title:
Astrometric and Timing Effects of Gravitational Waves from Localized
  Sources

abstract:
  A consistent approach for an exhaustive solution of the problem of
propagation of light rays in the field of gravitational waves emitted by a
localized source of gravitational radiation is developed in the first
post-Minkowskian and quadrupole approximation of General Relativity. We
demonstrate that the equations of light propagation in the retarded
gravitational field of an arbitrary localized source emitting quadrupolar
gravitational waves can be integrated exactly. The influence of the
gravitational field on the light propagation is examined not only in the wave
zone but also in cases when light passes through the intermediate and near
zones of the source. Explicit analytic expressions for light deflection and
integrated time delay (Shapiro effect) are obtained accounting for all possible
retardation effects and arbitrary relative locations of the source of
gravitational waves, that of light rays, and the observer. It is shown that the
ADM and harmonic gauge conditions can both be satisfied simultaneously outside
the source of gravitational waves. Their use drastically simplifies the
integration of light propagation equations and those for the motion of light
source and observer in the field of the source of gravitational waves, leading
to the unique interpretation of observable effects. The two limiting cases of
small and large values of impact parameter are elaborated in more detail.
Explicit expressions for Shapiro effect and deflection angle are obtained in
terms of the transverse-traceless part of the space-space components of the
metric tensor. We also discuss the relevance of the developed formalism for
interpretation of radio interferometric and timing observations, as well as for
data processing algorithms for future gravitational wave detectors.


title: Angular momentum near the black hole threshold in scalar field collapse

abstract:
  For the formation of a black hole in the gravitational collapse of a massless
scalar field, we calculate a critical exponent that governs the black hole
angular momentum for slightly non-spherical initial data near the black hole
threshold. We calculate the scaling law by second-order perturbation theory. We
then use the numerical results of a previous first-order perturbative analysis
to obtain the numerical value mu ~ 0.76 for the angular momentum critical
exponent. A quasi-periodic fine structure is superimposed on the overall power
law.


title:
Asymptotically Flat Initial Data for Gravitational Wave Spacetimes,
  Conformal Compactification and Conformal Symmetry

abstract:
  We study the utilization of conformal compactification within the conformal
approach to solving the constraints of general relativity for asymptotically
flat initial data. After a general discussion of the framework, particular
attention is paid to simplifications that arise when restricting to a class of
initial data which have a certain $U(1)\times U(1)$ conformal symmetry.


title:
Classical and Quantum Fields in Curved Spacetime: Canonical Theory
  versus Conventional Construction

abstract:
  We argue that the conventional construction for quantum fields in curved
spacetime has a grave drawback: It involves an uncountable set of physical
field systems which are nonequivalent with respect to the Bogolubov
transformations, and there is, in general, no canonical way for choosing a
single system. Thus the construction does not result in a definite theory. The
problem of ambiguity pertains equally both to quantum and classical fields. The
canonical theory is advanced, which is based on a canonical, or natural choice
of field modes. The principal characteristic feature of the theory is
relativistic-gravitational nonlocality: The field at a spacetime point $(s,t)$
depends on the metric at $t$ in the whole 3-space. The most fundamental and
shocking result is the following: In the case of a free field in curved
spacetime, there is no particle creation. Applications to cosmology and black
holes are given. The results for particle energies are in complete agreement
with those of general relativity. A model of the universe is advanced, which is
an extension of the Friedmann universe; it lifts the problem of missing dark
matter.


title: A note on the Penrose junction conditions

abstract:
  Impulsive pp-waves are commonly described either by a distributional
spacetime metric or, alternatively, by a continuous one. The transformation $T$
relating these forms clearly has to be discontinuous, which causes two basic
problems: First, it changes the manifold structure and second, the pullback of
the distributional form of the metric under $T$ is not well defined within
classical distribution theory. Nevertheless, from a physical point of view both
pictures are equivalent. In this work, after calculating $T$ als well as the
''Rosen''-form of the metric in the general case of a pp-wave with arbitrary
wave profile we give a precise meaning to the term ``physically equivalent'' by
interpreting $T$ as the distributional limit of a suitably regularized sequence
of diffeomorphisms. Moreover, it is shown that $T$ provides an example of a
generalized coordinate transformation in the sense of Colombeau's generalized
functions.


title: A note on light velocity anisotropy

abstract:
  It is proved that in experiments on or near the Earth, no anisotropy in the
one-way velocity of light may be detected. The very accurate experiments which
have been performed to detect such an effect are to be considered significant
tests of both special relativity and the equivalence principle


title:
Fermi Coordinates of an Observer Moving in a Circle in Minkowski Space:
  Apparent Behavior of Clocks

abstract:
  Coordinate transformations are derived from global Minkowski coordinates to
the Fermi coordinates of an observer moving in a circle in Minkowski
space-time. The metric for the Fermi coordinates is calculated directly from
the tensor transformation rule. The behavior of ideal clocks is examined from
the observer's reference frame using the Fermi coordinates. A complicated
relation exists between Fermi coordinate time and proper time on stationary
clocks (in the Fermi frame) and between proper time on satellite clocks that
orbit the observer. An orbital Sagnac-like effect exists for portable clocks
that orbit the Fermi coordinate origin. The coordinate speed of light is
isotropic but varies with Fermi coordinate position and time. The magnitudes of
these kinematic effects are computed for parameters that are relevant to the
Global Positioning System (GPS) and are found to be small; however, for future
high-accuracy time transfer systems, these effects may be of significant
magnitude.


abstract:
  On the non-minimal coupling of Riemann-flat Klein-Gordon Fields to Space-time
torsion} The energy spectrum of Klein-Gordon particles is obtained via the
non-minimal coupling of Klein-Gordon fields to Cartan torsion in the
approximation of Riemann-flatness and constant torsion.When the mass squared is
proportional to torsion coupling constant it is shown that the splitting of
energy does not occur.I consider that only the vector part of torsion does not
vanish and that it is constant.A torsion Hamiltonian operator is
constructed.The spectrum of Klein-Gordon fields is continuos.


title: Geodesics on non-Riemannian Geometric theory of Planar Defects

abstract:
  The method of Hamilton-Jacobi is used to obtain geodesics around non-
Riemannian planar torsional defects.It is shown that by perturbation expansion
in the Cartan torsion the geodesics obtained are parabolic curves along the
plane x-z when the wall is located at the plane x-y.In the absence of defects
the geodesics reduce to straight lines.The family of parabolas depend on the
torsion parameter and describe a gravitationally repulsive domain wall.Torsion
here plays the role of the Burgers vector in solid state physics.


title: New Black Hole Solutions in Brans-Dicke Theory of Gravity

abstract:
  Existence check of non-trivial, stationary axisymmetric black hole solutions
in Brans-Dicke theory of gravity in different direction from those of Penrose,
Thorne and Dykla, and Hawking is performed. Namely, working directly with the
known explicit spacetime solutions in Brans-Dicke theory, it is found that
non-trivial Kerr-Newman-type black hole solutions different from general
relativistic solutions could occur for the generic Brans-Dicke parameter values
-5/2\leq \omega <-3/2. Finally, issues like whether these new black holes carry
scalar hair and can really arise in nature and if they can, what the associated
physical implications would be are discussed carefully.


title:
Cosmological perturbations in a gravity with quadratic order curvature
  couplings

abstract:
  We present a set of equations describing the evolution of the scalar-type
cosmological perturbation in a gravity with general quadratic order curvature
coupling terms. Equations are presented in a gauge ready form, thus are ready
to implement various temporal gauge conditions depending on the problems. The
Ricci-curvature square term leads to a fourth-order differential equation for
describing the spacetime fluctuations in a spatially homogeneous and isotropic
cosmological background.


title:
Effective spacetime and Hawking radiation from moving domain wall in
  thin film of 3He-A

abstract:
  An event horizon for "relativistic" fermionic quasiparticles can be
constructed in a thin film of superfluid 3He-A. The quasiparticles see an
effective "gravitational" field which is induced by a topological soliton of
the order parameter. Within the soliton the "speed of light" crosses zero and
changes sign. When the soliton moves, two planar event horizons (black hole and
white hole) appear, with a curvature singularity between them. Aside from the
singularity, the effective spacetime is incomplete at future and past
boundaries, but the quasiparticles cannot escape there because the
nonrelativistic corrections become important as the blueshift grows, yielding
"superluminal" trajectories. The question of Hawking radiation from the moving
soliton is discussed but not resolved.


title:
Three Dimensional Numerical General Relativistic Hydrodynamics I:
  Formulations, Methods, and Code Tests

abstract:
  This is the first in a series of papers on the construction and validation of
a three-dimensional code for general relativistic hydrodynamics, and its
application to general relativistic astrophysics. This paper studies the
consistency and convergence of our general relativistic hydrodynamic treatment
and its coupling to the spacetime evolutions described by the full set of
Einstein equations with a perfect fluid source. The numerical treatment of the
general relativistic hydrodynamic equations is based on high resolution shock
capturing schemes. These schemes rely on the characteristic information of the
system. A spectral decomposition for general relativistic hydrodynamics
suitable for a general spacetime metric is presented. Evolutions based on three
different approximate Riemann solvers coupled to four different discretizations
of the Einstein equations are studied and compared. The coupling between the
hydrodynamics and the spacetime (the right and left hand side of the Einstein
equations) is carried out in a treatment which is second order accurate in {\it
both} space and time. Convergence tests for all twelve combinations with a
variety of test beds are studied, showing consistency with the differential
equations and correct convergence properties. The test-beds examined include
shocktubes, Friedmann-Robertson-Walker cosmology tests, evolutions of
self-gravitating compact (TOV) stars, and evolutions of relativistically
boosted TOV stars. Special attention is paid to the numerical evolution of
strongly gravitating objects, e.g., neutron stars, in the full theory of
general relativity, including a simple, yet effective treatment for the surface
region of the star (where the rest mass density is abruptly dropping to zero).


title:
Creation of unstable particles and decoherence in semiclassical
  cosmology

abstract:
  We consider a simple cosmological model in order to show the importance of
unstable particle creation for the validity of the semiclassical approximation.
Using the mathematical structure of rigged Hilbert spaces we show that particle
creation is the seed of decoherence which enables the quantum to classical
transition.


