title: Toward Quantum Gravity II: Quantum Tests

abstract:
  This study toward quantum gravity (QG) introduces an SU(N) gauge theory with
the \Theta vacuum term for gravitational interactions, which leads to a group
SU(2)_L x U(1)_Y x SU(3)_C for weak and strong interactions through dynamical
spontaneous symmetry breaking (DSSB). Newton gravitation constant G_N and the
effective cosmological constant are realized as the effective coupling constant
and the effective vacuum energy, respectively, due to massive gauge bosons. A
gauge theory relevant for the non-zero gauge bosons, 10^{-12} GeV, and the
massless gauge boson (photon) is predicted as a new dynamics for the universe
expansion: this is supported by the repulsive force, indicated in BUMERANG-98
and MAXIMA-1 experiments, and cosmic microwave background radiation. Under the
constraint of the flat universe, \Omega = 1 - 10^{-61}, the large cosmological
constant in the early universe becomes the source of the exponential expansion
in 10^{30} order as expected in the inflation theory, nearly massless gauge
bosons are regarded as strongly interacting mediators of dark matter, and the
baryon asymmetry is related to the DSSB mechanism.


title: An introduction to quantum cosmology

abstract:
  This is an introductory set of lecture notes on quantum cosmology, given in
1995 to an audience with interests ranging from astronomy to particle physics.
Topics covered: 1. Introduction: 1.1 Quantum cosmology and quantum gravity; 1.2
A brief history of quantum cosmology. 2. Hamiltonian formulation of general
relativity: 2.1 The 3+1 decomposition; 2.2 The action. 3. Quantisation: 3.1
Superspace; 3.2 Canonical quantisation; 3.3 Path integral quantisation; 3.4
Minisuperspace; 3.5 The WKB approximation; 3.6 Probability measures; 3.7
Minisuperspace for the Friedmann universe with massive scalar field. 4.
Boundary Conditions: 4.1 The no-boundary proposal; 4.2 The tunneling proposal.
5. The predictions of quantum cosmology: 5.1 The period of inflation; 5.2 The
origin of density perturbations; 5.3 The arrow of time.


title: Notes on a quantum gravitational collaps

abstract:
  Everybody knows what the classical black holes are. In short, this is a
spacetime region beyond the so-called event horizon. The notion of the event
horizon is mathematically well defined. The situation with a definition of
quantum black hole is not so clear. The problem is that the classical event
horizon can be defined only globally, i.e. in order to be sure we have a black
hole we would need an infinite time interval. But, in classical physics we have
trajectories off all the particles and equations of motion for all the fields
and can, in principle, construct some ideal models for the gravitational
collapse and study the black hole formation under different conditions.


title:
X-fluid and viscous fluid in D-dimensional anisotropic integrable
  cosmology

abstract:
  D-dimensional cosmological model describing the evolution of a perfect fluid
with negative pressure (x-fluid) and a fluid possessing both shear and bulk
viscosity in n Ricci-flat spaces is investigated. The second equations of state
are chosen in some special form of metric dependence of the shear and bulk
viscosity coefficients. The equations of motion are integrated and the
dynamical properties of the exact solutions are studied. It is shown the
possibility to resolve the cosmic coincidence problem when the x-fluid plays
role of quintessence and the viscous fluid is used as cold dark matter.


title: A rigidity theorem for nonvacuum initial data

abstract:
  In this note we prove a theorem on non-vacuum initial data for general
relativity. The result presents a ``rigidity phenomenon'' for the extrinsic
curvature, caused by the non-positive scalar curvature.
  More precisely, we state that in the case of asymptotically flat non-vacuum
initial data if the metric has everywhere non-positive scalar curvature then
the extrinsic curvature cannot be compactly supported.


title:
Bosonic string - Kaluza Klein theory exact solutions using 5D-6D
  dualities

abstract:
  We present the explicit formulae which allow to transform the general
solution of the 6D Kaluza--Klein theory on a 3--torus into the special solution
of the 6D bosonic string theory on a 3--torus as well as into the general
solution of the 5D bosonic string theory on a 2--torus. We construct a new
family of the extremal solutions of the 3D chiral equation for the
SL(4,R)/SO(4) coset matrix and interpret it in terms of the component fields of
these three duality related theories.


title: Geometric Characterizations of the Kerr Isolated Horizon

abstract:
  We formulate conditions on the geometry of a non-expanding horizon $\Delta$
which are sufficient for the space-time metric to coincide on $\Delta$ with the
Kerr metric. We introduce an invariant which can be used as a measure of how
different the geometry of a given non-expanding horizon is from the geometry of
the Kerr horizon. Directly, our results concern the space-time metric at $\IH$
at the zeroth and the first orders. Combained with the results of Ashtekar,
Beetle and Lewandowski, our conditions can be used to compare the space-time
geometry at the non-expanding horizon with that of Kerr to every order. The
results should be useful to numerical relativity in analyzing the sense in
which the final black hole horizon produced by a collapse or a merger
approaches the Kerr horizon.


title: Black Hole Configurations with Total Entropy Less than A/4

abstract:
  If one surrounds a black hole with a perfectly reflecting shell and
adiabatically squeezes the shell inward, one can increase the black hole area A
to exceed four times the total entropy S, which stays fixed during the process.
A can be made to exceed 4S by a factor of order unity before the one enters the
Planck regime where the semiclassical approximation breaks down. One
interpretation is that the black hole entropy resides in its thermal
atmosphere, and the shell restricts the atmosphere so that its entropy is less
than A/4.


title:
Reflection symmetry breaking scenarios with minimal gauge form coupling
  in brane world cosmology

abstract:
  This article synthesises and extends recent work on the cosmological
consequences of dropping the usual Z_2 reflection symmetry postulate in brane
world scenarios. It is observed that for a cosmological model of homogeneous
isotropic type, the relevant generalised Birkhoff theorem establishing
staticity of the external vacuum in the maximally symmetric ``bulk'' outside a
freely moving world brane will remain valid for the case of motion that is
forced by minimal (generalised Wess Zumino type) coupling to an external
antisymmetric gauge field provided its kinetic action contribution has the
usual homogeneous quadratic form. This means that the geometry on each side of
the brane worldsheet will still be of the generalised Schwarzschild anti de
Sitter type. The usual first integrated Friedmann equation for the Hubble
expansion rate can thereby be straightforwardly generalised by inclusion of new
terms involving 2 extra parameters respectively measuring the strength of the
gauge coupling and the degree of deviation from reflection symmetry. Some
conceivable phenomenological implications are briefly outlined, and
corresponding limitations are derived for possible values of relevant
parameters.


title: On the derivation of the equations of motion in theories of gravity

abstract:
  The equations of motion of massive particles in GR are completely determined
by the field equation. We utilize the particular form of Einstein's field
equation and propose for the $N$-body problem of the equations that are Lorentz
invariant a novel algorithm for the derivation of the equations of motion from
the field equations. It is: 1. Compute a static, spherically symmetric solution
of the field equation. It will be singular at the origin. This will be taken to
be the field generated by a single particle. 2. Move the solution on a
trajectory $ {\psi(t)}$ and apply the instantaneous Lorentz transformation
based on instantaneous velocity $\dot{\psi}(t)$. 3. Take, as first
approximation, the field generated by $N$ particles to be the superposition of
the fields generated by the single particles. 4. Compute the leading part of
the equation. Hopefully, only terms that involves $\ddot{\psi}(t)$ will be
dominant. This is the ``inertial'' part. 5. Compute by the quadratic part of
the equation. This is the agent of the ``force''. 6. Equate for each
singularity, the highest order terms of the singularities that came from the
linear part and the quadratic parts, respectively. This is an equation between
the inertial part and the force. The algorithm was applied to Einstein
equations. The approximate evolution of scalar curvature lends, in turn, to an
invariant scalar equation. The algorithm for it did produce Newton's law of
gravitation. This is, also, the starting point for the embedding the
trajectories in a common field.


title: Exact Solutions of Einstein Equations

abstract:
  We use a metric of the type Friedmann-Robertson-Walker to obtain new exact
solutions of Einstein equations for a scalar and massive field. The solutions
have a permanent or transitory inflationary behavior.


title:
Probing Quantum General Relativity Through Exactly Soluble
  Midi-Superspaces II: Polarized Gowdy Models

abstract:
  Canonical quantization of the polarized Gowdy midi-superspace with a 3-torus
spatial topology is carried out. As in an earlier work on the Einstein-Rosen
cylindrical waves, symmetry reduction is used to cast the original problem in
4-dimensional space-times to a 3-dimensional setting. To our knowledge, this is
the first complete, systematic treatment of the Gowdy model in the
geometrodynamical setting.


title: The twin paradox in compact spaces

abstract:
  Twins travelling at constant relative velocity will each see the other's time
dilate leading to the apparent paradox that each twin believes the other ages
more slowly. In a finite space, the twins can both be on inertial, periodic
orbits so that they have the opportunity to compare their ages when their paths
cross. As we show, they will agree on their respective ages and avoid the
paradox. The resolution relies on the selection of a preferred frame singled
out by the topology of the space.


title: Collision of spinning black holes in the close limit

abstract:
  In this paper we consider the collision of spinning holes using first order
perturbation theory of black holes (Teukolsky formalism). With these results
(along with ones, we published in the past) one can predict the properties of
the gravitational waves radiated from the late stage inspiral of two spinning,
equal mass black holes. Also we note that the energy radiated by the head-on
collision of two spinning holes with spins (that are equal and opposite)
aligned along the common axis is more than the case in which the spins are
perpendicular to the axis of the collision.


title: Bubbles created from vacuum fluctuation

abstract:
  We show that the bubbles $S^2\times S^2$can be created from vacuum
fluctuation in certain De Sitter universe, so the space-time foam-like
structure might really be constructed from bubbles of $S^2\times S^2$ in the
very early inflating phase of our universe. But whether such foam-like
structure persisted during the later evolution of the universe is a problem
unsolved now.


title:
Generation of exact solutions in cosmology on the basis of
  five-dimensional Projective Unified Field Theory

abstract:
  A homogeneous and isotropic model of the Universe is considered in the
framework of the five-dimensional Projective Unified Field Theory in which the
gravitation is described by both space-time curvature and some hypothetical
scalar field (sigma-field). We propose a generation method for obtaining exact
solutions. New exact Friedmann-like solutions for a dust model and inflationary
solutions are found. It is shown that in the framework of exponential type
inflation we obtain a natural explanation of why at present we do not observe
sigma-field effects or why these effects are negligible.


