the statement of any physical theory, recalling that diffeomorphisms are at the
heart of the principle of general relativity. Some of the history of the
discovery of exotic, i.e., non-standard, differentiable structures is reviewed.
Some new results suggesting the spatial localization of such exotic structures
are described and speculations are made on the possible opportunities that such
structures present for the further development of physical theories.


title:
Classical and Quantum Solutions of Conformally Related Multidimensional
  Cosmological Models

abstract:
  Consider multidim. universes M= R x M_1 x ... x M_n with D = 1+ d_1 .. + d_n,
where M_i of dimension d_i are of have constant curvature and compact for i>1.
For Lagrangian models L(R,phi) on M which depend only on Ricci curvature R and
a scalar field phi, there exists an explicit description of conformal
equivalence, with the minimal coupling model and the conformal coupling model
as distinguished representatives of a conformal class. For the conformally
coupled model we study classical solutions and their relation to solutions in
the equivalent minimally coupled model. The domains of equivalence are
separated by certain critical values of the scalar field phi. Furthermore the
coupling constant xi of the coupling between phi and R is critical at both, the
minimal value xi=0 and the conformal value xi_c={D-2}/{4(D-1)}. In different
noncritical regions of $xi$ the solutions behave qualitatively different. For
vanishing potential of the minimally coupled scalar field we find a
multidimensional generalization of Kasner's solution. Its scale factor
singularity vanishes in the conformal coupling model. Static internal spaces in
the minimal model become dynamical in the conformal one. The nonsingular
conformal solution has a particular interesting region, where internal spaces
shrink while the external space expands. While the Lorentzian solution relates
to a creation of the universe at finite scale, it Euclidean counterpart is an
(instanton) wormhole. Solving the Wheeler de Witt equation we obtain the
quantum counterparts to the classical solutions. A real Euclidean quantum
wormhole is obtained in a special case.


title: Non-commutative black holes in $D$ dimensions

abstract:
  Recently introduced classical theory of gravity in non-commutative geometry
is studied. The most general (four parametric) family of $D$ dibensional static
spherically symmetric spacetimes is identified and its properties are studied
in detail. For wide class of the choices of parameters, the corresponding
spacetimes have the structure of asymptotically flat black holes with a smooth
event horizon hiding the curvature singularity. A specific attention is devoted
to the behavior of components of the metric in non-commutative direction, which
are interpreted as the black hole hair.


title: Gravity as a Higgs Field. I.the Geometric Equivalence Principle

abstract:
  {\it If gravity is a metric field by Einstein, it is a Higgs field.}
Gravitation theory meets spontaneous symmetry breaking in accordance with the
Equivalence Principle reformulated in the spirit of Klein-Chern geometries of
invariants. In gravitation theory, the structure group of the principal linear
frame bundle $LX$ over a world manifold $X^4$ is reducible to the connected
Lorentz group $SO(3,1)$. The physical underlying reason of this reduction is
Dirac fermion matter possessing only exact Lorentz symmetries. The associated
Higgs field is a tetrad gravitational field $h$ represented by a global section
of the quotient $\Si$ of $LX$ by $SO(3,1)$. The feature of gravity as a Higgs
field issues from the fact that, in the presence of different tetrad fields,
Dirac fermion fields are described by spinor bundles associated with different
reduced Lorentz subbundles of $LX$, and we have nonequivalent representations
of cotangent vectors to $X^4$ by Dirac's matrices. It follows that a fermion
field must be regarded only in a pair with a certain tetrad field. These pairs
fail to be represented by sections of any product bundle $S\times\Si$, but
sections of the composite spinor bundle $S\to\Si\to X^4$. They constitute the
so-called fermion-gravitation complex where values of tetrad gravitational
fields play the role of coordinate parameters, besides the familiar world
coordinates. In Part 1 of the article, geometry of the fermion-gravitation
complex is investigated. The goal is the total Dirac operator into which
components of a connection on $S\to\Si$ along tetrad coordinate directions make
contribution. The Part II will be devoted to dynamics of fermion-gravitation
complex. It is a constraint system to describe which we use the covariant
multisymplectic generalization of the Hamiltonian formalism when canonical
momenta correspond to derivatives of fields with respect to all world
coordinates, not only the time.


title: On the Limiting Solution of the Bartnik-McKinnon Family

abstract:
  We analyze the limiting solution of the Bartnik-McKinnon family and show that
its exterior is an extremal Reissner-Nordstr{\o}m black hole and not a new type
of non-abelian black hole as claimed in a recent article by Smoller and
Wasserman.


