title: Exotic Smoothness on Spacetime

abstract:
  Recent discoveries in differential topology are reviewed in light of their
possible implications for spacetime models and related subjects in theoretical
physics. Although not often noted, a particular smoothness (differentiability)
structure must be imposed on a topological manifold before geometric or other
structures of physical interest can be discussed. The recent discoveries of
interest here are of various surprising ``exotic'' smoothness structures on
topologically trivial manifolds such as ${S^7}$ and ${\bf R^4}$. Since no two
of these are diffeomorphic to each other, each such manifold represents a
physically distinct model of topologically trivial spacetime. That is, these
are not merely different coordinate representations of a given spacetime. The
path to such structures intertwines many branches of mathematics and
theoretical physics (Yang-Mills and other gauge theories). An overview of these
topics is provided, followed by certain results concerning the geometry and
physics of such manifolds. Although exotic ${\bf R^4}$'s cannot be effectively
exhibited by finite constructions, certain existence and non-existence results
can be stated. For example, it is shown that the ``exoticness'' can be confined
to a time-like world tube, providing a possible model for an exotic source.
Other suggestions and conjectures for future research are made.


title: On cosmic rotation

abstract:
  We overview our recent studies of cosmological models with expansion and
global rotation. Problems of the early rotating models are discussed, and the
class of new viable cosmologies is described in detail. Particular attention is
paid to the observational effects of the cosmic rotation.


title: Cosmic Crystallography

abstract:
  We assume that the Universe has a non trivial topology whose compact spatial
sections have a volume significantly smaller than the horizon volume. By a
topological lens effect, such a "folded" space configuration generates multiple
images of cosmic sources, e.g. clusters of galaxies. We present a simple and
powerful method to unveil non ambiguous observational effects, independently of
the sign of the curvature and of the topological type.


title: The Origin of Black Hole Entropy in String Theory

abstract:
  I review some recent work in which the quantum states of string theory which
are associated with certain black holes have been identified and counted. For
large black holes, the number of states turns out to be precisely the
exponential of the Bekenstein-Hawking entropy. This provides a statistical
origin for black hole thermodynamics in the context of a potential quantum
theory of gravity.


title: Gravitons and Lightcone Fluctuations II: Correlation Functions

abstract:
  A model of a fluctuating lightcone due to a bath of gravitons is further
investigated. The flight times of photons between a source and a detector may
be either longer or shorter than the light propagation time in the background
classical spacetime, and will form a Gaussian distribution centered around the
classical flight time. However, a pair of photons emitted in rapid succession
will tend to have correlated flight times. We derive and discuss a correlation
function which describes this effect. This enables us to understand more fully
the operational significance of a fluctuating lightcone. Our results may be
combined with observational data on pulsar timing to place some constraints on
the quantum state of cosmological gravitons.


title: Ashtekar Constraint Surface as Projection of Hilbert-Palatini One

abstract:
  The Hilbert-Palatini (HP) Lagrangian of general relativity being written in
terms of selfdual and antiselfdual variables contains Ashtekar Lagrangian
(which governs the dynamics of the selfdual sector of the theory on condition
that the dynamics of antiselfdual sector is not fixed). We show that
nonequivalence of the Ashtekar and HP quantum theories is due to the specific
form (of the "loose relation" type) of constraints which relate self- and
antiselfdual variables so that the procedure of (canonical) quantisation of
such the theory is noncommutative with the procedure of excluding antiselfdual
variables.


title: On Newton-Cartan Cosmology

abstract:
  After a brief summary of the Newton-Cartan theory in a form which emphasizes
its close analogy to general relativity, we illustrate the theory with
selective applications in cosmology. The geometrical formulation of this
nonrelativistic theory of gravity, pioneered by Cartan and further developed by
various workers, leads to a conceptually sound basis of Newtonian cosmology. In
our discussion of homogeneous models and cosmological perturbation theory, we
stress the close relationship with their general relativistic treatments.
Spatially compact flat models also fit into this framework.


title: Conserved masses in GHS Einstein and string black holes

abstract:
  We analyze the relationship between quasilocal masses calculated for
solutions of conformally related theories. We show that the ADM mass of a
static, spherically symmetric solution is conformally invariant (up to a
constant factor) only if the background action functional is conformally
invariant. Thus, the requirement of conformal invariance places restrictions on
the choice of reference spacetimes. We calculate the mass of the black hole
solutions obtained by Garfinkle, Horowitz, and Strominger (GHS) for both the
string and the Einstein metrics. In addition, the quasilocal thermodynamic
quantities in the string metrics are computed and discussed.


title: Dynamics of compact homogeneous universes

abstract:
  A complete description of dynamics of compact locally homogeneous universes
is given, which, in particular, includes explicit calculations of Teichm\"uller
deformations and careful counting of dynamical degrees of freedom. We regard
each of the universes as a simply connected four dimensional spacetime with
identifications by the action of a discrete subgroup of the isometry group. We
then reduce the identifications defined by the spacetime isometries to ones in
a homogeneous section, and find a condition that such spatial identifications
must satisfy. This is essential for explicit construction of compact
homogenoeus universes. Some examples are demonstrated for Bianchi II, VI${}_0$,
VII${}_0$, and I universal covers.


title: Volterra Distortions, Spinning Strings, and Cosmic Defects

abstract:
  Cosmic strings, as topological spacetime defects, show striking resemblance
to defects in solid continua: distortions, which can be classified into
disclinations and dislocations, are line-like defects characterized by a delta
function-valued curvature and torsion distribution giving rise to rotational
and translational holonomy. We exploit this analogy and investigate how
distortions can be adapted in a systematic manner from solid state systems to
Einstein-Cartan gravity. As distortions are efficiently described within the
framework of a $SO(3) {\rlap{$\supset$}\times}} T(3)$ gauge theory of solid
continua with line defects, we are led in a straightforward way to a Poincar\'e
gauge approach to gravity which is a natural framework for introducing the
notion of distorted spacetimes. Constructing all ten possible distorted
spacetimes, we recover, inter alia, the well-known exterior spacetime of a
spin-polarized cosmic string as a special case of such a geometry. In a second
step, we search for matter distributions which, in Einstein-Cartan gravity, act
as sources of distorted spacetimes. The resulting solutions, appropriately
matched to the distorted vacua, are cylindrically symmetric and are interpreted
as spin-polarized cosmic strings and cosmic dislocations.


title: Quantum Gravity and Turning Points in the Semiclassical Approximation

abstract:
  The wavefunctional in quantum gravity gives an amplitude for 3-geometries and
matter fields. The four-space is usually recovered in a semiclassical
approximation where the gravity variables are taken to oscillate rapidly
compared to matter variables; this recovers the Schrodinger evolution for the
matter. We examine turning points in the gravity variables where this
approximation appears to be troublesome. We investigate the effect of such a
turning point on the matter wavefunction, in simple quantum mechanical models
and in a closed minisuperspace cosmology. We find that after evolving
sufficiently far from the turning point the matter wavefunction recovers to a
form close to that predicted by the semiclassical approximation, and we compute
the leading correction (from `backreaction') in a simple model. We also show
how turning points can appear in the gravitational sector in dilaton gravity.
We give some remarks on the behavior of the wavefunctional in the vicinity of
turning points in the context of dilaton gravity black holes.


title: Extracting Gravitational Energy From The Homogeneous Isotropic Universe

abstract:
  The kinetic energy of a local system of objects placed in a curved spacetime
is gained by the subsequent acceleration of the object following the more
contracted region of spacetime. Normally this happens near massive gravitating
stars. However, the gravitational dipole moment has been shown to be capable of
self creating asymmetrically distorted spacetime in its vicinity, therby,
capable of being accelerated indefinitely following the successive self created
loophole of the spacetime. Localization of this kinetic energy may be possible
by designing a system that uses the artificially created gavitational dipole
moments to rotate the main axis. A mechanical constraint is derived for the
extraction of unlimited gravitational energy from such system.


title:
Isothermal spherical perfect fluid model: Uniqueness and Conformal
  mapping

abstract:
  We prove the theorem: The necessary and sufficient condition for a
spherically symmetric spacetime to represent an isothermal perfect fluid
(barotropic equation of state with density falling off as inverse square of the
curvature radius) distribution without boundary is that it is conformal to the
``minimally'' curved (gravitation only manifesting in tidal acceleration and
being absent in particle trajectory) spacetime.


title: A Conformal Mapping and Isothermal Perfect Fluid Model

abstract:
  Instead of conformal to flat spacetime, we take the metric conformal to a
spacetime which can be thought of as ``minimally'' curved in the sense that
free particles experience no gravitational force yet it has non-zero curvature.
The base spacetime can be written in the Kerr-Schild form in spherical polar
coordinates. The conformal metric then admits the unique three parameter family
of perfect fluid solution which is static and inhomogeneous. The density and
pressure fall off in the curvature radial coordinates as $R^{-2}, $ for
unbounded cosmological model with a barotropic equation of state. This is the
characteristic of isothermal fluid. We thus have an ansatz for isothermal
perfect fluid model. The solution can also represent bounded fluid spheres.


title: Canonical reduction of two-dimensional gravity for Particle Dynamics

abstract:
  We develop the formalism for canonical reduction of $(1+1)$--dimensional
gravity coupled with a set of point particles by eliminating constraints and
imposing coordinate conditions. The formalism itself is quite analogous to the
$(3+1)$--dimensional case; however in $(1+1)$ dimensions an auxiliary scalar
field is shown to have an important role. The reduced Hamiltonian is expressed
as a form of spatial integral of the second derivative of the scalar field.
Since in $(1+1)$ dimensions there exists no dynamical degree of freedom of the
gravitational field ({\it i.e.} the transverse-traceless part of the metric
tensor is zero), the reduced Hamiltonian is completely determined in terms of
the particles' canonical variables (coordinates and momenta). The explicit form
of the Hamiltonian is calculated both in post-linear and post-Newtonian
approximations.


title:
First-order symmetric-hyperbolic Einstein equations with arbitrary fixed
  gauge

abstract:
  We find a one-parameter family of variables which recast the 3+1 Einstein
equations into first-order symmetric-hyperbolic form for any fixed choice of
gauge. Hyperbolicity considerations lead us to a redefinition of the lapse in
terms of an arbitrary factor times a power of the determinant of the 3-metric;
under certain assumptions, the exponent can be chosen arbitrarily, but
positive, with no implication of gauge-fixing.