title: Generalised hyperbolicity: hypersurface singularities

abstract:
  Sufficient conditions for the well-posedness of the initial value problem for
the scalar wave equation are obtained in space-times with hypersurface
singularities


title: Gravitational waves in non-singular string cosmologies

abstract:
  We study the evolution of tensor metric fluctuations in a class of
non-singular models based on the string effective action, by including in the
perturbation equation the higher-derivative and loop corrections needed to
regularise the background solutions. We discuss the effects of such
higher-order corrections on the final graviton spectrum, and we compare the
results of analytical and numerical computations.


title: Spacetime Ehlers group: Transformation law for the Weyl tensor

abstract:
  The spacetime Ehlers group, which is a symmetry of the Einstein vacuum field
equations for strictly stationary spacetimes, is defined and analyzed in a
purely spacetime context (without invoking the projection formalism). In this
setting, the Ehlers group finds its natural description within an infinite
dimensional group of transformations that maps Lorentz metrics into Lorentz
metrics and which may be of independent interest. The Ehlers group is shown to
be well defined independently of the causal character of the Killing vector
(which may become null on arbitrary regions). We analyze which global
conditions are required on the spacetime for the existence of the Ehlers group.
The transformation law for the Weyl tensor under Ehlers transformations is
explicitly obtained. This allows us to study where, and under which
circumstances, curvature singularities in the transformed spacetime will arise.
The results of the paper are applied to obtain a local characterization of the
Kerr-NUT metric.


title: The Wahlquist-Newman solution

abstract:
  Based on a geometrical property which holds both for the Kerr metric and for
the Wahlquist metric we argue that the Kerr metric is a vacuum subcase of the
Wahlquist perfect-fluid solution. The Kerr-Newman metric is a physically
preferred charged generalization of the Kerr metric. We discuss which geometric
property makes this metric so special and claim that a charged generalization
of the Wahlquist metric satisfying a similar property should exist. This is the
Wahlquist-Newman metric, which we present explicitly in this paper. This family
of metrics has eight essential parameters and contains the Kerr-Newman-de
Sitter and the Wahlquist metrics, as well as the whole Pleba\'nski limit of the
rotating C-metric, as particular cases. We describe the basic geometric
properties of the Wahlquist-Newman metric, including the electromagnetic field
and its sources, the static limit of the family and the extension of the
spacetime across the horizon.


title: Correlation between Gamma-Ray bursts and Gravitational Waves

abstract:
  The cosmological origin of $\gamma$-ray bursts (GRBs) is now commonly
accepted and, according to several models for the central engine, GRB sources
should also emit at the same time gravitational waves bursts (GWBs). We have
performed two correlation searches between the data of the resonant
gravitational wave detector AURIGA and GRB arrival times collected in the BATSE
4B catalog. No correlation was found and an upper limit \bbox{$h_{\text{RMS}}
\leq 1.5 \times 10^{-18}$} on the averaged amplitude of gravitational waves
associated with $\gamma$-ray bursts has been set for the first time.


title: Nearly horizon skimming orbits of Kerr black holes

abstract:
  An unusual set of orbits about extreme Kerr black holes resides at the
Boyer-Lindquist radius $r = M$, the coordinate of the hole's event horizon.
These ``horizon skimming'' orbits have the property that their angular momentum
$L_z$ {\it increases} with inclination angle, opposite to the familiar behavior
one encounters at larger radius. In this paper, I show that this behavior is
characteristic of a larger family of orbits, the ``nearly horizon skimming''
(NHS) orbits. NHS orbits exist in the very strong field of any black hole with
spin $a\agt 0.952412M$. Their unusual behavior is due to the locking of
particle motion near the event horizon to the hole's spin, and is therefore a
signature of the Kerr metric's extreme strong field. An observational hallmark
of NHS orbits is that a small body spiraling into a Kerr black hole due to
gravitational-wave emission will be driven into orbits of progressively smaller
inclination angle, toward the equator. This is in contrast to the ``normal''
behavior. For circular orbits, the change in inclination is very small, and
unlikely to be of observational importance. I argue that the change in
inclination may be considerably larger when one considers the evolution of
inclined eccentric orbits. If this proves correct, then the gravitational waves
produced by evolution through the NHS regime may constitute a very interesting
and important probe of the strong-field nature of rotating black holes.


title: Comment on "Gravity Waves, Chaos, and Spinning Compact Binaries"

abstract:
  In this comment, I argue that chaotic effects in binary black hole inspiral
will not strongly impact the detection of gravitational waves from such
systems.


title:
Einstein General Relativity In Bi-metric Spacetime Contains Exponential
  Metrics Which Dynamically Preserve Bi-metric "Light Cone Causality"

abstract:
  It is well known that Einstein General Relativity can be expressed
covariantly in bi-metric spacetime, without the uncertainties which arise from
the effects of gravitational energy-momentum pseudo-tensors. However the effect
that the Strong Principle of Equivalence (SPOE) has on the curved and flat
bi-metric spacetime tetrad structure has not been fully explored. In the
context of bi-metric General Relativity the (SPOE) requires that: a) in the
absence of gravitation due to spacetime curvature a Global Inertial Cartesian
Minkowski (GICM) spacetime frame exists in which Special Relativity is valid
and, b) in the presence of gravitation due to spacetime curvature a bi-metric
Local Free Fall frame (LFF) must always exist. These two conditions required by
the (SPOE) are then shown to imply that a symmetric gravitational potential
tensor must exist in the bi-metric spacetime which is connected exponentially
to the tetrad inner product between the curved symmetric tetrads and the flat
background symmetric tetrads. It is then shown that this (SPOE) generated
gravitational potential tensor has the property of exponentially connecting the
curved metric tensor with the flat background metric tensor in a manner which
allows the condition of "Light Cone Causality" (LCC) to be dynamically
satisfied in the bi-metric spacetime. Substitution of this (LCC) conserving
exponential metric into the bi-metric Einstein field equations, subject to an
appropriate choice of tensor gauge conditions, yields an equivalent set of
(LCC) conserving bi-metric Einstein field equations for the gravitational
potential tensor, the full implications of which will be explored in future
papers.


title: Energy and Momentum in Expansive Nondecelerative Universe

abstract:
  Incorporation of the Vaidya metric in the model of Expansive Nondecelerative
Universe allows to precisely localize gravitational energy for weak fields and
obtain the components of the Einstein energy-momentum pseudotensor for strong
gravitational fields. The components are identical to those calculated by
Virbhadra.


title:
Determination of Upper Limit of Stars Mass Based on Model of Expansive
  Nondecelerative Universe

abstract:
  Incorporation of the Vaidya metric in the model of Expansive Nondecelerative
Universe allows to localize the energy density of gravitational field that,
subsequently, enables to determine the upper limit of stars mass. The upper
limit decreases with cosmological time and at present is close to 30-fold of
our Sun mass.


title: A brief review of Regge calculus in classical numerical relativity

abstract:
  We briefly review past applications of Regge calculus in classical numerical
relativity, and then outline a programme for the future development of the
field. We briefly describe the success of lattice gravity in constructing
initial data for the head-on collision of equal mass black holes, and discuss
recent results on the efficacy of Regge calculus in the continuum limit.


title: Anti-de Sitter-type 2+1 spacetime of a charged rotating mass

abstract:
  The exact charged rotating solution of 2+1 Einstein-Maxwell equations with
$\Lambda$ term is obtained and its properties outlined. It generalizes the
Cataldo-Cruz-del Campo-Garc{\'\i}a relativistic charged massive black hole on
the 2+1 anti-de Sitter cosmological background. We show that rotating solutions
correspond to inhomogeneous field equations, thus presence of sources in 2+1
Maxwell's equations cannot be identified with existence of a charge
distribution. Instead, these sources are related to the 2+1 Machian 2-form
field, and the overall Lagrangian structure of the rotating system is
reconstructed.


title: Tidal satellite perturbations and the Lense-Thirring effect

abstract:
  The tiny general relativistic Lense-Thirring effect can be measured by means
of a suitable combination of the orbital residuals of the nodes of LAGEOS and
LAGEOS II and the perigee of LAGEOS II. This observable is affected, among
other factors, by the Earth' s solid and ocean tides. They induce long-period
orbital perturbations that, over observational periods of few years, may alias
the detection of the gravitomagnetic secular trend of interest. In this paper
we calculate explicitly the most relevant tidal perturbations acting upon
LAGEOSs and assess their influence on the detection of the Lense-Thirring
effect. The present day level of knowledge of the solid and ocean tides allow
us to conclude that their influence on it ranges from almost 4% over 4 years to
less than 2% over 7 years.

categories: gr-qc astro-ph physics.geo-ph physics.space-ph


title: Gravitational Statistical Mechanics: A model

abstract:
  Using the quantum Hamiltonian for a gravitational system with boundary, we
find the partition function and derive the resulting thermodynamics. The
Hamiltonian is the boundary term required by functional differentiability of
the action for Lorentzian general relativity. In this model, states of quantum
geometry are represented by spin networks. We show that the statistical
mechanics of the model reduces to that of a simple non-interacting gas of
particles with spin. Using both canonical and grand canonical descriptions, we
investigate two temperature regimes determined by the fundamental constant in
the theory, m. In the high temperature limit (kT > m), the model is
thermodynamically stable. For low temperatures (kT < m) and for macroscopic
areas of the bounding surface, the entropy is proportional to area (with
logarithmic correction), providing a simple derivation of the
Bekenstein-Hawking result. By comparing our results to known semiclassical
relations we are able to fix the fundamental scale. Also in the low
temperature, macroscopic limit, the quantum geometry on the boundary forms a
`condensate' in the lowest energy level (j=1/2).


title: New Operators for Spin Net Gravity: Definitions and Consequences

abstract:
  Two operators for quantum gravity, angle and quasilocal energy, are briefly
reviewed. The requirements to model semi-classical angles are discussed. To
model semi-classical angles it is shown that the internal spins of the vertex
must be very large, ~10^20.


title: Effective action for scalar fields in two-dimensional gravity

abstract:
  We consider a general two-dimensional gravity model minimally or nonminimally
coupled to a scalar field. The canonical form of the model is elucidated, and a
general solution of the equations of motion in the massless case is reviewed.
In the presence of a scalar field all geometric fields (zweibein and Lorentz
connection) are excluded from the model by solving exactly their Hamiltonian
equations of motion. In this way the effective equations of motion and the
corresponding effective action for a scalar field are obtained. It is written
in a Minkowskian space-time and does not include any geometric variables. The
effective action arises as a boundary term and is nontrivial both for open and
closed universes. The reason is that unphysical degrees of freedom cannot be
compactly supported because they must satisfy the constraint equation. As an
example we consider spherically reduced gravity minimally coupled to a massless
scalar field. The effective action is used to reproduce the Fisher and Roberts
solutions.