title:
The Chern-Simons Invariant as the Natural Time Variable for Classical
  and Quantum Cosmology

abstract:
  We propose that the Chern-Simons invariant of the Ashtekar-Sen connection is
the natural internal time coordinate for classical and quantum cosmology. The
reasons for this are a number of interesting properties of this functional,
which we describe here. 1)It is a function on the gauge and diffeomorphism
invariant configuration space, whose gradient is orthogonal to the two physical
degrees of freedom, in the metric defined by the Ashtekar formulation of
general relativity. 2)The imaginary part of the Chern-Simons form reduces in
the limit of small cosmological constant, $\Lambda$, and solutions close to
DeSitter spacetime, to the York extrinsic time coordinate. 3)Small matter-field
excitations of the Chern-Simons state satisfy, by virtue of the quantum
constraints, a functional Schroedinger equation in which the matter fields
evolve on a DeSitter background in the Chern-Simons time. We then n propose
this is the natural vacuum state of the theory for $\Lambda \neq 0$. 4)This
time coordinate is periodic on the configuration space of Euclideanized
spacetimes, due to the large gauge transformations, which means that physical
expectation values for all states in non-perturbative quantum gravity will
satisfy the $KMS$ condition, and may then be interpreted as thermal states.
5)Forms for the physical hamiltonians and inner product which support the
proposal are suggested, and a new action principle for general relativity, as a
geodesic principle on the connection superspace, is found.


title:
Behavior of Friedmann-Robertson-Walker Cosmological Models in
  Scalar-Tensor Gravity

abstract:
  We analyze solutions to Friedmann-Robertson-Walker cosmologies in Brans-Dicke
theory, where a scalar field is coupled to gravity. Matter is modelled by a
$\gamma$-law perfect fluid, including false-vacuum energy as a special case.
Through a change of variables, we reduce the field equations from fourth order
to second order, and they become equivalent to a two-dimensional dynamical
system. We then analyze the entire solution space of this dynamical system, and
find that many qualitative features of these cosmologies can be gleaned,
including standard non-inflationary or extended inflationary expansion, but
also including bifurcations of stable or unstable expansion or contraction,
noninflationary vacuum-energy dominated models, and several varieties of
``coasting," ``bouncing," ``hesitating," and ``vacillating" universes. It is
shown that inflationary dogma, which states that a universe with curvature and
dominated by inflationary matter will always approach a corresponding
flat-space solution at late times, does not hold in general for the
scalar-tensor theory, but rather that the occurence of inflation depends upon
the initial energy of the scalar field relative to the expansion rate. In the
case of flat space ($k=0$), the dynamical system formalism generates some
previously known exact power-law solutions.


title: Gravitational Force by Point Particle in Static Einstein Universe

abstract:
  The gravitaional force produced by a point particle, like the sun, in the
background of the static Einstein universe is studied. Both the approximate
solution in the weak field limit and exact solution are obtained. The main
properties of the solution are {\it i}) near the point particle, the metric
approaches the Schwarzschild one and the radius of its singularity becomes
larger than that of the Schwarzschild singularity, {\it ii}) far from the point
particle, the metric approaches the static Einstein closed universe. The
maximum length of the equator of the universe becomes smaller than that of the
static Einstein universe due to the existence of the point particle. These
properties show the strong correlation betweem the particle and the universe.


title: Mass Bounds for Multidimensional Charged Dilatonic Black Holes

abstract:
  The multidimensional charged dilatonic black hole solution with $n$ internal
Ricci-flat spaces is considered. The bound on the mass of the black hole is
obtained. In the strong dilatonic coupling limit the critical mass becomes
zero. The case $n = \infty$ is also considered.


title:
Classical and Quantum Behaviour of Multidimensional Integrable
  Cosmologies

abstract:
  Multidimensional cosmological models with $n~(n > 1)$ Einstein spaces are
discussed classically and with respect to canonical quantization. These models
are integrable in the case of Ricci flat internal spaces. For negative
curvature of the external space we find exact classical solutions modelling
dynamical as well as spontaneous compactification of the internal spaces.
Spontaneous compactification turns out to be an attractor solution. Solutions
of the quantum Wheeler-DeWitt equation are also obtained. Some of them describe
the tunneling process to be interpreted as the birth of the universe from
''nothing''.