title:
Integration in the GHP formalism II: An operator approach for spacetimes
  with killing vectors, with applications to twisting type n spaces

abstract:
  Held has proposed a coordinate- and gauge-free integration procedure within
the GHP formalism built around four functionally independent zero-weighted
scalars constructed from the spin coefficients and the Riemann tensor
components. Unfortunately, a spacetime with Killing vectors will be unable to
supply the full quota of four scalars of this type. However, for such a
spacetime additional scalars are supplied by the components of the Killing
vectors; by using these alongside the spin coefficients and the Riemann tensor
components we have the possibility of constructing the full quota of four
functionally independent zero-weighted scalars, and of exploiting Held's
procedure.
  As an illustration we investigate the vacuum Type N spaces admitting a
Killing vector and a homothetic Killing vector. In a direct manner, we reduce
the problem to a pair of ordinary differential operator `master equations',
making use of a new zero-weighted GHP operator. By first rewriting the master
equations as a closed set of complex first order equations, we reduce the
problem to one real third order operator differential equation for a complex
function of a real variable --- but with still the freedom to choose explicitly
our fourth coordinate. An alternative, more algorithmic approach, using a
closed chain of real first order equations for real functions, reduces the
problem to the same order, but in a more natural and much more concise form. It
is also outlined how the various other third order differential equations,
which have been derived previously by other workers on this problem, can be
deduced from our master equations.


title:
Quantum fields interacting with colliding plane waves: the stress-energy
  tensor and backreaction

abstract:
  Following a previous work on the quantization of a massless scalar field in a
spacetime representing the head on collision of two plane waves which fucus
into a Killing-Cauchy horizon, we compute the renormalized expectation value of
the stress-energy tensor of the quantum field near that horizon in the physical
state which corresponds to the Minkowski vacuum before the collision of the
waves. It is found that for minimally coupled and conformally coupled scalar
fields the respective stress-energy tensors are unbounded in the horizon. The
specific form of the divergences suggests that when the semiclassical Einstein
equations describing the backreaction of the quantum fields on the spacetime
geometry are taken into account, the horizon will acquire a curvature
singularity. Thus the Killing-Cauchy horizon which is known to be unstable
under ``generic" classical perturbations is also unstable by vacuum
polarization. The calculation is done following the point splitting
regularization technique. The dynamical colliding wave spacetime has four quite
distinct spacetime regions, namely, one flat region, two single plane wave
regions, and one interaction region. Exact mode solutions of the quantum field
equation cannot be found exactly, but the blueshift suffered by the initial
modes in the plane wave and interaction regions makes the use of the WKB
expansion a suitable method of solution. To ensure the correct regularization
of the stress-energy tensor, the initial flat modes propagated into the
interaction region must be given to a rather high adiabatic order of
approximation.


title: Self-Similar Collapse in Brans-Dicke Theory and Critical Behavior

abstract:
  We use the technique of conformal transformations to generate self-similar
collapse in Brans-Dicke theory. We analyze the solutions concerning the
critical behavior found recently by Choptuik. The critical exponent associated
to the formation of black hole for near critical evolution is obtained. The
role of the coupling parameter is discussed.


title: Rindler and Minkowski particles relationship revisited

abstract:
  We show that the emission of a Minkowski particle by a general class of
scalar sources as described by inertial observers corresponds to either the
emission or the absorption of a Rindler particle as described by uniformly
accelerated observers. Our results are discussed in connection with the current
controversy whether uniformly accelerated detectors radiate.


title: Cosmic Topology

abstract:
  General relativity does not allow one to specify the topology of space,
leaving the possibility that space is multi-- rather than simply--connected. We
review the main mathematical properties of multi--connected spaces, and the
different tools to classify them and to analyse their properties. Following the
mathematical classification, we describe the different possible muticonnected
spaces which may be used to construct universe models. We briefly discuss some
implications of multi--connectedness for quantum cosmology, and its
consequences concerning quantum field theory in the early universe. We consider
in details the properties of the cosmological models where space is
multi--connected, with emphasis towards observable effects. We then review the
analyses of observational results obtained in this context, to search for a
possible signature of multi--connectedness, or to constrain the models. They
may concern the distribution of images of cosmic objects like galaxies,
clusters, quasars,..., or more global effects, mainly those concerning the
Cosmic Microwave Background, and the present limits resulting from them.


title: Consistently Implementing the Fields Self-Energy in Newtonian Gravity

abstract:
  We consider in a pedagogical fashion alterations to Newtonian gravity due to
the postulate that all energy corresponds to active gravitational mass when
applied to the self-energy of the gravitational field. We show why a simple
addition of ${1\over c^2}$ times the gravitational field energy to the matter
density in Newton's field equation is inconsistent. A consistent prescription
is shown and discussed. The connection to general relativity is pointed out.


title:
Classical solutions in five dimensional induced matter theory and its
  relation to an imperfect fluid

abstract:
  We study five dimensional cosmological models with four dimensional
hypersufaces of the Bianchi type I and V. In this way the five dimensional
vacuum field equations $\rm G_{AB} = 0$, led us to four dimensional matter
equations $\rm G_{\mu\nu}=T_{\mu\nu}$ and the matter is interpreted as a purely
geometrical property of a fifth dimension. Also, we find that the
energy-momentum tensor induced from the fifth dimension has the structure of an
imperfect fluid that has dissipative terms.


title:
Post-Relativistic Gravity - A Hidden Variable Theory For General
  Relativity

abstract:
  Post-relativistic gravity is a hidden variable theory for general relativity.
It introduces the pre-relativistic notions absolute space, absolute time, and
ether as hidden variables into general relativity. Evolution is defined by the
equations of general relativity and the harmonic coordinate condition
interpreted as a physical equation. There are minor differences in predictions
compared with general relativity (i.e. trivial topology of the universe is
predicted).
  The unobservable absolute time is designed to solve the problem of time in
quantization of general relativity. Background space and time define a
Newtonian frame for the quantization of the gravitational field. By the way, a
lot of other conceptual problems of quantization will be solved (i.e. no
constraints, no topological foam, no black hole and bib bang singularities,
natural vacuum definition for quantum fields on classical background).


title: Geometrical Hyperbolic Systems for General Relativity and Gauge Theories

abstract:
  The evolution equations of Einstein's theory and of Maxwell's theory---the
latter used as a simple model to illustrate the former--- are written in gauge
covariant first order symmetric hyperbolic form with only physically natural
characteristic directions and speeds for the dynamical variables. Quantities
representing gauge degrees of freedom [the spatial shift vector
$\beta^{i}(t,x^{j})$ and the spatial scalar potential $\phi(t,x^{j})$,
respectively] are not among the dynamical variables: the gauge and the physical
quantities in the evolution equations are effectively decoupled. For example,
the gauge quantities could be obtained as functions of $(t,x^{j})$ from
subsidiary equations that are not part of the evolution equations. Propagation
of certain (``radiative'') dynamical variables along the physical light cone is
gauge invariant while the remaining dynamical variables are dragged along the
axes orthogonal to the spacelike time slices by the propagating variables. We
obtain these results by $(1)$ taking a further time derivative of the equation
of motion of the canonical momentum, and $(2)$ adding a covariant spatial
derivative of the momentum constraints of general relativity (Lagrange
multiplier $\beta^{i}$) or of the Gauss's law constraint of electromagnetism
(Lagrange multiplier $\phi$). General relativity also requires a harmonic time
slicing condition or a specific generalization of it that brings in the
Hamiltonian constraint when we pass to first order symmetric form. The
dynamically propagating gravity fields straightforwardly determine the
``electric'' or ``tidal'' parts of the Riemann tensor.


title:
String dynamics in cosmological and black hole backgrounds: The null
  string expansion

abstract:
  We study the classical dynamics of a bosonic string in the $D$--dimensional
flat Friedmann--Robertson--Walker and Schwarzschild backgrounds. We make a
perturbative development in the string coordinates around a {\it null} string
configuration; the background geometry is taken into account exactly. In the
cosmological case we uncouple and solve the first order fluctuations; the
string time evolution with the conformal gauge world-sheet $\tau$--coordinate
is given by $X^0(\sigma, \tau)=q(\sigma)\tau^{1\over1+2\beta}+c^2B^0(\sigma,
\tau)+\cdots$, $B^0(\sigma,\tau)=\sum_k b_k(\sigma)\tau^k$ where $b_k(\sigma)$
are given by Eqs.\ (3.15), and $\beta$ is the exponent of the conformal factor
in the Friedmann--Robertson--Walker metric, i.e. $R\sim\eta^\beta$. The string
proper size, at first order in the fluctuations, grows like the conformal
factor $R(\eta)$ and the string energy--momentum tensor corresponds to that of
a null fluid. For a string in the black hole background, we study the planar
case, but keep the dimensionality of the spacetime $D$ generic. In the null
string expansion, the radial, azimuthal, and time coordinates $(r,\phi,t)$ are
$r=\sum_n A^1_{n}(\sigma)(-\tau)^{2n/(D+1)}~,$ $\phi=\sum_n
A^3_{n}(\sigma)(-\tau)^{(D-5+2n)/(D+1)}~,$ and $t=\sum_n A^0_{n}
(\sigma)(-\tau)^{1+2n(D-3)/(D+1)}~.$ The first terms of the series represent a
{\it generic} approach to the Schwarzschild singularity at $r=0$. First and
higher order string perturbations contribute with higher powers of $\tau$. The
integrated string energy-momentum tensor corresponds to that of a null fluid in
$D-1$ dimensions. As the string approaches the $r=0$ singularity its proper
size grows indefinitely like $\sim(-\tau)^{-(D-3)/(D+1)}$. We end the paper
giving three particular exact string solutions inside the black hole.


title: Dynamical Constraints in the Nonsymmetric Gravitational Theory

abstract:
  We impose in the nonsymmetric gravitational theory, by means of Lagrange
multiplier fields in the action, a set of covariant constraints on the
antisymmetric tensor field. The canonical Hamiltonian constraints in the weak
field approximation for the antisymmetric sector yield a Hamiltonian energy
bounded from below. An analysis of the Cauchy evolution, in terms of an
expansion of the antisymmetric sector about a symmetric Einstein background,
shows that arbitrarily small antisymmetric Cauchy data can lead to smooth
evolution.


