title: Smooth Manifolds of Kinematic Type

abstract:
  We give a short historical review of early Kaluza-Klein theories. We study
various causal structures on manifolds, especially those which cannot be
described by a metric tensor with signature (+---). The smooth structure
(atlas) on a manifold is found to be related with its causal structure.


title: On one connection between Lorentzian and Euclidean metrics

abstract:
  We investigate connections between pairs of (pseudo-)Riemannian metrics whose
sum is a (tensor) product of a covector field with itself. A bijective mapping
between the classes of Euclidean and Lorentzian metrics is constructed as a
special result. The existence of such maps on a differentiable manifold is
discussed. Similar relations for metrics of arbitrary signature on a manifold
are considered. We point the possibility that any physical theory based on real
Lorentzian metric(s) can be (re)formulated equivalently in terms of real
Euclidean metric(s).


title:
On metric-connection compatibility and the signature change of
  space-time

abstract:
  We discuss and investigate the problem of existence of metric-compatible
linear connections for a given space-time metric which is, generally, assumed
to be semi-pseudo-Riemannian. We prove that under sufficiently general
conditions such connections exist iff the rank and signature of the metric are
constant. On this base we analyze possible changes of the space-time signature.


title:
Dynamics of scalar fields in the background of rotating black holes II:
  A note on superradiance

abstract:
  We analyze the amplification due to so-called superradiance from the
scattering of pulses off rotating black holes as a numerical time evolution
problem. We consider the "worst possible case" of scalar field pulses for which
superradiance effects yield amplifications $< 1%$. We show that this small
effect can be isolated by numerically evolving quasi-monochromatic, modulated
pulses with a recently developed Teukolsky code. The results show that it is
possible to study superradiance in the time domain, but only if the initial
data is carefully tuned. This illustrates the intrinsic difficulties of
detecting superradiance in more general evolution scenarios.


title:
Acoustic phase lenses in superfluid helium as models of composite
  spacetimes in general relativity: Classical and quantum features

abstract:
  In the spirit of the well-known analogy between inviscid fluids and
pseudo-Riemannian manifolds we study spherical singular hypersurfaces in the
static superfluid. Such hypersurfaces turn out to be the interfaces dividing
the superfluid into the pairs of spherical domains, examples of which are
``superfluid A - superfluid B'' or ``impurity - superfluid'' phases. It is
shown that these shells form the acoustic lenses which are the sonic
counterparts of the usual optical ones. The exact equations of motion of the
lens interfaces are obtained. Also some quantum aspects of the theory are
considered. We calculate energy spectra for bound states of acoustic lenses in
dynamical equilibrium, taking into account the analogy to a material shell
model of a black hole (we consider the cases of spatial topology of a black
hole and a wormhole type).


title: Scaling of curvature in sub-critical gravitational collapse

abstract:
  We perform numerical simulations of the gravitational collapse of a
spherically symmetric scalar field. For those data that just barely do not form
black holes we find the maximum curvature at the position of the central
observer. We find a scaling relation between this maximum curvature and
distance from the critical solution. The scaling relation is analogous to that
found by Choptuik for black hole mass for those data that do collapse to form
black holes. We also find a periodic wiggle in the scaling exponent.


title: Comment on `Quantum Creation of an Open Universe', by Andrei Linde

abstract:
  We comment on Linde's claim that one should change the sign in the action for
a Euclidean instanton in quantum cosmology, resulting in the formula $P \sim
e^{+S}$ for the probability of various classical universes. There are serious
problems with doing so. If one reverses the sign of the action of both the
instanton and the fluctuations, the latter are unsupressed and the calculation
becomes meaningless. So for a sensible result one would have to reverse the
sign of the action for the background, while leaving the sign for the
perturbations fixed by the usual Wick rotation. The problem with this approach
is that there is no invariant way to split a given four geometry into
background plus perturbations. So the prescription would have to violate
general coordinate invariance. There are other indications that a sign change
is problematic. With the choice $P \sim e^{+S}$ the nucleation of primordial
black holes during inflation is unsuppressed, with a disastrous resulting
cosmology. We regard these as compelling arguments for adhering to the usual
sign given by the Wick rotation.


title:
The collision of boosted black holes: second order close limit
  calculations

abstract:
  We study the head-on collision of black holes starting from unsymmetrized,
Brill--Lindquist type data for black holes with non-vanishing initial linear
momentum. Evolution of the initial data is carried out with the ``close limit
approximation,'' in which small initial separation and momentum are assumed,
and second-order perturbation theory is used. We find agreement that is
remarkably good, and that in some ways improves with increasing momentum. This
work extends a previous study in which second order perturbation calculations
were used for momentarily stationary initial data, and another study in which
linearized perturbation theory was used for initially moving holes. In addition
to supplying answers about the collisions, the present work has revealed
several subtle points about the use of higher order perturbation theory, points
that did not arise in the previous studies. These points include issues of
normalization, and of comparison with numerical simulations, and will be
important to subsequent applications of approximation methods for collisions.


title: On the Asserted Clash between the Freud and the Bianchi Identities

abstract:
  Through a constructive method it is shown that the claim advanced in recent
times about a clash that should occur between the Freud and the Bianchi
identities in Einstein's general theory of relativity is based on a faulty
argument.


title: Spherical Self-Similar Solutions in Einstein-Multi-Scalar Gravity

abstract:
  We consider a general non-linear sigma model coupled to Einstein gravity and
show that in spherical symmetry and for a simple realization of
self-similarity, the spacetime can be completely determined. We also examine
some more specific matter models and discuss their relation to critical
collapse.


title: Ringing the eigenmodes from compact manifolds

abstract:
  We present a method for finding the eigenmodes of the Laplace operator acting
on any compact manifold. The procedure can be used to simulate cosmic microwave
background fluctuations in multi-connected cosmological models. Other
applications include studies of chaotic mixing and quantum chaos.


title: Free Field Realization of Cylindrically Symmetric Einstein Gravity

abstract:
  Cylindrically reduced Einstein gravity can be regarded as an $SL(2,R)/SO(2)$
sigma model coupled to 2D dilaton gravity. By using the corresponding 2D
diffeomorphism algebra of constraints and the asymptotic behaviour of the Ernst
equation we show that the theory can be mapped by a canonical transformation
into a set of free fields with a Minkowskian target space. We briefly discuss
the quantization in terms of these free-field variables, which is considerably
simpler than in the other approaches.


title:
Inextendible Schwarzschild black hole with a single exterior: How
  thermal is the Hawking radiation?

abstract:
  Several approaches to Hawking radiation on Schwarzschild spacetime rely in
some way or another on the fact that the Kruskal manifold has two causally
disconnected exterior regions. We investigate the Hawking(-Unruh) effect for a
real scalar field on the $\RPthree$ geon: an inextendible, globally hyperbolic,
space and time orientable eternal black hole spacetime that is locally
isometric to Kruskal but contains only one exterior region. The
Hartle-Hawking-like vacuum~$\hhvacgeon$, which can be characterized
alternatively by the positive frequency properties along the horizons or by the
complex analytic properties of the Feynman propagator, turns out to contain
exterior region Boulware modes in correlated pairs, and any operator in the
exterior that only couples to one member of each correlated Boulware pair has
thermal expectation values in the usual Hawking temperature. Generic operators
in the exterior do not have this special form; however, we use a Bogoliubov
transformation, a particle detector analysis, and a particle
emission-absorption analysis that invokes the analytic properties of the
Feynman propagator, to argue that $\hhvacgeon$ appears as a thermal bath with
the standard Hawking temperature to any exterior observer at asymptotically
early and late Schwarzschild times. A~(naive) saddle-point estimate for the
path-integral-approach partition function yields for the geon only half of the
Bekenstein-Hawking entropy of a Schwarzschild black hole with the same ADM
mass: possible implications of this result for the validity of path-integral
methods or for the statistical interpretation of black-hole entropy are
discussed. Analogous results hold for a Rindler observer in a flat spacetime
whose global properties mimic those of the geon.


title: Adaptive computation of gravitational waves from black hole interactions

abstract:
  We construct a class of linear partial differential equations describing
general perturbations of non-rotating black holes in 3D Cartesian coordinates.
In contrast to the usual approach, a single equation treats all radiative $\ell
-m$ modes simultaneously, allowing the study of wave perturbations of black
holes with arbitrary 3D structure, as would be present when studying the full
set of nonlinear Einstein equations describing a perturbed black hole. This
class of equations forms an excellent testbed to explore the computational
issues of simulating black spacetimes using a three dimensional adaptive mesh
refinement code. Using this code, we present results from the first fully
resolved 3D solution of the equations describing perturbed black holes. We
discuss both fixed and adaptive mesh refinement, refinement criteria, and the
computational savings provided by adaptive techniques in 3D for such model
problems of distorted black holes.


title: Time-Symmetric Approach to Gravity

abstract:
  Quantization of the time symmetric system of interacting strings requires
that gravity, just as electromagnetism in Wheeler-Feynman's time symmetric
electro- dynamics, also be an "adjunct field" instead of an independent entity.
The "adjunct field" emerges, at a scale large compared to that of the strings,
as a "statistic" that summarizes how the string positions in the underlying
space- time are "compactified" into those in Minkowski space. We are able to
show, WITHOUT adding a scalar curvature term to the string action, that the
"adjunct gravitational field" satisfies Einstein's equation with no
cosmological term.


title: Is It Possible to Disentangle an Entangled Quantum State?

abstract:
  Experimental tests of the suggestion that the generalization of Wheeler and
Feynman's time symmetric system is the dynamical basis underlying quantum
mechanics are considered. In a time-symmetric system, the instantaneous
correlations exhibited by two spatially separated particles in an entangled
state can be established through other particles, and can reveal advanced
interaction effects. In particular, the existence of advanced gravity waves may
be detectable through suitable arrangements at the Laser Interferometer
Gravitation- Wave Observatory.


title: Phase Transitions and the Mass-Radius Curves of Relativistic Stars

abstract:
  The properties of the mass-radius curves of relativistic stellar models
constructed from an equation of state with a first-order phase transition are
examined. It is shown that the slope of the mass-radius curve is continuous
unless the discontinuity in the density at the phase transition point has a
certain special value. The curve has a cusp if the discontinuity is larger than
this value. The curvature of the mass-radius curve becomes singular at the
point where the high density phase material first appears. This singularity
makes the mass-radius curve appear on large scales to have a discontinuity in
its slope at this point, even though the slope is in fact continuous on
microscopic scales. Analytical formulae describing the behavior of these curves
are found for the simple case of models with two-zone uniform-density equations
of state.


