title: Vacuum Effects in Gravitational Fields: Theory and Detectability

abstract:
  In this thesis, we investigate quantum vacuum effects in the presence of
gravitational fields. After discussing the general theory of vacuum effects in
strong fields we apply it to the relevant issue of the interaction of the
quantum vacuum with black hole geometries. In particular we consider the
long-standing problem of the interpretation of gravitational entropy. After
these investigations, we discuss the possible experimental tests of particle
creation from the quantum vacuum. This leads us to study acoustic geometries
and their way of ``simulating'' gravitational structures, such as horizons and
black holes. We study the stability of these structures and the problems
related to setting up experimental detection of ``phonon Hawking flux'' from
acoustic horizons. This line of research then leads us to propose a new model
for explaining the emission of light in the phenomenon of Sonoluminescence,
based on the dynamical Casimir effect. This is possibly amenable to
experimental investigation. Finally we consider high energy phenomena in the
early universe. In particular we discuss inflation and possible alternative
frameworks for solving the cosmological puzzles.


title: Hawking radiation and Hawking flux from spherical reduction

abstract:
  Using heat kernel techniques we show that the relation between Hawking
temperature and radiation flux known from Einstein gravity in D dimensions can
be reproduced from the spherically reduced action. A recent controversy
regarding the D=2 anomaly for that case is discussed. The generalized effective
Polyakov action in the presence of a dilaton field is presented.


title: Quantum Theory within the Framework of General Relativity

abstract:
  A local conception is proposed to reconcile quantum theory with general
relativity, which allows one to avoid some difficulties --- as e.g. vacuum
catastrophe --- of the global approach.


title:
Distributional Sources in General Relativity: two point-like examples
  revisited

abstract:
  A regularization procedure, that allows one to relate singularities of
curvature to those of the Einstein tensor without some of the shortcomings of
previous approaches, is proposed. This regularization is obtained by requiring
that (i) the density $|det {\bf g}|^{{1/2}}G^a_{b}$, associated to the Einstein
tensor $G^a_{b}$ of the regularized metric, rather than the Einstein tensor
itself, be a distribution and (ii) the regularized metric be a continuous
metric with a discontinuous extrinsic curvature across a non-null hypersurface
of codimension one. In this paper, the curvature and Einstein tensors of the
geometries associated to point sources in the 2+1-dimensional gravity and the
Schwarzschild spacetime are considered. In both examples the regularized
metrics are continuous regular metrics, as defined by Geroch and Traschen, with
well defined distributional curvature tensors at all the intermediate steps of
the calculation. The limit in which the support of these curvature tensors
tends to the singular region of the original spacetime is studied and the
results are contrasted with the ones obtained in previous works.


title: Static black holes in scalar tensor gravity

abstract:
  We study static black hole solutions in scalar tensor gravity. We present
exact solutions in hiperextended models with a quadratic scalar potential.


title:
Gravitational waves from a spinning particle scattered by a relativistic
  star: Axial mode case

abstract:
  We study gravitational waves from a spinning test particle scattered by a
relativistic star using a perturbation method. The present analysis is
restricted to axial modes. By calculating the energy spectrum, the waveforms
and the total energy and angular momentum of gravitational waves, we analyze
the dependence of the emitted gravitational waves on a particle spin. For a
normal neutron star, the energy spectrum has one broad peak whose
characteristic frequency corresponds to the angular velocity at the turning
point (a periastron). Since the turning point is determined by the orbital
parameter, there exists the dependence of the gravitational wave on a particle
spin. We find that the total energy of $l = 2$ gravitational waves gets larger
as the spin increases in the anti-parallel direction to the orbital angular
momentum. For an ultracompact star, in addition to such an orbital
contribution, we find the quasi-normal modes exited by a scattered particle,
whose excitation rate to gravitational waves depends on the particle spin. We
also discuss the ratio of the total angular momentum to the total energy of
gravitational waves and explain its spin dependence.


title: Dust-filled axially symmetric universes with a cosmological constant

abstract:
  Following the recent recognition of a positive value for the vacuum energy
density and the realization that a simple Kantowski-Sachs model might fit the
classical tests of cosmology, we study the qualitative behavior of three
anisotropic and homogeneous models: Kantowski-Sachs, Bianchi type-I and Bianchi
type-III universes, with dust and a cosmological constant, in order to find out
which are physically permitted. We find that these models undergo
isotropization up to the point that the observations will not be able to
distinguish between them and the standard model, except for the Kantowski-Sachs
model $(\Omega_{k_{0}}<0)$ and for the Bianchi type-III $(\Omega_{k_{0}}>0)$
with $\Omega_{\Lambda_{0}}$ smaller than some critical value
$\Omega_{\Lambda_{M}}$. Even if one imposes that the Universe should be nearly
isotropic since the last scattering epoch ($z\approx 1000$), meaning that the
Universe should have approximately the same Hubble parameter in all directions
(considering the COBE 4-Year data), there is still a large range for the matter
density parameter compatible with Kantowsky-Sachs and Bianchi type-III if
$|\Omega_0+\Omega_{\Lambda_0}-1|\leq \delta$, for a very small $\delta$ . The
Bianchi type-I model becomes exactly isotropic owing to our restrictions and we
have $\Omega_0+\Omega_{\Lambda_0}=1$ in this case. Of course, all these models
approach locally an exponential expanding state provided the cosmological
constant $\Omega_\Lambda>\Omega_{\Lambda_{M}}$.


title: Matching Spherical Dust Solutions to Construct Cosmological Models

abstract:
  Conditions for smooth cosmological models are set out and applied to
inhomogeneous spherically symmetric models constructed by matching together
different Lemaitre-Tolman-Bondi solutions to the
  Einstein field equations. As an illustration the methods are applied to a
collapsing dust sphere in a curved background. This describes a region which
expands and then collapses to form a black hole in an
  Einstein de Sitter background. We show that in all such models if there is no
vacuum region then the singularity must go on accreting matter for an infinite
LTB time.


title: A Rotating Vacuum and the Quantum Mach's Principle

abstract:
  In this work we consider a quantum analog of Newton's bucket experiment in a
flat spacetime: we take an Unruh-DeWitt detector in interaction with a real
massless scalar field. We calculate the detector's excitation rate when it is
uniformly rotating around some fixed point and the field is prepared in the
Minkowski vacuum and also when the detector is inertial and the field is in the
Trocheries-Takeno vacuum state. These results are compared and the relations
with a quantum analog of Mach's principle are discussed.


title: Graviton Production in Relativistic Heavy-Ion Collisions

abstract:
  We study the feasibility of producing the graviton of the novel Kaluza-Klein
theory in which there are d large compact dimensions in addition to the 4
dimensions of Minkowski spacetime. We calculate the cross section for producing
such a graviton in nucleus-nucleus collisions via t-channel photon-photon
fusion using the semiclassical Weizsacker-Williams method and show that it can
exceed the cross section for graviton production in electron-positron
scattering by several orders of magnitude.


title:
Matters of Gravity, the newsletter of the APS Topical Group on
  Gravitation

abstract:
  Research Briefs:
  Cosmic microwave background anisotropy experiments, by Sean Carroll
  LISA Project Update by Bill Folkner
  An update on the r-mode instability, by Nils Andersson
  Laboratory experiments: news from MG9, by Riley Newman
  Progress toward Commissioning the LIGO detectors, by Stan Whitcomb
  160 Hours of Data Taken on TAMA300, by Seiji Kawamura
  Conference reports:
  Kipfest, by Richard Price
  Third Capra meeting, by Eric Poisson
  GR at the XIIIth Congress on Mathematical Physics, by Abhay Ashtekar
  3rd International LISA Symposium, by Curt Cutler


title: Quantized Fields and Chronology Protection

abstract:
  Several recent possible counterexamples to the Chronology Protection
Conjecture are critically examined. The ``adapted'' Rindler vacuum state
constructed by Li and Gott for a conformal scalar field in Misner space is
extended to nonconformally coupled and self-interacting scalar fields. For
these fields, the vacuum stress-energy always diverges on the chronology
horizons. The divergence of the vacuum stress-energy on Misner space chronology
horizons cannot be generally avoided by choosing a Rindler-type vacuum state.