title:
Inflationary and Deflationary Branches in Extended Pre--Big Bang
  Cosmology

abstract:
  The pre--big bang cosmological scenario is studied within the context of the
Brans--Dicke theory of gravity. An epoch of superinflationary expansion may
occur in the pre--big bang phase of the Universe's history in a certain region
of parameter space. Two models are considered that contain a cosmological
constant in the gravitational and matter sectors of the theory, respectively.
Classical pre-- and post--big bang solutions are found for both models. The
existence of a curvature singularity forbids a classical transition between the
two branches. On the other hand, a quantum cosmological approach based on the
tunneling boundary condition results in a non--zero transition probability. The
transition may be interpreted as a spatial reflection of the wavefunction in
minisuperspace.


title: Pregeometric modelling of the spacetime phenomenology

abstract:
  At present we have only the very successful but phenomenological Einstein
geometrical modelling of the spacetime phenomenon. This geometrical model
provides a `container' for other theories, in particular the quantum field
theories. Here we report progress in developing a {\em Heraclitean Quantum
System}. This is a particular pregeometric theory for space and time in which
no classical or geometric structures are assumed, but rather the emergence of
such phenomena is sought.


title: On the interpretation of quantum cosmology

abstract:
  We formulate a ''minimal'' interpretational scheme for fairly general
(minisuperspace) quantum cosmological models. Admitting as few exact
mathematical structure as is reasonably possible at the fundamental level, we
apply approximate WKB-techniques locally in minisuperspace in order to make
contact with the realm of predictions, and propose how to deal with the
problems of mode decomposition and almost-classicality without introducing
further principles. In order to emphasize the general nature of approximate
local quantum mechanical structures, we modify the standard WKB-expansion
method so as to rely on exact congruences of classical paths, rather than a
division of variables into classical and quantum. The only exact mathematical
structures our interpretation needs are the space of solutions of the
Wheeler-DeWitt equation and the Klein-Gordon type indefinite scalar product.
The latter boils down to plus or minus the ordinary quantum mechanical scalar
product in the local quantum structures. According to our approach all further
structures, in particular the concepts encountered in conventional physics,
such as observables, time and unitarity, are approximate. Our interpretation
coincides to some extent with the standard WKB-oriented view, but the way in
which the conventional concepts emerge, and the accuracy at which they are
defined at all, are more transparent. A simpler book-keeping of normalization
issues is automatically achieved. Applying our scheme to the Hawking model, we
find hints that the no-boundary wave function predicts a cosmic catastrophe
with some non-zero probability.


title: Time Gauge Fixing and Hilbert Space in Quantum String Cosmology

abstract:
  Recently the low-energy effective string theory has been used by Gasperini
and Veneziano to elaborate a very interesting scenario for the early history of
the universe (``birth of the universe as quantum scattering''). Here we
investigate the gauge fixing and the problem of the definition of a global time
parameter for this model, and we obtain the positive norm Hilbert space of
states.


title: Quantum cosmology in the energy representation

abstract:
  The Hawking minisuperspace model (closed FRW geometry with a homogeneous
massive scalar field) provides a fairly non-trivial testing ground for
fundamental problems in quantum cosmology. We provide evidence that the
Wheeler-DeWitt equation admits a basis of solutions that is distinguished by
analyticity properities in a large scale factor expansion. As a consequence,
the space of solutions decomposes in a preferred way into two Hilbert spaces
with positive and negative definite scalar product, respectively. These results
may be viewed as a hint for a deeper significance of analyticity. If a similar
structure exists in full (non-minisuperspace) models as well, severe
implications on the foundations of quantum cosmology are to be expected.
Semiclassically, the elements of the preferred basis describe contracting and
expanding universes with a prescribed value of the matter (scalar field)
energy. Half of the basis elements have previously been constructed by Hawking
and Page in a wormhole context, and they appear in a new light here. The
technical tools to arrive at these conclusions are transformations of the wave
function into several alternative representations that are based on the
harmonic oscillator form of the matter energy operator, and that are called
oscillator, energy and Fock representation. The framework defined by these may
be of some help in analyzing the Wheeler-DeWitt equation for other purposes as
well.


title:
Existence of constant mean curvature foliations in spacetimes with
  two-dimensional local symmetry

abstract:
  It is shown that in a class of maximal globally hyperbolic spacetimes
admitting two local Killing vectors, the past (defined with respect to an
appropriate time orientation) of any compact constant mean curvature
hypersurface can be covered by a foliation of compact constant mean curvature
hypersurfaces. Moreover, the mean curvature of the leaves of this foliation
takes on arbitrarily negative values and so the initial singularity in these
spacetimes is a crushing singularity. The simplest examples occur when the
spatial topology is that of a torus, with the standard global Killing vectors,
but more exotic topologies are also covered. In the course of the proof it is
shown that in this class of spacetimes a kind of positive mass theorem holds.
The symmetry singles out a compact surface passing through any given point of
spacetime and the Hawking mass of any such surface is non-negative. If the
Hawking mass of any one of these surfaces is zero then the entire spacetime is
flat.


title:
Higher Dimensional Self-similar Spherical Symmetric Scalar Field
  Collapse and Critical Phenomena in Black Hole Formation

abstract:
  The higher dimensional spherical symmetric scalar field collapse problem is
studied in the light of the critical behavior in black hole formation. To make
the analysis tractable, the self similarity is also imposed. By giving a new
view to the self-similar scalar field collapse problem, we give the general
formula for the critical exponents in higher dimensions. In the process, the
explanation of the universality of the critical phenomena is given within the
self-similar context.


title: Evolution of Structures in Generalized Gravity Theories

abstract:
  A broad class of generalized Einstein's gravity can be cast into Einstein's
gravity with a minimally coupled scalar field using suitable conformal
rescaling of the metric. Using this conformal equivalence between the theories,
we derive the equations for the background and the perturbations, and the
general asymptotic solutions for the perturbations in the generalized
Einstein's gravity from the simple results known in the minimally coupled
scalar field. Results for the scalar and tensor perturbations can be presented
in unified forms. The large scale evolutions for both modes are characterized
by corresponding conserved quantities. We also present the normalization
condition for canonical quantization.


title: Some remarks on singularities in quantum cosmology

abstract:
  We discuss to what extent classical singularities persist upon quantization
in two simple cosmological models.


title:
The Principle of Non-Gravitating Vacuum Energy and some of its
  consequences

abstract:
  For Einstein's General Relativity (GR) or the alternatives suggested up to
date the vacuum energy gravitates. We present a model where a new measure is
introduced for integration of the total action in the D-dimensional space-time.
This measure is built from D scalar fields $\varphi_{a}$. As a consequence of
such a choice of the measure, the matter lagrangian $L_{m}$ can be changed by
adding a constant while no gravitational effects, like a cosmological term, are
induced. Such Non-Gravitating Vacuum Energy (NGVE) theory has an infinite
dimensional symmetry group which contains volume-preserving diffeomorphisms in
the internal space of scalar fields $\varphi_{a}$. Other symmetries contained
in this symmetry group, suggest a deep connection of this theory with theories
of extended objects. In general {\em the theory is different from GR} although
for certain choices of $L_{m}$, which are related to the existence of an
additional symmetry, solutions of GR are solutions of the model. This is
achieved in four dimensions if $L_{m}$ is due to fundamental bosonic and
fermionic strings. Other types of matter where this feature of the theory is
realized, are for example: scalars without potential or subjected to nonlinear
constraints, massless fermions and point particles. The point particle plays a
special role, since it is a good phenomenological description of matter at
large distances. de Sitter space is realized in an unconventional way, where
the de Sitter metric holds, but such de Sitter space is supported by the
existence of a variable scalar field which in practice destroys the maximal
symmetry. The only space - time where maximal symmetry is not broken, in a
dynamical sense, is Minkowski space. The theory has non trivial dynamics in 1+1
dimensions, unlike GR.


title: Workshop on gravitational waves

abstract:
  In this article we summarise the proceedings of the Workshop on Gravitational
Waves held during ICGC-95. In the first part we present the discussions on 3PN
calculations (L. Blanchet, P. Jaranowski), black hole perturbation theory (M.
Sasaki, J. Pullin), numerical relativity (E. Seidel), data analysis (B.S.
Sathyaprakash), detection of gravitational waves from pulsars (S. Dhurandhar),
and the limit on rotation of relativistic stars (J. Friedman). In the second
part we briefly discuss the contributed papers which were mainly on detectors
and detection techniques of gravitational waves.


title: Autoparallels From a New Action Principle

abstract:
  We present a simpler and more powerful version of the recently-discovered
action principle for the motion of a spinless point particle in spacetimes with
curvature and torsion. The surprising feature of the new principle is that an
action involving only the metric can produce an equation of motion with a
torsion force, thus changing geodesics to autoparallels. This additional
torsion force arises from a noncommutativity of variations with parameter
derivatives of the paths due to the closure failure of parallelograms in the
presence of torsion


title: The mixmaster universe is chaotic

abstract:
  For the past decade there has been a considerable debate about the existence
of chaos in the mixmaster cosmological model. The debate has been hampered by
the coordinate, or observer dependence of standard chaotic indicators such as
Lyapanov exponents. Here we use coordinate independent, fractal methods to show
the mixmaster universe is indeed chaotic.


title: Bremsstrahlung by static charges outside a static black hole ?

abstract:
  We show that in complete analogy with the usual bremsstrahlung process, when
studied from the coaccelerated observer's point of view, a charge moving along
the integral curves of the static Killing field in the exterior of a static
black hole gives rise to the emission of zero-energy photons, induced by the
thermal bath of Hawking Radiation.


title:
On the Ionization of a Keplerian Binary System by Periodic Gravitational
  Radiation

abstract:
  The gravitational ionization of a Keplerian binary system via normally
incident periodic gravitational radiation of definite helicity is discussed.
The periodic orbits of the planar tidal equation are investigated on the basis
of degenerate continuation theory. The relevance of the Kolmogorov-Arnold-Moser
theory to the question of gravitational ionization is elucidated, and it is
conjectured that the process of ionization is closely related to the Arnold
diffusion of the perturbed system.


title:
On the Estimates to Measure Hawking Effect and Unruh Effect in the
  Laboratory

abstract:
  A comparison between the proposals made to measure Hawking-like effects and
the Unruh effect in the laboratory is given at the level of their estimates. No
satisfactory scheme exists as yet for their detection.