title:
Multidimensional Classical and Quantum Wormholes in Models with
  Cosmological Constant

abstract:
  A multidimensional cosmological model with space-time consisting of $n (n \ge
2)$ Einstein spaces $M_{i}$ is investigated in the presence of a cosmological
constant $\Lambda$ and a homogeneous minimally coupled scalar field
$\varphi(t)$ as a matter source. Classical and quantum wormhole solutions are
obtained for $\Lambda < 0$ and all $M_{i}$ being Ricci-flat. Classical wormhole
solutions are also found for $\Lambda < 0$ and only one of the $M_{i}$ being
Ricci-flat for the case of spontaneous compactification of the internal
dimensions with fine tuning of parameters.


title: On Black Hole Stability in Multidimensional Gravity

abstract:
  Exact static, spherically symmetric solutions to the Einstein-Maxwell-scalar
equations, with a dilatonic-type scalar-vector coupling, in $D$-dimensional
gravity with a chain of $n$ Ricci-flat internal spaces are considered. Their
properties and special cases are discussed. A family of multidimensional
dilatonic black-hole solutions is singled out, depending on two integration
constants (related to black hole mass and charge) and three free parameters of
the theory (the coordinate sphere, internal space dimensions, and the coupling
constant). The behaviour of the solutions under small perturbations preserving
spherical symmetry, is studied. It is shown that the black-hole solutions
without a dilaton field are stable, while other solutions, possessing naked
singularities, are catastrophically unstable.


title: On Spontaneous Compactification in Multidimensional Cosmology

abstract:
  Mutidimensional cosmological models with $n\left( n\geq 2\right) $ Einstein
spaces $M_i\left( i=1,\ldots ,n\right) $ are investigated. The cosmological
constant and homogeneous minimally coupled scalar field as a matter sources are
considered. The scalar field has a potential of general form depending on the
scalar field as well as on the scale factors of $M_i$ . The general condition
of existence of the solutions with spontaneous compactification is obtained and
applied to physically important cases. Two particular kinds of solutions are
found. One of them has a wormhole-type continuation into the Euclidean region.
Another one represents the generalization of the de Sitter universe to the
multidimensional model under consideration.


title:
Reduced phase space quantization of Ashtekar's gravity on de Sitter
  background

abstract:
  We solve perturbative constraints and eliminate gauge freedom for Ashtekar's
gravity on de Sitter background. We show that the reduced phase space consists
of transverse, traceless, symmetric fluctuations of the triad and of
transverse, traceless, symmetric fluctuations of the connection. A part of
gauge freedom corresponding to the conformal Killing vectors of the
three-manifold can be fixed only by imposing conditions on Lagrange multiplier.
The reduced phase space is equivalent to that of ADM gravity on the same
background.


title: The Path Integral Formulation of Gravitational Thermodynamics

abstract:
  The first objective of this article is to show that the black hole partition
function can be placed on a firm logical foundation by enclosing the black hole
in a spatially finite "box" or boundary. The presence of the box has the effect
of stabilizing the black hole and yields a system with a positive heat
capacity. The second objective of this article is to explore the origin of
black hole entropy. This is accomplished through the construction of a path
integral expression for the density matrix for the gravitational field, and
through an analysis of the connection between the density matrix and the black
hole density of states. Our results suggest that black hole entropy can be
associated with an absence of certain "inner boundary information" for the
system. (Based on the talk presented by J.D. Brown at the conference "The Black
Hole 25 Years After", Santiago, Chile, January 1994.)


title: Massless Fileds in Scalar-Tensor Cosmologies

abstract:
  We derive exact Friedmann--Robertson--Walker cosmological solutions in
general scalar--tensor gravity theories, including Brans--Dicke gravity, for
stiff matter or radiation. These correspond to the long or short wavelength
modes respectively of massless scalar fields. If present, the long wavelength
modes of such fields would be expected to dominate the energy density of the
universe at early times and thus these models provide an insight into the
classical behaviour of these scalar--tensor cosmologies near an initial
singularity, or bounce. The particularly simple exact solutions also provide a
useful example of the possible evolution of the Brans--Dicke (or dilaton)
field, $\phi$, and the Brans--Dicke parameter, $\omega(\phi)$, at late times in
spatially curved as well as flat universes. We also discuss the corresponding
solutions in the conformally related Einstein metric.


title: The Vacuum of de~Sitter Space

abstract:
  To resolve infrared problems with the de~Sitter invariant vacuum, we argue
that the history of the de~Sitter phase is crucial. We illustrate how either
(1)~the diagonalization of the Hamiltonian for long-wavelength modes or (2)~an
explicit modification of the metric in the distant past leads to natural
infrared cutoffs. The former case resembles a bosonic superconductor in which
graviton-pairing occurs between non-adiabatic modes. While the dynamical
equations respect de~Sitter symmetry, the vacuum is not de~Sitter invariant
because of the introduction of an initial condition at a finite time. The
implications for the one-loop stress tensor and the production of particles are
also discussed.