title: A self-similar inhomogeneous dust cosmology

abstract:
  A detailed study of an inhomogeneous dust cosmology contained in a
$\gamma$-law family of perfect-fluid metrics recently presented by Mars and
Senovilla is performed. The metric is shown to be the most general orthogonally
transitive, Abelian, $G_2$ on $S_2$ solution admitting an additional homothety
such that the self-similar group $H_3$ is of Bianchi type VI and the fluid flow
is tangent to its orbits. The analogous cases with Bianchi types I, II, III, V,
VIII and IX are shown to be impossible thus making this metric privileged from
a mathematical viewpoint. The differential equations determining the metric are
partially integrated and the line-element is given up to a first order
differential equation of Abel type of first kind and two quadratures. The
solutions are qualitatively analyzed by investigating the corresponding
autonomous dynamical system. The spacetime is regular everywhere except for the
big bang and the metric is complete both into the future and in all spatial
directions. The energy-density is positive, bounded from above at any instant
of time and with an spatial profile (in the direction of inhomogeneity) which
is oscillating with a rapidly decreasing amplitude. The generic asymptotic
behaviour at spatial infinity is a homogeneous plane wave. Well-known dynamical
system results indicate that this metric is very likely to describe the
asymptotic behaviour in time of a much more general class of inhomogeneous
$G_2$ dust cosmologies.


title: Higher Dimensional Chern-Simons Theories and Topological Black Holes

abstract:
  It has been recently pointed out that black holes of constant curvature with
a "chronological singularity" can be constructed in any spacetime dimension.
These black holes share many common properties with the 2+1 black hole. In this
contribution we give a brief summary of these new black holes and consider them
as solutions of a Chern-Simons gravity theory. We also provide a brief
introduction to some aspects of higher dimensional Chern-Simons theories.


title: Gravitating $\sigma$ Model Solitons

abstract:
  We study axially symmetric static solitons of O(3) nonlinear $\sigma$ model
coupled to (2+1)-dimensional anti-de Sitter gravity. The obtained solutions are
not self-dual under static metric. The usual regular topological lump solution
cannot form a black hole even though the scale of symmetry breaking is
increased. There exist nontopological solitons of half integral winding in a
given model, and the corresponding spacetimes involve charged Ba$\tilde
n$ados-Teitelboim-Zanelli black holes without non-Abelian scalar hair.


title:
Mass-Inflation in Dynamical Gravitational Collapse of a Charged
  Scalar-Field

abstract:
  We study the inner-structure of a charged black-hole which is formed from the
gravitational collapse of a self-gravitating charged scalar-field. Starting
with a regular spacetime, we follow the evolution through the formation of an
apparent horizon, a Cauchy horizon and a final central singularity. We find a
null, weak, mass-inflation singularity along the Cauchy horizon, which is a
precursor of a strong, spacelike singularity along the $r=0$ hypersurface.


title: Colliding black holes: analytic insights

abstract:
  We summarize the state of the art of the ``close approximation'' to black
hole collisions. We discuss results to first and second order in perturbation
theory for head-on collisions of momentarily-stationary and non-stationary
black holes and discuss the near-future prospect of non-axisymmetric
collisions.


title: Particle creation in the effective action method

abstract:
  The effect of particle creation by nonstationary external fields is
considered as a radiation effect in the expectation-value spacetime. The energy
of created massless particles is calculated as the vacuum contribution in the
energy-momentum tensor of the expectation value of the metric. The calculation
is carried out for an arbitrary quantum field coupled to all external fields
entering the general second-order equation. The result is obtained as a
functional of the external fields. The paper gives a systematic derivation of
this result on the basis of the nonlocal effective action. Although the
derivation is quite involved and touches on many aspects of the theory, the
result itself is remarkably simple. It brings the quantum problem of particle
creation to the level of complexity of the classical radiation problem. For
external fields like the electromagnetic or gravitational field there appears a
quantity, the radiation moment, that governs both the classical radiation of
waves and the quantum particle production. The vacuum radiation of an
electrically charged source is considered as an example. The research is aimed
at the problem of backreaction of the vacuum radiation.


title: Relativistic thermodynamics

abstract:
  A generally relativistic theory of thermodynamics is developed, based on four
main physical principles: heat is a local form of energy, therefore described
by a thermal energy tensor; conservation of mass, equivalent to conservation of
heat, or the local first law; entropy is a local current; and non-destruction
of entropy, or the local second law. A fluid is defined by the thermostatic
energy tensor being isotropic. The entropy current is related to the other
fields by certain equations, including a generalised Gibbs equation for the
thermostatic entropy, followed by linear and quadratic terms in the dissipative
(thermal minus thermostatic) energy tensor. Then the second law suggests
certain equations for the dissipative energy tensor, generalising the Israel-
Stewart dissipative relations, which describe heat conduction and viscosity
including relativistic effects and relaxation effects. In the thermostatic
case, the perfect-fluid model is recovered. In the linear approximation for
entropy, the Eckart theory is recovered. In the quadratic approximation for
entropy, the theory is similar to that of Israel & Stewart, but involving
neither state-space differentials, nor a non-equilibrium Gibbs equation, nor
non-material frames. Also, unlike conventional thermodynamics, the thermal
energy density is not assumed to be purely thermostatic, though this is derived
in the linear approximation. Otherwise, the theory reduces in the non-
relativistic limit to the extended thermodynamics of irreversible processes due
to Mueller. The dissipative energy density seems to be a new thermodynamical
field, but also exists in relativistic kinetic theory of gases.


title:
GR15 Workshop A3 --- Mathematical Studies of Field Equations --- A
  report

abstract:
  This is a report of the A3 workshop ("Mathematical Studies of Field
Equations"), which was held in Poone during the GR15 Conference in December
1997.


title: Einstein-Weyl structures and Bianchi metrics

abstract:
  We analyse in a systematic way the (non-)compact four dimensional
Einstein-Weyl spaces equipped with a Bianchi metric. We show that Einstein-Weyl
structures with a Class A Bianchi metric have a conformal scalar curvature of
constant sign on the manifold. Moreover, we prove that most of them are
conformally Einstein or conformally K\"ahler ; in the non-exact Einstein-Weyl
case with a Bianchi metric of the type $VII_0, VIII$ or $IX$, we show that the
distance may be taken in a diagonal form and we obtain its explicit
4-parameters expression. This extends our previous analysis, limited to the
diagonal, K\"ahler Bianchi $IX$ case.


title: Uniqueness of the Trautman--Bondi mass

abstract:
  It is shown that the only functionals, within a natural class, which are
monotonic in time for all solutions of the vacuum Einstein equations admitting
a smooth ``piece'' of conformal null infinity Scri, are those depending on the
metric only through a specific combination of the Bondi `mass aspect' and other
next--to--leading order terms in the metric. Under the extra condition of
passive BMS invariance, the unique such functional (up to a multiplicative
factor) is the Trautman--Bondi energy. It is also shown that this energy
remains well-defined for a wide class of `polyhomogeneous' metrics.


title: Summary of GR15 Session D1(1), Quantum General Relativity

abstract:
  This summary was prepared for the proceedings of the GR15 conference in Pune,
India in Dec. 1997.


title: Pleba\'nski-Demia\'nski-like solutions in metric-affine gravity

abstract:
  We consider a (non--Riemannian) metric--affine gravity theory, in particular
its nonmetricity--torsion sector ``isomorphic'' to the Einstein--Maxwell
theory. We map certain Einstein--Maxwell electrovacuum solutions to it, namely
the Pleba\'nski--Demia\'nski class of Petrov type D metrics.


title:
Interplay of gravitation and linear superposition of different mass
  eigenstates

abstract:
  The interplay of gravitation and the quantum-mechanical principle of linear
superposition induces a new set of neutrino oscillation phases. These ensure
that the flavor-oscillation clocks, inherent in the phenomenon of neutrino
oscillations, redshift precisely as required by Einstein's theory of
gravitation. The physical observability of these phases in the context of the
solar neutrino anomaly, type-II supernovae, and certain atomic systems is
briefly discussed.


title: A White Hole Model of the Big Bang

abstract:
  A model of the universe as a very large white hole provides a useful
alternative inhomogeneous theory to pit against the homogeneous standard FLRW
big bang models. The white hole would have to be sufficiently large that we can
fit comfortably inside the event horizon at the present time, so that the
inhomogeneities of space-time are not in contradiction with current
observational limits. A specific Lemaitre-Tolman model of a spherically
symmetric non-rotating white hole with a few adjustable parameters is
investigated. Comparison of calculated anisotropy in the Hubble flow and the
CMB against observational limits constrain the parameter space. A Copernican
principle would require that we are not too near the centre of the white hole.
As an additional constraint this predicts a value of Omega between 0.9999 and
1.


title:
Two Boosted Black Holes in Asymptotically de Sitter Space-Time -
  Relation between Mass and Apparent Horizon Formation -

abstract:
  We study the apparent horizon for two boosted black holes in the
asymptotically de Sitter space-time by solving the initial data on a space with
punctures. We show that the apparent horizon enclosing both black holes is not
formed if the conserved mass of the system (Abbott-Deser mass) is larger than a
critical mass. The black hole with too large AD mass therefore cannot be formed
in the asymptotically de Sitter space-time even though each black hole has any
inward momentum. We also discuss the dynamical meaning of AD mass by examining
the electric part of the Weyl tensor (the tidal force) for various initial
data.


title: Continuous coordinates for all impulsive pp - waves

abstract:
  We present a coordinate system for a general impulsive gravitational pp -
wave in vacuum in which the metric is explicitly continuous, synchronous and
"transverse". Also, it is more appropriate for investigation of particle
motions.


title: On the spin-rotation-gravity coupling

abstract:
  The inertial and gravitational properties of intrinsic spin are discussed and
some of the recent work in this area is briefly reviewed. The extension of
relativistic wave equations to accelerated systems and gravitational fields is
critically examined. A nonlocal theory of accelerated observers is presented
and its predictions are compared with observation.