title: Naked strong curvature singularities in Szekeres space-times

abstract:
  We investigate the occurrence and nature of naked singularities in the
Szekeres space-times. These space-times represent irrotational dust. They do
not have any Killing vectors and they are generalisations of the
Tolman-Bondi-Lemaitre space-times. It is shown that in these space-times there
exist naked singularities that satisfy both the limiting focusing condition and
the strong limiting focusing condition. The implications of this result for the
cosmic censorship hypothesis are discussed.


title:
`` Rerum Universitas Sententia ex Susy'' (A View of the Universe
  according to Supersymmetry)

abstract:
  The question if conserved currents can be sensibly defined in supersymmetric
minisuperspaces is investigated in this essay. The objective is to employ
exclusively the differential equations obtained {\em directly} from the Lorentz
and supersymmetry quantum constraints. The ``square-root'' structure of N=1
supergravity is the motivation to contemplate this tempting idea. However, it
is shown that such prospect is not feasible but for some very simple scenarios.
Otherwise, conserved currents (and consistent probability densities) can be
derived from subsequent Wheeler-DeWitt like equations obtained from the
supersymmetric algebra of constraints.


title:
Exact quantum states for the diagonal Bianchi type IX model with
  negative cosmological constant

abstract:
  Quantum states of the diagonal Bianchi type IX model with negative
cosmological constant $\Lambda$ are obtained by transforming the Chern-Simons
solution in Ashtekar's variables to the metric representation. We apply our
method developed earlier for $\Lambda>0$ and obtain five linearly independent
solutions by using the complete set of topologically inequivalent integration
contours in the required generalized Fourier-transformation. A caustic in
minisuperspace separates two Euclidean regimes at small and large values of the
scale parameter from a single classically interpretable Lorentzian regime in
between, corresponding to the fact that classically these model-Universes
recollapse. Just one particular solution out of the five we find gives a
normalizable probability distribution on both branches of the caustic. However,
in contrast to the case of positive cosmological constant, this particular
solution neither satisfies the semi-classical no-boundary condition, nor does
the special initial condition it picks out for $\hbar \to 0$ evolve into a
classically interpretable Universe.


title: Finite Action Yang-Mills Solutions on the Group Manifold

abstract:
  We demonstrate that the left (and right) invariant Maurer-Cartan forms for
any semi-simple Lie group enable one to construct solutions of the Yang-Mills
equations on the group manifold equipped with the natural Cartan-Killing
metric. For the unitary unimodular groups the Yang-Mills action integral is
finite for such solutions. This is explicitly exhibited for the case of
$SU(3)$.


title:
The Construction of Spinor Fields on Manifolds with Smooth Degenerate
  Metrics

abstract:
  We examine some of the subtleties inherent in formulating a theory of spinors
on a manifold with a smooth degenerate metric. We concentrate on the case where
the metric is singular on a hypersurface that partitions the manifold into
Lorentzian and Euclidean domains. We introduce the notion of a complex spinor
fibration to make precise the meaning of continuity of a spinor field and give
an expression for the components of a local spinor connection that is valid in
the absence of a frame of local orthonormal vectors. These considerations
enable one to construct a Dirac equation for the discussion of the behavior of
spinors in the vicinity of the metric degeneracy. We conclude that the theory
contains more freedom than the spacetime Dirac theory and we discuss some of
the implications of this for the continuity of conserved currents.


title:
On the Quantum Levels of Isolated Spherically Symmetric Gravitational
  Systems

abstract:
  The known canonical quantum theory of a spherically symmetric pure
(Schwarzschild) gravitational system describes isolated black holes by plane
waves exp(-iMc^2\tau/\hbar) with respect to their continuous masses M and the
proper time \tau of obsevers at spatial infinity. On the other hand Bekenstein
and Mukhanov postulated discrete mass levels for such black holes in the spirit
of the Bohr-Sommerfeld quantisation in atomic physics. The two approaches can
be related by postulating periodic boundary conditions in time for the plane
waves and by identifying the period \Delta in real time with the period
\Delta_H= 8\pi GM/c^3 in Euclidean time. This yields the mass spectrum
M_n=(1/2)\sqrt{n}m_P, n=1,2,... .


title: Testing the Equivalence Principle in the Quantum Regime

abstract:
  We consider possible tests of the Einstein Equivalence Principle for physical
systems in which quantum-mechanical vacuum energies cannot be neglected.
Specific tests include a search for the manifestation of non-metric effects in
Lamb-shift transitions of Hydrogenic atoms and in anomalous magnetic moments of
massive leptons. We discuss how current experiments already set bounds on the
violation of the equivalence principle in this sector and how new
(high-precision) measurements of these quantities could provide further
information to this end.


title: Superposition of a static perfect fluid and a radial elecric field

abstract:
  We obtain a two-parameter set of solutions, which represents a spherically
symmetric space-time with a superposition of a neutral fluid and an electric
field. The electromagnetic four-potential of this Einstein-Maxwell space-time
is taken in the form A=(q/n)(r^n)dt, when n=/0 and A=q*ln(r)dt, when n=0 (where
q and n are arbitrary constants)


title: Compact hyperbolic universe and singularities

abstract:
  Recently many people have discussed the possibility that the universe is
hyperbolic and was in an inflationary phase in the early stage. Under these
assumptions, it is shown that the universe cannot have compact hyperbolic
time-slices. Though the universal covering space of the universe has a past
Cauchy horizon and can be extended analytically beyond it, the extended region
has densely many points which correspond to singularities of the compact
universe. The result is essentially attributed to the ergodicity of the
geodesic flow on a compact negatively curved manifold. Validity of the result
is also discussed in the case of inhomogeneous universe. Relationship with the
strong cosmic censorship conjecture is also discussed.


title: Long-wavelength iteration scheme and scalar-tensor gravity

abstract:
  Inhomogeneous and anisotropic cosmologies are modeled withing the framework
of scalar-tensor gravity theories. The inhomogeneities are calculated to
third-order in the so-called long-wavelength iteration scheme. We write the
solutions for general scalar coupling and discuss what happens to the
third-order terms when the scalar-tensor solution approaches at first-order the
general relativistic one. We work out in some detail the case of Brans-Dicke
coupling and determine the conditions for which the anisotropy and
inhomogeneity decay as time increases. The matter is taken to be that of
perfect fluid with a barotropic equation of state.


title: Reply to "A Comment on Singularities in Quantum Cosmology"

abstract:
  We argue that the reasonings that underlie a recent comment by Gotay and
Demaret [1, gr-qc/9605025] are defective. We maintain that, contrary to what
they assert, our previous papers [2,3,4] are correct and indeed disprove their
conjecture that quantum cosmological singularities are predetermined on the
classical level by the choice of time.


title: Hawking radiation and masses in generalized dilaton theories

abstract:
  A generalized dilaton action is considered of which the standard dilaton
black hole and spherically reduced gravity are particular cases. The
Arnowitt-Deser-Misner (ADM) and the Bondi-Sachs (BS) mass are calculated.
Special attention is paid to both the asymptotic conditions for the metric as
well as for the reference space-time. For the latter one we suggest a modified
expression thereby obtaining a new definition of energy. Depending on the
parameters of the model the Hawking radiation behaves like a positive or
negative power of the mass.


title: Cosmological Solution To Einstein-Vlasov System

abstract:
  Einstein-Vlasov system is solved for a homogeneous isotropic spacetime with
positive curvature. In the case of the Universe consisting of massless
particles the equation for R(t) is solved analytically.


title: Anholonomic Transformations of Mechanical Action Principle

abstract:
  We exhibit the transformation properties of the mechanical action principle
under anholonomic transformations. Using the fact that spaces with torsion can
be produced by anholonomic transformations we derive the correct action
principle in these spaces which is quite different from the conventional action
principle.


title: On Quantum Statistical Mechanics of a Schwarzschild Black Hole

abstract:
  Quantum theory of geometry, developed recently in the framework of
non-perturbative quantum gravity, is used in an attempt to explain
thermodynamics of Schwarzschild black holes on the basis of a microscopical
(quantum) description of the system. We work with the formulation of
thermodynamics in which the black hole is enclosed by a spherical surface B and
a macroscopic state of the system is specified by two parameters: the area of
the boundary surface and a quasilocal energy contained within. To derive
thermodynamical properties of the system from its microscopics we use the
standard statistical mechanical method of Gibbs. Under a certain number of
assumptions on the quantum behavior of the system, we find that its microscopic
(quantum) states are described by states of quantum Chern-Simons theory defined
by sets of points on B labelled with spins. The level of the Chern-Simons
theory turns out to be proportional to the horizon area of black hole measured
in Planck units. The statistical mechanical analysis turns out to be especially
simple in the case when the entire interior of B is occupied by a black hole.
We find in this case that the entropy contained within B, that is, the black
hole entropy, is proportional to the horizon surface area.


title:
Results of the First Coincident Observations by Two
  Laser-Interferometric Gravitational Wave Detectors

abstract:
  We report an upper bound on the strain amplitude of gravitational wave bursts
in a waveband from around 800Hz to 1.25kHz. In an effective coincident
observing period of 62 hours, the prototype laser interferometric gravitational
wave detectors of the University of Glasgow and Max Planck Institute for
Quantum Optics, have set a limit of 4.9E-16, averaging over wave polarizations
and incident directions. This is roughly a factor of 2 worse than the
theoretical best limit that the detectors could have set, the excess being due
to unmodelled non-Gaussian noise. The experiment has demonstrated the viability
of the kind of observations planned for the large-scale interferometers that
should be on-line in a few years time.


title: Static Einstein-Maxwell Solutions in 2+1 dimensions

abstract:
  We obtain the Einstein-Maxwell equations for (2+1)-dimensional static
space-time, which are invariant under the transformation
$q_0=i\,q_2,q_2=i\,q_0,\alpha \rightleftharpoons \gamma$. It is shown that the
magnetic solution obtained with the help of the procedure used in
Ref.~\cite{Cataldo}, can be obtained from the static BTZ solution using an
appropriate transformation. Superpositions of a perfect fluid and an electric
or a magnetic field are separately studied and their corresponding solutions
found.