title: Wormholes as Basis for the Hilbert Space in Lorentzian Gravity

abstract:
  We carry out to completion the quantization of a Friedmann-Robertson-Walker
model provided with a conformal scalar field, and of a Kantowski-Sachs
spacetime minimally coupled to a massless scalar field. We prove that the
Hilbert space determined by the reality conditions that correspond to
Lorentzian gravity admits a basis of wormhole wave functions. This result
implies that the vector space spanned by the quantum wormholes can be equipped
with an unique inner product by demanding an adequate set of Lorentzian reality
conditions, and that the Hilbert space of wormholes obtained in this way can be
identified with the whole Hilbert space of physical states for Lorentzian
gravity. In particular, all the normalizable quantum states can then be
interpreted as superpositions of wormholes. For each of the models considered
here, we finally show that the physical Hilbert space is separable by
constructing a discrete orthonormal basis of wormhole solutions.


title:
Multidimensional Integrable Cosmological Models with Dynamical and
  Spontaneous Compactification

abstract:
  Multidimensional cosmological models with $n (n > 1)$ spaces of constant
curvature are discussed classically and with respect to canonical quantization.
These models are integrable in the case of Ricci flat internal spaces. For
positive curvature in the external space we find exact solutions modelling
dynamical as well as spontaneous compactification of internal spaces.


title:
Quantum temporal logic and decoherence functionals in the histories
  approach to generalised quantum theory

abstract:
  We analyse and develop the recent suggestion that a temporal form of quantum
logic provides the natural mathematical framework within which to discuss the
proposal by Gell-Mann and Hartle for a generalised form of quantum theory based
on the ideas of histories and decoherence functionals. Particular stress is
placed on properties of the space of decoherence functionals, including one way
in which certain global and topological properties of a classical system are
reflected in a quantum history theory.


title:
Linearized Constraints in the Connection Representation: Hamilton-Jacobi
  Solution

abstract:
  Newman and Rovelli have used singular Hamilton-Jacobi transformations to
reduce the phase space of general relativity in terms of the Ashtekar
variables. Their solution of the gauge constraint cannot be inverted and indeed
has no Minkowski space limit. Nonetheless, we exhibit an explicit
Hamilton-Jacobi solution of all the linearized constraints. The result does not
encourage an iterative solution, but it does indicate the origin of the
singularity of the Newman-Rovelli result.


title: New Loop Representations for 2+1 Gravity

abstract:
  Since the gauge group underlying 2+1-dimensional general relativity is
non-compact, certain difficulties arise in the passage from the connection to
the loop representations. It is shown that these problems can be handled by
appropriately choosing the measure that features in the definition of the loop
transform. Thus, ``old-fashioned'' loop representations - based on ordinary
loops - do exist. In the case when the spatial topology is that of a two-torus,
these can be constructed explicitly; {\it all} quantum states can be
represented as functions of (homotopy classes of) loops and the scalar product
and the action of the basic observables can be given directly in terms of
loops.


title: The Ernst Equation on a Riemann Surface

abstract:
  The Ernst equation is formulated on an arbitrary Riemann surface.
Analytically, the problem reduces to finding solutions of the ordinary Ernst
equation which are periodic along the symmetry axis. The family of (punctured)
Riemann surfaces admitting a non-trivial Ernst field constitutes a ``partially
discretized'' subspace of the usual moduli space. The method allows us to
construct new exact solutions of Einstein's equations in vacuo with non-trivial
topology, such that different ``universes'', each of which may have several
black holes on its symmetry axis, are connected through necks bounded by cosmic
strings. We show how the extra topological degrees of freedom may lead to an
extension of the Geroch group and discuss possible applications to string
theory.


title: Quasilocal Energy for a Kerr black hole

abstract:
  The quasilocal energy associated with a constant stationary time slice of the
  Kerr spacetime is presented. The calculations are based on a recent proposal
\cite{by} in which quasilocal energy is derived from the Hamiltonian of
spatially bounded gravitational systems. Three different classes of boundary
surfaces for the Kerr slice are considered (constant radius surfaces, round
spheres, and the ergosurface). Their embeddings in both the Kerr slice and flat
three-dimensional space (required as a normalization of the energy) are
analyzed. The energy contained within each surface is explicitly calculated in
the slow rotation regime and its properties discussed in detail. The energy is
a positive, monotonically decreasing function of the boundary surface radius.
It approaches the Arnowitt-Deser-Misner (ADM) mass at spatial infinity and
reduces to (twice) the irreducible mass at the horizon of the Kerr black hole.
The expressions possess the correct static limit and include negative
contributions due to gravitational binding. The energy at the ergosurface is
compared with the energies at other surfaces. Finally, the difficulties
involved in an estimation of the energy in the fast rotation regime are
discussed.