title: Vassiliev invariants: a new framework for quantum gravity

abstract:
  We show that Vassiliev invariants of knots, appropriately generalized to the
spin network context, are loop differentiable in spite of being diffeomorphism
invariant. This opens the possibility of defining rigorously the constraints of
quantum gravity as geometrical operators acting on the space of Vassiliev
invariants of spin nets. We show how to explicitly realize the diffeomorphism
constraint on this space and present proposals for the construction of
Hamiltonian constraints.


title: No Scalar Hair Theorem for a Charged Spherical Black Hole

abstract:
  This paper consolidates noscalar hair theorem for a charged spherically
symmetric black hole in four dimension in general relativity as well as in all
scalar tensor theories, both minimally and nonminimally coupled, when the
effective Newtonian constant of gravity is positive. However, there is an
exception when the matter field itself is coupled to the scalar field, such as
in dilaton gravity.


title: Chronology Protection and Non-Naked Singularity

abstract:
  We test the chronology protection conjecture in classical general relativity
by investigating finitely vicious space-times. First we present singularity
theorems in finitely vicious space-times by imposing some restrictions on the
chronology violating sets. In the theorems we can refer to the location of an
occurring singularity and do not assume any asymptotic conditions such as the
existence of null infinities. Further introducing the concept of a non-naked
singularity, we show that a restricted class of chronology violations cannot
arise if all occurring singularities are the non-naked singularities. Our
results suggest that the causal feature of the occurring singularities is the
key to prevent the appearance of causality violation.


title:
Phase-plane analysis of Friedmann-Robertson-Walker cosmologies in
  Brans-Dicke gravity

abstract:
  We present an autonomous phase-plane describing the evolution of
Friedmann-Robertson-Walker models containing a perfect fluid (with barotropic
index gamma) in Brans-Dicke gravity (with Brans-Dicke parameter omega). We find
self-similar fixed points corresponding to Nariai's power-law solutions for
spatially flat models and curvature-scaling solutions for curved models. At
infinite values of the phase-plane variables we recover O'Hanlon and Tupper's
vacuum solutions for spatially flat models and the Milne universe for negative
spatial curvature. We find conditions for the existence and stability of these
critical points and describe the qualitative evolution in all regions of the
(omega,gamma) parameter space for 0<gamma<2 and omega>-3/2. We show that the
condition for inflation in Brans-Dicke gravity is always stronger than the
general relativistic condition, gamma<2/3.


title: Quantum black holes:unexpected results

abstract:
  The quantum black hole model with a self-gravitating spherically symmetric
thin dust shell as a source is considered. The shell Hamiltonian constraint is
written and the corresponding Schroedinger equation is obtained. This equation
appeared to be a finite differences equation. Its solutions are required to be
analytic functions on the relevant Riemannian surface. The method of finding
discrete spectra is suggested based on the analytic properties of the
solutions. The large black hole approximation is considered and the discrete
spectra for bound states of quantum black holes and wormholes are found. They
depend on two quantum numbers and are, in fact, quasi-continuous. The quantum
black hole bound state depends not only on mass but also on an additional
quantum number, and black holes with the same mass have different quantum
hairs. These hairs exhibit themselves at the Planckian distances near the black
hole horizon. For the observer who can not measure the distances smaller than
the Planckian length the black hole has the only parameter, its mass. The
other, non-measurable, parameter leads to the quantum corrections to the black
hole entropy. The quantum states with given mass are the mixed ones. It is
shown that there exists the ground quantum black hole state with minimal mass
equal approximately the Planckian mass. Its quantum state has zero entropy and
it is a pure state. The existence of the quantum hairs may solve (at least
partially) the well known information paradox in the black hole physics.


title: An Algorithm to Simplify Tensor Expressions

abstract:
  The problem of simplifying tensor expressions is addressed in two parts. The
first part presents an algorithm designed to put tensor expressions into a
canonical form, taking into account the symmetries with respect to index
permutations and the renaming of dummy indices. The tensor indices are split
into classes and a natural place for them is defined. The canonical form is the
closest configuration to the natural configuration. In the second part, the
Groebner basis method is used to simplify tensor expressions which obey the
linear identities that come from cyclic symmetries (or more general tensor
identities, including non-linear identities). The algorithm is suitable for
implementation in general purpose computer algebra systems. Some timings of an
experimental implementation over the Riemann package are shown.


title:
Strings, loops and others: a critical survey of the present approaches
  to quantum gravity

abstract:
  I review the present theoretical attempts to understand the quantum
properties of spacetime. In particular, I illustrate the main achievements and
the main difficulties in: string theory, loop quantum gravity, discrete quantum
gravity (Regge calculus, dynamical triangulations and simplicial models),
Euclidean quantum gravity, perturbative quantum gravity, quantum field theory
on curved spacetime, noncommutative geometry, null surfaces, topological
quantum field theories and spin foam models. I also briefly review several
recent advances in understanding black hole entropy and attempt a critical
discussion of our present understanding of quantum spacetime.


title: Quantum Cosmology in some Scalar-tensor Theories

abstract:
  The Wheeler-DeWitt equation is solved for some scalar-tensor theories of
gravitation in the case of homogeneous and isotropic cosmological models.We
present general solutions corresponding to cosmological term:
(i)\lambda(\phi)=0$ and $(ii) \lambda(\phi)=q\phi$.


title: The topology of the universe: the biggest manifold of them all

abstract:
  Clues as to the geometry of the universe are encoded in the cosmic background
radiation. Hot and cold spots in the primordial radiation may be randomly
distributed in an infinite universe while in a universe with compact topology
distinctive patterns can be generated. With improved vision, we could actually
see if the universe is wrapped into a hexagonal prism or a hyperbolic horn. We
discuss the search for such geometric patterns in predictive maps of the
microwave sky.


title: Rotating vacuum wormhole

abstract:
  We investigate whether self-maintained vacuum traversible wormhole can exist
described by stationary but nonstatic metric. We consider metric being the sum
of static spherically symmetric one and a small nondiagonal component which
describes rotation sufficiently slow to be taken into account in the linear
approximation. We study semiclassical Einstein equations for this metric with
vacuum expectation value of stress-energy of physical fields as the source. In
suggestion that the static traversible wormhole solution exists we reveal
possible azimuthal angle dependence of angular velocity of the rotation
(angular velocity of the local inertial frame) that solves semiclassical
Einstein equations. We find that in the macroscopic (in the Plank scale)
wormhole case a rotational solution exists but only such that, first, angular
velocity depends on radial coordinate only and, second, the wormhole connects
the two asymptotically flat spacetimes rotating with angular velocities
different in asymptotic regions.


title: High-Energy Physics with Gravitational-Wave Experiments

abstract:
  We discuss the possible relevance of gravitational-wave (GW) experiments for
physics at very high energy. We examine whether, from the experience gained
with the computations of various specific relic GW backgrounds, we can extract
statements and order of magnitude estimates that are as much as possible
model-independent, and we try to distinguish between general conclusions and
results related to specific cosmological mechanisms. We examine the statement
that the Virgo/LIGO experiments probe the Universe at temperatures $T\sim
10^{7}-10^{10}$ GeV (or timescales $t\sim 10^{-20}-10^{-26}$ sec) and we
consider the possibility that they could actually probe the Universe at much
higher energy scales, including the typical scales of grand unification, string
theory and quantum gravity. We consider possible scenarios, depending on how
the inflationary paradigm is implemented. We discuss the prospects for
detection with present and planned experiments. In particular, a second Virgo
interferometer correlated with the planned one, and located within a few tens
of kilometers from the first, could reach an interesting sensitivity for
stochastic GWs of cosmological origin.


title: Wormholes in spacetimes with cosmological horizons

abstract:
  A generalisation of the asymptotic wormhole boundary condition for the case
of spacetimes with a cosmological horizon is proposed. In particular, we
consider de Sitter spacetime with small cosmological constant. The wave
functions selected by this proposal are exponentially damped in WKB
approximation when the scale factor is large but still much smaller than the
horizon size. In addition, they only include outgoing gravitational modes in
the region beyond the horizon. We argue that these wave functions represent
quantum wormholes and compute the local effective interactions induced by them
in low-energy field theory. These effective interactions differ from those for
flat spacetime in terms that explicitly depend on the cosmological constant.


title: Non static local string in Brans-Dicke theory

abstract:
  A recent investigation shows that a local gauge string with a
phenomenological energy momentum tensor, as prescribed by Vilenkin, is
inconsistent in Brans-Dicke theory. In this work, it has been shown that such a
string is indeed consistent if one introduces time dependences in the metric. A
set of solutions of full nonlinear Einstein's equations for the interior region
of such a string are presented.


title: Gravitational-wave versus binary-pulsar tests of strong-field gravity

abstract:
  Binary systems comprising at least one neutron star contain strong
gravitational field regions and thereby provide a testing ground for
strong-field gravity. Two types of data can be used to test the law of gravity
in compact binaries: binary pulsar observations, or forthcoming
gravitational-wave observations of inspiralling binaries. We compare the
probing power of these two types of observations within a generic two-parameter
family of tensor-scalar gravitational theories. Our analysis generalizes
previous work (by us) on binary-pulsar tests by using a sample of realistic
equations of state for nuclear matter (instead of a polytrope), and goes beyond
a previous study (by C.M. Will) of gravitational-wave tests by considering more
general tensor-scalar theories than the one-parameter Jordan-Fierz-Brans-Dicke
one. Finite-size effects in tensor-scalar gravity are also discussed.


title: Gauge-invariant magnetic perturbations in perfect-fluid cosmologies

abstract:
  We develop further our extension of the Ellis-Bruni covariant and
gauge-invariant formalism to the general relativistic treatment of density
perturbations in the presence of cosmological magnetic fields. We present
detailed analysis of the kinematical and dynamical behaviour of perturbed
magnetized FRW cosmologies containing fluid with non-zero pressure. We study
the magnetohydrodynamical effects on the growth of density irregularities
during the radiation era. Solutions are found for the evolution of density
inhomogeneities on small and large scales in the presence of pressure, and some
new physical effects are identified.