title: Distributional torsion of charged domain walls with spin

abstract:
  An exact solution of Einstein-Cartan-Maxwell (ECM) field equations
representing a charged domain wall given by the jump on the electric charge and
spin density across the wall is obtained from the Riemannian theory of
distributions. The Gauss-Coddazzi equations are used to show that spin, charge
and Cartan torsion increases the repulsive character of the domain wall. Taub
and Vilenkin walls are discussed as well as their relations to wormhole
geometry. The electric and torsion fields are constants at the wall.


title: Geodesics around gravitational dislocations

abstract:
  A technique for generating spherically symmetric dislocation solutions of a
direct Poincar\'{e} gauge theory of gravity based on homogeneous functions
which makes Cartan torsion to vanish is presented.Static space supported
dislocation and time dependent solutions are supplied.Photons move along
geodesics in analogy to geodesics described by electrons around dislocations in
solid state physics.Tachyonic sectors are also found.


title:
Second order gauge invariant gravitational perturbations of a Kerr black
  hole

abstract:
  We investigate higher than the first order gravitational perturbations in the
Newman-Penrose formalism. Equations for the Weyl scalar $\psi_4,$ representing
outgoing gravitational radiation, can be uncoupled into a single wave equation
to any perturbative order. For second order perturbations about a Kerr black
hole, we prove the existence of a first and second order gauge (coordinates)
and tetrad invariant waveform, $\psi_I$, by explicit construction. This
waveform is formed by the second order piece of $\psi_4$ plus a term, quadratic
in first order perturbations, chosen to make $\psi_I$ totally invariant and to
have the appropriate behavior in an asymptotically flat gauge. $\psi_I$
fulfills a single wave equation of the form ${\cal T}\psi_I=S,$ where ${\cal
T}$ is the same wave operator as for first order perturbations and $S$ is a
source term build up out of (known to this level) first order perturbations. We
discuss the issues of imposition of initial data to this equation, computation
of the energy and momentum radiated and wave extraction for direct comparison
with full numerical approaches to solve Einstein equations.


title: Distributional Torsion of Cosmic Walls crossed by Cosmic Strings

abstract:
  Distributional sources of cosmic walls crossed by cosmic strings from
Riemann-Cartan (RC) Geometry. The matter density of the planar wall is maximum
at the point where the cosmic string crosses the cosmic wall. Cartan torsion is
has a support on the cosmic string given by the Dirac $ \delta $-function. Off
the sources are left with a torsionless vacuum.


title:
On the Rigidity Theorem for Spacetimes with a Stationary Event Horizon
  or a Compact Cauchy Horizon

abstract:
  We consider smooth electrovac spacetimes which represent either (A) an
asymptotically flat, stationary black hole or (B) a cosmological spacetime with
a compact Cauchy horizon ruled by closed null geodesics. The black hole event
horizon or, respectively, the compact Cauchy horizon of these spacetimes is
assumed to be a smooth null hypersurface which is non-degenerate in the sense
that its null geodesic generators are geodesically incomplete in one direction.
In both cases, it is shown that there exists a Killing vector field in a
one-sided neighborhood of the horizon which is normal to the horizon. We
thereby generalize theorems of Hawking (for case (A)) and Isenberg and Moncrief
(for case (B)) to the non-analytic case.


title:
The one-loop divergences of the linear gravity with the torsion terms in
  tetrad approach

abstract:
  In this paper we discuss the connection between the geometric and tetrad
approaches in the quantum affine-metric gravity. The corresponding transition
formulas are obtained at the one-loop level. As an example, the one-loop
counterterms are calculated in the tetrad formalism in the theory with terms
quadratic in the torsion field. This model possesses the extra local symmetries
connected with transformation of the connection field. It is shown that the
special gauge can be chosen so that the corresponding additional ghosts do not
contribute to the one-loop divergent terms.


title: Space-time defects :Domain walls and torsion

abstract:
  The theory of distributions in non-Riemannian spaces is used to obtain exact
static thin domain wall solutions of Einstein-Cartan equations of gravity.
Curvature $ \delta $-singularities are found while Cartan torsion is given by
Heaviside functions. Weitzenb\"{o}ck planar walls are caracterized by torsion
$\delta$-singularities and zero curvature. It is shown that Weitzenb\"{o}ck
static thin domain walls do not exist exactly as in general relativity. The
global structure of Weitzenb\"{o}ck nonstatic torsion walls is investigated.


title: Monopole Inflation in Brans-Dicke Theory

abstract:
  According to previous work, topological defects expand exponentially without
an end if the vacuum expectation value of the Higgs field is of the order of
the Planck mass. We extend the study of inflating topological defects to the
Brans-Dicke gravity. With the help of numerical simulation we investigate the
dynamics and spacetime structure of a global monopole. Contrary to the case of
the Einstein gravity, any inflating monopole eventually shrinks and takes a
stable configuration. We also discuss cosmological constraints on the model
parameters.


title: Approximate Canonical Quantization for Cosmological Models

abstract:
  In cosmology minisuperspace models are described by nonlinear
time-reparametrization invariant systems with a finite number of degrees of
freedom. Often these models are not explicitly integrable and cannot be
quantized exactly. Having this in mind, we present a scheme for the
(approximate) quantization of perturbed, nonintegrable, time-reparametrization
invariant systems that uses (approximate) gauge invariant quantities. We apply
the scheme to a couple of simple quantum cosmological models.


title: Quantum Gravity effects near the null black hole singularity

abstract:
  The structure of the Cauchy Horizon singularity of a black hole formed in a
generic collapse is studied by means of a renormalization group equation for
quantum gravity. It is shown that during the early evolution of the Cauchy
Horizon the increase of the mass function is damped when quantum fluctuations
of the metric are taken into account.


title:
Late time dynamics of scalar perturbations outside black holes: I. A
  shell toy-model

abstract:
  We present a new analytic approach for the study of late time evolution of
linear test-fields, propagating on the exterior of black holes. This method
provides a calculation scheme applicable to Kerr black holes (for which case no
analytic calculation of the late time tails has been presented so far). In this
paper we develop the new technique and apply it to the case of massless scalar
waves evolving on the background geometry of a static spherically-symmetric
thin shell with a Schwarzschild exterior. The late time behavior of the scalar
field at null infinity is calculated, and is explicitly related to the form of
(quite arbitrary) initial data. This reproduces the well-known late time
power-law decaying tails. In an accompanying paper we apply our approach to the
complete Schwarzschild black hole geometry, where we obtain the familiar
inverse-power late time tails at null infinity, as well as at time-like
infinity and along the event horizon. A calculation of the late time power-law
tails in the Kerr geometry, based on the same approach, will be presented in a
forthcoming paper.


title:
Late time dynamics of scalar perturbations outside black holes: II.
  Schwarzschild geometry

abstract:
  We apply a new analytic scheme, developed in a preceding paper, in order to
calculate the late time behavior of scalar test fields evolving outside a
Schwarzschild black hole. The pattern of the late time decay at future null
infinity is found to be the same as in the shell toy-model studied in the
preceding paper. A simple late time expansion of the scalar field is then used,
relying on the results at null infinity, to construct a complete picture of the
late time wave behavior anywhere outside the black hole. This reproduces the
well known power-law tails at time-like infinity and along the event horizon.
The main motivation for the introduction of the new approach arises from its
applicability to rotating black holes, as shall be discussed in a forthcoming
paper.


title:
Gravitational Effects of Quantum Fields in the Interior of a Cylindrical
  Black Hole

abstract:
  The gravitational back-reaction is calculated for the conformally invariant
scalar field within a black cosmic string interior with cosmological constant.
Using the perturbed metric, the gravitational effects of the quantum field are
calculated. It is found that the perturbations initially strengthen the
singularity. This effect is similar to the case of spherical symmetry (without
cosmological constant). This indicates that the behaviour of quantum effects
may be universal and not dependent on the geometry of the spacetime nor the
presence of a non-zero cosmological constant.


title:
An energy bound deduced from the vanishing of the radiation reaction
  force during uniform acceleration

abstract:
  We deduce from energy conservation a lower bound on the mass of any system
capable of imparting a constant acceleration to a charged body. We also point
out a connection between this bound and the so called dominant energy condition
of general relativity.


title: On the existence of Killing vector fields

abstract:
  In covariant metric theories of coupled gravity-matter systems the necessary
and sufficient conditions ensuring the existence of a Killing vector field are
investigated. It is shown that the symmetries of initial data sets are
preserved by the evolution of hyperbolic systems.


title:
Late-Time Evolution of Realistic Rotating Collapse and The No-Hair
  Theorem

abstract:
  We study analytically the asymptotic late-time evolution of realistic
rotating collapse. This is done by considering the asymptotic late-time
solutions of Teukolsky's master equation, which governs the evolution of
gravitational, electromagnetic, neutrino and scalar perturbations fields on
Kerr spacetimes. In accordance with the no-hair conjecture for rotating
black-holes we show that the asymptotic solutions develop inverse power-law
tails at the asymptotic regions of timelike infinity, null infinity and along
the black-hole outer horizon (where the power-law behaviour is multiplied by an
oscillatory term caused by the dragging of reference frames). The damping
exponents characterizing the asymptotic solutions at timelike infinity and
along the black-hole outer horizon are independent of the spin parameter of the
fields. However, the damping exponents at future null infinity are spin
dependent. The late-time tails at all the three asymptotic regions are
spatially dependent on the spin parameter of the field. The rotational dragging
of reference frames, caused by the rotation of the black-hole (or star) leads
to an active coupling of different multipoles.


title: A Metric Theory of Gravity with Condensed Matter Interpretation

abstract:
  We define a metric theory of gravity with preferred Newtonian frame
(X^i(x),T(x)) by
  L = L_{GR}
  + \Xi g^{mn}\delta_{ij}X^i_{,m}X^j_{,n}
  - \Upsilon g^{mn}T_{,m}T_{,n}
  It allows a condensed matter interpretation which generalizes LET to gravity.
  The \Xi-term influences the age of the universe. \Upsilon>0 allows to avoid
big bang singularity and black hole horizon formation. This solves the horizon
problem without inflation. An atomic hypothesis solves the ultraviolet problem
by explicit regularization. We give a prediction about cutoff length.