title: On gyroscopic precession

abstract:
  The vorticity of a congruence is often considered to be the rate of rotation
for the precession of a gyroscope moving along a world-line belonging to that
congruence. Our aim here was to determine the evolution equation for the
angular momentum of a gyrosocope with respect to an arbitrary time-like
congruence: i.e, a reference congruence not containing the curve described by
the gyroscope. In particular, we show the specific conditions needed to support
the introductory statement about the vorticity. We thus establish a
well-founded theoretical description for the analysis of the precession of
gyroscopes, providing suitable conclusions for possible experiments.


title:
On the "renormalization" transformations induced by cycles of expansion
  and contraction in causal set cosmology

abstract:
  We study the ``renormalization group action'' induced by cycles of cosmic
expansion and contraction, within the context of a family of stochastic
dynamical laws for causal sets derived earlier. We find a line of fixed points
corresponding to the dynamics of transitive percolation, and we prove that
there exist no other fixed points and no cycles of length two or more. We also
identify an extensive ``basin of attraction'' of the fixed points but find that
it does not exhaust the full parameter space. Nevertheless, we conjecture that
every trajectory is drawn toward the fixed point set in a suitably weakened
sense.


title:
Computing the Complete Gravitational Wavetrain from Relativistic Binary
  Inspiral

abstract:
  We present a new method for generating the nonlinear gravitational wavetrain
from the late inspiral (pre-coalescence) phase of a binary neutron star system
by means of a numerical evolution calculation in full general relativity. In a
prototype calculation, we produce 214 wave cycles from corotating polytropes,
representing the final part of the inspiral phase prior to reaching the ISCO.
Our method is based on the inequality that the orbital decay timescale due to
gravitational radiation is much longer than an orbital period and the
approximation that gravitational radiation has little effect on the structure
of the stars. We employ quasi-equilibrium sequences of binaries in circular
orbit for the matter source in our field evolution code. We compute the
gravity-wave energy flux, and, from this, the inspiral rate, at a discrete set
of binary separations. From these data, we construct the gravitational waveform
as a continuous wavetrain. Finally, we discuss the limitations of our current
calculation, planned improvements, and potential applications of our method to
other inspiral scenarios.


title:
Planck Scale Physics of the Single Particle Schr\"{o}dinger Equation
  with Gravitational Self-Interaction

abstract:
  We consider the modification of a single particle Schr\"{o}dinger equation by
the inclusion of an additional gravitational self-potential term which follows
from the prescription that the' mass-density'that enters this term is given by
$m |\psi (\vec {r},t)|^2$, where $\psi (\vec {r}, t)$ is the wavefunction and
$m$ is the mass of the particle. This leads to a nonlinear equation, the '
Newton Schrodinger' equation, which has been found to possess stationary
self-bound solutions, whose energy can be determined exactly using an
asymptotic method. We find that such a particle strongly violates superposition
and becomes a black hole as its mass approaches the Planck mass.


title:
Energetic Cosmic Rays observed by the resonant gravitational wave
  detector NAUTILUS

abstract:
  Cosmic ray showers interacting with the resonant mass gravitational wave
antenna NAUTILUS have been detected. The experimental results show large
signals at a rate much greater than expected. The largest signal corresponds to
an energy release in NAUTILUS of 87 TeV. We remark that a resonant mass
gravitational wave detector used as particle detector has characteristics
different from the usual particle detectors, and it could detect new features
of cosmic rays. Among several possibilities, one can invoke unexpected
behaviour of superconducting Aluminium as particle detector, producing enhanced
signals, the excitation of non-elastic modes with large energy release or
anomalies in cosmic rays (for instance, the showers might include exotic
particles as nuclearites or Q-balls). Suggestions for explaining these
observations are solicited.


title: Berry phase for spin--1/2 particles moving in a spacetime with torsion

abstract:
  Berry phase for a spin--1/2 particle moving in a flat spacetime with torsion
is investigated in the context of the Einstein-Cartan-Dirac model. It is shown
that if the torsion is due to a dense polarized background, then there is a
Berry phase only if the fermion is massless and its momentum is perpendicular
to the direction of the background polarization. The order of magnitude of this
Berry phase is discussed in other theoretical frameworks.


title: Fermi co-ordinates and relativistic effects in non-inertial frames

abstract:
  Fermi co-ordinates are proper co-ordinates of a local observer determined by
his trajectory in space-time. Two observers at different positions belong to
different Fermi frames even if there is no relative motion between them. Use of
Fermi co-ordinates leads to several physical conclusions related to
relativistic effects seen by observers in arbitrary motion. In flat space-time,
the relativistic length seen by an observer depends only on his instantaneous
velocity, not on his acceleration or rotation. In arbitrary space-time, for any
observer the velocity of light is isotropic and equal to $c$, provided that it
is measured by propagating a light beam in a small neighbourhood of the
observer. The value of a covariant field measured at the position of the
observer depends only on his instantaneous position and velocity, not on his
acceleration. The notion of radiation is observer independent. A "freely"
falling charge in curved space-time does not move along a geodesic and
therefore radiates.


title: Conformal Black Hole Solutions of Axi-Dilaton Gravity in D-dimensions

abstract:
  Static, spherically symmetric solutions of axi-dilaton gravity in $D$
dimensions is given in the Brans-Dicke frame for arbitrary values of the
Brans-Dicke constant $\omega$ and an axion-dilaton coupling parameter $k$. The
mass and the dilaton and axion charges are determined and a BPS bound is
derived. There exists a one parameter family of black hole solutions in the
scale invariant limit.


title: Gravitational waves and spinning test particles

abstract:
  The motion of a classical spinning test particle in the field of a weak plane
gravitational wave is studied. It is found that the characteristic dimensions
of the particle's orbit is sensitive to the ratio of the spin to the mass of
the particle. The results are compared with the corresponding motion of a
particle without spin.


title: On the possible role of superheavy particles in the early Universe

abstract:
  Different models of the role of creation of superheavy particles in the early
Friedmann Universe with their subsequent decay on light particles are
investigated. The observable numbers of baryon and entropy are predicted. The
possible role of superheavy particles in creation of cold dark matter is
discussed.


title: On a General Class of Wormhole Geometries

abstract:
  A general class of solutions is obtained which describe a spherically
symmetric wormhole system. The presence of arbitrary functions allows one to
describe infinitely many wormhole systems of this type. The source of the
stress-energy supporting the structure consists of an anisotropic brown dwarf
``star'' which smoothly joins the vacuum and may possess an arbitrary
cosmological constant. It is demonstrated how this set of solutions allows for
a non-zero energy density and therefore allows positive stellar mass as well as
how violations of energy conditions may be minimized. Unlike examples
considered thus far, emphasis here is placed on construction by manipulating
the matter field as opposed to the metric. This scheme is generally more
physical than the purely geometric method. Finally, explicit examples are
constructed including an example which demonstrates how multiple closed
universes may be connected by such wormholes. The number of connected universes
may be finite or infinite.


title: Ultracompact stars with multiple necks

abstract:
  We discuss ultracompact stellar objects which have multiple necks in their
optical geometry. There are in fact physically reasonable equations of state
for which the number of necks can be arbitrarily large. The proofs of these
statements rely on a recent regularized formulation of the field equations for
static spherically symmetric models due to Nilsson and Uggla. We discuss in
particular the equation of state p=\rho-\rho_s which plays a central role in
this context.


title:
Conditional Symmetries, the True Degree of Freedom and G.C.T. Invariant
  Wave functions for the general Bianchi Type II Vacuum Cosmology

abstract:
  The quantization of the most general Bianchi Type II geometry -with all six
scale factors, as well as the lapse function and the shift vector, present- is
considered. In an earlier work, a first reduction of the initial 6-dimensional
configuration space, to a 4-dimensional one, has been 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 unrevealling the extra
symmetries of the Hamiltonian. These symmetries appear in the form of -linear
in momenta- first integrals of motion. Most of these symmetries, correspond to
G.C.T.s through the action of the automorphism group. Thus, a G.C.T. invariant
wave function is found, which depends on the only true degree of freedom, i.e.
the unique curvature invariant, characterizing the hypersurfaces t=const.