title:
On Spacetimes Admitting Shear-free, Irrotational, Geodesic Timelike
  Congruences

abstract:
  A comprehensive analysis of general relativistic spacetimes which admit a
shear-free, irrotational and geodesic timelike congruence is presented. The
equations governing the models for a general energy-momentum tensor are written
down. Coordinates in which the metric of such spacetimes takes on a simplified
form are established. The general subcases of `zero anisotropic stress', `zero
heat flux vector' and `two component fluids' are investigated. In particular,
perfect fluid Friedmann-Robertson-Walker models and spatially homogeneous
models are discussed. Models with a variety of physically relevant
energy-momentum tensors are considered. Anisotropic fluid models and viscous
fluid models with heat conduction are examined. Also, models with a perfect
fluid plus a magnetic field or with pure radiation, and models with two
non-collinear perfect fluids (satisfying a variety of physical conditions) are
investigated. In particular, models with a (single) perfect fluid which is
tilting with respect to the shear-free, vorticity-free and acceleration-free
timelike congruence are discussed.


title: Shear-free, Irrotational, Geodesic, Anisotropic Fluid Cosmologies

abstract:
  General relativistic anisotropic fluid models whose fluid flow lines form a
shear-free, irrotational, geodesic timelike congruence are examined. These
models are of Petrov type D, and are assumed to have zero heat flux and an
anisotropic stress tensor that possesses two distinct non-zero eigenvalues.
Some general results concerning the form of the metric and the stress-tensor
for these models are established. Furthermore, if the energy density and the
isotropic pressure, as measured by a comoving observer, satisfy an equation of
state of the form $p = p(\mu)$, with $\frac{dp}{d\mu} \neq -\frac{1}{3}$, then
these spacetimes admit a foliation by spacelike hypersurfaces of constant Ricci
scalar. In addition, models for which both the energy density and the
anisotropic pressures only depend on time are investigated; both spatially
homogeneous and spatially inhomogeneous models are found. A classification of
these models is undertaken. Also, a particular class of anisotropic fluid
models which are simple generalizations of the homogeneous isotropic
cosmological models is studied.


title:
On the Role of Initial Data in the Gravitational Collapse of
  Inhomogeneous Dust

abstract:
  We consider here the gravitational collapse of a spherically symmetric
inhomogeneous dust cloud described by the Tolman-Bondi models. By studying a
general class of these models, we find that the end state of the collapse is
either a black hole or a naked singularity, depending on the parameters of the
initial density distribution, which are $\rho_{c}$, the initial central density
of the massive body, and $R_0$, the initial boundary. The collapse ends in a
black hole if the dimensionless quantity $\beta$ constructed out of this
initial data is greater than 0.0113, and it ends in a naked singularity if
$\beta$ is less than this number. A simple interpretation of this result can be
given in terms of the strength of the gravitational potential at the starting
epoch of the collapse.


title:
Analytic Results for the Gravitational Radiation from a Class of Cosmic
  String Loops

abstract:
  Cosmic string loops are defined by a pair of periodic functions ${\bf a}$ and
${\bf b}$, which trace out unit-length closed curves in three-dimensional
space. We consider a particular class of loops, for which ${\bf a}$ lies along
a line and ${\bf b}$ lies in the plane orthogonal to that line. For this class
of cosmic string loops one may give a simple analytic expression for the power
$\gamma$ radiated in gravitational waves. We evaluate $\gamma$ exactly in
closed form for several special cases: (1) ${\bf b}$ a circle traversed $M$
times; (2) ${\bf b}$ a regular polygon with $N$ sides and interior vertex angle
$\pi-2\pi M/N$; (3) ${\bf b}$ an isosceles triangle with semi-angle $\theta$.
We prove that case (1) with $M=1$ is the absolute minimum of $\gamma$ within
our special class of loops, and identify all the stationary points of $\gamma$
in this class.