title:
An Analysis of the Representations of the Mapping Class Group of a
  Multi-Geon Three-Manifold

abstract:
  It is well known that the inequivalent unitary irreducible representations
(UIR's) of the mapping class group $G$ of a 3-manifold give rise to ``theta
sectors'' in theories of quantum gravity with fixed spatial topology. In this
paper, we study several families of UIR's of $G$ and attempt to understand the
physical implications of the resulting quantum sectors. The mapping class group
of a three-manifold which is the connected sum of $\R^3$ with a finite number
of identical irreducible primes is a semi-direct product group. Following
Mackey's theory of induced representations, we provide an analysis of the
structure of the general finite dimensional UIR of such a group. In the picture
of quantized primes as particles (topological geons), this general
group-theoretic analysis enables one to draw several interesting qualitative
conclusions about the geons' behavior in different quantum sectors, without
requiring an explicit knowledge of the UIR's corresponding to the individual
primes.


title: Asymptotic freedom from induced gravity cosmology

abstract:
  We give conditions to obtain cosmological asymptotic freedom in scalar-tensor
theories of gravity. We show that this feature can be achieved in FRW flat
spacetimes since we obtain singularity free solutions where the effective
gravitational constant $G_{eff}\rightarrow 0$ for $t\rightarrow -\infty$ and,
for some of them, $G_{eff}\rightarrow G_{N}$ for $t\rightarrow\infty$, where
$G_{N}$ is the Newton constant.


title: Quantum Reference Frames and Quantum Transformations

abstract:
  A quantum frame is defined by a material object subject to the laws of
quantum mechanics. The present paper studies the relations between quantum
frames, which in the classical case are described by elements of the Poincare'
group. The possibility of using a suitable quantum group is examined, but some
arguments are given which show that a different mathematical structure is
necessary. Some simple examples in lower dimensional spacetimes are treated.
They indicate the necessity of taking into account some "internal" degrees of
freedom of the quantum frames, that can be disregarded in a classical
treatment.


title: Solitons of the Einstein-Yang-Mills Theory

abstract:
  Subject of this talk is an overview of results on self-gravitating solitons
of the classical Yang-Mills-Higgs theory. One finds essentially two classes of
solitons, one of them corresponding to the magnetic monopoles the other one to
the sphalerons of flat space. The coupling to the gravitational field leads to
new features absent in flat space. These are the gravitational instability of
these solitons at the Planck scale and the existence of black holes with
`non-abelian hair'' in addition to the regular solutions.


title:
An Iterative Approach to Twisting and Diverging, Type N, Vacuum Einstein
  Equations: A (Third-Order) Resolution of Stephani's `Paradox'

abstract:
  In 1993, a proof was published, within ``Classical and Quantum Gravity,''
that there are no regular solutions to the {\it linearized} version of the
twisting, type-N, vacuum solutions of the Einstein field equations. While this
proof is certainly correct, we show that the conclusions drawn from that fact
were unwarranted, namely that this irregularity caused such solutions not to be
able to truly describe pure gravitational waves. In this article, we resolve
the paradox---since such first-order solutions must always have singular lines
in space for all sufficiently large values of $r$---by showing that if we
perturbatively iterate the solution up to the third order in small quantities,
there are acceptable regular solutions. That these solutions become flat before
they become non-twisting tells us something interesting concerning the general
behavior of solutions describing gravitational radiation from a bounded source.


title: Thermodynamics of Decaying Vacuum Cosmologies

abstract:
  The thermodynamic behavior of vacuum decaying cosmologies is investigated
within a manifestly covariant formulation. Such a process corresponds to a
continuous irreversible energy flow from the vacuum component to the created
matter constituents. It is shown that if the specific entropy per particle
remains constant during the process, the equilibrium relations are preserved.
In particular, if the vacuum decays into photons, the energy density $\rho$ and
average number density of photons $n$ scale with the temperature as $\rho \sim
T^{4}$ and $n \sim T^{3}$. The temperature law is determined and a generalized
Planckian type form of the spectrum, which is preserved in the course of the
evolution, is also proposed. Some consequences of these results for decaying
vacuum FRW type cosmologies as well as for models with ``adiabatic'' photon
creation are discussed.


title: Cosmologies with Photon Creation and the 3K Relic Radiation Spectrum

abstract:
  A new Planckian distribution for cosmologies with photon creation is derived
using thermodynamics and semiclassical considerations. This spectrum is
preserved during the evolution of the universe and compatible with the present
spectral shape of the cosmic microwave background radiation(CMBR). Accordingly,
the widely spread feeling that cosmologies with continuous photon creation are
definitely ruled out by the COBE limits on deviation of the CMBR spectrum from
blackbody shape should be reconsidered. It is argued that a crucial test for
this kind of cosmologies is provided by measurements of the CMBR temperature at
high redshifts. For a given redshift $z$ greater than zero, the temperature is
smaller than the one predicted by the standard FRW model.


title:
Analytic Solutions of the Regge-Wheeler Equation and the
  Post-Minkowskian Expansion

abstract:
  Analytic solutions of the Regge-Wheeler equation are presented in the form of
series of hypergeometric functions and Coulomb wave functions which have
different regions of convergence. Relations between these solutions are
established. The series solutions are given as the Post-Minkowskian expansion
with respect to a parameter $\epsilon \equiv 2M\omega$, $M$ being the mass of
black hole. This expansion corresponds to the post-Newtonian expansion when
they are applied to the gravitational radiation from a particle in circular
orbit around a black hole. These solutions can also be useful for numerical
computations.


title: Area spectrum of the Schwarzschild black hole

abstract:
  We consider a Hamiltonian theory of spherically symmetric vacuum Einstein
gravity under Kruskal-like boundary conditions in variables associated with the
Einstein-Rosen wormhole throat. The configuration variable in the reduced
classical theory is the radius of the throat, in a foliation that is frozen at
the left hand side infinity but asymptotically Minkowski at the right hand side
infinity, and such that the proper time at the throat agrees with the right
hand side Minkowski time. The classical Hamiltonian is numerically equal to the
Schwarzschild mass. Within a class of Hamiltonian quantizations, we show that
the spectrum of the Hamiltonian operator is discrete and bounded below, and can
be made positive definite. The large eigenvalues behave asymptotically
as~$\sqrt{2k}$, where $k$ is an integer. The resulting area spectrum agrees
with that proposed by Bekenstein and others. Analogous results hold in the
presence of a negative cosmological constant and electric charge. The classical
input that led to the quantum results is discussed.


title: Black hole hair: twenty--five years after

abstract:
  Originally regarded as forbidden, black hole ``hair'' are fields associated
with a stationary black hole apart from the gravitational and electromagnetic
ones. Several stable stationary black hole solutions with gauge or Skyrme field
hair are known today within general relativity. We formulate here a ``no
scalar--hair'' conjecture, and adduce some new theorems that almost establish
it by ruling out - for all but a small parameter range - scalar field hair of
spherical black holes in general relativity, whether the field be
self--interacting, coupled to an Abelian gauge field, or nonminimally coupled
to gravity.


title: Generalised Functions and Distributional Curvature of Cosmic Strings

abstract:
  A new method is presented for assigning distributional curvature, in an
invariant manner, to a space-time of low differentiability, using the
techniques of Colombeau's `new generalised functions'. The method is applied to
show that curvature of a cone is equivalent to a delta function. The same is
true under small enough perturbations.


title:
Qualitative Analysis of Viscous Fluid Cosmological Models satisfying the
  Israel-Stewart theory of Irreversible Thermodynamics

abstract:
  Isotropic and spatially homogeneous viscous fluid cosmological models are
investigated using the truncated Israel-Stewart theory of irreversible
thermodynamics to model the bulk viscous pressure. The governing system of
differential equations is written in terms of dimensionless variables and a set
of dimensionless equations of state is then utilized to complete the system.
The resulting dynamical system is analyzed using geometric techniques from
dynamical systems theory to find the qualitative behaviour of the
Friedmann-Robertson-Walker models with bulk viscosity. In these models there
exists a free parameter such that the qualitative behaviour of the models can
be quite different (for certain ranges of values of this parameter) from that
found in models satisfying the Eckart theory studied previously. In addition,
the conditions under which the models inflate are investigated.


title:
Qualitative Analysis of Causal Anisotropic Viscous Fluid Cosmological
  Models

abstract:
  The truncated Israel-Stewart theory of irreversible thermodynamics is used to
describe the bulk viscous pressure and the anisotropic stress in a class of
spatially homogeneous viscous fluid cosmological models. The governing system
of differential equations is written in terms of dimensionless variables and a
set of dimensionless equations of state is utilized to complete the system. The
resulting dynamical system is then analyzed using standard geometric
techniques. It is found that the presence of anisotropic stress plays a
dominant role in the evolution of the anisotropic models. In particular, in the
case of the Bianchi type I models it is found that anisotropic stress leads to
models that violate the weak energy condition and to the creation of a periodic
orbit in some instances. The stability of the isotropic singular points is
analyzed in the case with zero heat conduction; it is found that there are
ranges of parameter values such that there exists an attracting isotropic
Friedmann-Robertson-Walker model. In the case of zero anisotropic stress but
with non-zero heat conduction the stability of the singular points is found to
be the same as in the corresponding case with zero heat conduction; hence the
presence of heat conduction does not apparently affect the global dynamics of
the model.


title: Qualitative Viscous Cosmology

abstract:
  The Full (non--truncated) Israel--Stewart theory of bulk viscosity is applied
to dissipative FRW spacetimes. Dimensionless variables and dimensionless
equations of state are used to write the Einstein--thermodynamic equations as a
plane autonomous system and the qualitative behaviour of this system is
determined. Entropy production in these models is also discussed.


title:
On the relation between the connection and the loop representation of
  quantum gravity

abstract:
  Using Penrose binor calculus for $SU(2)$ ($SL(2,C)$) tensor expressions, a
graphical method for the connection representation of Euclidean Quantum Gravity
(real connection) is constructed. It is explicitly shown that: {\it (i)} the
recently proposed scalar product in the loop-representation coincide with the
Ashtekar-Lewandoski cylindrical measure in the space of connections; {\it (ii)}
it is possible to establish a correspondence between the operators in the
connection representation and those in the loop representation. The
construction is based on embedded spin network, the Penrose graphical method of
$SU(2)$ calculus, and the existence of a generalized measure on the space of
connections modulo gauge transformations.