title: A comment on the Outgoing Radiation Condition and the Peeling Theorem

abstract:
  The connection between the Bondi-Sachs (BS) and the Newman-Penrose (NP)
framework for the study of the asymptotics of the gravitational field is done.
In particular the coordinate transformation relationg the BS luminosity
parameter and the NP affine parameter is obtained. Using this coordinate
transformation it is possible to express BS quantities in terms of NP
quantities, and to show that if the Outgoing Radiation Condition is not
satisfied then the spacetime will not decay in the way prescribed by the
Peeling theorem.


title: Evolution of the density contrast in inhomogeneous dust models

abstract:
  With the help of families of density contrast indicators, we study the
tendency of gravitational systems to become increasingly lumpy with time.
Depending upon their domain of definition, these indicators could be local or
global. We make a comparative study of these indicators in the context of
inhomogeneous cosmological models of Lemaitre--Tolman and Szekeres. In
particular, we look at the temporal asymptotic behaviour of these indicators
and ask under what conditions, and for which class of models, they evolve
monotonically in time. We find that for the case of ever-expanding models,
there is a larger class of indicators that grow monotonically with time,
whereas the corresponding class for the recollapsing models is more restricted.
Nevertheless, in the absence of decaying modes, indicators exist which grow
monotonically with time for both ever-expanding and recollapsing models
simultaneously. On the other hand, no such indicators may found which grow
monotonically if the decaying modes are allowed to exist. We also find the
conditions for these indicators to be non-divergent at the initial singularity
in both models. Our results can be of potential relevance for understanding
structure formation in inhomogeneous settings and in debates regarding
gravitational entropy and arrow of time. In particular, the spatial dependence
of turning points in inhomogeneous cosmologies may result in multiple density
contrast arrows in recollapsing models over certain epochs. We also find that
different notions of asymptotic homogenisation may be deduced, depending upon
the density contrast indicators used.


title:
The Confrontation between General Relativity and Experiment: A 1998
  Update

abstract:
  The status of experimental tests of general relativity and of theoretical
frameworks for analysing them are reviewed. Einstein's equivalence principle
(EEP) is well supported by experiments such as the E\"otv\"os experiment, tests
of special relativity, and the gravitational redshift experiment. Future tests
of EEP will search for new interactions arising from unification or quantum
gravity. Tests of general relativity have reached high precision, including the
light deflection, the Shapiro time delay, the perihelion advance of Mercury,
and the Nordtvedt effect in lunar motion. Gravitational wave damping has been
detected to half a percent using the binary pulsar, and new binary pulsar
systems promise further improvements. When direct observation of gravitational
radiation from astrophysical sources begins, new tests of general relativity
will be possible.


title: Causality and Cosmic Inflation

abstract:
  In the context of inflationary models with a pre-inflationary stage, in which
the Einstein equations are obeyed, the weak energy condition is satisfied, and
spacetime topology is trivial, we argue that homogeneity on super-Hubble scales
must be assumed as an initial condition. Models in which inflation arises from
field dynamics in a Friedman-Robertson-Walker background fall into this class
but models in which inflation originates at the Planck epoch, {\it eg.} chaotic
inflation, may evade this conclusion. Our arguments rest on causality and
general relativistic constraints on the structure of spacetime. We discuss
modifications to existing scenarios that may avoid the need for initial
large-scale homogeneity.


title: Spikes in Cosmic Crystallography

abstract:
  If the universe is multiply connected and small the sky shows multiple images
of cosmic objects, correlated by the covering group of the 3-manifold used to
model it. These correlations were originally thought to manifest as spikes in
pair separation histograms (PSH) built from suitable catalogues. Using
probability theory we derive an expression for the expected pair separation
histogram (EPSH) in a rather general topological-geometrical-observational
setting. As a major consequence we show that the spikes of topological origin
in PSH's are due to translations, whereas other isometries manifest as tiny
deformations of the PSH corresponding to the simply connected case. This result
holds for all Robertson-Walker spacetimes and gives rise to two basic
corollaries: (i) that PSH's of Euclidean manifolds that have the same
translations in their covering groups exhibit identical spike spectra of
topological origin, making clear that even if the universe is flat the
topological spikes alone are not sufficient for determining its topology; and
(ii) that PSH's of hyperbolic 3-manifolds exhibit no spikes of topological
origin. These corollaries ensure that cosmic crystallography, as originally
formulated, is not a conclusive method for unveiling the shape of the universe.
We also present a method that reduces the statistical fluctuations in PSH's
built from simulated catalogues.


title: Riemann-Hilbert Problems for the Ernst Equation and Fibre Bundles

abstract:
  Riemann--Hilbert techniques are used in the theory of completely integrable
differential equations to generate solutions that contain a free function which
can be used at least in principle to solve initial or boundary value problems.
The solution of a boundary value problem is thus reduced to the identification
of the jump data of the Riemann-Hilbert problem from the boundary data. But
even if this can be achieved,it is very difficult to get explicit solutions
since the matrix Riemann-Hilbert problem is equivalent to an integral equation.
In the case of the Ernst equation (the stationary axisymmetric Einstein
equations in vacuum), it was shown in a previous work that the matrix problem
is gauge equivalent to a scalar problem on a Riemann surface. If the jump data
of the original problem are rational functions, this surface will be compact
which makes it possible to give explicit solutions in terms of hyperelliptic
theta functions. In the present work, we discuss Riemann-Hilbert problems on
Riemann surfaces in the framework of fibre bundles. This makes it possible to
treat the compact and the non-compact case in the same setting and to apply
general existence theorems.


title: Early cosmology and the stochastic gravitational wave background

abstract:
  The epoch when the Universe had a temperature higher than a GeV is long
before any time at which we have reliable observations constraining the
cosmological evolution. For example, the occurrence of a second burst of
inflation (sometimes called thermal inflation) at a lower energy scale than
standard inflation, or a short epoch of early matter domination, cannot be
ruled out by present cosmological data. The cosmological stochastic
gravitational wave background, on scales accessible to interferometer
detection, is sensitive to non-standard cosmologies of this type. We consider
the implications of such alternative models both for ground-based experiments
such as LIGO and space-based proposals such as LISA. We show that a second
burst of inflation leads to a scale-dependent reduction in the spectrum.
Applied to conventional inflation, this further reduces an already
disappointingly low signal. In the pre big bang scenario, where a much more
potent signal is possible, the amplitude is reduced but the background remains
observable by LISA in certain parameter space regions. In each case, a second
epoch of inflation induces oscillatory features into the spectrum in a manner
analogous to the acoustic peaks in the density perturbation spectrum. On LIGO
scales, perturbations can only survive through thermal inflation with
detectable amplitudes if their amplitudes were at one time so large that linear
perturbation theory is inadequate. Although for an epoch of early matter
domination the reduction in the expected signal is not as large as the one
caused by a second burst of inflation, the detection in the context of the pre
big bang scenario may not be possible since the spectrum peaks around the LIGO
frequency window and for lower frequencies behaves as $f^3$.


title: Gauge Fixing in Higher Derivative Gravity

abstract:
  Linearized four-derivative gravity with a general gauge fixing term is
considered. By a Legendre transform and a suitable diagonalization procedure it
is cast into a second-order equivalent form where the nature of the physical
degrees of freedom, the gauge ghosts, the Weyl ghosts, and the intriguing
"third ghosts", characteristic to higher-derivative theories, is made explicit.
The symmetries of the theory and the structure of the compensating
Faddeev-Popov ghost sector exhibit non-trivial peculiarities.


title: Black Holes in Higher Curvature Gravity

abstract:
  A review of recent investigations of black holes in higher curvature theories
of gravity.


title: On Bose-Einstein condensation on closed Robertson-Walker spacetimes

abstract:
  In this letter we summarize our analysis of Bose-Einstein condensation on
closed Robertson-Walker spacetimes. In a previous work we defined an adiabatic
KMS state on the Weyl-algebra of the free massive Klein-Gordon field. This
state describes a free Bose gas on Robertson-Walker spacetimes. We use this
state to analyze the possibility of Bose-Einstein condensation on closed
Robertson-Walker spacetimes. We take into account the effects due to the
finiteness of the spatial volume and show that they are not relevant in the
early universe. Furthermore we show that a critical radius can be defined. The
condensate disappears above the critical radius.


title: Solitons of Induced Scalar Field and Their Stability

abstract:
  Exact particle-like static, spherically and/or cylindrically symmetric
solutions to the equations of interacting scalar and electromagnetic field
system have been obtained. We considered Freedman-Robertson-Walker (FRW)
space-time as an external homogenous and isotropic gravitational field whereas
the homogeneous and anisotropic Universe is given by the G$\ddot o$del model.
Beside the usual solitonian solutions some special regular solutions know as
droplets, anti-droplets and bags (confined in finite interval and having
trivial value beyond it) have been obtained. It has been shown that in FRW
space-time equations with different interaction terms may have stable solutions
while within the scope of G$\ddot o$del model only the droplet-like and the
hat-like configurations may be stable, if they are located in the region where
$g^{00}>0$.


title: Gravitational torsion kinks and thick domain walls

abstract:
  The dynamics of a gravitational torsion kink as a plane symmetric thick
domain wall solution of Einstein-Cartan (EC) field equation is given. The
spin-torsion energy has to be as high as the gravitational kink potential
otherwise torsion will not contribute as an appreciable effect to domain
wall.Cartan torsion also contributes to the orthonal pressure of the domain
wall.


title:
Global Dynamics of Cosmological Expansion with Minimally Coupled Scalar
  Field

abstract:
  We give a complete description of the asymptotic behavior of a
Friedmann-Robertson-Walker Universe with ``normal'' matter and a minimally
coupled scalar field. We classify the conditions under which the Universe is or
is not accelerating. In particular, we show that only two types of large time
behavior exist: an exponential regime, and a subexponential expansion with the
logarithmic derivative of the scale factor tending to zero. In the case of the
subexponetial expansion the Universe accelerates when the scalar field energy
density is dominant and the potential behaves in a specified manner, or if
matter violates the strong energy conditon $\rho + 3p >0$. When the expansion
is exponential the Universe accelerates, and the scalar field energy density is
dominant. We also find that the existence of the Big Bang and a never ending
expansion of the Universe constrain the equation of state of matter at large
and small densities, respectively.