title: General Cosmological Features of the Einstein-Yang-Mills-Dilaton System

abstract:
  We establish the main features of homogeneous and isotropic dilaton, metric
and Yang-Mills field configurations in a cosmological framework. Special
attention is paid to the energy exchange between the dilaton and the Yang-Mills
field and, in particular, a new energy exchange term is identified.
Implications for the Polonyi problem in 4-dimensional string models and in
dynamical supersymmetry breaking scenarios are discussed.


title: Semiclassical Gravity and the Problem of Time

abstract:
  I give a brief review of the recovery of semiclassical time from quantum
gravity and discuss possible extrapolations of this concept to the full theory.


title: Wheeler-Dewitt Metric and the Attractivity of Gravity

abstract:
  We investigate the class of ultralocal metrics on the configuration space of
canonical gravity. It is described by a parameter $\alpha$, where $\alpha=0.5$
corresponds to general relativity.
  For $\alpha$ less than a critical value the signature is positive definite,
while for all other values it is indefinite. We show that in the positive
definite case gravity becomes repulsive. From the primordial helium abundance
we find that $\alpha$ must lie between $0.4$ and $0.55$.


title: Eternal Black Holes and Quasilocal Energy

abstract:
  We present the gravitational action and Hamiltonian for a spatially bounded
region of an eternal black hole. The Hamiltonian is of the general form
$H=H_{+} - H_{-}$, where $H_{+}$ and $H_{-}$ are respectively the Hamiltonians
for the regions $M_+$ and $M_-$ located in the left and right wedges of the
spacetime. We construct explicitly the quasilocal energy for the system and
discuss its dependence on the time direction induced at the boundaries of the
manifold. This paper extends the analysis of Ref.~[1] to spacetimes possesing a
bifurcation surface and two timelike boundaries. The construction suggests that
an interpretation of black hole thermodynamics based on thermofield dynamics
ideas can be generalized beyond perturbations to the gravitational field itself
of a bounded spacetime region (based on the talk presented by E.A. Martinez at
the Lake Louise Winter School on Particle Physics and Cosmology, February
20-26, 1994.)


title: Singularity Free Quasi-Classical Schwarzschild Space-Times

abstract:
  Using canonical (Schrodinger) quantization of spherically symetric
gravitational dust systems, we find the quasi-classical (coherent) state,
|\alpha^{(s)}>, that corresponds to the classical Schwarzschild solution. We
calculate the ``quasi-classical Schwarzschild mertic", which is the expectation
value of the quantized metric in thhis quasi-classical state. Depending on the
quantization scheme that we use, we study three different quasi- classical
geometries, all of which turn out to be singularity free. Their maximal
extensions are complete manifolds with no singularities, describing a tower of
asymptotically flat universes connected through Planck size wormholes.


title: Time in (2+1)-Dimensional Quantum Gravity

abstract:
  General relativity in three spacetime dimensions is used to explore three
approaches to the ``problem of time'' in quantum gravity: the internal
Schr\"odinger approach with mean extrinsic curvature as a time variable, the
Wheeler-DeWitt equation, and covariant canonical quantization with ``evolving
constants of motion.'' (To appear in {\em Proc.\ of the Lanczos Centenary
Conference}, Raleigh, NC, December 1993.)


title: Conformal anomalies on Einstein spaces with Boundary

abstract:
  The anomalous rescaling for antisymmetric tensor fields, including gauge
bosons, and Dirac fermions on Einstein spaces with boundary has been prone to
errors and these are corrected here. The explicit calculations lead to some
interesting identities that indicate a deeper underlying structure.


title: Black hole formation from colliding bubbles

abstract:
  Some indication of conditions that are necessary for the formation of black
holes from the collision of bubbles during a supercooled phase transition in
the the early universe are explored. Two colliding bubbles can never form a
black hole. Three colliding bubbles can refocus the energy in their walls to
the extent that it becomes infinite.


title:
Standard and Generalized Newtonian Gravities as ``Gauge'' Theories of
  the Extended Galilei Group - I: The Standard Theory

abstract:
  Newton's standard theory of gravitation is reformulated as a {\it gauge}
theory of the {\it extended} Galilei Group. The Action principle is obtained by
matching the {\it gauge} technique and a suitable limiting procedure from the
ADM-De Witt action of general relativity coupled to a relativistic mass-point.