title: Gravitation as a Super SL(2,C) Gauge Theory

abstract:
  We present a gauge theory of the super SL(2,C) group. The gauge potential is
a connection of the Super SL(2,C) group. A MacDowell-Mansouri type of action is
proposed where the action is quadratic in the Super SL(2,C) curvature and
depends purely on gauge connection. By breaking the symmetry of the Super
SL(2,C) topological gauge theory to SL(2,C), a metric is naturally defined.


title: Quasi-Local "Conserved Quantities"

abstract:
  Using the Noether Charge formulation, we study a perturbation of the
conserved gravitating system. By requiring the boundary term in the variation
of the Hamiltonian to depend only on the symplectic structure, we propose a
general prescription for defining quasi-local ``conserved quantities'' (i.e. in
the situation when the gravitating system has a non-vanishing energy flux).
Applications include energy-momentum and angular momentum at spatial and null
infinity, asymptotically anti-deSitter spacetimes, and thermodynamics of the
isolated horizons.


title: Chiral models in dilaton-Maxwell gravity

abstract:
  We study symmetry properties of the Einstein-Maxwell theory nonminimaly
coupled to the dilaton field. We consider a static case with pure electric
(magnetic) Maxwell field and show that the resulting system becomes a nonlinear
sigma-model wich possesses a chiral representation. We construct the
corresponding chiral matrix and establish a representation which is related to
the pair of Ernst-like potentials. These potentials are used for separation of
the symmetry group into the gauge and nongauge (charging) sectors. New
variables, which linearize the action of charging symmetries, are also
established; a solution generation technique based on the use of charging
symmetries is formulated. This technique is used for generation of the
elecricaly (magneticaly) charged dilatonic fields from the static General
Relativity ones.


title: Soliton solution in dilaton-Maxwell gravity

abstract:
  The inverse scattering problem method application to construction of exact
solution for Maxwell dilaton gravity system ia considered. By use of Belinsky
and Zakharov L - A pair the solution of the theory is constructed. The rotating
Kerr - like configuration with NUT - parameter is obtained.


title: Geometric classification of the torsion tensor in space-time

abstract:
  Torsion appears in literature in quite different forms. Generally, spin is
considered to be the source of torsion, but there are several other
possibilities in which torsion emerges in different contexts. In some cases a
phenomenological counterpart is absent, in some other cases torsion arises from
sources without spin as a gradient of a scalar field. Accordingly, we propose
two classification schemes. The first one is based on the possibility to
construct torsion tensors from the product of a covariant bivector and a vector
and their respective space-time properties. The second one is obtained by
starting from the decomposition of torsion into three irreducible pieces. Their
space-time properties again lead to a complete classification. The
classifications found are given in a U_4, a four dimensional space-time where
the torsion tensors have some peculiar properties. The irreducible
decomposition is useful since most of the phenomenological work done for
torsion concerns four dimensional cosmological models. In the second part of
the paper two applications of these classification schemes are given. The
modifications of energy-momentum tensors are considered that arise due to
different sources of torsion. Furthermore, we analyze the contributions of
torsion to shear, vorticity, expansion and acceleration. Finally the
generalized Raychaudhuri equation is discussed.


title: Dilatonic current-carrying cosmic strings

abstract:
  We investigate the nature of ordinary cosmic vortices in some scalar-tensor
extensions of gravity. We find solutions for which the dilaton field condenses
inside the vortex core. These solutions can be interpreted as raising the
degeneracy between the eigenvalues of the effective stress-energy tensor,
namely the energy per unit length U and the tension T, by picking a privileged
spacelike or timelike coordinate direction; in the latter case, a phase
frequency threshold occurs that is similar to what is found in ordinary neutral
current-carrying cosmic strings. We find that the dilaton contribution for the
equation of state, once averaged along the string worldsheet, vanishes, leading
to an effective Nambu-Goto behavior of such a string network in cosmology, i.e.
on very large scales. It is found also that on small scales, the energy per
unit length and tension depend on the string internal coordinates in such a way
as to permit the existence of centrifugally supported equilibrium
configuration, also known as vortons, whose stability, depending on the very
short distance (unknown) physics, can lead to catastrophic consequences on the
evolution of the Universe.


title: The near-horizon geometry of dilaton-axion black holes

abstract:
  Static black holes of dilaton-axion gravity become singular in the extreme
limit, which prevents a direct determination of their near-horizon geometry.
This is addressed by first taking the near-horizon limit of extreme rotating
NUT-less black holes, and then going to the static limit. The resulting
four-dimensional geometry may be lifted to a Bertotti-Robinson-like solution of
six-dimensional vacuum gravity, which also gives the near-horizon geometry of
extreme Kaluza-Klein black holes in five dimensions.


abstract:
  Levin (gr-qc/9910040) has shown that spinning compact binaries can be chaotic
at second post-Newtonian order. However, when higher order dissipational
effects are included, the dynamics will no longer be chaotic, though the
evolution may still be unpredictable in a practical sense. I discuss some of
the additional work that needs to be done to decide how this unpredictability
might affect gravitational wave detectors such as LIGO.


title: Spin and statistics in quantum gravity

abstract:
  We present a review of the spin and statistics of topological geons,
particles in 3+1 quantum gravity. They can have half-odd-integral spin and
fermionic statistics and since the underlying gravitational field is tensorial
and bosonic, this is an example of ``emergent'' non-trivial spin and statistics
as displayed by familiar non-gravitating objects such as skyrmions. We give the
topological background and show that in a ``canonical'' quantization of gravity
there is no spin-statistics correlation for topological geons. Allowing the
topology of space to change, for example in a sum-over-histories approach,
raises the possibility that a spin-statistics correlation can be recovered for
geons. We review a conjectured set of rules powerful enough to give such a
spin-statistics correlation for all topological geons. These would appear to
rule out the possibility of parastatistics and may rule out spinorial and
fermionic geons altogether.


title: On quantum analogues of p-brane black holes

abstract:
  In a multidimensional model with several scalar fields and an m-form we deal
with classical spherically symmetric solutions with one (electric or magnetic)
p-brane and Ricci-flat internal spaces and the corresponding solutions to the
Wheeler--DeWitt (WDW) equation. Classical black holes are considered and their
quantum analogues (e.g. for M2 and M5 extremal solutions in D =11 supergravity,
electric and magnetic charges in D=4 gravity) are suggested when the curvature
coupling in the WDW equation is zero.


title:
Post-Newtonian parameters for general black hole and spherically
  symmetric p-brane solutions

abstract:
  Black hole p-brane solutions for a wide class of intersection rules are
considered. The solutions are defined on a manifold which contains a product of
n-1 Ricci-flat "internal'' spaces. The post-Newtonian parameters "beta" and
"gamma" corresponding to a 4-dimensional section of the metric for general
intersection rules are studied. It is shown that "beta" does not depend but
"gamma" depends on brane intersections. For "block-orthogonal" intersection
rules spherically symmetric solutions are considered, and explicit relations
for post-Newtonian parameters are obtained. The bounds on parameters of
solutions following from observational restrictions in the Solar system are
presented.


title: The Innermost Stable Circular Orbit in Compact Binaries

abstract:
  Newtonian point mass binaries can be brought into arbitrarily close circular
orbits. Neutron stars and black holes, however, are extended, relativistic
objects. Both finite size and relativistic effects make very close orbits
unstable, so that there exists an innermost stable circular orbit (ISCO). We
illustrate the physics of the ISCO in a simple model problem, and review
different techniques which have been employed to locate the ISCO in black hole
and neutron star binaries. We discuss different assumptions and approximations,
and speculate on how differences in the results may be explained and resolved.


title: Quantum cosmology at the turn of Millennium

abstract:
  A brief review of the modern state of quantum cosmology is presented as a
theory of quantum initial conditions for inflationary scenario. The no-boundary
and tunneling states of the Universe are discussed as a possible source of
probability peaks in the distribution of initial data for inflation. It is
emphasized that in the tree-level approximation the existence of such peaks is
in irreconcilable contradiction with the slow roll regime -- the difficulty
that is likely to be solved only on account of quantum gravitational effects.
The low-energy (typically GUT scale) mechanism of quantum origin of the
inflationary Universe with observationally justified parameters is presented
for closed and open inflation models with a strong non-minimal coupling.


title: Complete null data for a black hole collision

abstract:
  We discuss a sequence of numerically constructed geometries describing binary
black hole event horizons -- providing the necessary input for characteristic
evolution of the exterior spacetime. Our sequence approaches a single
Schwarzschild horizon as one limiting case and also includes cases where the
horizon's crossover surface is not hidden by a marginally anti-trapped surface
(MATS).


title: The Rest-Frame Instant Form of Metric Gravity

abstract:
  In a special class of globally hyperbolic, topologically trivial,
asymptotically flat at spatial infinity spacetimes selected by the requirement
of absence of supertranslations (compatible with Christodoulou-Klainermann
spacetimes) it is possible to define the {\it rest-frame instant form} of ADM
canonical gravity by using Dirac's strategy of adding ten extra variables at
spatial infinity and ten extra first class constraints implying the gauge
nature of these variables. The final canonical Hamiltonian is the weak ADM
energy and a discussion of the Hamiltonian gauge transformations generated by
the eight first class ADM constraints is given. When there is matter and the
Newton constant is switched off, one recovers the description of the matter on
the Wigner hyperplanes of the rest-frame instant form of dynamics in Minkowski
spacetime.


title: Chiral String in a Curved Space: Gravitational Self-Action

abstract:
  We analyze the effective action describing the linearised gravitational
self-action for a classical superconducting string in a curved spacetime. It is
shown that the divergent part of the effective action is equal to zero for the
both Nambu-Goto and chiral superconducting string.


title: A cosmological model in Weyl-Cartan spacetime

abstract:
  We present a cosmological model for early stages of the universe on the basis
of a Weyl-Cartan spacetime. In this model, torsion $T^{\alpha}$ and
nonmetricity $Q_{\alpha \beta}$ are proportional to the vacuum polarization.
Extending earlier work of one of us (RT), we discuss the behavior of the cosmic
scale factor and the Weyl 1-form in detail. We show how our model fits into the
more general framework of metric-affine gravity (MAG).