title:
Conformal transformations in classical gravitational theories and in
  cosmology

abstract:
  In recent years, the use of conformal transformation techniques has become
widespread in the literature on gravitational theories alternative to general
relativity, on cosmology, and on nonminimally coupled scalar fields. Typically,
the transformation to the Einstein frame is generated by a fundamental scalar
field already present in the theory. In this context, the problem of which
conformal frame is the physical one has to be dealt with and, in the general
case, it has been clarified only recently; the formulation of a theory in the
``new'' conformal frame leads to departures from canonical Einstein gravity. In
this article, we review the literature on conformal transformations in
classical gravitational theories and in cosmology, seen both as purely
mathematical tools and as maps with physically relevant aspects. It appears
particularly urgent to refer the analysis of experimental tests of Brans-Dicke
and scalar-tensor theories of gravity, as well as the predictions of
cosmological inflationary scenarios, to the physical conformal frame, in order
to have a meaningful comparison with the observations.


title: Locally Anisotropic (2+1)--Dimensional Black Holes

abstract:
  In this paper we analyze the conditions when the Einstein equations with
cosmological constant and matter describe (2+1)-dimensional generic locally
anisotropic (la) spacetimes of generalized Finsler type. New classes of
solutions for such la-spacetimes are constructed. There are investigated black
la-holes with the induced from general relativity la-curvature and la-torsion
and, as a particular case, the black la-hole solutions are found for
teleparallel la-spaces. In a more general context we consider the
la-renormalization of black hole constants via the receptivity of
la-spacetimes. We speculate on the properties of (2+1)-dimensional black
la-holes with unusual characteristics defined by la-interactions of matter and
gravity. The thermodynamics of black la-holes is discussed in connection with a
possible statistical mechanics background based on locally anisotropic variants
of Chern-Simons theories.


title: The Friedmannian model of our observed Universe

abstract:
  According to observations, in our Universe for gravitational phenomena in a
Newtonian approximation the Newtonian non-modified relations are valid. The
Friedmann equations of universe dynamics describe infinite number of
relativistic universe models in Newtonian approximation, but only in one of
them the Newtonian non-modified relations are valid. From these facts it
results that the Universe is described just by this only Friedmannian universe
model with Newtonian non-modified relations.


title:
Can the Decoherent Histories Description of Reality be Considered
  Satisfactory?

abstract:
  We discuss some features of the Decoherent Histories approach. We consider
four assumptions, the first three being in our opinion necessary for a sound
interpretation of the theory, while the fourth one is accepted by the
supporters of the DH approach, and we prove that they lead to a logical
contradiction. We discuss the consequences of relaxing any one of them.


title:
Dynamics of spatially homogeneous solutions of the Einstein-Vlasov
  equations which are locally rotationally symmetric

abstract:
  The dynamics of a class of cosmological models with collisionless matter and
four Killing vectors is studied in detail and compared with that of
corresponding perfect fluid models. In many cases it is possible to identify
asymptotic states of the spacetimes near the singularity or in a phase of
unlimited expansion. Bianchi type II models show oscillatory behaviour near the
initial singularity which is, however, simpler than that of the mixmaster
model.


title: The gravitational interaction of light: from weak to strong fields

abstract:
  An explanation is proposed for the fact that pp-waves superpose linearly when
they propagate parallely, while they interact nonlinearly, scatter and form
singularities or Cauchy horizons if they are antiparallel. Parallel pp-waves do
interact, but a generalized gravitoelectric force is exactly cancelled by a
gravitomagnetic force. In an analogy, the interaction of light beams in
linearized general relativity is also revisited and clarified, a new result is
obtained for photon to photon attraction, and a conjecture is proved. Given
equal energy density in the beams, the light-to-light attraction is twice the
matter-to-light attraction and four times the matter-to-matter attraction.


title:
The internal description of a causal set: What the universe looks like
  from the inside

abstract:
  We describe an algebraic way to code the causal information of a discrete
spacetime. The causal set C is transformed to a description in terms of the
causal pasts of the events in C. This is done by an evolving set, a functor
which to each event of C assigns its causal past. Evolving sets obey a Heyting
algebra which is characterised by a non-standard notion of complement.
Conclusions about the causal structure of the causal set can be drawn by
calculating the complement of the evolving set. A causal quantum theory can be
based on the quantum version of evolving sets, which we briefly discuss.


title: Colliding spherically symmetric null dust in equilibrium

abstract:
  We present two recently obtained solutions of the Einstein equations with
spherical symmetry and one additional Killing vector, describing colliding null
dust streams.


title: Spin effects in radiating compact binaries

abstract:
  We review and summarize our results concerning the influence of the spins of
a compact binary system on the motion of the binary and on its gravitational
reaction. We describe briefly our method which lead us to compute the secular
changes in the post-Newtonian motion and the averaged radiative losses. Our
description is valid to 1.5 post-Newtonian order. All spin-orbit and some
spin-spin effects are considered which contribute at this accuracy. This
approach enabled us to give both the evolutions of the constants of the
nonradiative motion and of the relevant angular variables under radiation
reaction.


title: Rotating incompressible perfect fluid source of the NUT metric

abstract:
  A global solution of the Einstein equations is given, consisting of a perfect
fluid interior and a vacuum exterior. The rigidly rotating and incompressible
perfect fluid is matched along the hypersurface of vanishing pressure with the
stationary part of the Taub-NUT metric. The fluid core generates a
negative-mass NUT space-time. The matching procedure leaves one parameter in
the global solution.


title: Gravitational Collapse of Perfect Fluid

abstract:
  The spherical gravitational collapse of a compact packet consisting of
perfect fluid is studied. The spacetime outside the fluid packet is described
by the out-going Vaidya radiation fluid. It is found that when the collapse has
continuous self-similarity the formation of black holes always starts with zero
mass, and when the collapse has no self-similarity, the formation of black
holes always starts with a finite non-zero mass. The packet is usually
accompanied by a thin matter shell. The effects of the shell on the collapse
are also studied.


title: Varying c cosmology and Planck value constraints

abstract:
  It has been suggested that by increasing the speed of light during the early
universe various cosmological problems of standard big bang cosmology can be
overcome, without requiring an inflationary phase. However, we find that as the
Planck length and Planck time are then made correspondingly smaller, and
together with the need that the universe should not re-enter a Planck epoch,
the higher $c$ models have very limited ability to resolve such problems. For a
constantly decreasing $c$ the universe will quickly becomes quantum
gravitationally dominated as time increases: the opposite to standard cosmology
where quantum behaviour is only ascribed to early times.


title: Dirac monopoles on Kerr black holes: comparing gauges

abstract:
  We update our previous work on the description of twisted configurations for
complex massless scalar field on the Kerr black holes as the sections of
complex line bundles over the Kerr black hole topology. From physical point of
view the appearance of twisted configurations is linked with the natural
presence of Dirac monopoles that arise as connections in the above line
bundles. We consider their description in the gauge inequivalent to the one
studied previously and discuss a row of new features appearing in this gauge.


title:
Quantum properties of the electron field in Kerr-Newman black hole
  manifolds

abstract:
  We study some spectral features of the one-particle electron Hamiltonian
obtained by separating the Dirac equation in a Kerr-Newman black hole
background. We find that the essential spectrum includes the whole real line.
As a consequence, there is no gap in the spectrum and discrete eigenvalues are
not allowed for any value of the black hole charge $Q$ and angular momentum
$J$. Our spectral analysis will be also related to the dissipation of the black
hole angular momentum and charge.


title: Exact Relativistic Two-Body Motion in Lineal Gravity

abstract:
  We consider the N-body problem in (1+1) dimensional lineal gravity. For 2
point masses (N=2) we obtain an exact solution for the relativistic motion. In
the equal mass case we obtain an explicit expression for their proper
separation as a function of their mutual proper time. Our solution gives the
exact Hamiltonian to infinite order in the gravitational coupling constant.


title: Mass Quantization of the Schwarzschild Black Hole

abstract:
  We examine the Wheeler-DeWitt equaton for a static, eternal Schwarzschild
black hole in Kucha\v r-Brown variables and obtain its energy eigenstates.
Consistent solutions vanish in the exterior of the Kruskal manifold and are
non-vanishing only in the interior. The system is reminiscent of a particle in
a box. States of definite parity avoid the singular geometry by vanishing at
the origin. These definite parity states admit a discrete energy spectrum,
depending on one quantum number which determines the Arnowitt-Deser-Misner
(ADM) mass of the black hole according to a relation conjectured long ago by
Bekenstein, $M \sim \sqrt{n}M_p$. If attention is restricted only to these
quantized energy states, a black hole is described not only by its mass but
also by its parity. States of indefinite parity do not admit a quantized mass
spectrum.


title: Causal Dissipative Cosmology With Variable G and Lambda

abstract:
  A cosmological model with variable G and Lambda is considered in the
framework of Israel-Stewart-Hiscock (ISH) causal theory. Power law as well as
inflationary solutions are obtained. The gravitational constant is found to
increase with time.


title: Spatially self-similar spherically symmetric perfect-fluid models

abstract:
  Einstein's field equations for spatially self-similar spherically symmetric
perfect-fluid models are investigated. The field equations are rewritten as a
first-order system of autonomous differential equations. Dimensionless
variables are chosen in such a way that the number of equations in the coupled
system is reduced as far as possible and so that the reduced phase space
becomes compact and regular. The system is subsequently analysed qualitatively
with the theory of dynamical systems.


title: Timelike self-similar spherically symmetric perfect-fluid models

abstract:
  Einstein's field equations for timelike self-similar spherically symmetric
perfect-fluid models are investigated. The field equations are rewritten as a
first-order system of autonomous differential equations. Dimensionless
variables are chosen in such a way that the number of equations in the coupled
system is reduced as far as possible and so that the reduced phase space
becomes compact and regular. The system is subsequently analysed qualitatively
using the theory of dynamical systems.


title: O(d,d)-invariance in inhomogeneous string cosmologies with perfect fluid

abstract:
  In the first part of the present paper, we show that O(d,d)-invariance
usually known in a homogeneous cosmological background written in terms of
proper time can be extended to backgrounds depending on one or several
coordinates (which may be any space-like or time-like coordinate(s)). In all
cases, the presence of a perfect fluid is taken into account and the equivalent
duality transformation in Einstein frame is explicitly given. In the second
part, we present several concrete applications to some four-dimensional
metrics, including inhomogeneous ones, which illustrate the different duality
transformations discussed in the first part. Note that most of the dual
solutions given here do not seem to be known in the literature.