title: Wiggly Strings in Linearized Brans-Dicke Gravity

abstract:
  The metric around a wiggly cosmic string is calculated in the linear
approximation of Brans-Dicke theory of gravitation. The equations of motion for
relativistic and non-relativistic particles in this metric are obtained.
  Light propagation is also studied and it is shown that photon trajectories
can be bounded.


title: Classical Scalar Fields and the Generalized Second Law

abstract:
  It has been shown that classical non-minimally coupled scalar fields can
violate all of the standard energy conditions in general relativity. Violations
of the null and averaged null energy conditions obtainable with such fields
have been suggested as possible exotic matter candidates required for the
maintenance of traversable wormholes. In this paper, we explore the possibility
that if such fields exist, they might be used to produce large negative energy
fluxes and macroscopic violations of the generalized second law (GSL) of
thermodynamics. We find that it appears to be very easy to produce large
magnitude negative energy fluxes in flat spacetime. However we also find,
somewhat surprisingly, that these same types of fluxes injected into a black
hole do {\it not} produce violations of the GSL. This is true even in cases
where the flux results in a decrease in the area of the horizon. We demonstrate
that two effects are responsible for the rescue of the GSL: the acausal
behavior of the horizon and the modification of the usual black hole entropy
formula by an additional term which depends on the scalar field.


title: The Bardeen Model as a Nonlinear Magnetic Monopole

abstract:
  The Bardeen model -- the first regular black hole model in General Relativity
-- is reinterpreted as the gravitational field of a nonlinear magnetic
monopole, i.e., as a magnetic solution to Einstein equations coupled to a
nonlinear electrodynamics.


title:
A data-analysis strategy for detecting gravitational-wave signals from
  inspiraling compact binaries with a network of laser-interferometric
  detectors

abstract:
  A data-analysis strategy based on the maximum-likelihood method (MLM) is
presented for the detection of gravitational waves from inspiraling compact
binaries with a network of laser-interferometric detectors having arbitrary
orientations and arbitrary locations around the globe. The MLM is based on the
network likelihood ratio (LR), which is a function of eight signal-parameters
that determine the Newtonian inspiral waveform. In the MLM-based strategy, the
LR must be maximized over all of these parameters. Here, we show that it is
possible to maximize it analytically over four of the eight parameters.
Maximization over a fifth parameter, the time of arrival, is handled most
efficiently by using the Fast-Fourier-Transform algorithm. This allows us to
scan the parameter space continuously over these five parameters and also cuts
down substantially on the computational costs. Maximization of the LR over the
remaining three parameters is handled numerically. This includes the
construction of a bank of templates on this reduced parameter space. After
obtaining the network statistic, we first discuss `idealized' networks with all
the detectors having a common noise curve for simplicity. Such an exercise
nevertheless yields useful estimates about computational costs, and also tests
the formalism developed here. We then consider realistic cases of networks
comprising of the LIGO and VIRGO detectors: These include two-detector
networks, which pair up the two LIGOs or VIRGO with one of the LIGOs, and the
three-detector network that includes VIRGO and both the LIGOs. For these
networks we present the computational speed requirements, network
sensitivities, and source-direction resolutions.


title: Constructing stellar objects with multiple necks

abstract:
  We discuss the construction of perfect fluid stellar objects having optical
geometries with multiple necks corresponding to spatially closed unstable
lightlike geodesics. We prove that there exist physically reasonable models
with arbitrarily many necks. We also show how a first order phase transition
can give rise to quite pronounced secondary double necks. The analysis is
carried out using a modification of a recent dynamical systems formulation of
the TOV equations due to Nilsson and Uggla. Our reformulation allows for a very
general family of equations of state including, for example, phase transitions.


title:
The Consistency of Causal Quantum Geometrodynamics and Quantum Field
  Theory

abstract:
  We consider quantum geometrodynamics and parametrized quantum field theories
in the framework of the Bohm-de Broglie interpretation. In the first case, and
following the lines of our previous work [1], where a hamiltonian formalism for
the bohmian trajectories was constructed, we show the consistency of the theory
for any quantum potential, completing the scenarios for canonical quantum
cosmology presented there. In the latter case, we prove the consistency of
scalar field theory in Minkowski spacetime for any quantum potential, and we
show, using this alternative hamiltonian method, a concrete example where
Lorentz invariance of individual events is broken.


title: The doomsday argument and the number of possible observers

abstract:
  If the human race comes to an end relatively shortly, then we have been born
at a fairly typical time in history of humanity. On the other hand, if humanity
lasts for much longer and trillions of people eventually exist, then we have
been born in the first surprisingly tiny fraction of all people. According to
the Doomsday Argument of Carter, Leslie, Gott, and Nielsen, this means that the
chance of a disaster which would obliterate humanity is much larger than
usually thought. Here I argue that treating possible observers in the same way
as those who actually exist avoids this conclusion. Under this treatment, it is
more likely to exist at all in a race which is long-lived, as originally
discussed by Dieks, and this cancels the Doomsday Argument, so that the chance
of a disaster is only what one would ordinarily estimate. Treating possible and
actual observers alike also allows sensible anthropic predictions from quantum
cosmology, which would otherwise depend on one's interpretation of quantum
mechanics.


title: Topologically massive gravity and black holes in three dimensions

abstract:
  We obtain a general class of exact solutions to topologically massive gravity
with or without a negative cosmological constant. In the first case, we show
that the solution is supersymmetric and asymptotically approaches the extremal
BTZ black hole solution, while in the latter case it goes to flat space-time.


title:
Information Erasure and the Generalized Second Law of Black Hole
  Thermodynamics

abstract:
  We consider the generalized second law of black hole thermodynamics in the
light of quantum information theory, in particular information erasure and
Landauer's principle (namely, that erasure of information produces at least the
equivalent amount of entropy). A small quantum system outside a black hole in
the Hartle-Hawking state is studied, and the quantum system comes into thermal
equilibrium with the radiation surrounding the black hole. For this scenario,
we present a simple proof of the generalized second law based on quantum
relative entropy. We then analyze the corresponding information erasure
process, and confirm our proof of the generalized second law by applying
Landauer's principle.


title: Cosmological models with flat spatial geometry

abstract:
  The imposition of symmetries or special geometric properties on submanifolds
is less restrictive than to impose them in the full space-time. Starting from
this idea, in this paper we study irrotational dust cosmological models in
which the geometry of the hypersurfaces generated by the fluid velocity is
flat, which supposes a relaxation of the restrictions imposed by the
Cosmological Principle. The method of study combines covariant and tetrad
methods that exploits the geometrical and physical properties of these models.
This procedure will allow us to determine all the space-times within this class
as well as to study their properties. Some important consequences and
applications of this study are also discussed.


title: Conflict between the Gravitational Field Energy and the Experiments

abstract:
  From the equivalence principle and true gravitational (G) time dilation
experiments it is concluded that ``matter is not invariable after a change of
relative position with respect to other bodies''. As a general principle (GP),
such variations cannot be locally detected because the basic parameters of all
of the 'well-defined parts' of the instruments change, lineally, in the same
proportion with respect to their original values''. Only observers that don't
change of position can detect them. Thus, to relate quantities measured by
observers in different G potentials they must be previously transformed after
Lorenz and G transformations derived from experiments. They are account for all
of the ``G tests''. However ``they are not consistent with the presumed energy
exchange between the field and the bodies''. The lack of energy of the G field
is justified from the GP, according to which particles models made up of
photons in stationary state obey same inertial and G laws as particle. Such
model has been previously tested with relativistic quantum-mechanics and all of
the G tests.
  PACS: 04.80.cc, 04.20.Cv, 04.80.-y, 98.80.Cq


title: Fermions without Vierbeins in Curved Space-Time

abstract:
  A general formulation of spinor fields in Riemannian space-time is given
without using vierbeins. The space-time dependence of the Dirac matrices
required by the anticommutation relation
{\gamma_{\mu},\gamma_{\nu}}=2g_{\mu\nu} determines the spin connection. The
action is invariant under any local spin base transformations in the 32
parameter group Gl(4,c) and not just under local Lorentz transformations. The
Dirac equation and the energy-momentum tensor are computed from the action.