title:
Detecting a non-Gaussian stochastic background of gravitational
  radiation

abstract:
  We derive a detection method for a stochastic background of gravitational
waves produced by events where the ratio of the average time between events to
the average duration of an event is large. Such a signal would sound something
like popcorn popping. Our derivation is based on the somewhat unrealistic
assumption that the duration of an event is smaller than the detector time
resolution.


title:
Scalar, electromagnetic and Weyl perturbations of BTZ black holes: quasi
  normal modes

abstract:
  We calculate the quasinormal modes and associated frequencies of the Banados,
Zanelli and Teitelboim (BTZ) non-rotating black hole. This black hole lives in
2+1-dimensions in an asymptotically anti-de Sitter spacetime. We obtain exact
results for the wavefunction and quasi normal frequencies of scalar,
electromagnetic and Weyl (neutrino) perturbations.


title: New constraints in dynamical torsion theory

abstract:
  The most general Lagrangian for dynamical torsion theory quadratic in
curvature and torsion is considered. We impose two simple and physically
reasonable constraints on the solutions of the equations of motion: (i) there
must be solutions with zero curvature and nontrivial torsion and (ii) there
must be solutions with zero torsion and non covariantly constant curvature. The
constraints reduce the number of independent coupling constants from ten to
five. The resulting theory contains Einstein's general relativity and
Weitzenbock's absolute parallelism theory as the two sectors.


title:
Oscillatory approach to the singularity in vacuum $T^2$ symmetric
  spacetimes

abstract:
  A combination of qualitative analysis and numerical study indicates that
vacuum $T^2$ symmetric spacetimes are, generically, oscillatory.


title:
Entropy of massive fields near a black hole and vacuum polarization:
  thermodynamics without statistical mechanics

abstract:
  Starting from the Frolov-Zel'nikov stress-energy tensor of quantum massive
fields in the Schwarzschild background, we recover the contribution $S_{q}$ of
these field into the entropy of a black hole. For fermions with the spin
$%s=1/2$ $S_{q}>0$, for scalar fields $S_{q}>0$ provided the coupling parameter
is restricted to some interval, and $S_{q}<0$ for vector fields. The appearance
of negative values of $S_{q}$ is attributed to the fact that in the situation
under discussion there are no real quanta to contribute to the entropy, so
$S_{q}$ is due to vacuum polarization entirely and has nothing to do with the
statistical-mechanical entropy. We also consider the spacetime with an
acceleration horizon - the Bertotti-Robison spacetime - and show that $S_{q}=0$
for massive fields similarly to what was proved earlier for massless fields.


title: The mass quantum and black hole entropy II

abstract:
  In gr-qc/9908036 [Phys. Lett. A 265 (2000) 1] a new method was given which
naturally led to a quantum of mass equal to twice the Planck mass. In the
present note which, for convenience, we write formally as a continuation of
that paper, we show that with spin one of the mass quantum, the physical
entropy of a rotating black hole is also given by the Bekenstein-Hawking
formula.


title: Relational time in generally covariant quantum systems: four models

abstract:
  We analize the relational quantum evolution of generally covariant systems in
terms of Rovelli's evolving constants of motion and the generalized Heisenberg
picture. In order to have a well defined evolution, and a consistent quantum
theory, evolving constants must be self-adjoint operators. We show that this
condition imposes strong restrictions to the choices of the clock variables. We
analize four cases. The first one is non- relativistic quantum mechanics in
parametrized form. We show that, for the free particle case, the standard
choice of time is the only one leading to self-adjoint evolving constants.
Secondly, we study the relativistic case. We show that the resulting quantum
theory is the free particle representation of the Klein Gordon equation in
which the position is a perfectly well defined quantum observable. The
admissible choices of clock variables are the ones leading to space-like
simultaneity surfaces. In order to mimic the structure of General Relativity we
study the SL(2R) model with two Hamiltonian constraints. The evolving constants
depend in this case on three independent variables. We show that it is possible
to find clock variables and inner products leading to a consistent quantum
theory. Finally, we discuss the quantization of a constrained model having a
compact constraint surface. All the models considered may be consistently
quantized, although some of them do not admit any time choice such that the
equal time surfaces are transversal to the orbits.


title: Slightly Bimetric Gravitation

abstract:
  The inclusion of a flat metric tensor in gravitation permits the formulation
of a gravitational stress-energy tensor and the formal derivation of general
relativity from a linear theory in flat spacetime. Building on the works of
Kraichnan and Deser, we present such a derivation using universal coupling and
gauge invariance.
  Next we slightly weaken the assumptions of universal coupling and gauge
invariance, obtaining a larger ``slightly bimetric'' class of theories, in
which the Euler-Lagrange equations depend only on a curved metric, matter
fields, and the determinant of the flat metric. The theories are equivalent to
generally covariant theories with an arbitrary cosmological constant and an
arbitrarily coupled scalar field, which can serve as an inflaton or dark
matter.
  The question of the consistency of the null cone structures of the two
metrics is addressed. A difficulty for Logunov's massive gravitation on this
front is noted.


title: Geometry and dynamics of the brane-world

abstract:
  Recent developments in string theory have led to 5-dimensional warped
spacetime models in which standard-model fields are confined to a 3-brane (the
observed universe), while gravity can propagate in the fifth dimension. Gravity
is localized near the brane at low energies, even if the extra dimension is
noncompact. A review is given of the classical geometry and dynamics of these
brane-world models. The field equations on the brane modify the general
relativity equations in two ways: local 5-D effects are imprinted on the brane
as a result of its embedding, and are significant at high energies; nonlocal
effects arise from the 5-D Weyl tensor. The Weyl tensor transmits tidal
(Coulomb), gravitomagnetic and gravitational wave effects to the brane from the
5-D nonlocal gravitational field. Local high-energy effects modify the dynamics
of inflation, and increase the amplitude of scalar and tensor perturbations
generated by inflation. Nonlocal effects introduce new features in cosmological
perturbations. They induce a non-adiabatic mode in scalar perturbations and
massive modes in vector and tensor perturbations, and they can support vector
perturbations even in the absence of matter vorticity. In astrophysics, local
and nonlocal effects introduce fundamental changes to gravitational collapse
and black hole solutions.


title:
Brane world cosmological constant in the models with large extra
  dimensions

abstract:
  We consider ``brane universe'' with nonzero tension in the models with large
extra dimensions. We find exact solutions of higher-dimensional Einstein
equations with single flat Minkowsky brane of arbitrary large tension (or brane
cosmological constant) and compact extra dimensions. The brane curves the bulk
space-time in a small region around it. There is no fine tuning of energy
scales in our model.


title: Symmetric States in Quantum Geometry

abstract:
  Symmetric states are defined in the kinematical sector of loop quantum
gravity and applied to spherical symmetry and homogeneity. Consequences for the
physics of black holes and cosmology are discussed.


title:
Fresh inflation: a warm inflationary model from a zero temperature
  initial state

abstract:
  A two-components mixture fluid which complies with the gamma law is
considered in the framework of inflation with finite temperature. The model is
developed for a quartic scalar potential without symmetry breaking. The
radiation energy density is assumed to be zero when inflation starts and
remains below the GUT temperature during the inflationary stage. Furthermore,
provides the necessary number of e-folds and sufficient radiation energy
density to GUT baryogenesis can take place near the minimum energetic
configuration.


title: Approximate Solutions to the Binary Black Hole Initial Value Problem

abstract:
  We present approximate analytical solutions to the Hamiltonian and momentum
constraint equations, corresponding to systems composed of two black holes with
arbitrary linear and angular momentum. The analytical nature of these initial
data solutions makes them easier to implement in numerical evolutions than the
traditional numerical approach of solving the elliptic equations derived from
the Einstein constraints.


title:
Convergence to a self-similar solution in general relativistic
  gravitational collapse

abstract:
  We study the spherical collapse of a perfect fluid with an equation of state
$P=k\rho$ by full general relativistic numerical simulations. For $0<k\alt
0.036$, it has been known that there exists a general relativistic counterpart
of the Larson-Penston self-similar Newtonian solution. The numerical
simulations strongly suggest that, in the neighborhood of the center, generic
collapse converges to this solution in an approach to a singularity and that
self-similar solutions other than this solution, including a ``critical
solution'' in the black hole critical behavior, are relevant only when the
parameters which parametrize initial data are fine-tuned. This result is
supported by a mode analysis on the pertinent self-similar solutions. Since a
naked singularity forms in the general relativistic Larson-Penston solution for
$0<k\alt0.0105$, this will be the most serious known counterexample against
cosmic censorship. It also provides strong evidence for the self-similarity
hypothesis in general relativistic gravitational collapse. The direct
consequence is that critical phenomena will be observed in the collapse of
isothermal gas in Newton gravity, and the critical exponent $\gamma$ will be
given by $\gamma\approx 0.11$, though the order parameter cannot be the black
hole mass.


title: Initial condition of a thick loop cosmic string and linear perturbations

abstract:
  The initial data of the gravitational field produced by a loop thick string
is considered. We show that a thick loop is not a geodesic on the initial
hypersurface, while a loop conical singularity is. This suggests that there is
the ``{\it critical thickness}'' of a string, at which the linear perturbation
theory with a flat space background fails to describe the gravity of a loop
cosmic string. Using the above initial data, we also show that the linear
perturbation around flat space is plausible if the string thickness is larger
than $\sim5\times10^{-3}a$, where $a$ is the curvature radius of the loop.


title:
Dirac Decomposition of Wheeler-DeWitt Equation on the Bianchi Class A
  Models

abstract:
  The Wheeler-DeWitt equation for the Bianchi Class A cosmological models is
expressed generally in terms of the second-order differential equation like the
Klein-Gordon equation. To obtain the positive-definite probability density, a
new method extending the Dirac-Square-Root formalism, which factorizes the
Wheeler-DeWitt equation into the first-order differential equation using the
Pauli matrices, is investigated. The solutions to the Dirac type equation thus
obtained are expressed in terms of two-component spinor form. The probability
density defined by the solution is positive-definite and there is a conserved
current. The newly found spin-like degree of freedom causes the universe to go
through an early quantum stage of evolution with agitated
anisotropy-oscillation like Zitterbewegung.