title: Must Quantum Spacetimes Be Euclidean?

abstract:
  The Bohm-de Broglie interpretation of quantum mechanics is applied to
canonical quantum cosmology. It is shown that, irrespective of any
regularization or choice of factor ordering of the Wheeler-DeWitt equation, the
unique relevant quantum effect which does not break spacetime is the change of
its signature from lorentzian to euclidean. The other quantum effects are
either trivial or break the four-geometry of spacetime. A Bohm-de Broglie
picture of a quantum geometrodynamics is constructed, which allows the
investigation of these latter structures. For instance, it is shown that any
real solution of the Wheeler-De Witt equation yields a generate four-geometry
compatible with the strong gravity limit of General Relativity and the Carroll
group. Due to the more detailed description of quantum geometrodynamics given
by the Bohm-de Broglie interpretation, some new boundary conditions on
solutions of the Wheeler-DeWitt equation must be imposed in order to preserve
consistency of this finer view.


title: Homogeneous cosmologies with cosmological constant

abstract:
  Spatially homogeneous cosmological models with a positive cosmological
constant are investigated, using dynamical systems methods. We focus on the
future evolution of these models. In particular, we address the question
whether there are models within this class that are de Sitter-like in the
future, but are tilted.


title: Noise induced inflation

abstract:
  We consider a closed Friedmann-Robertson-Walker Universe driven by the back
reaction from a massless, non-conformally coupled quantum scalar field. We show
that the back-reaction of the quantum field is able to drive the cosmological
scale factor over the barrier of the classical potential so that if the
universe starts near zero scale factor (initial singularity) it can make the
transition to an exponentially expanding de Sitter phase, with a probability
comparable to that from quantum tunneling processes. The emphasis throughout is
on the stochastic nature of back reaction, which comes from the quantum
fluctuations of the fundamental fields.


title: On the semiclassical Einstein-Langevin equation

abstract:
  We introduce a semiclassical Einstein-Langevin equation as a consistent
dynamical equation for a first order perturbative correction to semiclassical
gravity. This equation includes the lowest order quantum stress-energy
fluctuations of matter fields as a source of classical stochastic fluctuations
of the gravitational field. The Einstein-Langevin equation is explicitly solved
around one of the simplest solutions of semiclassical gravity: Minkowski
spacetime with a conformal scalar field in its vacuum state. We compute the
two-point correlation function of the linearized Einstein tensor. This
calculation illustrates the possibility of obtaining some ``non-perturbative''
behavior for the induced gravitational fluctuations that cannot be obtained in
perturbative quantum gravity.


title: BTZ Black Hole Entropy from Ponzano-Regge Gravity

abstract:
  The entropy of the BTZ black hole is computed in the Ponzano-Regge
formulation of three-dimensional lattice gravity. It is seen that the correct
semi-classical behaviour of entropy is reproduced by states that correspond to
all possible triangulations of the Euclidean black hole.


title:
Spectrum of radiation of a classical electron moving in the de Sitter
  spacetime

abstract:
  The radiation spectrum of a classical charged particle (electron) moving in
the de Sitter universe, has been calculated. The de Sitter metric is taken in
the quasi-Euclidean Robertson-Walker form. It is shown that in the de Sitter
spacetime an electron radiates as if it moved in a constant and homogeneous
electric field with the strength vector E collinear to the electron momentum P.


title: General Ether Theory and Graviton Mass

abstract:
  We introduce additional restriction into "general ether theory" - a
generalization of Lorentz ether theory to gravity - which fixes the signs of
the cosmological constants in this theory. This leads to an oscillating
universe, thus, solves the cosmological horizon problem without inflation.
  We prove the equivalence of the Lagrangian of this theory with Logunov's
"relativistic theory of gravity" with massive graviton and a variant of GR with
four non-standard scalar fields and negative cosmological constant.
  We consider the remaining differences between these theories.


title:
Exact analytic characteristic initial data for axisymmetric,
  non-rotating, vacuum spacetimes, with an application to the binary black hole
  problem

abstract:
  Bondi's approach to the construction of a coordinate system is used with a
different choice of gauge, in accordance with which the radial coordinate r is
an affine parameter, to cast the metric tensor into a form suitable for use
with the Newman-Penrose null tetrad formalism. The choice of tetrad has the
result that the equations and all the functions that appear in them are
real-valued. A group classification of the Sachs equations in this gauge leads
to a unique expression for the first of the five independent elements $\Psi_0$
of the Weyl spinor, and to the corresponding exact solutions for two of the
metric functions on an initial null hypersurface. A proof is presented that the
result for $\Psi_0$ constitutes the appropriate characteristic initial value
function for all physically realistic axisymmetric, non-rotating vacuum
spacetimes. Integration of the field equations on the axis of symmetry when an
equatorial symmetry plane is also present, and on the equatorial plane itself
when time rates of change can be neglected, shows that these data produce
results consistent with Newton's laws and with the Schwarzschild solution in
the appropriate limits. The solution on the axis of symmetry indicates that the
Weyl curvature increases without limit between black holes as their separation
decreases.


title:
Initial Hypersurface Formulation: Hamilton-Jacobi Theory for Strongly
  Coupled Gravitational Systems

abstract:
  Strongly coupled gravitational systems describe Einstein gravity and matter
in the limit that Newton's constant G is assumed to be very large. The
nonlinear evolution of these systems may be solved analytically in the
classical and semiclassical limits by employing a Green function analysis.
Using functional methods in a Hamilton-Jacobi setting, one may compute the
generating functional (`the phase of the wavefunctional') which satisfies both
the energy constraint and the momentum constraint. Previous results are
extended to encompass the imposition of an arbitrary initial hypersurface. A
Lagrange multiplier in the generating functional restricts the initial fields,
and also allows one to formulate the energy constraint on the initial
hypersurface. Classical evolution follows as a result of minimizing the
generating functional with respect to the initial fields. Examples are given
describing Einstein gravity interacting with either a dust field and/or a
scalar field. Green functions are explicitly determined for (1) gravity, dust,
a scalar field and a cosmological constant and (2) gravity and a scalar field
interacting with an exponential potential. This formalism is useful in solving
problems of cosmology and of gravitational collapse.


title: Boundary Terms and Noether Current of Sphereical Black Holes

abstract:
  We consider two proposals for defining black hole entropy in spherical
symmetry, where the horizon is defined locally as a trapping horizon. The first
case, boundary terms in a dual-null form of the reduced action in two
dimensions, gives a result that is proportional to the area. The second case,
Wald's Noether current method, is generalized to dynamic black holes, giving an
entropy that is just the area of the trapping horizon. These results are
compared with a generalized first law of thermodynamics.


title:
Modelling general relativistic perfect fluids in field theoretic
  language

abstract:
  Skew-symmetric massless fields, their potentials being $r$-forms, are close
analogues of Maxwell's field (though the non-linear cases also should be
considered). We observe that only two of them ($r=$2 and 3) automatically yield
stress-energy tensors characteristic to normal perfect fluids. It is shown that
they naturally describe both non-rotating ($r=2$) and rotating (then a
combination of $r=2$ and $r=3$ fields is indispensable) general relativistic
perfect fluids possessing every type of equations of state. Meanwile, a free
$r=3$ field is completely equivalent to appearance of the cosmological term in
Einstein's equations. Sound waves represent perturbations propagating on the
background of the $r=2$ field. Some exotic properties of these two fields are
outlined.


title: The action operator for continuous-time histories

abstract:
  We define the action operator in the consistent histories formalism, as the
quantum analogue of the classical action functional, for the simple harmonic
oscillator case. The action operator is shown to be the generator of time
transformations, and to be associated with the two types of time-evolution of
the standard quantum theory: the wave-packet reduction and the unitary
time-evolution. We construct the corresponding classical histories and
demonstrate the relevance with the quantum histories. Finally, we show the
relation of the action operator to the decoherence functional.


title: Instantons For Black Hole Pair Production

abstract:
  We address the issue of constructing continuous instantons representing the
pair creation of black holes in a cosmological context. The recent attempt at
constructing such solutions using virtual domain walls is reviewed first. We
then explore the existence of continuous instantons in higher curvature gravity
theories where the Lagrangian is polynomial in the Ricci scalar. Lastly, we
study continuous instanton solutions of ordinary gravity coupled to the
Narlikar C-field. For each theory, we first consider the case of finding
continuous instanton solutions which represent the "near-annihilation" of a de
Sitter universe and its subsequent recreation. In situations where these
solutions exist, we then ask whether solutions can be found that represent the
"near-annihilation" of a de Sitter spacetime and the subsequent creation of a
pair of Schwarzschild-de Sitter black holes.


title: On Duru-Kleinert Path Integral In Quantum Cosmology

abstract:
  We show that the Duru-Kleinert fixed energy amplitude leads to the path
integral for the propagation amplitude in the closed FRW quantum cosmology with
scale factor as one degree of freedom. Then, using the Duru-Kleinert
equivalence of corresponding actions, we calculate the tunneling rate, with
exact prefactor, through the dilute-instanton approximation to first order in
\hbar.


title:
Tunneling in a Cosmological Model with Violation of Strong Energy
  Condition

abstract:
  The tunneling rate, with exact prefactor, is calculated to first order in
\hbar for a closed FRW universe filled with perfect fluid violating the strong
energy condition. The calculations are performed by applying the
dilute-instanton approximation on the corresponding Duru-Kleinert path
integral. It is shown that a closed FRW universe filled with a perfect fluid
with small violation of strong energy condition is more probable to tunnel than
the same universe with large violation of strong energy condition.


title:
Tunneling in $\Lambda$ Decaying Cosmologies and the Cosmological
  Constant Problem

abstract:
  The tunneling rate, with exact prefactor, is calculated to first order in
$\hbar$ for an empty closed Friedmann-Robertson-Walker (FRW) universe with
decaying cosmological term $\Lambda \sim R^{-m}$ ($R$ is the scale factor and
$m$ is a parameter $0\leq m \leq 2$). This model is equivalent to a cosmology
with the equation of state $p_{\chi}=(m/3 -1)\rho_{\chi}$. The calculations are
performed by applying the dilute-instanton approximation on the corresponding
Duru-Kleinert path integral.
  It is shown that the highest tunneling rate occurs for $m=2$ corresponding to
the cosmic string matter universe. The obtained most probable cosmological
term, like one obtained by Strominger, accounts for a possible solution to the
cosmological constant problem.