title:
Standard and Generalized Newtonian Gravities as ``Gauge'' Theories of
  the Extended Galilei Group - II: Dynamical Three-Space Theories

abstract:
  In a preceding paper we developed a reformulation of Newtonian gravitation as
a {\it gauge} theory of the extended Galilei group. In the present one we
derive two true generalizations of Newton's theory (a {\it ten-fields} and an
{\it eleven-fields} theory), in terms of an explicit Lagrangian realization of
the {\it absolute time} dynamics of a Riemannian three-space. They turn out to
be {\it gauge invariant} theories of the extended Galilei group in the same
sense in which general relativity is said to be a {\it gauge} theory of the
Poincar\'e group. The {\it ten-fields} theory provides a dynamical realization
of some of the so-called ``Newtonian space-time structures'' which have been
geometrically classified by K\"{u}nzle and Kucha\v{r}. The {\it eleven-fields}
theory involves a {\it dilaton-like} scalar potential in addition to Newton's
potential and, like general relativity, has a three-metric with {\it two}
dynamical degrees of freedom. It is interesting to find that, within the linear
approximation, such degrees of freedom show {\it graviton-like} features: they
satisfy a wave equation and propagate with a velocity related to the scalar
Newtonian potential.


title:
The Emergence of an Effective two - dimensional Quantum Description from
  the study of Critical Phenomena in Black Holes

abstract:
  We study the occurrence of critical phenomena in four - dimensional, rotating
and charged black holes, derive the critical exponents and show that they
fulfill the scaling laws. Correlation functions critical exponents and
Renormalization Group considerations assign an effective (spatial) dimension,
$d=2$, to the system. The two - dimensional Gaussian approximation to critical
systems is shown to reproduce all the black hole's critical exponents. Higher
order corrections (which are always relevant) are discussed. Identifying the
two - dimensional surface with the event horizon and noting that generalization
of scaling leads to conformal invariance and then to string theory, we arrive
to 't Hooft's string interpretation of black holes. From this, a model for
dealing with a coarse grained black hole quantization is proposed. We also give
simple arguments that lead to a rough quantization of the black hole mass in
units of the Planck mass, i. e. $M\simeq{1\over\sqrt{2}}M_{pl} \sqrt{l}$ with a
$l$ positive integer and then, from this result, to the proportionality between
quantum entropy and area.


title:
On the Occurrence of Naked Singularity in Spherically Symmetric
  Gravitational Collapse

abstract:
  Generalizing earlier results of Joshi and Dwivedi (Commun. Math. Phys. 146,
333 (1992); Lett. Math. Phys. 27, 235 (1993)), we analyze here the spherically
symmetric gravitational collapse of a matter cloud with a general form of
matter for the formation of a naked singularity. It is shown that this is
related basically to the choice of initial data to the Einstein field
equations, and would therefore occur in generic situations from regular initial
data within the general context considered here, subject to the matter
satisfying the weak energy condition. The condition on initial data which leads
to the formation of black hole is also characterized.


title:
Do Inertial Electric Charges Radiate with Respect to Uniformly
  Accelerated Observers?

abstract:
  We revisit the long standing problem of analyzing an inertial electric charge
from the point of view of uniformly accelerated observers in the context of
semi-classical gravity. We choose a suitable set of accelerated observers with
respect to which there is no photon emission coming from the inertial charge.
We discuss this result against previous claims [F. Rohrlich, Ann. Phys. (N.Y.)
vol: 22, 169 (1963)]. (This Essay was awarded a Honorable Mention for 1994 by
the Gravity Research Foundation.)


title:
Collisions of boosted black holes: perturbation theory prediction of
  gravitational radiation

abstract:
  We consider general relativistic Cauchy data representing two nonspinning,
equal-mass black holes boosted toward each other. When the black holes are
close enough to each other and their momentum is sufficiently high, an
encompassing apparent horizon is present so the system can be viewed as a
single, perturbed black hole. We employ gauge-invariant perturbation theory,
and integrate the Zerilli equation to analyze these time-asymmetric data sets
and compute gravitational wave forms and emitted energies. When coupled with a
simple Newtonian analysis of the infall trajectory, we find striking agreement
between the perturbation calculation of emitted energies and the results of
fully general relativistic numerical simulations of time-symmetric initial
data.


title: Compact Homogeneous Universes

abstract:
  A thorough classification of the topologies of compact homogeneous universes
is given except for the hyperbolic spaces, and their global degrees of freedom
are completely worked out. To obtain compact universes, spatial points are
identified by discrete subgroups of the isometry group of the generalized
Thurston geometries, which are related to the Bianchi and the
Kantowski-Sachs-Nariai universes. Corresponding to this procedure their total
degrees of freedom are shown to be categorised into those of the universal
covering space and the Teichm\"uller parameters. The former are given by
constructing homogeneous metrics on simply connected manifold. The
Teichm\"uller spaces are also given by explicitly constructing expressions for
the discrete subgroups of the isometry group.