title: The many faces of superradiance

abstract:
  Inertial motion superradiance, the emission of radiation by an initially
unexcited system moving inertially but superluminally through a medium, has
long been known. Rotational superradiance, the amplification of radiation by a
rotating rigid object, was recognized much later, principally in connection
with black hole radiances. Here we review the principles of inertial motion
superradiance and prove thermodynamically that the Ginzburg--Frank condition
for superradiance coincides with the condition for superradiant amplification
of already existing radiation. Examples we cite include a new type of black
hole superradiance. We correct Zel'dovich's thermodynamic derivation of the
Zel'dovich--Misner condition for rotational superradiance by including the
radiant entropy in the bookkeeping . We work out in full detail the
electrodynamics of a Zel'dovich rotating cylinder, including a general
electrodynamic proof of the Zel'dovich--Misner condition, and explicit
calculations of the superradiant gain for both types of polarization. Contrary
to Zel'dovich's pessimistic conclusion we conclude that, if the cylinder is
surrounded by a dielectric jacket and the whole assembly is placed inside a
rotating cavity, the superradiance is measurable in the laboratory.

categories: gr-qc astro-ph physics.atom-ph physics.optics


title:
On the Completeness of the Quasinormal Modes of the Poeschl-Teller
  Potential

abstract:
  The completeness of the quasinormal modes of the wave equation with
Poeschl-Teller potential is investigated. A main result is that after a large
enough time $t_0$, the solutions of this equation corresponding to
$C^{\infty}$-data with compact support can be expanded uniformly in time with
respect to the quasinormal modes, thereby leading to absolutely convergent
series. Explicit estimates for $t_0$ depending on both the support of the data
and the point of observation are given. For the particular case of an ``early''
time and zero distance between the support of the data and observational point,
it is shown that the corresponding series is not absolutely convergent, and
hence that there is no associated sum which is independent of the order of
summation.


title: Wormhole effective interactions in anti-de Sitter spacetime

abstract:
  The effects of asymptotically anti-de Sitter wormholes in low-energy field
theory are calculated in full detail for three different matter contents: a
conformal scalar field, an electromagnetic field and gravitons. There exists a
close relation between the choice of vacuum for the matter fields and the
selection of a basis of the Hilbert space of anti-de Sitter wormholes. In the
presence of conformal matter (i.e., conformal scalar or electromagnetic
fields), this relation allows us to interpret the elements of these bases as
wormhole states containing a given number of particles. This interpretation is
subject to the same kind of ambiguity in the definition of particle as that
arising from quantum field theory in curved spacetime. In the case of
gravitons, owing to the non-conformal coupling, it is not possible to describe
wormhole states in terms of their particle content.


title: Global Properties of Vacuum States in de Sitter Space

abstract:
  Starting from the assumption that vacuum states in de Sitter space look for
any geodesic observer like equilibrium states with some a priori arbitrary
temperature, an analysis of their global properties is carried out in the
algebraic framework of local quantum physics. It is shown that these states
have the Reeh-Schlieder property and that any primary vacuum state is also pure
and weakly mixing. Moreover, the geodesic temperature of vacuum states has to
be equal to the Gibbons-Hawking temperature and this fact is closely related to
the existence of a discrete PCT-like symmetry. It is also shown that the global
algebras of observables in vacuum sectors have the same structure as their
counterparts in Minkowski space theories.


title:
Gauge theory of gravity: Electrically charged solutions within the
  metric--affine framework

abstract:
  We find a class of electrically charged exact solutions for a toy model of
metric-affine gravity. Their metric is of the Pleba\'nski-Demia\'nski type and
their nonmetricity and torsion are represented by a triplet of covectors with
dilation, shear, and spin charges.


title: Generalized Vaidya Solutions

abstract:
  A large family of solutions, representing, in general, spherically symmetric
Type II fluid, is presented, which includes most of the known solutions to the
Einstein field equations, such as, the monopole-de Sitter-charged Vaidya ones.


title:
Instability of cosmological event horizons of nonstatic global cosmic
  strings II: perturbations of gravitational waves and massless scalar field

abstract:
  The stability of the cosmological event horizons (CEHs) of a class of
non-static global cosmic strings is studied against perturbations of
gravitational waves and massless scalar field. It is found that the
perturbations of gravitational waves always turn the CEHs into non-scalar weak
spacetime curvature singularities, while the ones of massless scalar field turn
the CEHs either into non-scalar weak singularities or into scalar ones
depending on the particular cases considered. The perturbations of test
massless scalar field is also studied, and it is found that they do not always
give the correct prediction.


title: Radiation and String Atmosphere for Relativistic Stars

abstract:
  We extend the Vaidya radiating metric to include both a radiation field and a
string fluid. Assuming diffusive transport for the string fluid, we find new
analytic solutions of Einstein's field equations. Our new solutions represent
an extention of Xanthopoulos superposition.


title: Indeterministic Quantum Gravity and Cosmology XI. Quantum Measurement

abstract:
  This paper is a sequel to the series of papers [gr-qc/9409010, gr-qc/9505034,
gr-qc/9603022, gr-qc/9609035, gr-qc/9609046, gr-qc/9704033, gr-qc/9704038,
gr-qc/9708014, gr-qc/9802016, gr-qc/9802022]. We define a quantum measurement
as a sequence of binary quantum jumps caused by a macroscopic apparatus. A
dynamical theory of measurement is developed, the role of gravity and cosmology
being emphasized.


title:
The Dirac particle on central backgrounds and the anti-de Sitter
  oscillator

abstract:
  It is shown that, for spherically symmetric static backgrounds, a simple
reduced Dirac equation can be obtained by using the Cartesian tetrad gauge in
Cartesian holonomic coordinates. This equation is manifestly covariant under
rotations so that the spherical coordinates can be separated in terms of
angular spinors like in special relativity, obtaining a pair of radial
equations and a specific form of the radial scalar product. As an example, we
analytically solve the anti-de Sitter oscillator giving the formula of the
energy levels and the form of the corresponding eigenspinors.


title: The Husain-Kuchar Model: Time Variables and Non-degenerate Metrics

abstract:
  We study the Husain-Kuchar model by introducing a new action principle
similar to the self-dual action used in the Ashtekar variables approach to
Quantum Gravity. This new action has several interesting features; among them,
the presence of a scalar time variable that allows the definition of geometric
observables without adding new degrees of freedom, the appearance of a natural
non-degenerate four-metric and the possibility of coupling ordinary matter.


title:
Vacuum Fluctuations of a massless spin-1/2 field around multiple cosmic
  strings

abstract:
  We study the interaction of a massless quantized spinor field with the
gravitational filed of N parallel static cosmic strings by using a perturbative
approach. We show that the presence of more than one cosmic string gives rise
to an additional contribution to the energy density of vacuum fluctuations,
thereby leading to a vacuum force attraction between two parallel cosmic
strings.


title: The Background Field Approximation in (quantum) cosmology

abstract:
  We analyze the Hamilton-Jacobi action of gravity and matter in the limit
where gravity is treated at the background field approximation. The motivation
is to clarify when and how the solutions of the Wheeler-DeWitt equation lead to
the Schr\"odinger equation in a given background. To this end, we determine
when and how the total action, solution of the constraint equations of General
Relativity, leads to the HJ action for matter in a given background. This is
achieved by comparing two neighboring solutions differing slightly in their
matter energy content. To first order in the change of the 3-geometries, the
change of the gravitational action equals the integral of the matter energy
evaluated in the background geometry. Higher order terms are governed by the
``susceptibility'' of the geometry. These classical properties also apply to
quantum cosmology since the conditions which legitimize the use of WKB
gravitational waves are concomitant with those governing the validity of the
background field approximation.


title: Chaos in Preinflationary Friedmann-Robertson-Walker Universes

abstract:
  The dynamics of a preinflacionary phase of the universe, and its exit to
inflation, is discussed. This phase is modeled by a closed
Friedmann-Robertson-Walker geometry, the matter content of which is radiation
plus a scalar field minimally coupled to the gravitational field. The simple
configuration, with two effective degres of freedom only, presents a very
complicated dynamics connected to the existence of critical points of
saddle-center type and saddle type in phase space of the system. Each of these
critical points is associated to an extremum of the scalar field potential. The
Topology of the phase space about the saddle-center is characterized by
homoclinic cylinders emanating from unstable periodic orbits, and the
transversal crossing of the cylinders, due to the non-integrability of the
system, results in a chaotic dynamics. The topology of the homoclinic cylinders
provides an invariant characterization of chaos. The model exhibits one or more
exits to inflation, associated to one or more strong asymptotic de Sitter
attractors present in phase space, but the way out from the initial singularity
into any of the inflationary exits is chaotic. We discuss possible mechanisms,
connected to the spectrum of inhomogeneous fluctuations in the models, which
would allow us to distinguish physically the several exits to inflation.


title: Patching up the No-Boundary Proposal with virtual Euclidean wormholes

abstract:
  In quantum cosmology, one often considers tunneling phenomena which may have
occurred in the early universe. Processes requiring quantum penetration of a
potential barrier include black hole pair creation and the decay of vacuum
domain walls. Ideally, one calculates the rates for such processes by finding
an instanton, or Euclidean solution of the field equations, which interpolates
between the initial and final states. In practice, however, it has become
customary to calculate such amplitudes using the No-Boundary Proposal of Hartle
and Hawking. A criticism of this method is that it does not use a single path
which interpolates between the initial and final states, but two disjoint
instantons: One divides the probability to create the final state from nothing
by the probability to create the initial state from nothing and decrees the
answer to be the rate of tunneling from the initial to the final state. Here,
we demonstrate the validity of this approach by constructing continuous paths
connecting the ingoing and outgoing data, which may be viewed as perturbations
of the set of disconnected instantons. They are off-shell, but will still
dominate the path integral as they have action arbitrarily close to the
no-boundary action. In this picture, a virtual domain wall, or wormhole, is
created and annihilated in such a way as to interface between the disjoint
instantons. Decay rates calculated using our construction differ from decay
rates calculated using the No-Boundary Proposal only in the prefactor; the
exponent, which usually dominates the result, remains unchanged.