title:
Stochastic approach to inflation II: classicality, coarse-graining and
  noises

abstract:
  In this work we generalize a previously developed semiclassical approach to
inflation, devoted to the analysis of the effective dynamics of coarse-grained
fields, which are essential to the stochastic approach to inflation. We
consider general non-trivial momentum distributions when defining these fields.
The use of smooth cutoffs in momentum space avoids highly singular quantum
noise correlations and allows us to consider the whole quantum noise sector
when analyzing the conditions for the validity of an effective classical
dynamical description of the coarse-grained field. We show that the weighting
of modes has physical consequences, and thus cannot be considered as a mere
mathematical artifact. In particular we discuss the exponential inflationary
scenario and show that colored noises appear with cutoff dependent amplitudes.


title: A class of quasi-linear equations in coframe gravity

abstract:
  We have shown recently that the gravity field phenomena can be described by a
traceless part of the wave-type field equation. This is an essentially
non-Einsteinian gravity model. It has an exact spherically-symmetric static
solution, that yields to the Yilmaz-Rosen metric. This metric is very close to
the Schwarzchild metric. The wave-type field equation can not be derived from a
suitable variational principle by free variations, as it was shown by Hehl and
his collaborates. In the present work we are seeking for another field equation
having the same exact spherically-symmetric static solution. The
differential-geometric structure on the manifold endowed with a smooth
orthonormal coframe field is described by the scalar objects of anholonomity
and its exterior derivative. We construct a list of the first and second order
SO(1,3)-covariants (one- and two-indexed quantities) and a quasi-linear field
equation with free parameters. We fix a part of the parameters by a condition
that the field equation is satisfied by a quasi-conformal coframe with a
harmonic conformal function. Thus we obtain a wide class of field equations
with a solution that yields the Majumdar-Papapetrou metric and, in
particularly, the Yilmaz-Rosen metric, that is viable in the framework of three
classical tests.


title: Measures of gravitational entropy I. Self-similar spacetimes

abstract:
  We examine the possibility that the gravitational contribution to the entropy
of a system can be identified with some measure of the Weyl curvature. In this
paper we consider homothetically self-similar spacetimes. These are believed to
play an important role in describing the asymptotic properties of more general
models. By exploiting their symmetry properties we are able to impose
significant restrictions on measures of the Weyl curvature which could reflect
the gravitational entropy of a system. In particular, we are able to show, by
way of a more general relation, that the most widely used "dimensionless"
scalar is \textit{not} a candidate for this measure along homothetic
trajectories.


title:
Hamiltonian formulation and exact solutions of the Bianchi type I
  space-time in conformal gravity

abstract:
  We develop a Hamiltonian formulation of the Bianchi type I space-time in
conformal gravity, i.e. the theory described by a Lagrangian that is defined by
the contracted quadratic product of the Weyl tensor, in a four-dimensional
space-time. We derive the explicit forms of the super-Hamiltonian and of the
constraint expressing the conformal invariance of the theory and we write down
the system of canonical equations. To seek out exact solutions of this system
we add extra constraints on the canonical variables and we go through a global
involution algorithm which eventually leads to the closure of the constraint
algebra. The Painleve approach provides us with a proof of non-integrability,
as a consequence of the presence of movable logarithms in the general solution
of the problem. We extract all possible particular solutions that may be
written in closed analytical form. This enables us to demonstrate that the
global involution algorithm has brought forth the complete list of exact
solutions that may be written in closed analytical form. We discuss the
conformal relationship, or absence thereof, of our solutions with Einstein
spaces.


title:
Primordial Magnetic Fields via Spontaneous Breaking of Lorentz
  Invariance

abstract:
  Spontaneous breaking of Lorentz invariance compatible with observational
limits may realistically take place in the context of string theories, possibly
endowing the photon with a mass. In this process the conformal symmetry of the
electromagnetic action is broken allowing for the possibility of generating
large scale ($\sim Mpc$) magnetic fields within inflationary scenarios. We show
that for reheating temperatures safe from the point of view of the gravitino
and moduli problem, $T_{RH} \laq 10^{9} GeV$ for $m_{3/2} \approx 1 TeV$, the
strength of the generated seed fields is, in our mechanism, consistent with
amplification by the galactic dynamo processes and can be even as large as to
explain the observed galactic magnetic fields through the collapse of
protogalactic clouds.


title: Causal Set Dynamics: A Toy Model

abstract:
  We construct a quantum measure on the power set of non-cyclic oriented graphs
of N points, drawing inspiration from 1-dimensional directed percolation.
Quantum interference patterns lead to properties which do not appear to have
any analogue in classical percolation. Most notably, instead of the single
phase transition of classical percolation, the quantum model displays two
distinct crossover points. Between these two points, spacetime questions such
as "does the network percolate" have no definite or probabilistic answer.


title: Spectral methods in general relativistic astrophysics

abstract:
  We present spectral methods developed in our group to solve three-dimensional
partial differential equations. The emphasis is put on equations arising from
astrophysical problems in the framework of general relativity.


title: Scintillation in scalar-tensor theories of gravity

abstract:
  We study the scintillation produced by time-varying gravitational fields
within scalar-tensor theories of gravity. The problem is treated in the
geometrical optics approximation for a very distant light source emitting quasi
plane monochromatic electromagnetic waves. We obtain a general formula giving
the time dependence of the photon flux received by a freely falling observer.
In the weak-field approximation, we show that the contribution to the
scintillation effect due to the focusing of the light beam by a gravitational
wave is of first order in the amplitude of the scalar perturbation. Thus
scalar-tensor theories contrast with general relativity, which predicts that
the only first-order effect is due to the spectral shift. Moreover, we find
that the scintillation effects caused by the scalar field have a local
character: they depend only on the value of the perturbation at the observer.
This effect provides in principle a mean to detect the presence of a long range
scalar field in the Universe, but its smallness constitutes a tremendous
challenge for detection.


title: Effective one-body approach to general relativistic two-body dynamics

abstract:
  We map the general relativistic two-body problem onto that of a test particle
moving in an effective external metric. This effective-one-body approach
defines, in a non-perturbative manner, the late dynamical evolution of a
coalescing binary system of compact objects. The transition from the adiabatic
inspiral, driven by gravitational radiation damping, to an unstable plunge,
induced by strong spacetime curvature, is predicted to occur for orbits more
tightly bound than the innermost stable circular orbit in a Schwarzschild
metric of mass M = m1 + m2. The binding energy, angular momentum and orbital
frequency of the innermost stable circular orbit for the time-symmetric
two-body problem are determined as a function of the mass ratio.


title: Covariant Analysis of Gravitational Waves in a Cosmological Context

abstract:
  The propagation of gravitational waves or tensor perturbations in a perturbed
Friedmann-Robertson-Walker universe filled with a perfect fluid is re-examined.
It is shown that while the shear and magnetic part of the Weyl tensor satisfy
linear, homogeneous {\it second order} wave equations, for perfect fluids with
a $\gamma$\hs law equation of state satisfying $\case{2}/{3}<\gamma<2$, the
electric part of the Weyl tensor satisfies a linear homogeneous {\it third
order} equation. Solutions to these equations are obtained for a flat
Friedmann-Robertson-Walker background and we discuss implications of this
result.


title: Spacetime Exterior to a Star: Against Asymptotic Flatness

abstract:
  In many circumstances the perfect fluid conservation equations can be
directly integrated to give a Geometric-Thermodynamic equation: typically that
the lapse $N$ is the reciprocal of the enthalphy $h$, ($ N=1/h$). This result
is aesthetically appealing as it depends only on the fluid conservation
equations and does not depend on specific field equations such as Einstein's.
Here the form of the Geometric-Thermodynamic equation is derived subject to
spherical symmetry and also for the shift-free ADM formalism. There at least
three applications of the Geometric-Thermodynamic equation, the most important
being to the notion of asympotic flatness and hence to spacetime exterior to a
star. For asymptotic flatness one wants $h\to 0$ and $N\to 1$ simultaneously,
but this is incompatible with the Geometric-Thermodynamic equation.
Observational data and asymptotic flatness are discussed. It is argued that a
version of Mach's principle does not allow asymptotic flatness.


title: Geometry of 2d spacetime and quantization of particle dynamics

abstract:
  We analyze classical and quantum dynamics of a particle in 2d spacetimes with
constant curvature which are locally isometric but globally different. We show
that global symmetries of spacetime specify the symmetries of physical
phase-space and the corresponding quantum theory. To quantize the systems we
parametrize the physical phase-space by canonical coordinates. Canonical
quantization leads to unitary irreducible representations of $SO_\uparrow
(2.1)$ group.


title:
A dissipative algorithm for wave-like equations in the characteristic
  formulation

abstract:
  We present a dissipative algorithm for solving nonlinear wave-like equations
when the initial data is specified on characteristic surfaces. The dissipative
properties built in this algorithm make it particularly useful when studying
the highly nonlinear regime where previous methods have failed to give a stable
evolution in three dimensions. The algorithm presented in this work is directly
applicable to hyperbolic systems proper of Electromagnetism, Yang-Mills and
General Relativity theories. We carry out an analysis of the stability of the
algorithm and test its properties with linear waves propagating on a Minkowski
background and the scattering off a Scwharszchild black hole in General
Relativity.


title: Line Sources in Brans-Dicke Theory of Gravity

abstract:
  We investigate how the gravitational field generated by line sources can be
characterized in Brans-Dicke theory of gravity. Adapting an approach previously
developed by Israel who solved the same problem in general relativity we show
that in Brans-Dicke theory's case it is possible to work out the field
equations which relate the energy-momentum tensor of the source to the scalar
field, the coupling constant $\omega $ and the extrinsic curvature of a tube of
constant geodesic radius centered on the line in the limit when the radius
shrinks to zero. In this new scenario two examples are considered and an
account of the Gundlach and Ortiz solution is included. Finally, a brief
discussion of how to treat thin shells in Brans-Dicke theory is given.