title: The Ultrarelativistic Kerr-Geometry and its Energy-Momentum Tensor

abstract:
  The ultrarelativistic limit of the Schwarzschild and the Kerr-geometry
together with their respective energy-momentum tensors is derived. The approach
is based on tensor-distributions making use of the underlying Kerr-Schild
structure, which remains stable under the ultrarelativistic boost.


title: Is minimal coupling procedure compatible with minimal action principle?

abstract:
  When space-time is assumed to be non-Riemannian the minimal coupling
procedure (MCP) is not compatible, in general, with minimal action principle
(MAP). This means that the equations gotten by applying MCP to the
Euler-Lagrange equations of a Lagrangian $\cal L$ do not coincide with the
Euler-Lagrange equations of the Lagrangian obtained by applying MCP to $\cal
L$. Such compatibility can be restored if the space-time admits a
connection-compatible volume element. We show how these concepts can alter
qualitatively the predictions of the Einstein-Cartan theory of gravity.


title: Confinement by Black Holes

abstract:
  The question of whether an observer can escape from a black hole is
addressed, using a recent general definition of a black hole in the form of a
future outer trapping horizon. An observer on a future outer trapping horizon
must enter the neighbouring trapped region. It is possible for the observer to
subsequently escape from the trapped region. However, if the horizon separates
the space-time into two disjoint components, inside and outside the horizon,
then an observer inside a future outer trapping horizon cannot get outside,
assuming the null energy condition. A similar confinement property holds for
trapped, locally area-preserving cylinders, as suggested by Israel.


title: Phase Transition in Conformally Induced Gravity with Torsion

abstract:
  We have considered the quantum behavior of a conformally induced gravity in
the minimal Riemann-Cartan space. The regularized one-loop effective potential
considering the quantum fluctuations of the dilaton and the torsion fields in
the Coleman-Weinberg sector gives a sensible phase transition for an
inflationary phase in De Sitter space. For this effective potential, we have
analyzed the semi-classical equation of motion of the dilaton field in the
slow-rolling regime.


title:
General relativity as an effective field theory: The leading quantum
  corrections

abstract:
  I describe the treatment of gravity as a quantum effective field theory. This
allows a natural separation of the (known) low energy quantum effects from the
(unknown) high energy contributions. Within this framework, gravity is a well
behaved quantum field theory at ordinary energies. In studying the class of
quantum corrections at low energy, the dominant effects at large distance can
be isolated, as these are due to the propagation of the massless particles
(including gravitons) of the theory and are manifested in the
nonlocal/nonanalytic contributions to vertex functions and propagators. These
leading quantum corrections are parameter-free and represent necessary
consequences of quantum gravity. The methodology is illustrated by a
calculation of the leading quantum corrections to the gravitational interaction
of two heavy masses.


title: Unitarity Restoration in the Presence of Closed Timelike Curves

abstract:
  A proposal is made for a mathematically unambiguous treatment of evolution in
the presence of closed timelike curves. In constrast to other proposals for
handling the naively nonunitary evolution that is often present in such
situations, this proposal is causal, linear in the initial density matrix and
preserves probability. It provides a physically reasonable interpretation of
invertible nonunitary evolution by redefining the final Hilbert space so that
the evolution is unitary or equivalently by removing the nonunitary part of the
evolution operator using a polar decomposition.


title:
Density Perturbations of Quantum Mechanical Origin and Anisotropy of the
  Microwave Background

abstract:
  If the large-angular-scale anisotropy in the cosmic microwave background
radiation is caused by the long-wavelength cosmological perturbations of
quantum mechanical origin, they are, most likely, gravitational waves, rather
than density perturbations or rotational perturbations.


title: Disk collapse in general relativity

abstract:
  The radial collapse of a homogeneous disk of collisionless particles can be
solved analytically in Newtonian gravitation. To solve the problem in general
relativity, however, requires the full machinery of numerical relativity. The
collapse of a disk is the simplest problem that exhibits the two most
significant and challenging features of strong-field gravitation: black hole
formation and gravitational wave generation. We carry out dynamical
calculations of several different relativistic disk systems. We explore the
growth of ring instabilities in equilibrium disks, and how they are suppressed
by sufficient velocity dispersion. We calculate wave forms from oscillating
disks, and from disks that undergo gravitational collapse to black holes.
Studies of disk collapse to black holes should also be useful for developing
new techniques for numerical relativity, such as apparent horizon boundary
conditions for black hole spacetimes.