title: Godel Universes in String Theory

abstract:
  We show that homogeneous G\"odel spacetimes need not contain closed timelike
curves in low-energy-effective string theories. We find exact solutions for the
G\"odel metric in string theory for the full $O(\alpha ^{\prime})$ action
including both dilaton and axion fields. The results are valid for bosonic,
heterotic and super-strings. To first order in the inverse string tension
$\alpha ^{\prime}$, these solutions display a simple relation between the
angular velocity of the G\"odel universe, $\Omega ,$ and the inverse string
tension of the form $\alpha ^{\prime}=1/\Omega ^2$ in the absence of the axion
field. The generalization of this relationship is also found when the axion
field is present.


title: Towards a Full Quantum Theory of Black Holes

abstract:
  This review gives an introduction to various attempts to understand the
quantum nature of black holes. The first part focuses on thermodynamics of
black holes, Hawking radiation, and the interpretation of entropy. The second
part is devoted to the detailed treatment of black holes within canonical
quantum gravity. The last part adds a brief discussion of black holes in string
theory and quantum cosmology.


title: On the Hawking Turok solution to the Open Universe wave function

abstract:
  Hawking and Turok have recently published a solution to the WKB
"wave-function for the universe" which they claim leads in a natural way to an
open universe as the end point of the evolution for a universe dominated by a
scalar field. They furthermore argue that their solution a preferred solution
under the rules of the game. This paper will, I hope, clarify their solution
and the limits of validity of their argument.


title: Summary of Session A6: Alternative Theories of Gravity

abstract:
  This is a summary of the workshop A.6 on Alternative Theories of Gravity,
prepared for the proceedings for the GR15 conference.


title: Curing singularities: From the big bang to black holes

abstract:
  Singular spacetimes are a natural prediction of Einstein's theory. Most
memorable are the singular centers of black holes and the big bang. However,
dilatonic extensions of Einstein's theory can support nonsingular spacetimes.
The cosmological singularities can be avoided by dilaton driven inflation.
Furthermore, a nonsingular black hole can be constructed in two dimensions.


title: Gravitational Radiation Instability in Hot Young Neutron Stars

abstract:
  We show that gravitational radiation drives an instability in hot young
rapidly rotating neutron stars. This instability occurs primarily in the l=2
r-mode and will carry away most of the angular momentum of a rapidly rotating
star by gravitational radiation. On the timescale needed to cool a young
neutron star to about T=10^9 K (about one year) this instability can reduce the
rotation rate of a rapidly rotating star to about 0.076\Omega_K, where \Omega_K
is the Keplerian angular velocity where mass shedding occurs. In older colder
neutron stars this instability is suppressed by viscous effects, allowing older
stars to be spun up by accretion to larger angular velocities.


title:
A program for a problem free Cosmology within a framework of a rich
  class of scalar tensor theories

abstract:
  A search for a problem free cosmology within the framework of an effective
non - minimally coupled scalar tensor theory is suggested. With appropriate
choice of couplings in variants of a Lee - Wick model [as also in a model
supporting Q - ball solutions], non topological solutions [NTS's], varying in
size upto 10 kpc to 1 Mpc can exist. We explore the properties of a ``toy''
Milne model containing a distribution of NTS domains. The interior of these
domains would be regions where effective gravitational effects would be
indistinguishable from those expected in standard Einstein theory. For a large
class of non - minimal coupling terms and the scalar effective potential, the
effective cosmological constant identically vanishes. The model passes
classical cosmological tests and we describe reasons to expect it to fare well
as regards nucleosynthesis and structure formation.


title: Searching data for periodic signals

abstract:
  We present two statistical tests for periodicities in the time series. We
apply the two tests to the data taken from Glasgow prototype interferometer in
March 1996. We find that the data contain several very narrow spectral
features. We investigate whether these features can be confused with
gravitational wave signals from pulsars.


title: Quantization of gravity in the theory with the massive vector field

abstract:
  The quantum theory of gravity is considered based on the assumption that
gravitational interaction occurs by means of the vector field of the Planck
mass. Gravitational emission is considered as a process of the decay of proton
into some matter fields at the Planck scale. Within the framework of grand
unification vector field of the Planck mass may be thought of as those which
realize the interaction between leptons and quarks.


title: Astrophysical Evidence for Black Hole Event Horizons

abstract:
  Astronomers have discovered many potential black holes in X-ray binaries and
galactic nuclei. These black holes are usually identified by the fact that they
are too massive to be neutron stars. Until recently, however, there was no
convincing evidence that the objects identified as black hole candidates
actually have event horizons. This has changed with extensive applications of a
class of accretion models for describing the flow of gas onto compact objects;
for these solutions, called advection-dominated accretion flows (ADAFs), the
black hole nature of the accreting star, specifically its event horizon, plays
an important role. We review the evidence that, at low luminosities, accreting
black holes in both X-ray binaries and galactic nuclei contain ADAFs rather
than the standard thin accretion disk.


title:
The imposition of Cauchy data to the Teukolsky equation III: The
  rotating case

abstract:
  We solve the problem of expressing the Weyl scalars $\psi $ that describe
gravitational perturbations of a Kerr black hole in terms of Cauchy data. To do
so we use geometrical identities (like the Gauss-Codazzi relations) as well as
Einstein equations. We are able to explicitly express $\psi $ and $\partial
_t\psi $ as functions only of the extrinsic curvature and the three-metric (and
geometrical objects built out of it) of a generic spacelike slice of the
spacetime. These results provide the link between initial data and $\psi $ to
be evolved by the Teukolsky equation, and can be used to compute the
gravitational radiation generated by two orbiting black holes in the close
limit approximation. They can also be used to extract waveforms from spacetimes
completely generated by numerical methods.


title: The singularity in supercritical collapse of a spherical scalar field

abstract:
  We study the singularity created in the supercritical collapse of a spherical
massless scalar field. We first model the geometry and the scalar field to be
homogeneous, and find a generic solution (in terms of a formal series
expansion) describing a spacelike singularity which is monotonic, scalar
polynomial and strong. We confront the predictions of this analytical model
with the pointwise behavior of fully-nonlinear and inhomogeneous numerical
simulations, and find full compliance. We also study the phenomenology of the
spatial structure of the singularity numerically. At asymptotically late
advanced time the singularity approaches the Schwarzschild singularity, in
addition to discrete points at finite advanced times, where the singularity is
Schwarzschild-like. At other points the singularity is different from
Schwarzschild due to the nonlinear scalar field.


title:
The static spacetime relative acceleration for the general free fall and
  its possible experimental test

abstract:
  Mishra has recently established, using a generic static metric, the relative
local proper-time 3-acceleration of a test-particle in one-dimensional free
fall relative to a static reference frame in any static spacetime. In this
paper, on the grounds of gravitoelectromagnetism we establish, in a covariant
spacetime form, the relative 4-acceleration for the general free fall,
indicating its canonical representation with its 3-space cinematical content.
Then we obtain the relation between this representation and the very known
expression for the relative free fall acceleration in Fermi coordinates. Taking
this into account, it is shown that an experiment with relativistic beams in a
circular accelerator, modelled by Fermi coordinates, recently proposed by
Moliner et al, can test the here established covariant result and, therefore,
can also verify Mishra's formula. This possibility of experimental
verification, besides its intrinsic importance, can answer a recent inquire by
Vigier, related to his recent proposal of derivation of inertial forces.


title: Quantum Properties of Topological Black Holes

abstract:
  We examine quantum properties of topological black holes which are
asymptotically anti--de Sitter. First, massless scalar fields and Weyl spinors
which propagate in the background of an anti--de Sitter black hole are
considered in an exactly soluble two--dimensional toy model. The Boulware--,
Unruh--, and Hartle--Hawking vacua are defined. The latter results to coincide
with the Unruh vacuum due to the boundary conditions necessary in
asymptotically adS spacetimes. We show that the Hartle--Hawking vacuum
represents a thermal equilibrium state with the temperature found in the
Euclidean formulation. The renormalized stress tensor for this quantum state is
well--defined everywhere, for any genus and for all solutions which do not have
an inner Cauchy horizon, whereas in this last case it diverges on the inner
horizon. The four--dimensional case is finally considered, the equilibrium
states are discussed and a luminosity formula for the black hole of any genus
is obtained. Since spacelike infinity in anti--de Sitter space acts like a
mirror, it is pointed out how this would imply information loss in
gravitational collapse. The black hole's mass spectrum according to
Bekenstein's view is discussed and compared to that provided by string theory.


title:
No Time Machine Construction in Open 2+1 Gravity with Timelike Total
  Energy Momentum

abstract:
  It is shown that in 2+1 dimensional gravity an open spacetime with timelike
sources and total energy momentum cannot have a stable compactly generated
Cauchy horizon. This constitutes a proof of a version of Kabat's conjecture and
shows, in particular, that not only a Gott pair cannot be formed from processes
such as the decay of a single cosmic string as has been shown by Carroll et
al., but that, in a precise sense, a time machine cannot be constructed at all.


title: Vacuum fluctuations for spherical gravitational impulsive waves

abstract:
  We propose a method for calculating vacuum fluctuations on the background of
a spherical impulsive gravitational wave which results in a finite expression
for the vacuum expectation value of the stress-energy tensor. The method is
based on first including a cosmological constant as an auxiliary constant. We
show that the result for the vacuum expectation value of the stress-energy
tensor in second-order perturbation theory is finite if both the cosmological
constant and the infrared parameter tend to zero at the same rate.


title:
A method for calculating the imaginary part of the Hadamard Elementary
  function $G^{(1)}$ in static, spherically symmetric spacetimes

abstract:
  Whenever real particle production occurs in quantum field theory, the
imaginary part of the Hadamard Elementary function $G^{(1)}$ is non-vanishing.
A method is presented whereby the imaginary part of $G^{(1)}$ may be calculated
for a charged scalar field in a static spherically symmetric spacetime with
arbitrary curvature coupling and a classical electromagnetic field $A^{\mu}$.
The calculations are performed in Euclidean space where the Hadamard Elementary
function and the Euclidean Green function are related by $(1/2)G^{(1)}=G_{E}$.
This method uses a $4^{th}$ order WKB approximation for the Euclideanized mode
functions for the quantum field. The mode sums and integrals that appear in the
vacuum expectation values may be evaluated analytically by taking the large
mass limit of the quantum field. This results in an asymptotic expansion for
$G^{(1)}$ in inverse powers of the mass $m$ of the quantum field.
Renormalization is achieved by subtracting off the terms in the expansion
proportional to nonnegative powers of $m$, leaving a finite remainder known as
the ``DeWitt-Schwinger approximation.'' The DeWitt-Schwinger approximation for
$G^{(1)}$ presented here has terms proportional to both $m^{-1}$ and $m^{-2}$.
The term proportional to $m^{-2}$ will be shown to be identical to the
expression obtained from the $m^{-2}$ term in the generalized DeWitt-Schwinger
point-splitting expansion for $G^{(1)}$. The new information obtained with the
present method is the DeWitt-Schwinger approximation for the imaginary part of
$G^{(1)}$, which is proportional to $m^{-1}$ in the DeWitt-Schwinger
approximation for $G^{(1)}$ derived in this paper.