title:
Bohr's Correspondence Principle and The Area Spectrum of Quantum Black
  Holes

abstract:
  During the last twenty-five years evidence has been mounting that a
black-hole surface area has a {\it discrete} spectrum. Moreover, it is widely
believed that area eigenvalues are {\it uniformally} spaced. There is, however,
no general agreement on the {\it spacing} of the levels. In this letter we use
Bohr's correspondence principle to provide this missing link. We conclude that
the area spacing of a black-hole is $4\hbar \ln 3$. This is the unique spacing
consistent both with the area-entropy {\it thermodynamic} relation for black
holes, with Boltzmann-Einstein formula in {\it statistical physics} and with
{\it Bohr's correspondence principle}.


title: Instantaneous Action at a Distance in a Holistic Universe

abstract:
  The early work of Lorentz, Abraham and others, evolved through the work of
Fokker, Dirac and others to ultimately culminate in the Feynman- Wheeler direct
action at a distance theory. However this theory has encountered certain
conceptual difficulties like non-locality in time, self force of the electron,
pre acceleration and the perfect absorption condition of Feynman and Wheeler,
that is the instantaneous action of the remaining charges in the universe on
the charge in question. More recently, Hoyle and Narlikar have resurrected this
theory, but within the context of a Steady State or Quasi Steady State
cosmology. They argue that the theory infact has a better standing than the
generally accepted quantum theoretic description. In this article we consider a
quantum theoretic description and a cosmology which parallels the
Hoyle-Narlikar approach. This leads to a synthesis and justification of the
Dirac and Feynman-Wheeler approaches, clarifying the conceptual problems in the
process. We deduce a scenario with quantized space-time and a holistic
cosmology, consistent with physical and astrophysical data. The non-locality is
now seen to be meaningful within the minimum space-time intervals, as also the
perfect absorption within the holistic description. Local realism, and the
usual causal field theory are seen to have an underpinning of direct action.
For example this is brought out by the virtual photons which mediate
interactions in Quantum Electro Dynamics, and the emergence of the inverse
square law in the above approach from a background Zero Point Field.


title:
Logarithmic Newman-Penrose constants for arbitrary polyhomogeneous
  spacetimes

abstract:
  A discussion of how to calculate asymptotic expansions for polyhomogeneous
spacetimes using the Newman-Penrose formalism is made. The existence of
logarithmic Newman-Penrose constants for a general polyhomogeneous spacetime
(i.e. a polyhomogeneous spacetime such that $\Psi_0=\O(r^{-3}\ln ^{N_3})$) is
addressed. It is found that these constants exist for the generic case.


title:
Chaos in closed isotropic cosmological models with steep scalar field
  potential

abstract:
  The dynamics of closed scalar field FRW cosmological models is studied for
several types of exponentially and more than exponentially steep potentials.
The parameters of scalar field potentials which allow a chaotic behaviour are
found from numerical investigations. It is argued that analytical studies of
equation of motion at the Euclidean boundary can provide an important
information about the properties of chaotic dynamics. Several types of
transition from chaotic to regular dynamics are described.


title: Existence of Spinorial States in Pure Loop Quantum Gravity

abstract:
  We demonstrate the existence of spinorial states in a theory of canonical
quantum gravity without matter. This should be regarded as evidence towards the
conjecture that bound states with particle properties appear in association
with spatial regions of non-trivial topology. In asymptotically trivial general
relativity the momentum constraint generates only a subgroup of the spatial
diffeomorphisms. The remaining diffeomorphisms give rise to the mapping class
group, which acts as a symmetry group on the phase space. This action induces a
unitary representation on the loop state space of the Ashtekar formalism.
Certain elements of the diffeomorphism group can be regarded as asymptotic
rotations of space relative to its surroundings. We construct states that
transform non-trivially under a $2\pi$-rotation: gravitational quantum states
with fractional spin.


title: Gravitational Instantons from Minimal Surfaces

abstract:
  Physical properties of gravitational instantons which are derivable from
minimal surfaces in 3-dimensional Euclidean space are examined using the
Newman-Penrose formalism for Euclidean signature. The gravitational instanton
that corresponds to the helicoid minimal surface is investigated in detail.
This is a metric of Bianchi Type $VII_0$, or E(2) which admits a hidden
symmetry due to the existence of a quadratic Killing tensor. It leads to a
complete separation of variables in the Hamilton-Jacobi equation for geodesics,
as well as in Laplace's equation for a massless scalar field. The scalar Green
function can be obtained in closed form which enables us to calculate the
vacuum fluctuations of a massless scalar field in the background of this
instanton.


title: Primordial Fluctuations from Inflation: a Consistent Histories Approach

abstract:
  We show how the quantum-to-classical transition of the cosmological
fluctuations produced during an inflationary stage can be described using the
consistent histories approach. We identify the corresponding histories in the
limit of infinite squeezing. To take the decaying mode into account, we propose
an extension to coarse-grained histories.


title: On Local Constraints of D=4 Supergravity in Terms of Dirac Eigenvalues

abstract:
  It has been recently shown that in order to have Dirac eigenvalues as
observables of Euclidean supergravity, certain constraints should be imposed on
the covariant phase space as well as on Dirac eigenspinors. We investigate the
relationships among the constraints in the first set and argue that these
relationships are not linear. We also derive a set of equations expressing the
linear dependency of the constraints in order that the second set of
constraints be linearly independent.


title: Asymptotic self-similarity breaking at late times in cosmology

abstract:
  We study the late time evolution of a class of exact anisotropic cosmological
solutions of Einstein's equations, namely spatially homogeneous cosmologies of
Bianchi type VII$_0$ with a perfect fluid source. We show that, in contrast to
models of Bianchi type VII$_h$ which are asymptotically self-similar at late
times, Bianchi VII$_0$ models undergo a complicated type of self-similarity
breaking. This symmetry breaking affects the late time isotropization that
occurs in these models in a significant way: if the equation of state parameter
$\gamma$ satisfies $\gamma \leq 4/3$ the models isotropize as regards the shear
but not as regards the Weyl curvature. Indeed these models exhibit a new
dynamical feature that we refer to as Weyl curvature dominance: the Weyl
curvature dominates the dynamics at late times. By viewing the evolution from a
dynamical systems perspective we show that, despite the special nature of the
class of models under consideration, this behaviour has implications for more
general models.


title: Constraints on Covariance

abstract:
  Based on the principle of relativity, we find that the sufficient and
necessary condition for the general covariance of a field theory actually
requires more than the invariance of its local Langrangian density. If the
spacetime is not a flat one, its derivative requirement from the analysis of
the parallel transportation of tensor fields over spacetime restricts the
generally supposed covariance group, the group of differmorphisms, to the group
of linear coordinate transformations. Moreover, for any a field theory with
linear equations of motion, it stipulates for a universal physical propagation
speed of interaction over the spacetime manifold.


title:
On the gravitational field of static and stationary axial symmetric
  bodies with multi-polar structure

abstract:
  We give a physical interpretation to the multi-polar Erez-Rozen-Quevedo
solution of the Einstein Equations in terms of bars. We find that each
multi-pole correspond to the Newtonian potential of a bar with linear density
proportional to a Legendre Polynomial. We use this fact to find an integral
representation of the $\gamma$ function. These integral representations are
used in the context of the inverse scattering method to find solutions
associated to one or more rotating bodies each one with their own multi-polar
structure.


title: Dimensionally Challenged Gravities

abstract:
  I review some ways in which spacetime dimensionality enters explicitly in
gravitation. In particular, I recall some unusual geometrical gravity models
that are constructible in dimensions different from four, especially in D=3
where even ordinary Einstein theory is "different", e.g., fully Machian.


title: Searching for periodic sources with LIGO. II: Hierarchical searches

abstract:
  The detection of quasi-periodic sources of gravitational waves requires the
accumulation of signal-to-noise over long observation times. If not removed,
Earth-motion induced Doppler modulations, and intrinsic variations of the
gravitational-wave frequency make the signals impossible to detect. These
effects can be corrected (removed) using a parameterized model for the
frequency evolution. We compute the number of independent corrections
$N_p(\Delta T,N)$ required for incoherent search strategies which use stacked
power spectra---a demodulated time series is divided into $N$ segments of
length $\Delta T$, each segment is FFTed, the power is computed, and the $N$
spectra are summed up. We estimate that the sensitivity of an all-sky search
that uses incoherent stacks is a factor of 2--4 better than would be achieved
using coherent Fourier transforms; incoherent methods are computationally
efficient at exploring large parameter spaces. A two-stage hierarchical search
which yields another 20--60% improvement in sensitivity in all-sky searches for
old (>= 1000 yr) slow (<= 200 Hz) pulsars, and for young (>= 40 yr) fast (<=
1000 Hz) pulsars. Assuming 10^{12} flops of effective computing power for data
analysis, enhanced LIGO interferometers should be sensitive to: (i) Galactic
core pulsars with gravitational ellipticities of $\epsilon\agt5\times 10^{-6}$
at 200 Hz, (ii) Gravitational waves emitted by the unstable r-modes of newborn
neutron stars out to distances of ~8 Mpc, and (iii) neutron stars in LMXB's
with x-ray fluxes which exceed $2 \times 10^{-8} erg/(cm^2 s)$. Moreover,
gravitational waves from the neutron star in Sco X-1 should be detectable is
the interferometer is operated in a signal-recycled, narrow-band configuration.


title: Detection of gravitational wave bursts by interferometric detectors

abstract:
  We study in this paper some filters for the detection of burst-like signals
in the data of interferometric gravitational-wave detectors. We present first
two general (non-linear) filters with no {\it a priori} assumption on the
waveforms to detect. A third filter, a peak correlator, is also introduced and
permits to estimate the gain, when some prior information is known about the
waveforms. We use the catalogue of supernova gravitational-wave signals built
by Zwerger and M\"uller in order to have a benchmark of the performance of each
filter and to compare to the performance of the optimal filter. The three
filters could be a part of an on-line triggering in interferometric
gravitational-wave detectors, specialised in the selection of burst events.


title: Gravitational Scattering of Cosmic Strings by Non-Rotating Black Holes

abstract:
  This paper discusses the gravitational scattering of a straight, infinitely
long test cosmic string by a black hole. We present numerical results that
probe the two-dimensional parameter space of impact parameter and initial
velocity and compare them to approximate perturbative solutions derived
previously. We analyze string scattering and loop formation in the
ultra-relativistic regime and compare these results with analytical results for
string scattering by a gravitational shock wave. Special attention is paid to
regimes where the string approaches the black hole at near-critical impact
parameters. The dynamics of string scattering in this case are highly sensitive
to initial data and transient phenomena arise while portions of the string
dwell in the strong gravitational field near the event horizon of the black
hole. The role of string tension is also investigated by comparing the
scattering of a cosmic string to the scattering of a tensionless "dust" string.
Finally, the problem of string capture is revisited in light of these new
results, and a capture curve covering the entire velocity range ($0 < v \le c$)
is given.