title: On the Equivalence Principle in Quantum Theory

abstract:
  The role of the equivalence principle in the context of non-relativistic
quantum mechanics and matter wave interferometry, especially atom beam
interferometry, will be discussed. A generalised form of the weak equivalence
principle which is capable of covering quantum phenomena too, will be proposed.
It is shown that this generalised equivalence principle is valid for matter
wave interferometry and for the dynamics of expectation values. In addition,
the use of this equivalence principle makes it possible to determine the
structure of the interaction of quantum systems with gravitational and inertial
fields. It is also shown that the path of the mean value of the position
operator in the case of gravitational interaction does fulfill this generalised
equivalence principle.


title: From Euclidean to Lorentzian General Relativity: The Real Way

abstract:
  We study in this paper a new approach to the problem of relating solutions to
the Einstein field equations with Riemannian and Lorentzian signatures. The
procedure can be thought of as a "real Wick rotation". We give a modified
action for general relativity, depending on two real parameters, that can be
used to control the signature of the solutions to the field equations. We show
how this procedure works for the Schwarzschild metric and discuss some possible
applications of the formalism in the context of signature change, the problem
of time, black hole thermodynamics...


title:
On Parallel Transport in Quantum Bundles over Robertson-Walker
  Spacetimes

abstract:
  A recently-developed theory of quantum general relativity provides a
propagator for free-falling particles in curved spacetimes. These propagators
are constructed by parallel-transporting quantum states within a quantum bundle
associated to the Poincare frame bundle. We consider such parallel transport in
the case that the spacetime is a classical Robertson-Walker universe. An
explicit integral formula is developed which expresses the propagators for
parallel transport between any two points of such a spacetime. The integrals in
this formula are evaluated in closed form for a particular spatially-flat
model.


title: Hamiltonian Gravity and Noncommutative Geometry

abstract:
  A version of foliated spacetime is constructed in which the spatial geometry
is described as a time dependent noncommutative geometry. The ADM version of
the gravitational action is expressed in terms of these variables. It is shown
that the vector constraint is obtained without the need for an extraneous shift
vector in the action.


title: Black Hole Singularity and Generalized Quantum Affine Parameter

abstract:
  We study a behavior of quantum generalized affine parameter (QGAP), which has
been recently proposed by one of the present authors, near the singularity and
the event horizon in three and four spacetime dimensions in terms of a
minisuperspace model of quantum gravity. It is shown that the QGAP is infinite
to the singularity while it remains finite to the event horizon. This fact
indicates a possible interpretation that the singularity is wiped out in
quantum gravity in this particular model of black hole.


title: Topological Inflation in Dual Superstring Models

abstract:
  We study the possibility of obtaining inflationary solutions from S-dual
superstring potentials. We find, in particular, that such solutions occur at
the core of domain walls separating degenerate minima whose positions differ by
modular transformations.


title: Decoherence and Localization in Quantum Two-Level Systems

abstract:
  We study and compare the decoherent histories approach, the
environment-induced decoherence and the localization properties of thesolutions
to the stochastic Schr\"{o}dinger equation in quantum jump simulationand
quantum state diffusion approaches, for a quantum two-level system model. We
show, in particular, that there is a close connection between the decoherent
histories and the quantum jump simulation, complementing a connection with the
quantum state diffusion approach noted earlier by Di\'{o}si, Gisin, Halliwell
and Percival. In the case of the decoherent histories analysis, the degree of
approximate decoherence is discussed in detail.


title: Spectrum of relic gravitational waves in string cosmology

abstract:
  We compute the spectrum of relic gravitons in a model of string cosmology. In
the low- and in the high-frequency limits we reproduce known results. The full
spectrum, however, also displays a series of oscillations which could give a
characteristic signature at the planned LIGO/VIRGO detectors. For special
values of the parameters of the model the signal reaches its maximum already at
frequencies accessible to LIGO and VIRGO and it is close to the sensitivity of
first generation experiments.


title:
An Analogue of the Kac-Wakimoto Formula and Black Hole Conditional
  Entropy

abstract:
  A local formula for the dimension of a superselection sector in Quantum Field
Theory is obtained as vacuum expectation value of the exponential of the proper
Hamiltonian. In the particular case of a chiral conformal theory, this provides
a local analogue of a global formula obtained by Kac and Wakimoto within the
context of representations of certain affine Lie algebras. Our formula is model
independent and its version in general Quantum Field Theory applies to black
hole thermodynamics. The relative free energy between two thermal equilibrium
states associated with a black hole turns out to be proportional to the
variation of the conditional entropy in different superselection sectors, where
the conditional entropy is defined as the Connes-Stoermer entropy associated
with the DHR localized endomorphism representing the sector. The constant of
proportionality is half of the Hawking temperature. As a consequence the
relative free energy is quantized proportionally to the logarithm of a rational
number, in particular it is equal to a linear function the logarithm of an
integer once the initial state or the final state is taken fixed.


title: Comment on "Gravitationally Induced Neutrino-Oscillation Phases"

abstract:
  We critically examine the recent claim (gr-qc/9603008) of a ``new effect'' of
gravitationally induced quantum mechanical phases in neutrino oscillations. A
straightforward exercise in the Schwarzschild coordinates appropriate to a
spherically symmetric non-rotating star shows that, although there is a general
relativistic effect of the star's gravity on neutrino oscillations, it is not
of the form claimed, and is too small to be measured.


title: Well Posed Reduced Systems for the Einstein Equations

abstract:
  We review some well posed formulations of the evolution part of the Cauchy
problem of General Relativity that we have recently obtained. We include also a
new first order symmetric hyperbolic system based directly on the Riemann
tensor and the full Bianchi identities. It has only physical characteristics
and matter sources can be included. It is completely equivalent to our other
system with these properties.


title: Nonsingular global strings

abstract:
  We examine the possibility that time dependence might remove the singular
nature of global string spacetimes. We first show that this time dependence
takes a specific form -- a de-Sitter like expansion along the length of the
string and give an argument for the existence of such a solution, estimating
the rate of expansion. We compare our solution to the singular Cohen-Kaplan
spacetime.


title: Dynamics of Scalar Fields in the Background of Rotating Black Holes

abstract:
  A numerical study of the evolution of a massless scalar field in the
background of rotating black holes is presented. First, solutions to the wave
equation are obtained for slowly rotating black holes. In this approximation,
the background geometry is treated as a perturbed Schwarzschild spacetime with
the angular momentum per unit mass playing the role of a perturbative
parameter. To first order in the angular momentum of the black hole, the scalar
wave equation yields two coupled one-dimensional evolution equations for a
function representing the scalar field in the Schwarzschild background and a
second field that accounts for the rotation. Solutions to the wave equation are
also obtained for rapidly rotating black holes. In this case, the wave equation
does not admit complete separation of variables and yields a two-dimensional
evolution equation. The study shows that, for rotating black holes, the late
time dynamics of a massless scalar field exhibit the same power-law behavior as
in the case of a Schwarzschild background independently of the angular momentum
of the black hole.


title: Directional naked singularity in general relativity

abstract:
  We consider a static, axially symmetric, and asymptotically flat exact
solution of the Einstein vacuum equations, known as the gamma metric. This is
characterized by two constant parameters $m$ and $\gamma$. We find that the
total energy associated with this metric is $m \gamma$. Considering the total
energy to be positive, we investigate the nature of a curvature singularity
$r=2m$ ($r$ is the radial coordinate) in this metric. For $\gamma < 1$, this
singularity is globally visible along $\theta = 0$ as well as $\theta = \pi
/2$. However, for $\gamma > 1$, this singularity is though globally naked along
$\theta =\pi/2$, it is not visible (even locally) along $\theta = 0$. Thus,
this exhibits ``directional nakedness'' for $\gamma > 1$. This could have
implications for astrophysics.


title: Solutions of the Regge Equations on some Triangulations of CP^2

abstract:
  Simplicial geometries are collections of simplices making up a manifold
together with an assignment of lengths to the edges that define a metric on
that manifold. The simplicial analogs of the Einstein equations are the Regge
equations. Solutions to these equations define the semiclassical approximation
to simplicial approximations to a sum-over-geometries in quantum gravity. In
this paper, we consider solutions to the Regge equations with cosmological
constant that give Euclidean metrics of high symmetry on a family of
triangulations of CP^2 presented by Banchoff and Kuhnel. This family is
characterized by a parameter p. The number of vertices grows larger with
increasing p. We exhibit a solution of the Regge equations for p=2 but find no
solutions for p=3. This example shows that merely increasing the number of
vertices does not ensure a steady approach to a continuum geometry in the Regge
calculus.


title: Wave Packet in Quantum Cosmology and Definition of Semiclassical Time

abstract:
  We consider a quantum cosmology with a massless background scalar field $\pb$
and adopt a wave packet as the wave function. This wave packet is a
superposition of the WKB form wave functions, each of which has a definite
momentum of the scalar field $\pb$. In this model it is shown that to trace the
formalism of the WKB time is seriously difficult without introducing a complex
value for a time. We define a semiclassical real time variable $\tp$ from the
phase of the wave packet and calculate it explicitly. We find that, when a
quantum matter field $\pq$ is coupled to the system, an approximate
Schr\"odinger equation for $\pq$ holds with respect to $\tp$ in a region where
the size $a$ of the universe is large and $|\pb|$ is small.


title: Can the Equivalence Principle Survive Quantization?

abstract:
  It is well known that Einstein gravity is non-renormalizable; however a
generalized approach is proposed that leads to Einstein gravity {\it after}
renormalization. This them implies that at least one candidate for quantum
gravity treats all matter on an equal footing with regard to the gravitational
behaviour.


title: Eluding the No-Hair Conjecture for Black Holes

abstract:
  I discuss a recent analytic proof of bypassing the no-hair conjecture for two
interesting (and quite generic) cases of four-dimensional black holes: (i)
black holes in Einstein-Yang-Mills-Higgs (EYMH) systems and (ii) black holes in
higher-curvature (Gauss-Bonnet (GB) type) string-inspired gravity. Both systems
are known to possess black-hole solutions with non-trivial scalar hair outside
the horizon. The `spirit' of the no-hair conjecture, however, seems to be
maintained either because the black holes are unstable (EYMH), or because the
hair is of secondary type (GB), i.e. it does not lead to new conserved quantum
numbers.