title: Quantum Gravity/String/M-theory/ as we approach the 3rd Millennium

abstract: I review some recent progress in String/M-theory


title: Long range correlations in quantum gravity

abstract:
  Smolin has pointed out that the spin network formulation of quantum gravity
will not necessarily possess the long range correlations needed for a proper
classical limit; typically, the action of the scalar constraint is too local.
Thiemann's length operator is used to argue for a further restriction on the
action of the scalar constraint: it should not introduce new edges of color
unity into a spin network, but should rather change preexisting edges by $\pm$
one unit of color. Smolin has proposed a specific ansatz for a correlated
scalar constraint. This ansatz does not introduce color unity edges, but the
[scalar, scalar] commutator is shown to be anomalous. In general, it will be
hard to avoid anomalies, once correlation is introduced into the constraint;
but it is argued that the scalar constraint may not need to be anomaly-free
when acting on the kinematic basis.


title: A Non-Singular Universe in String Cosmology

abstract:
  We consider the low-energy effective string action in four dimensions
including the leading order-$\alpha'$ terms. An exact homogeneous solution is
obtained. It represents a non-singular expanding cosmological model in which
the tensor fields tend to vanish as $t\to \infty$. The scale factor $a(t)$ of
the very early universe in this model has the time dependence
$a(t)^2=a_0^2+t^2$. The violation of the strong energy condition of classical
General Relativity to avoid the initial singularity requires that the central
charge deficit of the theory be larger than a certain value. The significance
of this solution is discussed.


title:
Quantum Creation of a Universe with $\Omega \not = 1$: Singular and
  Non-Singular Instantons

abstract:
  We propose two new classes of instantons which describe the tunneling and/or
quantum creation of closed and open universes. The instantons leading to an
open universe can be considered as generalizations of the Coleman-De-Luccia
solution. They are non-singular, unlike the instantons recently studied by
Hawking and Turok, whose prescription has the problem that the singularity is
located on the hypersurface connecting to the Lorentzian region, which makes it
difficult to remove. We argue that such singularities are harmless if they are
located purely in the Euclidean region. We thus obtain new singular instantons
leading to a closed universe; unlike the usual regular instantons used for this
purpose, they do not require complex initial conditions. The singularity gives
a boundary contribution to the action which is small for the instantons leading
to sufficient inflation, but changes the sign of the action for small $\phi$
corresponding to short periods of inflation.


title: G_2 cosmological models separable in non-comoving coordinates

abstract:
  We study new separable orthogonally transitive abelian G_2 on S_2 models with
two mutually orthogonal integrable Killing vector fields. For this purpose we
consider separability of the metric functions in a coordinate system in which
the velocity vector field of the perfect fluid does not take its canonical
form, providing thereby solutions which are non-separable in comoving
coordinates in general. Some interesting general features concerning this class
of solutions are given. We provide a full classification for these models and
present several families of explicit solutions with their properties.


title: Black holes and gravitational waves in string cosmology

abstract:
  Pre--big bang models of inflation based on string cosmology produce a
stochastic gravitational wave background whose spectrum grows with decreasing
wavelength, and which may be detectable using interferometers such as LIGO. We
point out that the gravitational wave spectrum is closely tied to the density
perturbation spectrum, and that the condition for producing observable
gravitational waves is very similar to that for producing an observable density
of primordial black holes. Detection of both would provide strong support to
the string cosmology scenario.


title: Relativistic Static Thin Disks with Radial Stress Suport

abstract:
  New solutions for static non-rotating thin disks of finite radius with
nonzero radial stress are studied. A method to introduce either radial pressure
or radial tension is presented. The method is based on the use of conformal
transformations.


title: GR 15 Proceedings A5(ii) Computer Methods in GR: Algebraic computing

abstract:
  Algebraic computing in relativity and gravitation dates back more than thirty
years, but only relatively recently has hardware of sufficient power to tackle
large scale calculations become commonplace. Whereas it is generally understood
throughout the relativity community that there are a number of packages
available, the diversity of problems that the available packages can help with
is not so widely appreciated. This session was devoted to computer algebra for
relativity and gravitation from the point of view of developers. In this
summary I expand this to include some background and outline what is available
for users in the field.


title: Where do all the supercurvature modes go?

abstract:
  In the hyperbolic slicing of de Sitter space appropriate for open universe
models, a curvature scale is present and supercurvature fluctuations are
possible. In some cases, the expansion of a scalar field in the Bunch-Davies
vacuum includes supercurvature modes, as shown by Sasaki, Tanaka and Yamamoto.
We express the normalizable vacuum supercurvature modes for a massless scalar
field in terms of the basis modes for the spatially-flat slicing of de Sitter
space.


title: The Area Spectrum in Quantum Gravity

abstract:
  We show that, apart from the usual area operator of non-perturbative quantum
gravity, there exists another, closely related, operator that measures areas of
surfaces. Both corresponding classical expressions yield the area. Quantum
mechanically, however, the spectra of the two operators are different,
coinciding only in the limit when the spins labelling the state are large. We
argue that both operators are legitimate quantum operators, and which one to
use depends on the context of a physical problem of interest. Thus, for
example, we argue that it is the operator proposed here that is relevant in the
black hole context to measure the area of black hole horizon. We show that the
difference between the two operators is due to non-commutativity that is known
to arise in the quantum theory. We give a heuristic picture explaining the
difference between the two area spectra in terms of quantum fluctuations of the
surface whose area is being measured.


title: The (Unstable) Threshold of Black Hole Formation

abstract:
  In recent years it has become apparent that intriguing phenomenology exists
at the threshold of black hole formation in a large class of general
relativistic collapse models. This phenomenology, which includes scaling,
self-similarity and universality, is largely analogous to statistical
mechanical critical behaviour, a fact which was first noted empirically, and
subsequently clarified by perturbative calculations which borrow on ideas and
techniques from dynamical systems theory and renormalization group theory. This
contribution, which closely parallels my talk at the conference, consists of an
overview of the considerable ``zoo''' of critical solutions which have been
discovered thus far, along with a brief discussion of how we currently
understand the nature of these solutions from the point of view of perturbation
theory.


title: Particle production from nonlocal gravitational effective action

abstract:
  In this paper we show how the nonlocal effective action for gravity, obtained
after integrating out the matter fields, can be used to compute particle
production and spectra for different space-time metrics. Applying this
technique to several examples, we find that the perturbative calculation of the
effective action up to second order in curvatures yields exactly the same
results for the total number of particles as the Bogolyubov transformations
method, in the case of masless scalar fields propagating in a Robertson-Walker
space-time. Using an adiabatic approximation we also obtain the corresponding
spectra and compare the results with the traditional WKB approximation.


title: Symmetric hyperbolic system in the Ashtekar formulation

abstract:
  We present a first-order symmetric hyperbolic system in the Ashtekar
formulation of general relativity for vacuum spacetime. We add terms from
constraint equations to the evolution equations with appropriate combinations,
which is the same technique used by Iriondo, Leguizam\'on and Reula [Phys. Rev.
Lett. 79, 4732 (1997)]. However our system is different from theirs in the
points that we primarily use Hermiticity of a characteristic matrix of the
system to characterize our system "symmetric", discuss the consistency of this
system with reality condition, and show the characteristic speeds of the
system.


title:
On the evolution of a large class of inhomogeneous scalar field
  cosmologies

abstract:
  The asymptotic behaviour of a family of inhomogeneous scalar field
cosmologies with exponential potential is studied. By introducing new variables
we can perform an almost complete analysis of the evolution of these
cosmologies. Unlike the homogeneous case (Bianchi type solutions), when k^2<2
the models do not isotropize due to the presence of the inhomogeneities


title: Inhomogeneous Universe Models with Varying Cosmological Term

abstract:
  The evolution of a class of inhomogeneous spherically symmetric universe
models possessing a varying cosmological term and a material fluid, with an
adiabatic index either constant or not, is studied.


title: Quasi-Spherical Light Cones of the Kerr Geometry

abstract:
  Quasi-spherical light cones are lightlike hypersurfaces of the Kerr geometry
that are asymptotic to Minkowski light cones at infinity. We develop the
equations of these surfaces and examine their properties. In particular, we
show that they are free of caustics for all positive values of the Kerr radial
coordinate r. Useful applications include the propagation of high-frequency
waves, the definition of Kruskal-like coordinates for a spinning black hole and
the characteristic initial-value problem.


title:
Breakdown of the linear approximation in the perturbative analysis of
  heat conduction in relativistic systems

abstract:
  We analyze the effects of thermal conduction in a relativistic fluid just
after its departure from spherical symmetry, on a time scale of the order of
relaxation time. Using first order perturbation theory, it is shown that, as in
spherical systems, at a critical point the effective inertial mass density of a
fluid element vanishes and becomes negative beyond that point. The impact of
this effect on the reliability of causality conditions is discussed.


title:
Irrotational Binary Neutron Stars in Quasiequilibrium in General
  Relativity

abstract:
  Neutron stars in binary orbit emit gravitational waves and spiral slowly
together. During this inspiral, they are expected to have very little
vorticity. It is in fact a good approximation to treat the system as having
zero vorticity, i.e., as irrotational. Because the orbital period is much
shorter than the radiation reaction time scale, it is also an excellent
approximation to treat the system as evolving through a sequence of equilibrium
states, in each of which the gravitational radiation is neglected. In Newtonian
gravity, one can simplify the hydrodynamic equations considerably for an
equilibrium irrotational binary by introducing a velocity potential. The
equations reduce to a Poisson-like equation for the potential, and a
Bernoulli-type integral for the density. We show that a similar simplification
can be carried out in general relativity. The resulting equations are much
easier to solve than other formulations of the problem.