title:
Tanaka-Tagoshi Parametrization of post-1PN Spin-Free Gravitational Wave
  Chirps: Equispaced and Cardinal Interpolated Lattices For First Generation
  Interferometric Antennas

abstract:
  The spin-free binary-inspiral parameter-space introduced by Tanaka and
Tagoshi to construct a uniformly-spaced lattice of templates at (and possibly
beyond) $2.5PN$ order is shown to work for all first generation interferometric
gravitational wave antennas. This allows to extend the minimum-redundant
cardinal interpolation techniques of the correlator bank developed by the
Authors to the highest available order PN templates. The total number of 2PN
templates to be computed for a minimal match $\Gamma=0.97$ is reduced by a
factor 4, as in the 1PN case.


title: Geometry of Non-expanding Horizons and Their Neighborhoods

abstract:
  This is a contribution to MG9 session BHT4. Certain geometrically
distinguished frame on a non-expanding horizon and in its space-time
neighborhood, as well as the Bondi-like coordinates are constructed. The
construction provides free degrees of freedom, invariants, and the existence
conditions for a Killing vector field. The reported results come from the joint
works with Ashtekar and Beetle.


title: A 2-Surface Quantization of the Lorentzian Gravity

abstract:
  This is a contribution to the MG9 session QG1-a. A new quantum representation
for the Lorentzian gravity is created from the Pullin vaccum by the operators
assigned to 2-complexes. The representation uses the original, spinorial
Ashtekar variables, the reality conditions are well posed and Thiemann's
Hamiltonian is well defined. The results on the existence of a suitable Hilbert
product are partial. They were derived in collaboration with Abhay Ashtekar.


title:
Matter seen at many scales and the geometry of averaging in relativistic
  cosmology

abstract:
  We investigate the scale-dependence of Eulerian volume averages of scalar
functions on Riemannian three-manifolds. We propose a complementary view of a
Lagrangian scaling of variables as opposed to their Eulerian averaging on
spatial domains. This program explains rigorously the origin of the Ricci
deformation flow for the metric, a flow which, on heuristic grounds, has been
already suggested as a possible candidate for averaging the initial data set
for cosmological spacetimes.


title: Rotational Instabilities and Centrifugal Hangup

abstract:
  One interesting class of gravitational radiation sources includes rapidly
rotating astrophysical objects that encounter dynamical instabilities. We have
carried out a set of simulations of rotationally induced instabilities in
differentially rotating polytropes. An $n$=1.5 polytrope with the Maclaurin
rotation law will encounter the $m$=2 bar instability at $T/|W| \gtrsim 0.27$.
Our results indicate that the remnant of this instability is a persistent
bar-like structure that emits a long-lived gravitational radiation signal.
Furthermore, dynamical instability is shown to occur in $n$=3.33 polytropes
with the $j$-constant rotation law at $T/|W| \gtrsim 0.14$. In this case, the
dominant mode of instability is $m$=1. Such instability may allow a
centrifugally-hung core to begin collapsing to neutron star densities on a
dynamical timescale. If it occurs in a supermassive star, it may produce
gravitational radiation detectable by LISA.


title:
Some results on the integrability of Einstein's field equations for
  axistationary perfect fluids

abstract:
  Using an orthonormal Lorentz frame approach to axistationary perfect fluid
spacetimes, we have formulated the necessary and sufficient equations as a
first order system, and investigated the integrability conditions of this set
of equations. The integrability conditions are helpful tools when it comes to
check the consequences and/or compatibility of certain simplifying assumptions,
e.g. Petrov types. Furthermore, using this method, a relation between the fluid
shear and vorticity is found for barotropic fluids. We collect some results
concerning Petrov types, and it is found that an incompressible axistationary
perfect fluid must be of Petrov type I.


title:
Analytical treatment of critical collapse in 2+1 dimensional AdS
  spacetime: a toy model

abstract:
  We present an exact collapsing solution to 2+1 gravity with a negative
cosmological constant minimally coupled to a massless scalar field, which
exhibits physical properties making it a candidate critical solution. We
discuss its global causal structure and its symmetries in relation with those
of the corresponding continously self-similar solution derived in the
$\Lambda=0$ case. Linear perturbations on this background lead to approximate
black hole solutions. The critical exponent is found to be $\gamma = 2/5$.


title: Hydrodynamics of Neutron Star Mergers

abstract:
  The final burst of gravitational radiation emitted by coalescing binary
neutron stars carries direct information about the neutron star fluid, and, in
particular, about the equation of state of nuclear matter at extreme densities.
The final merger may also be accompanied by a detectable electromagnetic
signal, such as a gamma-ray burst. In this paper, we summarize the results of
theoretical work done over the past decade that has led to a detailed
understanding of this hydrodynamic merger process for two neutron stars, and we
discuss the prospects for the detection and physical interpretation of the
gravity wave signals by ground-based interferometers such as LIGO. We also
present results from our latest post-Newtonian SPH calculations of binary
neutron star coalescence, using up to 10^6 SPH particles to compute with higher
spatial resolution than ever before the merger of an initially irrotational
system. We discuss the detectability of our calculated gravity wave signals
based on power spectra.


title:
An Alternative to Matter Localization in the "Brane World": An Early
  Proposal and its Later Improvements

abstract:
  Here we place the Latex typeset of the paper M. Pavsic, Phys. Lett. A116
(1986) 1-5. In the paper we presented the picture that our spacetime is a
3-brane moving in a higher dimensional space. The dynamical equations were
derived from the action which is just that for the usual Dirac-Nambu-Goto
$p$-brane. We also considered the case where not only one, but many branes of
various dimensionalities are present, and showed that their intersections with
the 3-brane manifest as matter in 4-dimensional spacetime. We considered a
particular case, where the intersections behaved as point particles, and found
out that they follow the geodesics on the 3-brane worldsheet (identified with
our spacetime). In a series of subsequent papers the original idea has been
further improved and developped. This is discussed in a note at the end, where
it is also pointed out that such a model resolves the problem of massive matter
confinement on the brane, recently discussed by Rubakov et al. and Mueck et al.


title: On the Green functions of gravitational radiation theory

abstract:
  Previous work in the literature has studied gravitational radiation in
black-hole collisions at the speed of light. In particular, it had been proved
that the perturbative field equations may all be reduced to equations in only
two independent variables, by virtue of a conformal symmetry at each order in
perturbation theory. The Green function for the perturbative field equations is
here analyzed by studying the corresponding second-order hyperbolic operator
with variable coefficients, instead of using the reduction method from the
retarded flat-space Green function in four dimensions. After reduction to
canonical form of this hyperbolic operator, the integral representation of the
solution in terms of the Riemann function is obtained. The Riemann function
solves a characteristic initial-value problem for which analytic formulae
leading to the numerical solution are derived.


title: Navigation in Curved Space-Time

abstract:
  A covariant and invariant theory of navigation in curved space-time with
respect to electromagnetic beacons is written in terms of J. L. Synge's
two-point invariant world function. Explicit equations are given for navigation
in space-time in the vicinity of the Earth in Schwarzschild coordinates and in
rotating coordinates. The restricted problem of determining an observer's
coordinate time when their spatial position is known is also considered.


title:
Exact static solutions in Einstein-Maxwell-Dilaton gravity with
  arbitrary dilaton coupling parameter

abstract:
  We present solution generating methods which allow to construct exact static
solutions to the equations of four-dimensional Einstein-Maxwell-Dilaton gravity
starting with arbitrary static solutions to the pure vacuum Einstein equations,
Einstein-dilaton or Einstein-Maxwell equations.


title: Note on Scalar Fields Non-Minimally Coupled to (2+1)-Gravity

abstract:
  Scalar fields non--minimally coupled to (2+1)-gravity, in the presence of
cosmological constant term, are considered. Non-minimal couplings are described
by the term $\zeta R \Psi^2$ in the Lagrangian. Within a class of static
circularly symmetric space-times, it is shown that the only existing physically
relevant solutions are the anti-de Sitter space-time for $\zeta=0$, and the
Martinez-Zanelli black hole for $\zeta=1/8$. We obtain also two new solutions
with non-trivial scalar field, for $\zeta=1/6$ and $\zeta=1/8$ respectively,
nevertheless, the corresponding space-times can be reduced, via coordinate
transformations, to the standard anti-de Sitter space.


title: Statistical geometry of random weave states

abstract:
  I describe the first steps in the construction of semiclassical states for
non-perturbative canonical quantum gravity using ideas from classical,
Riemannian statistical geometry and results from quantum geometry of spin
network states. In particular, I concentrate on how those techniques are
applied to the construction of random spin networks, and the calculation of
their contribution to areas and volumes.


title:
The Post-Newtonian Approximation of the Rigidly Rotating Disc of Dust to
  Arbitrary Order

abstract:
  Using the analytic, global solution for the rigidly rotating disc of dust as
a starting point, an iteration scheme is presented for the calculation of an
arbitrary coefficient in the post-Newtonian (PN) approximation of this
solution. The coefficients were explicitly calculated up to the 12th PN level
and are listed in this paper up to the 4th PN level. The convergence of the
series is discussed and the approximation is found to be reliable even in
highly relativistic cases. Finally, the ergospheres are calculated at
increasing orders of the approximation and for increasingly relativistic
situations.


title: Non-Commutative Topology for Curved Quantum Causality

abstract:
  A quantum causal topology is presented. This is modeled after a
non-commutative scheme type of theory for the curved finitary spacetime sheaves
of the non-abelian incidence Rota algebras that represent `gravitational
quantum causal sets'. The finitary spacetime primitive algebra scheme
structures for quantum causal sets proposed here are interpreted as the
kinematics of a curved and reticular local quantum causality. Dynamics for
quantum causal sets is then represented by appropriate scheme morphisms, thus
it has a purely categorical description that is manifestly `gauge-independent'.
Hence, a schematic version of the Principle of General Covariance of General
Relativity is formulated for the dynamically variable quantum causal sets. We
compare our non-commutative scheme-theoretic curved quantum causal topology
with some recent $C^{*}$-quantale models for non-abelian generalizations of
classical commutative topological spaces or locales, as well as with some
relevant recent results obtained from applying sheaf and topos-theoretic ideas
to quantum logic proper. Motivated by the latter, we organize our finitary
spacetime primitive algebra schemes of curved quantum causal sets into a
topos-like structure, coined `quantum topos', and argue that it is a sound
model of a structure that Selesnick has anticipated to underlie Finkelstein's
reticular and curved quantum causal net. At the end we conjecture that the
fundamental quantum time-asymmetry that Penrose has expected to be the main
characteristic of the elusive `true quantum gravity' is possibly of a
kinematical or structural rather than of a dynamical character, and we also
discuss the possibility of a unified description of quantum logic and quantum
gravity in quantum topos-theoretic terms.