title: On the link between Shrodinger and Vlasov Equations

abstract:
  It is shown that well-known Vlasov equation can be derived by adding "hidden"
degrees of freedom and subsequent quantization. The Shrodinger equation
obtained in this manner coincides (in x-representation) with the kinetic
equation for the original dynamical system


title: Implementing an apparent-horizon finder in three dimensions

abstract:
  Locating apparent horizons is not only important for a complete understanding
of numerically generated spacetimes, but it may also be a crucial component of
the technique for evolving black-hole spacetimes accurately. A scheme proposed
by Libson et al., based on expanding the location of the apparent horizon in
terms of symmetric trace-free tensors, seems very promising for use with
three-dimensional numerical data sets. In this paper, we generalize this scheme
and perform a number of code tests to fully calibrate its behavior in
black-hole spacetimes similar to those we expect to encounter in solving the
binary black-hole coalescence problem. An important aspect of the
generalization is that we can compute the symmetric trace-free tensor expansion
to any order. This enables us to determine how far we must carry the expansion
to achieve results of a desired accuracy. To accomplish this generalization, we
describe a new and very convenient set of recurrence relations which apply to
symmetric trace-free tensors.


title: The Torus Universe in the Polygon Approach to 2+1-Dimensional Gravity

abstract:
  In this paper we describe the matter-free toroidal spacetime in 't Hooft's
polygon approach to 2+1-dimensional gravity (i.e. we consider the case without
any particles present). Contrary to earlier results in the literature we find
that it is not possible to describe the torus by just one polygon but we need
at least two polygons. We also show that the constraint algebra of the polygons
closes.


title: Inhomogeneity of Spatial Curvature for Inflation

abstract:
  We study how the initial inhomogeneities of the spatial curvature affect the
onset of inflation in the closed universe. We consider a cosmological model
which contains a radiation and a cosmological constant. In order to treat the
inhomogeneities in the closed universe, we improve the long wavelength
approximation such that the non-small spatial curvature is tractable in the
lowest order. Using the improved scheme, we show how large inhomogeneities of
the spatial curvature prevent the occurrence of inflation.


title: Graphical Evolution of Spin Network States

abstract:
  The evolution of spin network states in loop quantum gravity can be described
by introducing a time variable, defined by the surfaces of constant value of an
auxiliary scalar field. We regulate the Hamiltonian, generating such an
evolution, and evaluate its action both on edges and on vertices of the spin
network states. The analytical computations are carried out completely to yield
a finite, diffeomorphism invariant result. We use techniques from the
recoupling theory of colored graphs with trivalent vertices to evaluate the
graphical part of the Hamiltonian action. We show that the action on edges is
equivalent to a diffeomorphism transformation, while the action on vertices
adds new edges and re-routes the loops through the vertices.


title: Hidden Symmerties in Dilaton--Axion Gravity

abstract:
  Four--dimensional Einstein--Maxwell--dilaton--axion system restricted to
space--times with one non--null Killing symmetry is formulated as the
three--dimensional gravity coupled sigma--model. Several alternative
representations are discussed and the associated hidden symmetries are
revealed. The action of target space isometries on the initial set of
(non--dualized ) variables is found. New mulicenter solutions are obtained via
generating technique based on the formulation in terms of the non--dualized
variables.


title: A Quasi-Spherical Gravitational Wave Solution in Kaluza-Klein Theory

abstract:
  An exact solution of the source-free Kaluza-Klein field equations is
presented. It is a 5D generalization of the Robinson-Trautman quasi-spherical
gravitational wave with a cosmological constant. The properties of the 5D
solution are briefly described.


title: Gravitational Collapse and Cosmic Censorship

abstract:
  This article gives an elementary overview of the end-state of gravitational
collapse according to classical general relativity. The focus of discussion is
the formation of black holes and naked singularities in various physically
reasonable models of gravitational collapse. Possible implications for the
cosmic censorship hypothesis are outlined.


title: `Thermal' ambience and fluctuations in classical field theory

abstract:
  A plane monochromatic wave will not appear monochromatic to a noninertial
observer. We show that this feature leads to a `thermal' ambience in an
accelerated frame {\it even in classical field theory}. When a real,
monochromatic, mode of a scalar field is Fourier analyzed with respect to the
proper time of a uniformly accelerating observer, the resulting power spectrum
consists of three terms: (i)~a factor $(1/2)$ that is typical of the ground
state energy of a quantum oscillator, (ii)~a Planckian distribution $N(\Omega)$
and---most importantly---(iii)~a term $\sqrt{N(N+1)}$, which is the root mean
square fluctuations about the Planckian distribution. It is the appearance of
the root mean square fluctuations that motivates us to attribute a `thermal'
nature to the power spectrum. This result shows that some of the `purely'
quantum mechanical results might have a classical analogue. The `thermal'
ambience that we report here also proves to be a feature of observers stationed
at a constant radius in the Schwarzschild and de-Sitter spacetimes.


title: Gravitational Radiation Reaction to a Particle Motion

abstract:
  In this paper, we discuss the leading order correction to the equation of
motion of the particle, which presumably describes the effect of gravitational
radiation reaction. We derive the equation of motion in two different ways. The
first one is an extension of the well-known formalism by DeWitt and Brehme
developed for deriving the equation of motion of an electrically charged
particle. In contrast to the electromagnetic case, in which there are two
different charges, i.e., the electric charge and the mass, the gravitational
counterpart has only one charge. This fact prevents us from using the same
renormalization scheme that was used in the electromagnetic case. To make clear
the subtlety in the first approach, we then consider the asymptotic matching of
two different schemes, i.e., the internal scheme in which the small particle is
represented by a spherically symmetric black hole with tidal perturbations and
the external scheme in which the metric is given by small perturbations on the
given background geometry. The equation of motion is obtained from the
consistency condition of the matching. We find that in both ways the same
equation of motion is obtained. The resulting equation of motion is analogous
to that derived in the electromagnetic case. We discuss implications of this
equation of motion.


title: The Gravitational Energy of a Point Mass is Finite

abstract:
  We argue that our equation of gravitation ( Phys.Lett. A 156 (1991) 404 )
lead in pseudo-Euclidean space-time to the finite energy of the gravitational
field of a point mass.


title: Black Hole Area in Brans-Dicke Theory

abstract:
  We have shown that the dynamics of the scalar field $\phi (x)= ``G^{-1}(x)"$
in Brans-Dicke theories of gravity makes the surface area of the black hole
horizon {\it oscillatory} during its dynamical evolution. It explicitly
explains why the area theorem does not hold in Brans-Dicke theory. However, we
show that there exists a certain non-decreasing quantity defined on the event
horizon which is proportional to the black hole entropy for the case of
stationary solutions in Brans-Dicke theory. Some numerical simulations have
been demonstrated for Oppenheimer-Snyder collapse in Brans-Dicke theory.


title: The Princess and the Pea

abstract:
  Like a fairy-tale princess, trajectories around black holes can be sensitive
to small disturbances. We describe how a small disturbance can lead to erratic
orbits and an increased production of gravitational waves.


title:
Ill-posedness of a double null free evolution scheme for black hole
  spacetimes

abstract:
  We suggest that ``free evolution'' integration schemes for the Einstein
equations (that do not enforce constraints) may contain exponentially growing
modes that render them useless in numerical integrations of black hole
spacetimes, independently of how the equations are differenced. As an example
we consider the evolution of Schwarzschild and Reissner-Nordstr\"om spacetimes
in double null coordinates.


title: Critical phenomena in gravitational collapse

abstract:
  Lecture given at the workshop "Mathematical aspects of theories of
gravitation", Stefan Banach International Mathematical Centre, 7 March 1996. A
mini-introduction to critical phenomena in gravitational collapse is combined
with a more detailed discussion of the regularity of the ``critical
spacetimes'' dominating these phenomena.


title:
Measuring black-hole parameters and testing general relativity using
  gravitational-wave data from space-based interferometers

abstract:
  Among the expected sources of gravitational waves for the Laser
Interferometer Space Antenna (LISA) is the capture of solar-mass compact stars
by massive black holes residing in galactic centers. We construct a simple
model for such a capture, in which the compact star moves freely on a circular
orbit in the equatorial plane of the massive black hole. We consider the
gravitational waves emitted during the late stages of orbital evolution,
shortly before the orbiting mass reaches the innermost stable circular orbit.
We construct a simple model for the gravitational-wave signal, in which the
phasing of the waves plays the dominant role. The signal's behavior depends on
a number of parameters, including $\mu$, the mass of the orbiting star, $M$,
the mass of the central black hole, and $J$, the black hole's angular momentum.
We calculate, using our simplified model, and in the limit of large
signal-to-noise ratio, the accuracy with which these quantities can be
estimated during a gravitational-wave measurement. Our simplified model also
suggests a method for experimentally testing the strong-field predictions of
general relativity.


title: Killing spinors, the adS black hole and I(ISO(2,1)) gravity

abstract:
  We construct a supersymmetric extension of the $I\big(ISO(2,1)\big)$
Chern-Simons gravity and show that certain particle-like solutions and the adS
black-hole solution of this theory are supersymmetric.


title: Spacetime model with superluminal phenomena

abstract:
  recent theoretical results show the existence of arbitrary speeds ($0\leq v
<\infty$) solutions of the wave equations of mathematical physics. Some recent
experiments confirm the results for sound waves. The question arises naturally:
What is the appropriate spacetime model to describe superluminal phenomena? In
this paper we present a spacetime model that incorporates the valid results of
Relativity Theory and yet describes coherently superluminal phenomena without
paradoxes.


title:
Stress-Energy Must be Singular on the Misner Space Horizon even for
  Automorphic Fields

abstract:
  We use the image sum method to reproduce Sushkov's result that for a massless
automorphic field on the initial globally hyperbolic region $IGH$ of Misner
space, one can always find a special value of the automorphic parameter
$\alpha$ such that the renormalized expectation value
$\langle\alpha|T_{ab}|\alpha\rangle$ in the {\it Sushkov state}
``$\langle\alpha|\cdot|\alpha\rangle$'' (i.e. the automorphic generalization of
the Hiscock-Konkowski state) vanishes. However, we shall prove by elementary
methods that the conclusions of a recent general theorem of
Kay-Radzikowski-Wald apply in this case. I.e. for any value of $\alpha$ and any
neighbourhood $N$ of any point $b$ on the chronology horizon there exists at
least one pair of non-null related points $(x,x') \in (N\cap IGH)\times (N\cap
IGH)$ such that the renormalized two-point function of an automorphic field
$G^\alpha_{\rm ren}(x,x')$ in the Sushkov state is singular. In consequence
$\langle\alpha|T_{ab}|\alpha\rangle$ (as well as other renormalized expectation
values such as $\langle\alpha|\phi^2|\alpha\rangle$) is necessarily singular
{\it on} the chronology horizon. We point out that a similar situation (i.e.
singularity {\it on} the chronology horizon) holds for states on Gott space and
Grant space.