title: Einstein and the Kaluza-Klein particle

abstract:
  In his search for a unified field theory that could undercut quantum
mechanics, Einstein considered five dimensional classical Kaluza-Klein theory.
He studied this theory most intensively during the years 1938-1943. One of his
primary objectives was finding a non-singular particle solution. In the full
theory this search got frustrated and in the x^5-independent theory Einstein,
together with Pauli, argued it would be impossible to find these structures.


title:
Solution of Stationary and Axisymmetric Problem in General
  Relativity.Nontraditional Approach

abstract:
  Physically admissible choice of the "essential" coordinates identified with
components of the metric tensor and co-moving frame of reference reduced to the
formulation of the stationary axisymmetric GR problem. Such nontraditional
approach allows to obtain new 4-parametric vacuum solution. In special static
case this solution becomes the set well-known GR exact solutions for degenerate
vacuum gravitational fields, in some special stationary case, after
transformations coincides with Kerr solution. In other special stationary case
the founded solution turn into modified NUT solution.


title: Slowly Rotating General Relativistic Superfluid Neutron Stars

abstract:
  We present a general formalism to treat slowly rotating general relativistic
superfluid neutron stars. As a first approximation, their matter content can be
described in terms of a two-fluid model, where one fluid is the neutron
superfluid, which is believed to exist in the core and inner crust of mature
neutron stars, and the other fluid represents a conglomerate of all other
constituents (crust nuclei, protons, electrons, etc.). We obtain a system of
equations, good to second-order in the rotational velocities, that determines
the metric and the matter variables, irrespective of the equation of state for
the two fluids. In particular, allowance is made for the so-called entrainment
effect, whereby the momentum of one constituent (e.g. the neutrons) carries
along part of the mass of the other constituent. As an illustration of the
developed framework, we consider a simplified equation of state for which the
two fluids are described by different polytropes. We determine numerically the
effects of the two fluids on the rotational frame-dragging, the induced changes
in the neutron and proton densities and the inertial mass, as well as the
change in shape of the star. We further discuss issues regarding conservation
of the two baryon numbers, the mass-shedding (Kepler) limit and chemical
equilibrium.


title:
"Self-dual" solutions of topologically massive gravity coupled with the
  Maxwell-Chern-Simons theory

abstract:
  We give a general class of exact solutions to the (1+2)-dimensional
topologically massive gravity model coupled with Maxwell-Chern-Simons theory
where a "self-duality" condition is imposed on the Maxwell field.


title: Waveforms for Gravitational Radiation from Cosmic String Loops

abstract:
  We obtain general formulae for the plus- and cross- polarized waveforms of
gravitational radiation emitted by a cosmic string loop in transverse,
traceless (synchronous, harmonic) gauge. These equations are then specialized
to the case of piecewise linear loops, and it is shown that the general
waveform for such a loop is a piecewise linear function. We give several simple
examples of the waveforms from such loops. We also discuss the relation between
the gravitational radiation by a smooth loop and by a piecewise linear
approximation to it.


title: Complete null data for a black hole collision

abstract:
  We present an algorithm for calculating the complete data on an event horizon
which constitute the necessary input for characteristic evolution of the
exterior spacetime. We apply this algorithm to study the intrinsic and
extrinsic geometry of a binary black hole event horizon, constructing a
sequence of binary black hole event horizons which approaches a single
Schwarzschild black hole horizon as a limiting case. The linear perturbation of
the Schwarzschild horizon provides global insight into the close limit for
binary black holes, in which the individual holes have joined in the infinite
past. In general there is a division of the horizon into interior and exterior
regions, analogous to the division of the Schwarzschild horizon by the r=2M
bifurcation sphere. In passing from the perturbative to the strongly nonlinear
regime there is a transition in which the individual black holes persist in the
exterior portion of the horizon. The algorithm is intended to provide the data
sets for production of a catalog of nonlinear post-merger wave forms using the
PITT null code.


title:
The Friedmann universe of dust by Regge Calculus: study of its ending
  point

abstract:
  We develop an evolution scheme, based on Sorkin algorithm, to evolve the most
complex regular tridimensional polytope, the 600-cell. This application has
been already studied before and all authors found a stop point for the
evolution of the spatial section. In our opinion a clear and satisfactory
meaning to this behaviour has not been given. In this paper we propose a reason
why the evolution of the 600-cell stops when its volume is still far from 0. We
find that the 600-cell meets a causality-breaking singularity of space-time. We
study the nature of this singularity by embedding the 600-cell into a
five-dimensional Lorentzian manifold. We fit 600-cell's evolution with a
continuos metric and study it as a solution of Einstein equations.


title: Data Analysis of Continuous Gravitational Wave Signal: Fourier Transform

abstract:
  We present the Fourier Transform of continuous gravitational wave for
arbitrary location of detector and source and for any duration of observation
time in which both rotational motion of earth about its spin axis and orbital
motion around sun has been taken into account. We also give the method to
account the spin down of continuous gravitational wave.


title: Effects of Pair Creation on Charged Gravitational Collapse

abstract:
  We investigate the effects of pair creation on the internal geometry of a
black hole, which forms during the gravitational collapse of a charged massless
scalar field. Classically, strong central Schwarzschild-like singularity forms,
and a null, weak, mass-inflation singularity arises along the Cauchy horizon,
in such a collapse. We consider here the discharge, due to pair creation, below
the event horizon and its influence on the {\it dynamical formation} of the
Cauchy horizon. Within the framework of a simple model we are able to trace
numerically the collapse. We find that a part of the Cauchy horizon is replaced
by the strong space-like central singularity. This fraction depends on the
value of the critical electric field, $E_{\rm cr}$, for the pair creation.


title: On the solutions of the Cartan equation in Metric Affine Gravity

abstract:
  In the Tucker-Wang approach to Metric Affine gravity we review some
particular solutions of the Cartan equation for the non-riemannian part of the
connection. As application we show how a quite general non Riemannian model
gives a Proca type equation for the trace of the nonmetricity 1-forms Q.


title: Dilaton Gravity with a Non-minmally Coupled Scalar Field

abstract:
  We discuss the two-dimensional dilaton gravity with a scalar field as the
source matter. The coupling between the gravity and the scalar, massless, field
is presented in an unusual form. We work out two examples of these couplings
and solutions with black-hole behaviour are discussed and compared with those
found in the literature.


title: Production and detection of relic dilatons in string cosmology

abstract:
  This paper summarizes the contribution presented at the {\sl IX Marcel
Grossmann Meeting} (Rome, July 2000). It is stressed, in particular, that a
non-relativistic background of ultra-light dilatons, produced in the context of
string cosmology, could represent today a significant fraction of cold dark
matter. If the dilaton mass lies within the resonant band of present
gravitational antennas, a stochastic dilaton background with a nearly critical
density could be visible, in principle, already at the level of sensitivity of
the detectors in operation and presently under construction.


title: Unimodular relativity and cosmological constant

abstract:
  Unimodular relativity is a theory of gravity and space-time with a fixed
absolute space-time volume element, the modulus, which we suppose is
proportional to the number of microscopic modules in that volume element. In
general relativity an arbitrary fixed measure can be imposed as a gauge
condition, while in unimodular relativity it is determined by the events in the
volume. Since this seems to break general covariance, some have suggested that
it permits a non-zero covariant divergence of the material stress-energy tensor
and a variable cosmological ``constant.'' In Lagrangian unimodular relativity,
however, even with higher-derivatives of the gravitational field in the
dynamics, the usual covariant continuity holds and the cosmological constant is
still a constant of integration of the gravitational field equations.