title: Dyonic BIon black hole in string inspired model

abstract:
  We construct static and spherically symmetric particle-like and black hole
solutions with magnetic and/or electric charge in the
Einstein-Born-Infeld-dilaton-axion system, which is a generalization of the
Einstein-Maxwell-dilaton-axion (EMDA) system and of the Einstein-Born-Infeld
(EBI) system. They have remarkable properties which are not seen for the
corresponding solutions in the EMDA and the EBI system.


title:
Axisymmetric electrovacuum spacetimes with an additional Killing vector
  and radiation

abstract:
  Main results concerning allowable additional symmetries of axially symmetric
electrovacuum spacetimes are summarized. These are translational Killing
vectors and the boost Killing vector. However, this is only the boost symmetry
that does not exclude radiation and permit a spacetime to be asymptotically
flat with global null infinity.


title: Curvature invariants in algebraically special spacetimes

abstract:
  It is well known that all curvature invariants of the order zero vanish for
type-III and type-N vacuum spacetimes. We briefly summarize properties of
higher order curvature invariants for these spacetimes.


title:
Cylindrically Symmetric Solitons with Nonlinear Self-Gravitating Scalar
  Fields

abstract:
  Static, cylindrically symmetric solutions to nonlinear scalar-Einstein
equations are considered. Regularity conditions on the symmetry axis and flat
or string asymptotic conditions are formulated in order to select soliton-like
solutions. Some non-existence theorems are proved, in particular, theorems
asserting (i) the absence of black-hole and wormhole-like cylindrically
symmetric solutions for any static scalar fields minimally coupled to gravity
and (ii) the absence of solutions with a regular axis for scalar fields with
the Lagrangian $L=F(I)$, $I=\phi^\alpha \phi_\alpha$, for any function $F(I)$
possessing a correct weak field limit. Exact solutions for scalar fields with
an arbitrary potential function $V(\phi)$ are obtained by quadratures and are
expressed in a parametric form in a few ways, where the parameter may be either
the coordinate $x$, or the $\phi$ field, or one of the metric coefficients.
Soliton-like solutions are shown to exist only with $V(\phi)$ having a variable
sign. Some explicit examples of solutions (including a soliton-like one) and
their flat-space limit are discussed.}


title:
Cosmological Adiabatic Geometric Phase of a Scalar Field in a Bianchi
  Spacetime

abstract:
  A two-component formulation of the Klein-Gordon equation is used to
investigate the cyclic and noncyclic adiabatic geometric phases due to
spatially homogeneous (Bianchi) cosmological models. It is shown that no
adiabatic geometric phases arise for Bianchi type I models. For general Bianchi
type IX models the problem of the adiabatic geometric phase is shown to be
equivalent to the one for nuclear quadrupole interactions of a spin. For these
models nontrivial non-Abelian adiabatic geometrical phases may occur in
general.


title:
Length versus time-interval discreteness in 2+1 Lorentzian canonical
  quantum gravity

abstract: Paper withdrawn. Replaced by by gr-qc/0212077 .


title: Some aspects on the observation of the gravitomagnetic clock effect

abstract:
  As a consequence of gravitomagnetism, which is a fundamental weak-field
prediction of general relativity and ubiquitous in gravitational phenomena,
clocks show a difference in their proper periods when moving along identical
orbits in opposite directions about a spinning mass. This time shift is induced
by the rotation of the source and may be used to verify the existence of the
terrestrial gravitomagnetic field by means of orbiting clocks. A possible
mission scenario is outlined with emphasis given to some of the major
difficulties which inevitably arise in connection with such a venture.


title: Asymptotic Freedom in Curvature-Satured Gravity

abstract:
  For a spatially flat Friedmann model with line element $ds^2=a^2 [
da^2/B(a)-dx^2-dy^2-dz^2 ] $, the 00-component of the Einstein field equation
reads $8\pi G T_{00}=3/a^2$ containing no derivative. For a nonlinear
Lagrangian ${\cal L}(R)$, we obtain a second--order differential equation for
$B$ instead of the expected fourth-order equation. We discuss this equation for
the curvature-saturated model proposed by Kleinert and Schmidt. Finally, we
argue that asymptotic freedom $G_{{\rm eff}}^{-1}\to 0$ is fulfilled in
curvature-saturated gravity.


title: Black Holes under External Influence

abstract:
  The work on black holes immersed in external fields is reviewed in both
test-field approximation and within exact solutions. In particular we pay
attention to the effect of the expulsion of the flux of external fields across
charged and rotating black holes which are approaching extremal states.
Recently this effect has been shown to occur for black hole solutions in string
theory. We also discuss black holes surrounded by rings and disks and rotating
black holes accelerated by strings.


title:
Nonlinear mode coupling in rotating stars and the r-mode instability in
  neutron stars

abstract:
  We develop the formalism required to study the nonlinear interaction of modes
in rotating Newtonian stars in the weakly nonlinear regime. The formalism
simplifies and extends previous treatments. At linear order, we elucidate and
extend slightly a formalism due to Schutz, show how to decompose a general
motion of a rotating star into a sum over modes, and obtain uncoupled equations
of motion for the mode amplitudes under the influence of an external force.
Nonlinear effects are added perturbatively via three-mode couplings. We
describe a new, efficient way to compute the coupling coefficients, to zeroth
order in the stellar rotation rate, using spin-weighted spherical harmonics.
  We apply this formalism to derive some properties of the coupling
coefficients relevant to the nonlinear interactions of unstable r-modes in
neutron stars, postponing numerical integrations of the coupled equations of
motion to a later paper. From an astrophysical viewpoint, the most interesting
result of this paper is that many couplings of r-modes to other rotational
modes (modes with zero frequencies in the non-rotating limit) are small: either
they vanish altogether because of various selection rules, or they vanish to
lowest order in the angular velocity. In zero-buoyancy stars, the coupling of
three r-modes is forbidden entirely and the coupling of two r-modes to one
hybrid rotational mode vanishes to zeroth order in rotation frequency. In
incompressible stars, the coupling of any three rotational modes vanishes to
zeroth order in rotation frequency.


title: Field Theories from the Relativistic Law of Motion

abstract:
  From the relativistic law of motion we attempt to deduce the field theories
corresponding to the force law being linear and quadratic in 4-velocity of the
particle. The linear law leads to the vector gauge theory which could be the
abelian Maxwell electrodynamics or the non-abelian Yang-Mills theory. On the
other hand the quadratic law demands spacetime metric as its potential which is
equivalent to demanding the Principle of Equivalence. It leads to the tensor
theory of gravitational field -- General Relativity. It is remarkable that a
purely dynamical property of the force law leads uniquely to the corresponding
field theories.

categories: gr-qc astro-ph hep-th math-ph math.MP physics.class-ph


title: Signature transition and compactification

abstract:
  It is shown that a change in the signature of the space-time metric together
with compactification of internal dimensions could occure in a six-dimensional
cosmological model. We also show that this is due to interaction with Maxwell
fields having support in the internal part of the space-time.


title: Testing the Dirac equation

abstract:
  The dynamical equations which are basic for the description of the dynamics
of quantum felds in arbitrary space--time geometries, can be derived from the
requirements of a unique deterministic evolution of the quantum fields, the
superposition principle, a finite propagation speed, and probability
conservation. We suggest and describe observations and experiments which are
able to test the unique deterministic evolution and analyze given experimental
data from which restrictions of anomalous terms violating this basic principle
can be concluded. One important point is, that such anomalous terms are
predicted from loop gravity as well as from string theories. Most accurate data
can be obtained from future astrophysical observations. Also, laboratory tests
like spectroscopy give constraints on the anomalous terms.


title: Symmetries of the Gowdy Equations and Spatial Topologies

abstract:
  We examine some kinds of discrete symmetries which are dynamically preserved,
using the (generalized) Gowdy models of the first kind.


title: Light Cone Consistency in Bimetric General Relativity

abstract:
  General relativity can be formally derived as a flat spacetime theory, but
the consistency of the resulting curved metric's light cone with the flat
metric's null cone has not been adequately considered. If the two are
inconsistent, then gravity is not just another field in flat spacetime after
all.
  Here we discuss recent progress in describing the conditions for consistency
and prospects for satisfying those conditions.


title: Falaco Solitons, Cosmic Strings in a Swimming Pool

abstract:
  Topological defects experimentally induced by rotational dynamics in a
continuous media replicate the coherent structure features of cosmic strings as
well as hadrons.


title: Flat Spacetime Gravitation with a Preferred Foliation

abstract:
  Paralleling the formal derivation of general relativity as a flat spacetime
theory, we introduce in addition a preferred temporal foliation. The physical
interpretation of the formalism is considered in the context of 5-dimensional
``parametrized'' and 4-dimensional preferred frame contexts. In the former
case, we suggest that our earlier proposal of unconcatenated parametrized
physics requires that the dependence on $\tau$ be rather slow. In the
4-dimensional case, we consider and tentatively reject several areas of physics
that might require a preferred foliation, but find a need for one in the
process (``flowing'') theory of time. We then suggest why such a foliation
might reasonably be unobservable.


title:
Quantization Near Violent Singularities in Einstein-Yang-Mills Black
  Holes

abstract:
  Classical singularities inside black holes in the Einstein-Yang-Mills theory
exhibit unusual features. Only for discrete values of the black hole mass one
encounters singularities of the Schwarzschild type (timelike) and the
Reissner-Nordstrom type (spacelike). For a generic mass the approach to
singularity is not smooth: the metric oscillates with an infinitely growing
amplitude and decreasing period. In spite of some similarity with the BKL
oscillations, here the behavior is not chaotic. However the oscillation
amplitude exceeds classical limits after few cycles, so the question arises how
this behavior gets modified by quantum effects. We discuss this issue both in
the framework of QFT and in the string theory.


title: Solitons in Non-Abelian Born-Infeld Theory

abstract:
  Born-Infeld generalization of the Yang-Mills action suggested by the
superstring theory gives rise to modification of previously known as well as to
some new classical soliton solutions. Earlier it was shown that within the
model with the usual trace over the group generators classical glueballs exist
which form an infinite sequence similar to the Bartnik-McKinnon family of the
Einstein-Yang-Mills solutions. Here we give the generalization of this result
to the 'realistic' model with the symmetrized trace and show the existence of
excited monopoles (in presence of triplet Higgs) which can be regarded as a
non-linear superposition of monopoles and sphalerons.