title:
Complex Paths and the Hartle Hawking Wave-function for Slow Roll
  Cosmologies

abstract:
  A large set of complex path solutions for the Hartle Hawking semi-classical
wave function are found for an inflationary universe in the "slow roll" regime.
The implication of these for the semi-classical evolution of the universe is
also studied.


title:
Symmetries and conservation laws in histories-based generalized quantum
  mechanics

abstract:
  Symmetries are defined in histories-based generalized quantum mechanics
paying special attention to the class of history theories admitting
quasitemporal structure (a generalization of the concept of `temporal
sequences' of `events' using partial semigroups) and logic structure for
`single time histories'. Symmetries are classified into orthochronous (those
preserving the `temporal order' of `events') and non-orthochronous. A
straightforward criterion for physical equivalence of histories is formulated
in terms of orthochronous symmetries; this criterion covers various notions of
physical equivalence considered by Gell-Mann and Hartle as special cases. In
familiar situations, a reciprocal relationship between traditional symmetries
(Wigner symmetries in quantum mechanics and Borel-measurable transformations of
phase space in classical mechanics) and symmetries defined in this work is
established. In a restricted class of theories, a definition of conservation
law is given in the history language which agrees with the standard ones in
familiar situations; in a smaller subclass of theories, a Noether type theorem
(implying a connection between continuous symmetries of dynamics and
conservation laws) is proved.


title: Where are the r-modes of isentropic stars?

abstract:
  Almost none of the r-modes ordinarily found in rotating stars exist, if the
star and its perturbations obey the same one-parameter equation of state; and
rotating relativistic stars with one-parameter equations of state have no pure
r-modes at all, no modes whose limit, for a star with zero angular velocity, is
a perturbation with axial parity. Similarly (as we show here) rotating stars of
this kind have no pure g-modes, no modes whose spherical limit is a
perturbation with polar parity and vanishing perturbed pressure and density.
Where have these modes gone?
  In spherical stars of this kind, r-modes and g-modes form a degenerate
zero-frequency subspace. We find that rotation splits the degeneracy to zeroth
order in the star's angular velocity $\Omega$, and the resulting modes are
generically hybrids, whose limit as $\Omega\to 0$ is a stationary current with
axial and polar parts. Because each mode has definite parity, its axial and
polar parts have alternating values of $l$. We show that each mode belongs to
one of two classes, axial-led or polar-led, depending on whether the spherical
harmonic with lowest value of $l$ that contributes to its velocity field is
axial or polar. We numerically compute these modes for slowly rotating
polytropes and for Maclaurin spheroids, using a straightforward method that
appears to be novel and robust. Timescales for the gravitational-wave driven
instability and for viscous damping are computed using assumptions appropriate
to neutron stars.


title: Static Bondi Energy in the Teleparallel Equivalent of General Relativity

abstract:
  We consider Bondi's radiating metric in the context of the teleparallel
equivalent of general relativity (TEGR). This metric describes the asymptotic
form of a radiating solution of Einstein's equations. The total gravitational
energy for this solution can be calculated by means of pseudo-tensors in the
static case. In the nonstatic case, Bondi defines the {\it mass aspect} $m(u)$,
which describes the mass of an isolated system. In this paper we express
Bondi's solution in asymptotically spherical 3+1 coordinates, not in radiation
coordinates, and obtain Bondi's energy in the static limit by means of the
expression for the gravitational energy in the framework of the TEGR. We can
either obtain the total energy or the energy inside a large (but finite)
portion of the three-dimensional spacelike hypersurface, whose boundary is far
away from the source. The relationship of the present energy expression with
Moller's energy is established.


title:
Fully Anisotropic String Cosmologies, Maxwell Fields and Primordial
  Shear

abstract:
  We present a class of exact cosmological solutions of the low energy string
effective action in the presence of a homogeneous magnetic fields. We discuss
the physical properties of the obtained (fully anisotropic) cosmologies paying
particular attention to their vacuum limit and to the possible isotropization
mechanisms. We argue that quadratic curvature corrections are able to
isotropize fully anisotropic solutions whose scale factors describe accelerated
expansion. Moreover, the degree of isotropization grows with the duration of
the string phase. We follow the fate of the shear parameter in a decelerated
phase where, dilaton, magnetic fields and radiation fluid are simultaneously
present. In the absence of any magnetic field a long string phase immediately
followed by radiation is able to erase large anisotropies. Conversely, if a
short string phase is followed by a long dilaton dominated phase the
anisotropies can be present, in principle, also at later times. The presence of
magnetic seeds after the end of the string phase can induce further
anisotropies which can be studied within the formalism reported in this paper.


title: Cosmological models with isotropic singularities

abstract:
  In 1985 Goode and Wainwright devised the concept of an isotropic singularity.
Since that time, numerous authors have explored the interesting consequences,
in mathematical cosmology, of assuming the existence of this type of
singularity. In this paper, we collate all examples of cosmological models
which are known to admit an isotropic singularity, and make a number of
observations regarding their general characteristics.


title: Geodesics in the Gamma spacetime

abstract:
  Circular and radial geodesics are studied in the spacetime described by the
$\gamma$ metric. Their behaviour is compared with the spherically symmetric
situation, bringing out the sensitivity of the trajectories to deviations from
spherical symmetry.


title: On the Generality of Refined Algebraic Quantization

abstract:
  The Dirac quantization `procedure' for constrained systems is well known to
have many subtleties and ambiguities. Within this ill-defined framework, we
explore the generality of a particular interpretation of the Dirac procedure
known as refined algebraic quantization. We find technical conditions under
which refined algebraic quantization can reproduce the general implementation
of the Dirac scheme for systems whose constraints form a Lie algebra with
structure constants. The main result is that, under appropriate conditions, the
choice of an inner product on the physical states is equivalent to the choice
of a ``rigging map'' in refined algebraic quantization.


title: Relativistically Rotating Frames and Non-time-orthogonality

abstract:
  This paper is a brief overview of a more extensive article recently published
in Found. Phys. Lett. [2]. Apparent disagreement with experiment as well as
internal inconsistencies found in the traditional analysis of relativistically
rotating frames/disks are summarized. As one example, a point p at 0 degrees on
the circumference of a rotating disk does not, according to the standard
theory, exist at the same moment in time as the same point p at 360 degrees.
This and other problems with the standard theory are completely resolved by a
novel analysis that directly addresses, apparently for the first time, the
non-time-orthogonal nature of rotating frames. Though ultimately consonant with
the special and general theories of relativity, due to non-time-orthogonality,
the analysis predicts several peculiar (i.e., not traditionally relativistic)
results. For example, the local circumferential speed of light is not invariant
(thereby agreeing with the Sagnac experiment), and no Lorentz contraction
exists along the disk rim. Other experimental results, including time dilation,
mass-energy dependence on speed, and what has heretofore been considered a
"spurious" signal in the most accurate Michelson-Morley experiment performed to
date, are accurately predicted. Further, the widely accepted postulate for the
equivalence of co-moving inertial and non-inertial rods, used liberally with
prior rotating frame analyses, is shown to be invalid for non-time-orthogonal
frames. This understanding of the ramifications of non-time-orthogonality
resolves paradoxes inherent in the traditional theory.


title: Static Cylindrically Symmetric Solution

abstract:
  A static axisymmetric solution with an additional cylindrical symmetry is
considered and that the matter consists in a cosmological and a dust term.


title: The quantum cosmology debate

abstract:
  I review the tunneling, Hartle-Hawking and Linde proposals for the wave
function of the universe and comment on the recent work on quantum creation of
open universes.


title: Particle production and complex path analysis

abstract:
  This paper discusses particle production in Schwarzchild-like spacetimes and
in an uniform electric field. Both problems are approached using the method of
complex path analysis. Particle production in Schwarzchild-like spacetimes with
a horizon is obtained here by a new and simple semi-classical method based on
the method of complex paths. Hawking radiation is obtained in the (t,r)
co-ordinate system of the standard Schwarzchild metric {\it without} requiring
the Kruskal extension. The co-ordinate singularity present at the horizon
manifests itself as a singularity in the expression for the semi-classical
propagator for a scalar field. We give a prescription whereby this singularity
is regularised with Hawking's result being recovered. In the case of the
electric field, standard quantum field theoretic methods can be used to obtain
particle production in a purely time-dependent gauge. In a purely
space-dependent gauge, however, the tunnelling interpretation has to be
resorted to. We attempt, in this paper, to provide a tunnelling description for
both the time and space dependent gauges. The usefulness of such a common
description becomes evident when `mixed' gauges, which are functions of both
space and time variables, are analysed. We report, in this paper, certain mixed
gauges which have the interesting property that mode functions in these gauges
are found to be a combination of {\it elementary} functions unlike the standard
modes. Finally, we present an attempt to interpret particle production by the
electric field as a tunnelling process between the two sectors of the Rindler
spacetime.


title: From Superstrings to M Theory

abstract:
  In this talk I will survey some of the basic facts about superstring theories
in 10 dimensions and the dualities that relate them to M theory in 11
dimensions. Then I will mention some important unresolved issues.


title: Harmonic Map Formulation of Colliding Electrovac Plane Waves

abstract:
  The formulation of the Einstein field equations admitting two Killing vectors
in terms of harmonic mappings of Riemannian manifolds is a subject in which
Charlie Misner has played a pioneering role. We shall consider the hyperbolic
case of the Einstein-Maxwell equations admitting two hypersurface orthogonal
Killing vectors which physically describes the interaction of two electrovac
plane waves. Following Penrose's discussion of the Cauchy problem we shall
present the initial data appropriate to this collision problem. We shall also
present three different ways in which the Einstein-Maxwell equations for
colliding plane wave spacetimes can be recognized as a harmonic map. The goal
is to cast the Einstein-Maxwell equations into a form adopted to the initial
data for colliding impulsive gravitational and electromagnetic shock waves in
such a way that a simple harmonic map will directly yield the metric and the
Maxwell potential 1-form of physical interest.
  For Charles W. Misner on his 60th birthday