title: Spin 2 in 2+1 dimensions

abstract:
  The distinct models that describe spin 1 and 2 massive excitations in 2+1
dimensions are analized, showing their equivalence (between models of same
spin) and analogies (between models of different spin). Topics as spontaneous
symmetry breaking and anyonic behaviour, in these models, are analized. A
massive gravity model is introduced. This model is diffeomophism invariant, but
it is not Lorentz invariant.


title: Neutron star in presence of torsion-dilaton field

abstract:
  We develop the general theory of stars in Saa's model of gravity with
propagating torsion and study the basic stationary state of neutron star. Our
numerical results show that the torsion force decreases the role of the gravity
in the star configuration leading to significant changes in the neutron star
masses depending on the equation of state of star matter. The inconsistency of
the Saa's model with Roll-Krotkov-Dicke and Braginsky-Panov experiments is
discussed.


title:
A relativistic formalism for computation of irrotational binary stars in
  quasi equilibrium states

abstract:
  We present relativistic hydrostatic equations for obtaining irrotational
binary neutron stars in quasi equilibrium states in 3+1 formalism. Equations
derived here are different from those previously given by Bonazzola,
Gourgoulhon, and Marck, and have a simpler and more tractable form for
computation in numerical relativity. We also present hydrostatic equations for
computation of equilibrium irrotational binary stars in first post-Newtonian
order.


title:
Equivalence of black hole thermodynamics between a generalized theory of
  gravity and the Einstein theory

abstract:
  We analyze black hole thermodynamics in a generalized theory of gravity whose
Lagrangian is an arbitrary function of the metric, the Ricci tensor and a
scalar field. We can convert the theory into the Einstein frame via a
"Legendre" transformation or a conformal transformation. We calculate
thermodynamical variables both in the original frame and in the Einstein frame,
following the Iyer--Wald definition which satisfies the first law of
thermodynamics. We show that all thermodynamical variables defined in the
original frame are the same as those in the Einstein frame, if the spacetimes
in both frames are asymptotically flat, regular and possess event horizons with
non-zero temperatures. This result may be useful to study whether the second
law is still valid in the generalized theory of gravity.


title:
Relativistic Hydrodynamics around Black Holes and Horizon Adapted
  Coordinate Systems

abstract:
  Despite the fact that the Schwarzschild and Kerr solutions for the Einstein
equations, when written in standard Schwarzschild and Boyer-Lindquist
coordinates, present coordinate singularities, all numerical studies of
accretion flows onto collapsed objects have been widely using them over the
years. This approach introduces conceptual and practical complications in
places where a smooth solution should be guaranteed, i.e., at the gravitational
radius. In the present paper, we propose an alternative way of solving the
general relativistic hydrodynamic equations in background (fixed) black hole
spacetimes. We identify classes of coordinates in which the (possibly rotating)
black hole metric is free of coordinate singularities at the horizon,
independent of time, and admits a spacelike decomposition. In the spherically
symmetric, non-rotating case, we re-derive exact solutions for dust and perfect
fluid accretion in Eddington-Finkelstein coordinates, and compare with
numerical hydrodynamic integrations. We perform representative axisymmetric
computations. These demonstrations suggest that the use of those coordinate
systems carries significant improvements over the standard approach, especially
for higher dimensional studies.


title:
Quantum Fields in Curved Spacetimes and Semiclassical Approaches: A
  Workshop Summary

abstract:
  I briefly review some of the recent progress in quantum field theory in
curved spacetime and other aspects of semiclassical gravity, as reported at the
D3 Workshop at GR15.


title:
Summary report of the workshop D2: Conceptual Issues, Foundational
  Questions and Quantum Cosmology

abstract:
  This is a summary report of the workshop D2 in GR15. In this workshop rather
diverging problems related to quantum gravity and quantum cosmology were
discussed. Since it is almost impossible to summarize all these discussions in
coherent and integrated expressions, in this report, I give a brief description
of the content of each paper in order, with some additional comments on their
backgrounds.


title: Connes duality in Lorentzian geometry

abstract:
  The Connes formula giving the dual description for the distance between
points of a Riemannian manifold is extended to the Lorentzian case. It resulted
that its validity essentially depends on the global structure of spacetime. The
duality principle classifying spacetimes is introduced. The algebraic account
of the theory is suggested as a framework for quantization along the lines
proposed by Connes. The physical interpretation of the obtained results is
discussed.


title:
Group Theoretical Examination of the Relativistic Wave Equations on
  Curved Spaces. I.Basic Principles

abstract:
  The basic principles of generalization of the group theoretical approach to
the relativistic wave equations on curved spaces are examined. The general
method of the determination of wave equations from the known symmetry group of
a symmetrical curved space is described. The method of obtaining the
symmetrical spaces in which invariant wave equations admit the limiting passage
to the relativistic wave equations on the flat (not necessarily real) spaces is
explained. Starting from the equations for massless particles and from the
Dirac equation in the Minkowski space, admissible real symmetrical spaces are
founded. The mentioned procedure is carried out also for the complex spaces. As
the basic point, the wave equations on the flat complex space are considered.
It is shown that the usual Dirac equation written down in the complex variables
does not lead to any curved space. By "decomposition" of the mentioned form of
the Dirac equation the equation leading to the space ${\Bbb C}{\Bbb P}^{n}$ and
being alternative to the usual Dirac equation on ${\Bbb C}^{n}$ is constructed.


title:
Group Theoretical Examination of the Relativistic Wave Equations on
  Curved Spaces. II. De Sitter and Anti-de Sitter Spaces

abstract:
  The group theoretical approach to the relativistic wave equations in the de
Sitter and Anti-de Sitter spaces for spin~0 and 1/2 massive particles is
considered. The invariant wave equations which determines the appropriate
irreducible representations are constructed. The explicit solutions of these
equations possessing a simplicity and physical transparency are obtained
without use of the separation of variables method. The connection with the
general-covariant approach to wave equations in a curved space is established.
It is shown that the Anti-de Sitter space is the solution of the Einstein-Dirac
equations. The geometrical meaning of the mass quantization in the Anti-de
Sitter space and of the particle creation in de Sitter space is shown.


title:
Binary Neutron-Star Systems: From the Newtonian Regime to the Last
  Stable Orbit

abstract:
  We report on the first calculations of fully relativistic binary circular
orbits to span a range of separation distances from the innermost stable
circular orbit (ISCO), deeply inside the strong field regime, to a distance
($\sim$ 200 km) where the system is accurately described by Newtonian dynamics.
We consider a binary system composed of two identical corotating neutron stars,
with 1.43 $M_\odot$ gravitational mass each in isolation. Using a conformally
flat spatial metric we find solutions to the initial value equations that
correspond to semi-stable circular orbits. At large distance, our numerical
results agree exceedingly well with the Newtonian limit. We also present a self
consistent determination of the ISCO for different stellar masses.


title:
Brans-Dicke Boson Stars: Configurations and Stability through Cosmic
  History

abstract:
  We make a detailed study of boson star configurations in Jordan--Brans--Dicke
theory, studying both equilibrium properties and stability, and considering
boson stars existing at different cosmic epochs. We show that boson stars can
be stable at any time of cosmic history and that equilibrium stars are denser
in the past. We analyze three different proposed mass functions for boson star
systems, and obtain results independently of the definition adopted. We study
how the configurations depend on the value of the Jordan--Brans--Dicke coupling
constant, and the properties of the stars under extreme values of the
gravitational asymptotic constant. This last point allows us to extract
conclusions about the stability behaviour concerning the scalar field. Finally,
other dynamical variables of interest, like the radius, are also calculated. In
this regard, it is shown that the radius corresponding to the maximal boson
star mass remains roughly the same during cosmological evolution.


title: Black Holes and Strings: the Polymer Link

abstract:
  Quantum aspects of black holes represent an important testing ground for a
theory of quantum gravity. The recent success of string theory in reproducing
the Bekenstein-Hawking black hole entropy formula provides a link between
general relativity and quantum mechanics via thermodynamics and statistical
mechanics. Here we speculate on the existence of new and unexpected links
between black holes and polymers and other soft-matter systems.


title: Particles As Bound States In Their Own Potentials

abstract:
  I consider the problem of computing the mass of a charged, gravitating
particle in quantum field theory. It is shown how solving for the first
quantized propagator of a particle in the presence of its own potentials
reproduces the gauge and general coordinate invariant sum over an infinite
class of diagrams. The distinguishing feature of this class of diagrams is that
all closed loops contain part of the continuous matter line running from early
to late times. The next order term would have one closed loop external to the
continuous matter line, and so on. I argue that the gravitational potentials in
the 0-th order term may permit the formation of bound states, which would then
dominate the propagator. It is conceivable that this provides an tractable
technique for computing the masses of fundamental particles from first
principles. It is also conceivable that the expansion in external loops permits
gravity to regulate certain ultraviolet divergences.


title: Does loop quantum gravity imply Lambda=0?

abstract:
  We suggest that in a recently proposed framework for quantum gravity, where
Vassiliev invariants span the the space of states, the latter is dramatically
reduced if one has a non-vanishing cosmological constant. This naturally
suggests that the initial state of the universe should have been one with
$\Lambda=0$.


title: Rotating traversable wormholes

abstract:
  The general form of a stationary, axially symmetric traversable wormhole is
discussed. This provides an explicit class of rotating wormholes that
generalize the static, spherically symmetric ones first considered by Morris
and Thorne. In agreement with general analyses, it is verified that such a
wormhole generically violates the null energy condition at the throat. However,
for suitable model wormholes, there can be classes of geodesics falling through
it which do not encounter any energy-condition-violating matter. The possible
presence of an ergoregion surrounding the throat is also noted.


title:
Topological Appearance of Event Horizon: What Is the Topology of the
  Event Horizon That We Can See?