title: On rigidity of spacetimes with a compact Cauchy horizon

abstract:
  Smooth spacetimes with a compact Cauchy horizon ruled by closed null
geodesics are considered. The compact Cauchy horizon is assumed to be
non-degenerate. Then, supporting the validity of Penrose's strong cosmic censor
hypothesis, the existence of a smooth Killing vector field in a neighbourhood
of the horizon on the Cauchy development side is shown.


title:
Conditional Symmetries and Phase Space Reduction towards G.C.T.
  Invariant Wave Functions, for the Class A Bianchi Type VI & VII Vacuum
  Cosmologies

abstract:
  The quantization of Class A Bianchi Type VI and VII geometries -with all six
scale factors, as well as the lapse function and the shift vector present- is
considered. A first reduction of the initial 6-dimensional configuration space
is achieved by the usage of the information furnished by the quantum form of
the linear constraints. Further reduction of the space in which the wave
function -obeying the Wheeler-DeWitt equation- lives, is accomplished by
revealing a classical integral of motion, tantamount to an extra symmetry of
the corresponding classical Hamiltonian. This symmetry generator -member of a
larger group- is linear in momenta and corresponds to G.C.T.s through the
action of the automorphism group -especially through the action of the outer
automorphism subgroup. Thus, a G.C.T. invariant wave function is found, which
depends on one combination of the two curvature invariants --which uniquely and
irreducibly characterizes the hypersurfaces t=const.


title: Quantum nondemolition measurements and non-Newtonian Gravity

abstract:
  In the present work the detection, by means of a nondemolition measurement,
of a Yukawa term, coexisting simultaneously with gravity, has been considered.
In other words, a nondemolition variable for the case of a particle immersed in
a gravitational field containing a Yukawa term is obtained. Afterwards the
continuous monitoring of this nondemolition parameter is analyzed, the
corresponding propagator is evaluated, and the probabilities associated with
the possible measurement outputs are found. The relevance of these kind of
proposals in connection with some unified theories of elementary particles has
been underlined.


title:
On the r-mode spectrum of relativistic stars in the low-frequency
  approximation

abstract:
  The axial modes for non-barotropic relativistic rotating neutron stars with
uniform angular velocity are studied, using the slow-rotation formalism
together with the low-frequency approximation, first investigated by Kojima.
The time independent form of the equations leads to a singular eigenvalue
problem, which admits a continuous spectrum. We show that for $l=2$, it is
nevertheless also possible to find discrete mode solutions (the $r$-modes).
However, under certain conditions related to the equation of state and the
compactness of the stellar model, the eigenfrequency lies inside the continuous
band and the associated velocity perturbation is divergent; hence these
solutions have to be discarded as being unphysical. We corroborate our results
by explicitly integrating the time dependent equations. For stellar models
admitting a physical $r$-mode solution, it can indeed be excited by arbitrary
initial data. For models admitting only an unphysical mode solution, the
evolutions do not show any tendency to oscillate with the respective frequency.
For higher values of $l$, it seems that in certain cases there are no mode
solutions at all.


title:
Statistical Mechanics of Relativistic One-Dimensional Self-Gravitating
  Systems

abstract:
  We consider the statistical mechanics of a general relativistic
one-dimensional self-gravitating system. The system consists of $N$-particles
coupled to lineal gravity and can be considered as a model of $N$
relativistically interacting sheets of uniform mass. The partition function and
one-particle distitrubion functions are computed to leading order in $1/c$
where $c$ is the speed of light; as $c\to\infty$ results for the
non-relativistic one-dimensional self-gravitating system are recovered. We find
that relativistic effects generally cause both position and momentum
distribution functions to become more sharply peaked, and that the temperature
of a relativistic gas is smaller than its non-relativistic counterpart at the
same fixed energy. We consider the large-N limit of our results and compare
this to the non-relativistic case.


title: Integrability for Relativistic Spin Networks

abstract:
  The evaluation of relativistic spin networks plays a fundamental role in the
Barrett-Crane state sum model of Lorentzian quantum gravity in 4 dimensions. A
relativistic spin network is a graph labelled by unitary irreducible
representations of the Lorentz group appearing in the direct integral
decomposition of the space of L^2 functions on three-dimensional hyperbolic
space. To `evaluate' such a spin network we must do an integral; if this
integral converges we say the spin network is `integrable'. Here we show that a
large class of relativistic spin networks are integrable, including any whose
underlying graph is the 4-simplex (the complete graph on 5 vertices). This
proves a conjecture of Barrett and Crane, whose validity is required for the
convergence of their state sum model.


title: Is Minisuperspace Quantum Gravity Reliable?

abstract:
  We study a minisuperspace quantum cosmology for a 2+1 dimensional de Sitter
universe and find the wave function both exactly and in WKB approximation. Then
we extend the model to a canonically quantized field theory for quantum
gravity, i.e., a midisuperspace, and obtain the wave functional of the
resulting field theory in the saddle point approximation. It is shown that
these two approaches yield different results.


title: Curvature and torsion of implicit hypersurfaces and the origin of charge

abstract:
  A formal correspondence is established between the curvature theory of
generalized implicit hypersurfaces, electromagnetism as expressed in terms of
exterior differential systems, and thermodynamics. Starting with a generalized
implicit surface whose normal field is represented by an exterior differential
1-form, it is possible to deduce the curvature invariants of the implicit
surface and to construct a globally closed vector density in terms of the
Jacobian properties of the normal field. When the closed vector density is
assigned the role of an intrinsic charge current density, and the components of
the normal field are assigned the roles of the electromagnetic potentials, the
theory is formally equivalent to an exterior differential system that generates
the PDE's of both the Maxwell Faraday equations and the Maxwell Ampere
equations. The interaction energy density between the potentials and the
induced closed charge current density is exactly the similarity curvature
invariant of highest degree (N-1) for the implicit surface. Although developed
without direct contact with M-brane theory, these ideas of generalized implicit
surfaces should have application to the study of p-branes that can have
multiple components and envelopes. The theory suggests that gravitational
collapse of mass energy density should include terms that involve the
interaction between charge-current densities and electromagnetic potentials.


title:
Some remarks on the thermal and vacuum fluctuations of a massive scalar
  field

abstract:
  Thermal fluctuations of a massive scalar field in the Rindler wedge have been
recently obtained. As a by product, the Minkowski vacuum fluctuations seen by a
uniformly accelerated observer have been determined and confronted with the
corresponding Minkowski thermal fluctuations of the same field, seen by an
inertial observer. Since some of the calculations of this previous work have
not been detailed on it, and they present some important subtleties, they are
explicitly done here. These subtleties have to do with the leading order
behaviour of certain parameter dependent integrals. Some of the leading order
expansions are derived using the Riemann-Lebesgue lemma.


title: Vacuum energy and cosmological constant: View from condensed matter

abstract:
  The condensed matter examples, in which the effective gravity appears in the
low-energy corner as one of the collective modes of quantum vacuum, provide a
possible answer to the question, why the vacuum energy is so small. This answer
comes from the fundamental ``trans-Planckian'' physics of quantum liquids. In
the effective theory of the low energy degrees of freedom the vacuum energy
density is proportional to the fourth power of the corresponding ``Planck''
energy appropriate for this effective theory. However, from the exact ``Theory
of Everything'' of the quantum liquid it follows that its vacuum energy density
is exactly zero without fine tuning, if: there are no external forces acting on
the liquid; there are no quasiparticles which serve as matter; no space-time
curvature; and no boundaries which give rise to the Casimir effect. Each of
these four factors perturbs the vacuum state and induces the nonzero value of
the vacuum energy density of order of energy density of the perturbation. This
is the reason, why one must expect that in each epoch the vacuum energy density
is of order of matter density of the Universe, or/and of its curvature, or/and
of the energy density of smooth component -- the quintessence.


title: Uniqueness of the Machian Solution in the Brans-Dicke Theory

abstract:
  Machian solutions of which the scalar field exhibits the asymptotic behavior
$\phi =O(\rho /\omega)$ are generally explored for the homogeneous and
isotropic universe in the Brans-Dicke theory. It is shown that the Machian
solution is unique for the closed and the open space. Such a solution is
restricted to one that satisfies the relation $GM/c^{2}a=const$, which is fixed
to $\pi $ in the theory for the closed model. Another type of solution
satisfying $\phi =O(\rho /\omega)$ with the arbitrary coupling constant $%
\omega $ is obtained for the flat space. This solution has the scalar field $%
\phi \propto \rho t^{2}$ and also keeps the relation $GM/c^{2}R=const$ all the
time. This Machian relation and the asymptotic behavior $\phi =O(\rho /\omega)$
is equivalent to each other in the Brans-Dicke theory.


title:
Influence of the Particles Creation on the Flat and Negative Curved FLRW
  Universes

abstract:
  We present a dynamical analysis of the (classical) spatially flat and
negative curved Friedmann-Lameitre-Robertson-Walker (FLRW) universes evolving,
(by assumption) close to the thermodynamic equilibrium, in presence of a
particles creation process, described by means of a realiable phenomenological
approach, based on the application to the comoving volume (i. e. spatial volume
of unit comoving coordinates) of the theory for open thermodynamic systems. In
particular we show how, since the particles creation phenomenon induces a
negative pressure term, then the choice of a well-grounded ansatz for the time
variation of the particles number, leads to a deep modification of the very
early standard FLRW dynamics. More precisely for the considered FLRW models, we
find (in addition to the limiting case of their standard behaviours) solutions
corresponding to an early universe characterized respectively by an "eternal"
inflationary-like birth and a spatial curvature dominated singularity. In both
these cases the so-called horizon problem finds a natural solution.


title:
Equation of motion for relativistic compact binaries with the strong
  field point particle limit : the second and half post-Newtonian order

abstract:
  We study the equation of motion appropriate to an inspiralling binary star
system whose constituent stars have strong internal gravity. We use the
post-Newtonian approximation with the strong field point particle limit by
which we can introduce into general relativity a notion of a point-like
particle with strong internal gravity without using Dirac delta distribution.
Besides this limit, to deal with strong internal gravity we express the
equation of motion in surface integral forms and calculate these integrals
explicitly. As a result we obtain the equation of motion for a binary of
compact bodies accurate through the second and half post-Newtonian (2.5 PN)
order. This equation is derived in the harmonic coordinate. Our resulting
equation perfectly agrees with Damour and Deruelle 2.5 PN equation of motion.
Hence it is found that the 2.5 PN equation of motion is applicable to a
relativistic compact binary.