title: The Field Nature of Time in General Relativity

abstract:
  The paper is devoted to the description of the reparametrization - invariant
dynamics of general relativity obtained by resolving constraints and
constructing equivalent unconstrained systems. The constraint-shell action
reveals the "field nature" of the geometric time in general relativity. The
time measured by the watch of an observer coincides with one of field
variables, but not with the reparametrization-noninvariant coordinate evolution
parameter.
  We give new solution of such problem, as the derivation of the path integral
representation of the causal Green functions in the Hamiltonian scheme of
general relativity.


title: Stochastic GW backgrounds and Ground based detectors

abstract:
  The interplay between different ground based detectors and stochastic
backgrounds of relic GW is described. A simultaneous detection of GW in the kHz
and in the MHz--GHz region can point towards a cosmological nature of the
signal. The sensitivity of a pair of VIRGO detectors to string cosmological
models is presented. The implications of microwave cavities for stochastic GW
backgrounds are discussed.


title: Cosmic strings in axionic-dilatonic gravity

abstract:
  We first consider local cosmic strings in dilaton-axion gravity and show that
they are singular solutions. Then we take a supermassive Higgs limit and
present expressions for the fields at far distances from the core by applying a
Pecci-Quinn and a duality transformation to the dilatonic Melvin's magnetic
universe.


title: Boundary conditions and the entropy bound

abstract:
  The entropy-to-energy bound is examined for a quantum scalar field confined
to a cavity and satisfying Robin condition on the boundary of the cavity. It is
found that near certain points in the space of the parameter defining the
boundary condition the lowest eigenfrequency (while non-zero) becomes
arbitrarily small. Estimating, according to Bekenstein and Schiffer, the ratio
$S/E$ by the $\zeta$-function, $(24\zeta (4))^{1/4}$, we compute $\zeta (4)$
explicitly and find that it is not bounded near those points that signals
violation of the bound. We interpret our results as imposing certain
constraints on the value of the boundary interaction and estimate the forbidden
region in the parameter space of the boundary conditions.


title:
Thermoelastic effects at low temperatures and quantum limits in
  displacement measurements

abstract:
  The displacement fluctuations of mirrors in optomechanical devices, induced
via thermal expansion by temperature fluctuations due either to thermodynamic
fluctuations or to fluctuations in the photon absorption, can be made smaller
than quantum fluctuations, at the low temperatures, high reflectivities and
high light powers needed to readout displacements at the standard quantum
limit. The result is relevant for the design of quantum limited
gravitational-wave detectors, both "interferometers" and "bars", and for
experiments to study directly mechanical motion in the quantum regime.


title:
Global properties of gravitational lens maps in a Lorentzian manifold
  setting

abstract:
  In a general-relativistic spacetime (Lorentzian manifold), gravitational
lensing can be characterized by a lens map, in analogy to the lens map of the
quasi-Newtonian approximation formalism. The lens map is defined on the
celestial sphere of the observer (or on part of it) and it takes values in a
two-dimensional manifold representing a two-parameter family of worldlines. In
this article we use methods from differential topology to characterize global
properties of the lens map. Among other things, we use the mapping degree (also
known as Brouwer degree) of the lens map as a tool for characterizing the
number of images in gravitational lensing situations. Finally, we illustrate
the general results with gravitational lensing (a) by a static string, (b) by a
spherically symmetric body, (c) in asymptotically simple and empty spacetimes,
and (d) in weakly perturbed Robertson-Walker spacetimes.


title:
Gravitational Energy-Momentum in the Tetrad and Quadratic Spinor
  Representations of General Relativity

abstract:
  In the Tetrad Representation of General Relativity, the energy-momentum
expression, found by Moller in 1961, is a tensor wrt coordinate transformations
but is not a tensor wrt local Lorentz frame rotations. This local Lorentz
freedom is shown to be the same as the six parameter normalized spinor degrees
of freedom in the Quadratic Spinor Representation of General Relativity. From
the viewpoint of a gravitational field theory in flat space-time, these extra
spinor degrees of freedom allow us to obtain a local energy-momentum density
which is a true tensor over both coordinate and local Lorentz frame rotations.


title: Thurston's Geometrization Conjecture and cosmological models

abstract:
  We investigate a class of spatially compact inhomogeneous spacetimes.
Motivated by Thurston's Geometrization Conjecture, we give a formulation for
constructing spatially compact composite spacetimes as solutions for the
Einstein equations. Such composite spacetimes are built from the spatially
compact locally homogeneous vacuum spacetimes which have two commuting Killing
vectors by gluing them through a timelike hypersurface admitting a homogeneous
spatial slice spanned by the commuting Killing vectors. Topology of the spatial
section of the timelike boundary is taken to be the torus. We also assume that
the matter which will arise from the gluing is compressed on the boundary, i.e.
we take the thin-shell approximation. By solving the junction conditions, we
can see dynamical behavior of the connected (composite) spacetime. The
Teichm\"uller deformation of the torus also can be obtained. We apply our
formalism to a concrete model. The relation to the torus sum of 3-manifolds and
the difficulty of this problem are also discussed.


title: Measuring multipole moments of Weyl metrics by means of gyroscopes

abstract:
  Using the technique of Rindler and Perlick we calculate the total precession
per revolution of a gyroscope circumventing the source of Weyl metrics. We
establish thereby a link between the multipole moments of the source and an
``observable'' quantity. Special attention deserves the case of the
gamma-metric. As an extension of this result we also present the corresponding
expressions for some stationary space-times.


title: A Simple Line Element to the Dilaton Gravity

abstract:
  The metric to the two-dimensional dilaton gravity can be writen in an
alternative form, similar to the two-dimensional Schwarzschild metric, and
allow us the identification of some quantitiies with those equivalent in the
Schwarzschild solution. This new form, howewer, presents a non-physical
singularity at the horizon in the same way that in the realistic four
dimensional case. We show a procedure to eliminate this horizon singularity
and, as an application, the resulting metric is used to obtain the associated
Hawking temperature. We discuss also some differents between this metric and
the Schwarzcchild one.


title: Space-time as multidimensional elastic plate

abstract:
  It is suggested, that a curved 4-dimensional space-time manifold is a
strained elastic plate in multidimensional embedding space-time. Its
thicknesses along extradimensions are much less than 4-dimensional sizes.
Reduced 4-dimensional free energy density of the strained plate in a weak
strain case is similar to GR Lagrangian density of a gravitational field for
the particular value of the Poisson coefficient of the plate. Dynamical
equations of the theory are obtained by variation of the multidimensional free
energy over displacement vector components. In general case they are
inhomogeneous bewave equations.


title: Gravitational Perturbations of a Radiating Spacetime

abstract:
  This paper discusses the problem of gravitational perturbations of radiating
spacetimes. We lay out the theoretical framework for describing the interaction
of external gravitational fields with a radiating spacetime. This is done by
deriving the field perturbation equations for a radiating metric. The equations
are then specialized to a Vaidya spacetime. For the Hiscock ansatz of a linear
mass model of a radiating blackhole the equations are found separable. Further,
the resulting ordinary differential equations are found to admit analytic
solutions. We obtain the solutions and discuss their characteristics.


title:
Towards the solution of the relativistic gravitational radiation
  reaction problem for binary black holes

abstract:
  Here we present the results of applying the generalized Riemann zeta-function
regularization method to the gravitational radiation reaction problem. We
analyze in detail the headon collision of two nonspinning black holes with
extreme mass ratio. The resulting reaction force on the smaller hole is
repulsive. We discuss the possible extensions of these method to generic orbits
and spinning black holes. The determination of corrected trajectories allows to
add second perturbative corrections with the consequent increase in the
accuracy of computed waveforms.