abstract:
  The topology of the event horizon (TOEH) is usually believed to be a sphere.
Nevertheless, some numerical simulations of gravitational collapse with a
toroidal event horizon or the collision of event horizons are reported.
Considering the indifferentiability of the event horizon (EH), we see that such
non-trivial TOEHs are caused by the set of endpoints (the crease set) of the
EH. The two-dimensional (one-dimensional) crease set is related to the toroidal
EH (the coalescence of the EH). Furthermore, examining the stability of the
structure of the endpoints, it becomes clear that the spherical TOEH is
unstable under linear perturbation. On the other hand, a discussion based on
catastrophe theory reveals that the TOEH with handles is stable and generic.
Also, the relation between the TOEH and the hoop conjecture is discussed. It is
shown that the Kastor-Traschen solution is regarded as a good example of the
hoop conjecture by the discussion of its TOEH. We further conjecture that a
non-trivial TOEH can be smoothed out by rough observation in its mass scale.


title: On the Spectrum of the Radiation from a Naked Singularitry

abstract:
  In the final stages of collapse, quantum radiation due to particle creation
from a naked singularity is expected to be significantly different from black
hole radiation. In certain models of collapse it has been shown that,
neglecting the back reaction of spacetime, the particle flux on future null
infinity grows as the inverse square of the distance from the Cauchy horizon.
This is to be contrasted with the flux of radiation from a black hole, which
approaches a constant (inversely proportional to the square of its mass) in the
neighborhood of its event horizon. The spectrum of black hole radiation is
identical to that of a black body at temperature $T = (8\pi M)^{-1}$. We derive
the radiation spectrum for a naked singularity formed in the collapse of a
marginally bound inhomogeneous dust cloud and show that the spectrum is not
black body and admits no simple interpretation.


title: Testable Consequences of Curved-Spacetime Renormalization

abstract:
  I consider certain renormalization effects in curved spacetime quantum field
theory. In the very early universe these effects resemble those of a
cosmological constant, while in the present universe they give rise to a
significant finite renormalization of the gravitational constant. The relevant
renormalization term and its relation to elementary particle masses was first
found by Parker and Toms in 1985, as a consequence of the ``new partially
summed form'' of the propagator in curved spacetime. The significance of the
term is based on the contribution of massive particles to the vacuum. In the
present universe, this renormalization term appears to account for a large part
or even all of the Newtonian gravitational constant. This conjecture is
testable because it relates the value of Newton's constant to the elementary
particle masses.


title:
Formulation for the internal motion of quasi-equilibrium configurations
  in general relativity

abstract:
  We present a formulation for the internal motion of equilibrium
configurations with a rotational Killing vector in general relativity. As an
approximation, this formulation is applicable to investigation of the internal
motion of quasi-equilibrium configurations such as binary neutron stars. Based
on this simple formulation, a condition for the general relativistic counter
rotation has been obtained, though in the recent work by Bonazzola, Gourgoulhon
and Marck, their condition for the counter rotation is not enough to specify
the internal velocity field. Under the condition given in this paper, the
internal velocity field can be determined completely. Indeed, in the
counter-rotating case, we have also derived Poisson equations for the internal
velocity, which take tractable forms in numerical implementation.


title: On Quantization of Black Holes

abstract:
  A simple argument is presented in favour of the equidistant spectrum in
semiclassical limit for the horizon area of a black hole. The following
quantization rules for the mass $M_N$ and horizon area $A_{Nj}$ are proposed:
M_N = m_p [N(N+1)]^{1/4}; A_{Nj} = 8\pi l_p^2 [\sqrt{N(N+1)} + \sqrt{N(N+1) -
j(j+1)} ]. Here both $N$ and $j$ are nonnegative integers or half-integers.


title: Curvature invariants in type N spacetimes

abstract:
  Scalar curvature invariants are studied in type N solutions of vacuum
Einstein's equations with in general non-vanishing cosmological constant
Lambda. Zero-order invariants which include only the metric and Weyl (Riemann)
tensor either vanish, or are constants depending on Lambda. Even all
higher-order invariants containing covariant derivatives of the Weyl (Riemann)
tensor are shown to be trivial if a type N spacetime admits a non-expanding and
non-twisting null geodesic congruence.
  However, in the case of expanding type N spacetimes we discover a
non-vanishing scalar invariant which is quartic in the second derivatives of
the Riemann tensor.
  We use this invariant to demonstrate that both linearized and the third order
type N twisting solutions recently discussed in literature contain
singularities at large distances and thus cannot describe radiation fields
outside bounded sources.


title: Past and Future of Cosmic Topology

abstract:
  In the first part I set out some unexplored historical material about the
early development of cosmic topology. In the second part I briefly comment new
developments in the field since the Lachieze-Rey & Luminet report (1995), both
from a theoretical and an observational point of view.


title:
ADM and Bondi four-momenta for the ultrarelativistic Schwarzschild black
  hole

abstract:
  We argue that it is possible to assign Bondi as well as ADM four-momentum to
the ultrarelativistic limit of the Schwarzschild black hole in agreement to
what is expected on physical grounds: The Bondi-momentum is lightlike and equal
to the ADM-momentum up to the retarded time when particle and radiation escape
to infinity and drops to zero thereafter, leaving flat space behind.


title:
On Measuring Gravitomagnetism via Spaceborne Clocks: A Gravitomagnetic
  Clock Effect

abstract:
  The difference in the proper azimuthal periods of revolution of two standard
clocks in direct and retrograde orbits about a central rotating mass is
proportional to J/Mc^2, where J and M are, respectively, the proper angular
momentum and mass of the source. In connection with this gravitomagnetic clock
effect, we explore the possibility of using spaceborne standard clocks for
detecting the gravitomagnetic field of the Earth. It is shown that this
approach to the measurement of the gravitomagnetic field is, in a certain
sense, theoretically equivalent to the Gravity Probe-B concept.


title: Einstein's equation and geometric asymptotics

abstract:
  The intimate relations between Einstein's equation, conformal geometry,
geometric asymptotics, and the idea of an isolated system in general relativity
have been pointed out by Penrose many years ago. A detailed analysis of the
interplay of conformal geometry with Einstein's equation allowed us to deduce
from the conformal properties of the field equations a method to derive under
various assumptions definite statements about the feasibility of the idea of
geometric asymptotics.
  More recent investigations have demonstrated the possibility to analyse the
most delicate problem of the subject -- the behaviour of asymptotically flat
solutions to Einstein's equation in the region where ``null infinity meets
space-like infinity'' -- to an arbitrary precision. Moreover, we see now that
the, initially quite abstract, analysis yields methods for dealing with
practical issues. Numerical calculations of complete space-times in finite
grids without cut-offs become feasible now. Finally, already at this stage it
is seen that the completion of these investigations will lead to a
clarification and deeper understanding of the idea of an isolated system in
Einstein's theory of gravitation. In the following I wish to give a survey of
the circle of ideas outlined above, emphasizing the interdependence of the
structures and the naturalness of the concepts involved.


title:
Relation between the guessed and the derived super-Hamiltonians for
  spherically symmetric shells

abstract:
  The Hamiltonian dynamics of spherically symmetric massive thin shells in the
general relativity is studied. Two different constraint dynamical systems
representing this dynamics have been described recently; the relation of these
two systems is investigated. The symmetry groups of both systems are found. New
variables are used, which among other things simplify the complicated system a
great deal. The systems are reduced to presymplectic manifolds Gamma_1 and
Gamma_2, lest non-physical aspects like gauge fixings or embeddings in extended
phase spaces complicate the line of reasoning. The following facts are shown.
Gamma_1 is three- and Gamma_2 is five-dimensional; the description of the shell
dynamics by Gamma_1 is incomplete so that some measurable properties of the
shell cannot be predicted. Gamma_1 is locally equivalent to a subsystem of
Gamma_2 and the corresponding local morphisms are not unique, due to the large
symmetry group of Gamma_2. Some consequences for the recent extensions of the
quantum shell dynamics through the singularity are discussed.


title:
A Unique Continuation Result for Klein-Gordon Bisolutions on a
  2-dimensional Cylinder

abstract:
  We prove a novel unique continuation result for weak bisolutions to the
massive Klein-Gordon equation on a 2-dimensional cylinder M. Namely, if such a
bisolution vanishes in a neighbourhood of a `sufficiently large' portion of a
2-dimensional surface lying parallel to the diagonal in the product manifold of
M with itself, then it is (globally) translationally invariant. The proof makes
use of methods drawn from Beurling's theory of interpolation. An application of
our result to quantum field theory on 2-dimensional cylinder spacetimes will
appear elsewhere.


title:
Bisolutions to the Klein-Gordon Equation and Quantum Field Theory on
  2-dimensional Cylinder Spacetimes

abstract:
  We consider 2-dimensional cylinder spacetimes whose metrics differ from the
flat Minkowskian metric within a compact region. By choice of time orientation,
these spacetimes may be regarded as either globally hyperbolic timelike
cylinders or nonglobally hyperbolic spacelike cylinders. For generic metrics in
our class, we classify all possible candidate quantum field algebras for
massive Klein-Gordon theory which obey the F-locality condition introduced by
Kay. This condition requires each point of spacetime to have an intrinsically
globally hyperbolic neighbourhood, N, such that the commutator (in the
candidate algebra) of fields smeared with test functions supported in N agrees
with the value obtained in the usual construction of Klein-Gordon theory on N.
  By considering bisolutions to the Klein-Gordon equation, we prove that
generic timelike cylinders admit a unique F-local algebra -- namely the algebra
obtained by the usual construction -- and that generic spacelike cylinders do
not admit any F-local algebras, and are therefore non F-quantum compatible.
Refined versions of our results are obtained for subclasses of metrics
invariant under a symmetry group. Thus F-local field theory on 2-dimensional
cylinder spacetimes essentially coincides with the usual globally hyperbolic
theory. In particular the result of the author and Higuchi that the Minkowskian
spacelike cylinder admits infinitely many F-local algebras is now seen to
represent an anomalous case.


title: Anti-de Sitter wormhole kink

abstract:
  The metric describing a given finite sector of a four-dimensional
asymptotically anti-de Sitter wormhole can be transformed into the metric of
the time constant sections of a Tangherlini black hole in a five-dimensional
anti-de Sitter spacetime when one allows light cones to tip over on the
hypersurfaces according to the conservation laws of an one-kink. The resulting
kinked metric can be maximally extended, giving then rise to an instantonic
structure on the euclidean continuation of both the Tangherlini time and the
radial coordinate. In the semiclassical regime, this kink is related to the
existence of closed timelike curves.