title: r-modes of slowly rotating non-isentropic relativistic stars

abstract:
  We investigate properties of r-modes characterized by regular eigenvalue
problem in slowly rotating relativistic polytropes. Our numerical results
suggest that discrete r-mode solutions for the regular eigenvalue problem exist
only for restricted polytropic models. In particular the r-mode associated with
l=m=2, which is considered to be the most important for gravitational radiation
driven instability, do not have a discrete mode as solutions of the regular
eigenvalue problem for polytropes having the polytropic index N > 1.18 even in
the post-Newtonian order. Furthermore for a N=1 polytrope, which is employed as
a typical neutron star model, discrete r-mode solutions for regular eigenvalue
problem do not exist for stars whose relativistic factor M/R is larger than
about 0.1. Here M and R are stellar mass and stellar radius, respectively.


title: Eliminating Thermal Violin Spikes from LIGO Noise

abstract:
  We have developed a scheme for reducing LIGO suspension thermal noise close
to violin-mode resonances. The idea is to monitor directly the
thermally-induced motion of a small portion of (a ``point'' on) each suspension
fiber, thereby recording the random forces driving the test-mass motion close
to each violin-mode frequency. One can then suppress the thermal noise by
optimally subtracting the recorded fiber motions from the measured motion of
the test mass, i.e., from the LIGO output. The proposed method is a
modification of an analogous but more technically difficult scheme by
Braginsky, Levin and Vyatchanin for reducing broad-band suspension thermal
noise. The efficiency of our method is limited by the sensitivity of the sensor
used to monitor the fiber motion. If the sensor has no intrinsic noise (i.e.
has unlimited sensitivity), then our method allows, in principle, a complete
removal of violin spikes from the thermal-noise spectrum. We find that in
LIGO-II interferometers, in order to suppress violin spikes below the
shot-noise level, the intrinsic noise of the sensor must be less than
\~2*10^{-13}cm/sqrt(Hz). This sensitivity is two orders of magnitude greater
than that of currently available sensors.


title: Emission of gravitational radiation from ultra-relativistic sources

abstract:
  Recent observations suggest that blobs of matter are ejected with
ultra-relativistic speeds in various astrophysical phenomena such as supernova
explosions, quasars, and microquasars. In this paper we analyze the
gravitational radiation emitted when such an ultra-relativistic blob is ejected
from a massive object. We express the gravitational wave by the metric
perturbation in the transverse-traceless gauge, and calculate its amplitude and
angular dependence. We find that in the ultra-relativistic limit the
gravitational wave has a wide angular distribution, like $1+\cos\theta$. The
typical burst's frequency is Doppler shifted, with the blue-shift factor being
strongly beamed in the forward direction. As a consequence, the energy flux
carried by the gravitational radiation is beamed. In the second part of the
paper we estimate the anticipated detection rate of such bursts by a
gravitational-wave detector, for blobs ejected in supernova explosions. Dar and
De Rujula recently proposed that ultra-relativistic blobs ejected from the
central core in supernova explosions constitute the source of Gamma-ray bursts.
Substituting the most likely values of the parameters as suggested by their
model, we obtain an estimated detection rate of about 1 per year by the
advanced LIGO-II detector.


title: A diagrammatic approach to the spectrum of cosmological perturbations

abstract:
  We compute the spectral distribution of the quantum fluctuations of the
vacuum, amplified by inflation, after an arbitrary number of background
transitions. Using a graphic representation of the process we find that the
final spectrum can be completely determined trough a synthetic set of working
rules, and a list of simple algebraic computations.


title: A note on behaviour at an isotropic singularity

abstract:
  The behaviour of Jacobi fields along a time-like geodesic running into an
isotropic singularity is studied. It is shown that the Jacobi fields are
crushed to zero length at a rate which is the same in every direction
orthogonal to the geodesic. We show by means of a counter-example that this
crushing effect depends crucially on a technicality of the definition of
isotropic singularities, and not just on the uniform degeneracy of the metric
at the singularity.


title: Cosmological Black Holes

abstract:
  In this paper we propose a model for the formation of the cosmological voids.
We show that cosmological voids can form directly after the collapse of
extremely large wavelength perturbations into low-density black holes or
cosmological black holes (CBH). Consequently the voids are formed by the
comoving expansion of the matter that surrounds the collapsed perturbation. It
follows that the universe evolves, in first approximation, according to the
Einstein-Straus cosmological model. We discuss finally the possibility to
detect the presence of these black holes through their weak and strong lensing
effects and their influence on the cosmic background radiation.


title: New Proposal for a 5-dimensional Theory of Kaluza-Klein type

abstract:
  A new 5-dimensional Classical Unified Field Theory of Kaluza-Klein type is
formulated using 2 separate scalar fields which are related in such a way as to
make the 5-dimensional matter-geometry coupling parameter constant. It is shown
that this procedure solves the problem of the variability of the gravity
coupling parameter without having to assume a conformal invariance. The
corresponding Field equations are discussed paying particular attention to the
possible induction of scalar field gradients by Electromagnetic Fields. A new
correspondence limit in which the field equations lead to the usual
Einstein-Maxwell equations is obtained. This limit does not require the usual
condition that the usual scalar field be constant.


title: Delay Equations and Radiation Damping

abstract:
  Starting from delay equations that model field retardation effects, we study
the origin of runaway modes that appear in the solutions of the classical
equations of motion involving the radiation reaction force. When retardation
effects are small, we argue that the physically significant solutions belong to
the so-called slow manifold of the system and we identify this invariant
manifold with the attractor in the state space of the delay equation. We
demonstrate via an example that when retardation effects are no longer small,
the motion could exhibit bifurcation phenomena that are not contained in the
local equations of motion.


title:
Singular Behaviour of electric and magnetic fields in dielectric media
  in a non-linear gravitational wave background

abstract:
  Evolution of electric and magnetic fields in dielectric media, driven by the
influence of a strong gravitational wave, is considered for four exactly
integrable models. It is shown that the gravitational wave field gives rise to
new effects and to singular behaviour in the electromagnetic field.


title: Matter Collineations of Some Well Known Spacetimes

abstract:
  We derive matter collineations of the Bianchi types I, II, III, VIII and IX,
and Kantowski-Sachs spacetimes. It is found that matter collineations turn out
similar to Ricci collineations with different constranit equations. We solve
the constraint equation for a particular case and obtain three cosmological
models which represent perfect fluid dust solutions.


title: Diagrams for heat kernel expansions

abstract:
  A diagramatic heat kernel expansion technique is presented. The method is
especially well suited to the small-derivative expansion of the heat kernel,
but it can also be used to reproduce the results obtained by the approach known
as covariant perturbation theory. The new technique gives an expansion for the
heat kernel at coincident points. It can also be used to obtain the derivative
of the heat kernel and this is useful for evaluating the expectation values of
the stress-energy tensor.


title: A scalar-tensor cosmological model with dynamical light velocity

abstract:
  The dynamical consequences of a bimetric scalar-tensor theory of gravity with
a dynamical light speed are investigated in a cosmological setting. The model
consists of a minimally-coupled self-gravitating scalar field coupled to
ordinary matter fields in the standard way through the metric:
$\metric_{\mu\nu}+B\partial_\mu\phi\partial_\nu\phi$. We show that in a
universe with matter that has a radiation-dominated equation of state, the
model allows solutions with a de Sitter phase that provides sufficient
inflation to solve the horizon and flatness problems. This behaviour is
achieved without the addition of a potential for the scalar field, and is shown
to be largely independent of its introduction. We therefore have a model that
is fundamentally different than the potential-dominated, slowly-rolling scalar
field of the standard models inflationary cosmology. The speed of gravitational
wave propagation is predicted to be significantly different from the speed of
matter waves and photon propagation in the early universe.


title:
Integrability and explicit solutions in some Bianchi cosmological
  dynamical systems

abstract:
  The Einstein field equations for several cosmological models reduce to
polynomial systems of ordinary differential equations. In this paper we shall
concentrate our attention to the spatially homogeneous diagonal G_2
cosmologies. By using Darboux's theory in order to study ordinary differential
equations in the complex projective plane CP^2 we solve the Bianchi V models
totally. Moreover, we carry out a study of Bianchi VI models and first
integrals are given in particular cases.


title: Canonical quantization of two-dimensional gravity

abstract:
  A canonical quantization of two-dimensional gravity minimally coupled to real
scalar and spinor Majorana fields is presented. The physical state space of the
theory is completely described and calculations are also made of the average
value of the metric tensor relative to states close to the ground state


title:
Proposal for experimental verifying of Machian transient mass
  fluctuations

abstract:
  Starting from quoted papers it show that, applying Mach's principle, on
obtains transient mass fluctuation by varying proper energy. It is show why the
experiments performed until now measured a smaller effect than was predicted.
On establish conditions for using gravitational energy by means of transient
mass fluctuations. On suggest a new type of experiment for verify the effect of
transient mass fluctuation.


title:
Time-Variation of the Gravitational Constant and the Machian Solution in
  the Brans-Dicke Theory

abstract:
  The Machian cosmological solution satisfying $\phi =O(\rho /\omega)$ for the
perfect-fluid with negative pressure is discussed. When the coefficient of the
equation of state $\gamma \to -1/3$, the gravitational constant approaches to
constant. If we assume the present mass density $\rho_{0}\sim \rho_{c}$
(critical density), the parameter $\epsilon$ ($\gamma =(\epsilon -1)/3$) has a
value of order $10^{-3}$ to support the present gravitational constant. The
closed model is valid for $\omega <-3/2\epsilon$ and exhibits the slow
accelerating expansion. We understand why the coupling parameter $| \omega |$
is so large ($\omega \sim -10^{3}$). The time-variation of the gravitational
constant $| \dot{G}/G| \sim 10^{-13} yr^{-1}$ at present is derived in this
model.


title: Bianchi VIII Empty Futures

abstract:
  Using a qualitative analysis based on the Hamiltonian formalism and the
orthonormal frame representation we investigate whether the chaotic behaviour
which occurs close to the initial singularity is still present in the far
future of Bianchi VIII models. We describe some features of the vacuum Bianchi
VIII models at late times which might be relevant for studying the nature of
the future asymptote of the general vacuum inhomogeneous solution to the
Einstein field equations.


title:
Einstein's Field Equations for the Interior of a Uniformly Rotating
  Stationary Axisymmetric Perfect Fluid

abstract:
  We reduce Einstein's field equations for the interior of a uniformly
rotating, axisymmetric perfect fluid to a system of six second order partial
differential equations for the pressure p the energy density $\mu$ and four
dependent variables.Four of these equations do not depend on p and $\mu$ and
the other two determine p and $\mu$.