title:
Critical Behaviour in a Planar Dynamical Triangulation Model with a
  Boundary

abstract:
  We consider a canonical ensemble of dynamical triangulations of a
2-dimensional sphere with a hole where the number $N$ of triangles is fixed.
The Gibbs factor is $\exp (-\mu \sum \deg v)$ where $\deg v$ is the degree of
the vertex $v$ in the triangulation $T$. Rigorous proof is presented that the
free energy has one singularity, and the behaviour of the length $m$ of the
boundary undergoes 3 phases: subcritical $m=O(1)$, supercritical (elongated)
with $m$ of order $N$ and critical with $m=O(\sqrt{N})$. In the critical point
the distribution of $m$ strongly depends on whether the boundary is provided
with the coordinate system or not. In the first case $m$ is of order
$\sqrt{N}$, in the second case $m$ can have order $N^{\alpha}$ for any
$0<\alpha <{1/2}$.


title:
A Comparison of search templates for gravitational waves from binary
  inspiral

abstract:
  We compare the performances of the templates defined by three different types
of approaches: traditional post-Newtonian templates (Taylor-approximants),
``resummed'' post-Newtonian templates assuming the adiabatic approximation and
stopping before the plunge (P-approximants), and further ``resummed''
post-Newtonian templates going beyond the adiabatic approximation and
incorporating the plunge with its transition from the inspiral
(Effective-one-body approximants). The signal to noise ratio is significantly
enhanced (mainly because of the inclusion of the plunge signal) by using these
new effective-one-body templates relative to the usual post-Newtonian ones for
binary masses greater than $ 30 M_\odot$, the most likely sources for initial
laser interferometers. Independently of the question of the plunge signal, the
comparison of the various templates confirms the usefulness of using
resummation methods. The paper also summarizes the key elements of the
construction of various templates and thus can serve as a resource for those
involved in writing inspiral search software.


title: Conformal general relativity contains the quantum

abstract:
  Based on the de Broglie-Bohm relativistic quantum theory of motion we show
that the conformal formulation of general relativity, being linked with a
Weyl-integrable geometry, may implicitly contain the quantum effects of matter.
In this context the Mach's principle is discussed.


title:
Optical noise correlations and beating the standard quantum limit in
  advanced gravitational-wave detectors

abstract:
  The uncertainty principle, applied naively to the test masses of a
laser-interferometer gravitational-wave detector, produces a Standard Quantum
Limit (SQL) on the interferometer's sensitivity. It has long been thought that
beating this SQL would require a radical redesign of interferometers. However,
we show that LIGO-II interferometers, currently planned for 2006, can beat the
SQL by as much as a factor two over a bandwidth \Delta f \sim f, if their
thermal noise can be pushed low enough. This is due to dynamical correlations
between photon shot noise and radiation-pressure noise, produced by the LIGO-II
signal-recycling mirror.


title: Nonminimal Scalar-Tensor Theories and Quantum Gravity

abstract:
  Recentely, it is shown that the quantum effects of matter determine the
conformal degree of freedom of the space-time metric. This was done in the
framework of a scalar-tensor theory with one scalar field. A point with that
theory is that the form of quantum potential is preassumed. Here we present a
scalar-tensor theory with two scalar fields, and no assumption on the form of
quantum potential. It is shown that using the equations of motion one gets the
correct form of quantum potential plus some corrections.


title: Quantum, Gravity, and Geometry

abstract:
  Recently, it is shown that, the quantum effects of matter are well described
by the conformal degree of freedom of the space-time metric. On the other hand,
it is a wellknown fact that according to Einstein's gravity theory, gravity and
geometry are interconnected. In the new quantum gravity theory, matter quantum
effects completely determine the conformal degree of freedom of the space-time
metric, while the causal structure of the space-time is determined by the
gravitational effects of the matter, as well as the quantum effects through
back reaction effects. This idea, previousely, is realized in the framework of
scalar-tensor theories. In this work, it is shown that quantum gravity theory
can also be realized as a purely metric theory. Such a theory is developed, its
consequences and its properties are investigated. The theory is applied, then,
to black holes and the radiation-dominated universe. It is shown that the
initial singularity can be avoided.


title:
Gravitational field and equations of motion of spinning compact binaries
  to 2.5 post-Newtonian order

abstract:
  We derive spin-orbit coupling effects on the gravitational field and
equations of motion of compact binaries in the 2.5 post-Newtonian approximation
to general relativity, one PN order beyond where spin effects first appear. Our
method is based on that of Blanchet, Faye, and Ponsot, who use a post-Newtonian
metric valid for general (continuous) fluids and represent pointlike compact
objects with a delta-function stress-energy tensor, regularizing divergent
terms by taking the Hadamard finite part. To obtain post-Newtonian spin
effects, we use a different delta-function stress-energy tensor introduced by
Bailey and Israel. In a future paper we will use the 2.5PN equations of motion
for spinning bodies to derive the gravitational-wave luminosity and phase
evolution of binary inspirals, which will be useful in constructing matched
filters for signal analysis. The gravitational field derived here may help in
posing initial data for numerical evolutions of binary black hole mergers.


title: The structure of non-spacelike geodesics in dust collapse

abstract:
  We study here the behaviour of non-spacelike geodesics in dust collapse
models in order to understand the casual structure of the spacetime. The
geodesic families coming out, when the singularity is naked, corresponding to
different initial data are worked out and analyzed. We also bring out the
similarity of the limiting behaviour for different types of geodesics in the
limit of approach to the singularity.


title: Variable cosmological term - geometry and physics

abstract:
  We describe the dynamics of a cosmological term in the spherically symmetric
case by an r-dependent second rank symmetric tensor \Lambda_{\mu\nu} invariant
under boosts in the radial direction. The cosmological tensor \Lambda_{\mu\nu}
represents the extension of the Einstein cosmological term \Lambda g_{\mu\nu}
which allows a cosmological constant be variable. This possibility is based on
the Petrov classification scheme and Einstein field equations in the
spherically symmetric case. The inflationary equation of state is satisfied by
the radial pressure p_r^{\Lambda}=-\rho^{\Lambda}. The tangential pressure is
calculated from the conservation equation \Lambda^{\mu}_{\nu;\mu}=0. The
solutions to the Einstein equations with cosmological term \Lambda_{\mu\nu}
describe several types of globally regular self-gravitating vacuum
configurations including vacuum nonsingular black holes. In this case the
global structure of space-time contains an infinite set of black and white
holes whose singularities are replaced with the value of cosmological constant
of the scale of symmetry restoration, at the background of asymptotically flat
or asymptotically de Sitter universes. We outline \Lambda white hole geometry
and estimate probability of quantum birth of baby universes inside a \Lambda
black hole. In the course of Hawking evaporation of a \Lambda black hole, a
second-order phase transition occurs, and globally regular configuration
evolves towards a self-gravitating particlelike structure at the background of
the Minkowski or de Sitter space.


title: The static cylinder, gyroscopes, the C metric, and all that

abstract:
  The physical meaning of the Levi-Civita spacetime for some "critical" values
of the parameter sigma, is discussed in the light of gedanken experiments
performed with gyroscopes circumventing the axis of symmetry. The fact that
sigma=1/2 corresponds to flat space described from the point of view of an
accelerated frame of reference, led us to incorporate the C metric into
discussion. The interpretation of phi as an angle variable for any value of
sigma, appears to be at the origen of difficulties.


title:
The status of the Lambda term in quantum geometrodynamics in extended
  phase space

abstract:
  S. Weinberg pointed out a way to introduce a cosmological term by modifying
the theory of gravity. This modification would be justified if the Einstein
equations with the cosmological term could be obtained in the classical limit
of some physically satisfied quantum theory of gravity. We propose to consider
quantum geometrodynamics in extended phase space as a candidate for such a
theory. Quantum geometrodynamics in extended phase space aims at giving a
selfconsistent description of the integrated system ``the physical object (the
Universe) + observation means'', observation means being represented by a
reference frame. The Lambda term appears in classical equations under certain
gauge conditions and characterizes the state of gravitational vacuum related to
a chosen reference frame. The eigenvalue spectrum of Lambda depends on a
concrete cosmological model and can be found by solving the Schrodinger
equation for a wave function of the Universe. The proposed version of quantum
geometrodynamics enables one to make predictions concerning probable values of
the Lambda term at various stages of cosmological evolution.