title:
Relativistic Gravity Theory And Related Tests With A Mercury Orbiter
  Mission

abstract:
  Due to its relatively large eccentricity and proximity to the Sun, Mercury's
orbital motion provides one of the best solar-system tests of relativistic
gravity. We emphasize the number of feasible relativistic gravity tests that
can be performed within the context of the parameterized weak field and slow
motion approximation - a usefulframework for testing modern gravitational
theories in the solar system. We discuss a new approximation method, which
includes two Eddington parameters $(\gamma,\beta)$, proposed for construction
of the relativistic equations of motion of extended bodies. Within the present
accuracy of radio measurements, we discuss the generalized Fermi-normal-like
proper reference frame which is defined in the immediate vicinity of the
extended compact bodies. Based on the Hermean-centric equations of motion of
the spacecraft around the planet Mercury, we suggest a new test of the Strong
Equivalence Principle. The corresponding experiment could be performed with the
future {\it Mercury Orbiter} mission scheduled by the European Space Agency
({\small ESA}) for launch between 2006 and 2016. We discuss other relativistic
effects including the perihelion advance, redshift and geodetic precession of
the orbiter's orbital plane about Mercury.


title:
Localized Mass and Spin Sources in 2+1 Dimensional Topologically Massive
  Gravity

abstract:
  Stationary solutions to the full non-linear topologically massive gravity
(TMG) are obtained for localized sources of mass $m$ and spin $\sigma$. Our
results show that the topological term induces spin and that the total spin J
(which is the spin observed by an asymptotic observer) ranges from 0 to $\sigma
+ \frac{m}{\mu}(\frac{4\pi+m}{4\pi +2m})$ depending on the structure of the
spin source (here $\mu$ is the topological mass). We find that it is
inconsistent to consider actual delta function mass and spin sources. In the
point-like limit, however, we find no condition constraining $m$ and $\sigma$
contrary to a previous analysis by Clement.


title: Supersymmetric strictly isospectral FRW models for zero factor ordering

abstract:
  We apply the strictly isospectral technique of standard supersymmetric
quantum mechanics to the Q=0 factor ordered Wheeler-DeWitt equation for the
Friedmann-Robertson-Walker (FRW) minisuperspace model. The resulting strictly
isospectral one-parameter families of both FRW cosmological potentials and
"wavefunctions of the universe" are exhibited with relevant plots


title:
About the Interpretation of Gravitationally Induced Neutrino Oscillation
  Phases

abstract:
  We present some thoughts on how to interpret the gravitionally induced
neutrino oscillation phases presented by us in our 1996 Gravity Research
Foundation Essay.


title: Graviton Production in Elliptical and Hyperbolic Universes

abstract:
  The problem of cosmological graviton creation for homogeneous and isotropic
universes with elliptical ($\vae =+1$) and hyperbolical ($\vae =-1$) geometries
is addressed. The gravitational wave equation is established for a
self-gravitating fluid satisfying the barotropic equation of state $p=(\gamma
-1)\rho$, which is the source of the Einstein's equations plus a cosmological
$\Lambda$-term. The time dependent part of this equation is exactly solved in
terms of hypergeometric functions for any value of $\gamma$ and spatial
curvature $\vae$. An expression representing an adiabatic vacuum state is then
obtained in terms of associated Legendre functions whenever $\gamma\neq
\frac{2}{3}\; \frac{(2n+1)}{(2n-1)}$, where n is an integer. This includes most
cases of physical interest such as $\gamma =0,\;4/3\;,1$. The mechanism of
graviton creation is reviewed and the Bogoliubov coefficients related to
transitions between arbitrary cosmic eras are also explicitly evaluated.


title:
Anisotropy of fast-going processes in the Sun and new interaction in
  nature

abstract:
  The processing of the galactic coordinates of 3543 solar flares with a
magnitude of 2 or more has shown that the distribution of these fast-going
processes on the surface of the "nonrotating" Sun is irregular and non-random
what testifies that in the near-Sun space an anisotropy takes place which
practically coincides with that predicted and obtained in laboratory
experiments and caused by existence of the intergalactic vector potential ${\bf
A_g}$.


title: Dilatonic Black Holes with Gauss-Bonnet Term

abstract:
  We discuss black holes in an effective theory derived from a superstring
model, which includes a dilaton field, a gauge field and the Gauss-Bonnet term.
Assuming U(1) or SU(2) symmetry for the gauge field, we find four types of
spherically symmetric solutions, i.e., a neutral, an electrically charged, a
magnetically charged and a ``colored'' black hole, and discuss their
thermodynamical properties and fate via the Hawking evaporation process. For
neutral and electrically charged black holes, we find critical point and a
singular end point. Below the mass corresponding to the critical point,
nosolution exists, while the curvature on the horizon diverges and anaked
singularity appears at the singular point. A cusp structure in the mass-entropy
diagram is found at the critical point and black holes on the branch between
the critical and singular points become unstable. For magnetically charged and
``colored" black holes, the solution becomes singular just at the end point
with a finite mass. Because the black hole temperature is always finite even at
the critical point or the singular point, we may conclude that the evaporation
process will not be stopped even at the critical point or the singular point,
and the black hole will move to a dynamical evaporation phase or a naked
singularity will appear.


title: Relativity of Space-Time Geometry

abstract:
  We argue that space-time geometry is not absolute with respect to the frame
of reference being used. The space-time metric differential form $ds$ in
noninertial frames of reference (NIFR) is caused by the properties of the used
frames in accordance with the Berkley - Leibnitz - Mach - Poincar\'{e} ideas
about relativity of space and time . It is shown that the Sagnac effect and the
existence of inertial forces in NIFR can be considered from this point of view.
An experimental test is proposed.


title: Quantum black-hole kinks

abstract:
  By allowing the light cones to tip over on hypersurfaces according to the
conservation laws of an one-kink in static, Schwarzschild and five-dimensional
black hole metrics, we show that in the quantum regime there also exist
instantons whose finite imaginary action gives the probability of accurrence of
the kink metric corresponding to single chargeless, nonrotating black holes
taking place in pairs, joined on an interior surface beyond the horizon, with
each hole residing in a diffrent universe. Evaluation of the thermal properties
of each of the black holes in a neutral pair leads one to check that to an
asymptotic abserver in either universe, each black hole is exactly the
quantum-mechanically defined {\it anti-black hole} to the other hole in the
pair. The independent quantum states of black holes in neutral pairs have been
formulated by using the path integral method, and shown to be that of a
harmonic oscillator. Our results suggest that the boundary condition of a
single universe in the metauniverse is that this universe can never be
self-contained and must always have at least one boundary which connects it to
the rest of a self-contained metauniverse.


title: The no-defect conjecture in cosmic crystallography

abstract:
  The topology of space is usually assumed simply connected, but could be
multi-connected. We review in the latter case the possibility that topological
defects arising at high energy phase transitions might still be present and
find that either they are very unlikely to form at all, or space is effectively
simply connected on scales up to the horizon size.


title: Galactic periodicity and the oscillating G model

abstract:
  We consider the model involving the oscillation of the effective
gravitational constant that has been put forward in an attempt to reconcile the
observed periodicity in the galaxy number distribution with the standard
cosmological models. This model involves a highly nonlinear dynamics which we
analyze numerically. We carry out a detailed study of the bound that
nucleosynthesis imposes on this model. The analysis shows that for any assumed
value for $\Omega$ (the total energy density) one can fix the value of
$\Omega_{\rm bar}$ (the baryonic energy density) in such a way as to
accommodate the observational constraints coming from the $^4{\rm He}$
primordial abundance. In particular, if we impose the inflationary value
$\Omega=1$ the resulting baryonic energy density turns out to be $\Omega_{\rm
bar}\sim 0.021$. This result lies in the very narrow range $0.016 \leq
\Omega_{\rm bar} \leq 0.026$ allowed by the observed values of the primordial
abundances of the other light elements. The remaining fraction of $\Omega$
corresponds to dark matter represented by a scalar field.


title: Has cosmological dark matter been observed?

abstract:
  There are many indications that ordinary matter represents only a tiny
fraction of the matter content of the Universe, with the remainder assumed to
consist of some different type of matter, which, for various reasons must be
nonluminous (dark matter). Among these indications are the inflationary
scenarios which predicts that the average energy density of the Universe
coincides with the so called critical value (for which the expansion never
stops but the rate of expansion approaches zero at very late times). At the
same time it is known (from the predictions of Big Bang nucleosynthesis on the
abundances of the light elements, other than Helium) that the baryonic energy
density (ordinary matter) must represent ($1.5\pm 0.5)h^{-2}$ \% (where $h$ is
the Hubble constant in units of 100 km s$^{-1}$Mpc$^{-1}$) of this critical
value \cite{Copi,OstStein}. We present here evidence supporting the model in
which the rest of the energy density corresponds to a scalar field, which can
be observed, however indirectly, in the oscillation of the effective
gravitational constant, and manifests itself in the known periodicity of the
number distribution of galaxies \cite{Broad,Szalay}. We analyze this model
numerically and show that, the requirement that the model satisfy the bounds of
light element abundances in the Universe, as predicted by Big Bang
nucleosynthesis, yields a specific value for the red-shift-galactic-count
oscillation amplitude compatible with that required to explain the oscillations
described above \cite{hill,CritStein}, and, furthermore, yields a value for the
age of the Universe compatible with standard bounds \cite{OstStein}.


title:
Derivation of Field Equations from the Principle of the Fermionic
  Projector

abstract:
  With the concept of "discrete space-time" the space-time continuum is
resolved into discrete points at the scale of the Planck length. We postulate
with the "principle of the fermionic projector" that physical equations must be
formulated intrinsically in discrete space-time with the projector on fermionic
states. This principle combines the Pauli principle, a local gauge principle
and the principle of relativity, but does not include a locality or causality
principle. It is shown that a well-established limit yields the structure of a
Lorentzian manifold. The equations of discrete space-time reduce to classical
field equations.
  This preliminary text is intended as introduction. Detailed calculations can
be obtained from the author on request.