title:
Noise Kernel in Stochastic Gravity and Stress Energy Bi-Tensor of
  Quantum Fields in Curved Spacetimes

abstract:
  The noise kernel is the vacuum expectation value of the (operator-valued)
stress-energy bi-tensor which describes the fluctuations of a quantum field in
curved spacetimes. It plays the role in stochastic semiclassical gravity based
on the Einstein-Langevin equation similar to the expectation value of the
stress-energy tensor in semiclassical gravity based on the semiclassical
Einstein equation. According to the stochastic gravity program, this two point
function (and by extension the higher order correlations in a hierarchy) of the
stress energy tensor possesses precious statistical mechanical information of
quantum fields in curved spacetime and, by the self-consistency required of
Einstein's equation, provides a probe into the coherence properties of the
gravity sector (as measured by the higher order correlation functions of
gravitons) and the quantum nature of spacetime. It reflects the low and medium
energy (referring to Planck energy as high energy) behavior of any viable
theory of quantum gravity, including string theory. It is also useful for
calculating quantum fluctuations of fields in modern theories of structure
formation and for backreaction problems in cosmological and black holes
spacetimes.
  We discuss the properties of this bi-tensor with the method of
point-separation, and derive a regularized expression of the noise-kernel for a
scalar field in general curved spacetimes. One collorary of our finding is that
for a massless conformal field the trace of the noise kernel identically
vanishes. We outline how the general framework and results derived here can be
used for the calculation of noise kernels for Robertson-Walker and
Schwarzschild spacetimes.


title: LISA Sources in Globular Clusters

abstract:
  Globular clusters house a population of compact binaries that will be
interesting gravitational wave sources for LISA. We provide estimates for the
numbers of sources of several categories and discuss the sensitivity of LISA to
detecting these sources. The estimated total number of detectable sources
ranges from about 10 to about 1000 with gravitational wave frequencies above 1
mHz. These sources are typically undetectable by any other means and thus offer
an opportunity for doing true gravitational-wave astronomy. The detection of
these sources would provide information about both binary star evolution and
the dynamics of globular clusters.


title: Qualitative analysis of dissipative cosmologies

abstract:
  The evolution of an homogeneous and isotropic dissipative fluid is analyzed
using dynamical systems techniques. The dissipation is driven by bulk viscous
pressure and the truncated Israel-Stewart theory is used. Although almost all
solutions inflate, we show that only few of them can be considered as physical
solutions since the dominant energy condition is not satisfied.


title:
General Relativistic Contribution to Polarization of the Cosmic
  Microwave Background Anisotropy

abstract:
  We solve the wave equation for the electromagnetic field tensors associated
with the CMBR photons in a universe with scalar metric perturbations. We show
that the coupling of the electromagnetic fields with the curvature associated
with the scalar perturbations gives rise to an optical rotation of the
microwave background photons. The magnitude of the gravitationally generated
V-Stokes parameter anisotropy $\Delta_V$, is however very small compared to the
linear polarisation caused by Thomson scattering.


title: 2d quantum gravity with torsion, dilaton theory and black hole formation

abstract:
  Starting from the work of the author in 1990 with different collaborators,
essential progress in 2d gravity theories has been made. Now all such theories
(and not only certain special models) can be treated at the classical as well
as at the quantum level. New physical insights have been obtained, as e.g. the
``virtual black hole''. The formalism developed in this context recently also
finds increasing interest in mathematical physics.


title: Action and Energy of the Gravitational Field

abstract:
  We present a detailed examination of the variational principle for metric
general relativity as applied to a ``quasilocal'' spacetime region $\M$ (that
is, a region that is both spatially and temporally bounded). Our analysis
relies on the Hamiltonian formulation of general relativity, and thereby
assumes a foliation of $\M$ into spacelike hypersurfaces $\Sigma$. We allow for
near complete generality in the choice of foliation. Using a field--theoretic
generalization of Hamilton--Jacobi theory, we define the quasilocal
stress-energy-momentum of the gravitational field by varying the action with
respect to the metric on the boundary $\partial\M$. The gravitational
stress-energy-momentum is defined for a two--surface $B$ spanned by a spacelike
hypersurface in spacetime. We examine the behavior of the gravitational
stress-energy-momentum under boosts of the spanning hypersurface. The boost
relations are derived from the geometrical and invariance properties of the
gravitational action and Hamiltonian. Finally, we present several new examples
of quasilocal energy--momentum, including a novel discussion of quasilocal
energy--momentum in the large-sphere limit towards spatial infinity.


title: Operator ordering for generally covariant systems

abstract:
  The constraint operators belonging to a generally covariant system are found
out within the framework of the BRST formalism. The result embraces quadratic
Hamiltonian constraints whose potential can be factorized as a never null
function times a gauge invariant function. The building of the inner product
between physical states is analyzed for systems featuring either intrinsic or
extrinsic time.


title: Twisting type-N vacuum fields with a group $H_2$

abstract:
  We derive the equations corresponding to twisting type-N vacuum gravitational
fields with one Killing vector and one homothetic Killing vector by using the
same approach as that developed by one of us in order to treat the case with
two non-commuting Killing vectors. We study the case when the homothetic
parameter $\phi$ takes the value -1, which is shown to admit a reduction to a
third-order real ordinary differential equation for this problem, similar to
that previously obtained by one of us when two Killing vectors are present.


title: Gravitational Collapse and Cosmological Constant

abstract:
  We consider here the effects of a non-vanishing cosmological term on the
final fate of a spherical inhomogeneous collapsing dust cloud. It is shown that
depending on the nature of the initial data from which the collapse evolves,
and for a positive value of the cosmological constant, we can have a globally
regular evolution where a bounce develops within the cloud. We characterize
precisely the initial data causing such a bounce in terms of the initial
density and velocity profiles for the collapsing cloud. In the cases otherwise,
the result of collapse is either formation of a black hole or a naked
singularity resulting as the end state of collapse. We also show here that a
positive cosmological term can cover a part of the singularity spectrum which
is visible in the corresponding dust collapse models for the same initial data.


title: Casimir Effect for Spherical Shell in de Sitter Space

abstract:
  The Casimir stress on a spherical shell in de Sitter background for massless
scalar field satisfying Dirichlet boundary conditions on the shell is
calculated. The metric is written in conformally flat form. Although the metric
is time dependent no particles are created. The Casimir stress is calculated
for inside and outside of the shell with different backgrounds corresponding to
different cosmological constants. The detail dynamics of the bubble depends on
different parameter of the model. Specifically, bubbles with true vacuum inside
expand if the difference in the vacuum energies is small, otherwise they
collapse.


title: An effective model of the spacetime foam

abstract:
  An approximate model of the spacetime foam is offered in which each quantum
handle (wormhole) is a 5D wormhole-like solution. A spinor field is introduced
for an effective description of this foam. The topological handles of the
spacetime foam can be attached either to one space or connect two different
spaces. In the first case we have a wormhole with the quantum throat and such
object can demonstrate a model of preventing the formation the naked
singularity with relation $e > m$. In the second case the spacetime foam looks
as a dielectric with quantum handles as dipoles. It is supposed that
supergravity theories with a nonminimal interaction between spinor and
electromagnetic fields can be considered as an effective model approximately
describing the spacetime foam.


title: Dissipative Fluid in Brans Dicke theory and late time acceleration

abstract:
  We have investigated the possibility of having a late time accelerated
expansion phase for the universe. We have used a dissipative fluid in
Brans-Dicke(BD) theory for this purpose. The model does not involve any
potential for the BD scalar field. We have obtained the best fit values for the
different parameters in our model by comparing our model predictions with SNIa
data and the also with the data from the ultra-compact radio sources.


title:
Gluing 4-simplices: a derivation of the Barrett-Crane spin foam model
  for Euclidean quantum gravity

abstract:
  We derive the the Barrett-Crane spin foam model for Euclidean 4 dimensional
quantum gravity from a discretized BF theory, imposing the constraints that
reduce it to gravity at the quantum level. We obtain in this way a precise
prescription of the form of the Barrett-Crane state sum, in the general case of
an arbitrary manifold with boundary. In particular we derive the amplitude for
the edges of the spin foam from a natural procedure of gluing different
4-simplices along a common tetrahedron. The generalization of our results to
higher dimensions is also shown.


title: Sectors of spherical homothetic collapse

abstract:
  A study is undertaken of the gravitational collapse of spherically symmetric
thick shells admitting a homothetic Killing vector field under the assumption
that the energy momentum tensor corresponds to the absence of a pure outgoing
component of field. The energy-momentum tensor is not specified beyond this,
but is assumed to satisfy the strong and dominant energy conditions. The metric
tensor depends on only one function of the similarity variable and the energy
conditions identify a class of functions ${\cal F}$ to which the metric
function may belong. The possible global structure of such space-times is
determined, with particular attention being paid to singularities and their
temporal nature (naked or censored). It is shown that there are open subsets of
${\cal F}$ which correspond to naked singularities; in this sense, such
singularities are stable. Furthermore, it is shown that these singularities can
arise from regular (continuous), asymptotically flat initial data which deviate
from the trivial data by an arbitrarily small amount.


title:
Aperture synthesis for gravitational-wave data analysis: Deterministic
  Sources

abstract:
  Gravitational wave detectors now under construction are sensitive to the
phase of the incident gravitational waves. Correspondingly, the signals from
the different detectors can be combined, in the analysis, to simulate a single
detector of greater amplitude and directional sensitivity: in short, aperture
synthesis. Here we consider the problem of aperture synthesis in the special
case of a search for a source whose waveform is known in detail: \textit{e.g.,}
compact binary inspiral. We derive the likelihood function for joint output of
several detectors as a function of the parameters that describe the signal and
find the optimal matched filter for the detection of the known signal. Our
results allow for the presence of noise that is correlated between the several
detectors. While their derivation is specialized to the case of Gaussian noise
we show that the results obtained are, in fact, appropriate in a well-defined,
information-theoretic sense even when the noise is non-Gaussian in character.
  The analysis described here stands in distinction to ``coincidence
analyses'', wherein the data from each of several detectors is studied in
isolation to produce a list of candidate events, which are then compared to
search for coincidences that might indicate common origin in a gravitational
wave signal. We compare these two analyses --- optimal filtering and
coincidence --- in a series of numerical examples, showing that the optimal
filtering analysis always yields a greater detection efficiency for given false
alarm rate, even when the detector noise is strongly non-Gaussian.


title: Perturbations of the Kerr spacetime in horizon penetrating coordinates

abstract:
  We derive the Teukolsky equation for perturbations of a Kerr spacetime when
the spacetime metric is written in either ingoing or outgoing Kerr-Schild form.
We also write explicit formulae for setting up the initial data for the
Teukolsky equation in the time domain in terms of a three metric and an
extrinsic curvature. The motivation of this work is to have in place a
formalism to study the evolution in the ``close limit'' of two recently
proposed solutions to the initial value problem in general relativity that are
based on Kerr-Schild slicings. A perturbative formalism in horizon penetrating
coordinates is also very desirable in connection with numerical relativity
simulations using black hole ``excision''.


title: Brane-world inflation without inflaton on the brane

abstract:
  Inspired by the Randall-Sundrum brane-world scenario, we investigate the
possibility of brane-world inflation driven not by an inflaton field on the
brane, but by a bulk, dilaton-like gravitational field. As a toy model for the
dilaton-like gravitational field, we consider a minimally coupled massive
scalar field in the bulk 5-dimensional spacetime, and look for a perturbative
solution in the anti-de Sitter (AdS) background. For an adequate range of the
scalar field mass, we find a unique solution that has non-trivial dependence on
the 5th dimensional coordinate and that induces slow-roll inflation on the
brane.


title:
Gravitational reaction force on a particle in the Schwarzschild
  background

abstract:
  We formulate a new method to calculate the gravitational reaction force on a
particle of mass $\mu$ orbiting a massive black hole of mass $M$. In this
formalism, the tail part of the retarded Green function, which is responsible
for the reaction force, is calculated at the level of the Teukolsky equation.
Our method naturally allows a systematic post-Minkowskian (PM) expansion of the
tail part at short distances. As a first step, we consider the case of a
Schwarzschild black hole and explicitly calculate the first post-Newtonian
(1PN) tail part of the Green function. There are, however, a couple of issues
to be resolved before explicitly evaluating the reaction force by applying the
present method. We discuss possible resolutions of these issues.


title:
An efficient filter for detecting gravitational wave bursts in
  interferometric detectors

abstract:
  Typical sources of gravitational wave bursts are supernovae, for which no
accurate models exist. This calls for search methods with high efficiency and
robustness to be used in the data analysis of foreseen interferometric
detectors. A set of such filters is designed to detect gravitational wave burst
signals. We first present filters based on the linear fit of whitened data to
short straight lines in a given time window and combine them in a non linear
filter named ALF. We study the performances and efficiencies of these filters,
with the help of a catalogue of simulated supernova signals.
  The ALF filter is the most performant and most efficient of all filters. Its
performance reaches about 80% of the Optimal Filter performance designed for
the same signals. Such a filter could be implemented as an online trigger
(dedicated to detect bursts of unknown waveform) in interferometric detectors
of gravitational waves.


title: Space-time as strongly bent plate

abstract:
  Futher development is made of a consept of space-time as multidimensional
elastic plate, proposed earlier in [20,21]. General equilibrium equations,
including 4-dimensional tangent stress tensor - energy-momentum tensor of
matter - are derived. Comparative analysis of multidimensional elasticity
theory (MET) and GR is given. Variational principle, boundary conditions,
energy-momentum tensor, matter and space-time signature are reviewed within the
context of MET.


title:
General exact solution of the Einstein-Dirac equations with the
  cosmological constant in homogeneous space

abstract:
  The general exact solution of the Einstein-Dirac equations with cosmological
constant in the homogeneous Riemannian space of the Bianchi 1 type is obtained.


title:
Equivalence between the ADM-Hamiltonian and the harmonic-coordinates
  approaches to the third post-Newtonian dynamics of compact binaries

abstract:
  The third post-Newtonian approximation to the general relativistic dynamics
of two point-mass systems has been recently derived by two independent groups,
using different approaches, and different coordinate systems. By explicitly
exhibiting the map between the variables used in the two approaches we prove
their physical equivalence. Our map allows one to transfer all the known
results of the Arnowitt-Deser-Misner (ADM) approach to the harmonic-coordinates
one: in particular, it gives the value of the harmonic-coordinates Lagrangian,
and the expression of the ten conserved quantities associated to global
Poincar\'e invariance.


title: The Numerical Evolution of Neutron Star Oscillations

abstract:
  The present work investigates the numerical evolution of linearized
oscillations of non-rotating, spherically symmetric neutron stars within the
framework of general relativity. We derive the appropriate equations using the
(3+1)-formalism. We first focus on the evolution of radial oscillations, which
do not emit gravitational waves. We demonstrate how to handle a numerical
instability that also occurs in the non-radial case, when the stellar model is
constructed based on a realistic equation of state. We devise a coordinate
transformation that not only removes this instability but also provides much
more accurate results. [...] The main part deals with the evolution of
non-radial oscillations (l >= 2) of neutron stars. Here, we compare different
formulations of the equations and discuss how they have to be numerically dealt
with in order to avoid instabilities at the origin. We present results for
various polytropic stellar models and different initial data. [...] In the last
part of this thesis we consider a physical mechanism for exciting oscillations
of neutron stars. We use the time dependent gravitational field of a small
point mass \mu that orbits the neutron star to induce stellar oscillations.
With this particle we have a physical means which removes the arbitrariness in
choosing the initial data. [...] By sampling various orbital parameters of the
particle we show that in general the particle is not able to excite any
w-modes. It is only for speeds very close to the speed of light that the w-mode
is a significant part of the wave signal.


title:
Hawking radiation in different coordinate settings: Complex paths
  approach

abstract:
  We apply the technique of complex paths to obtain Hawking radiation in
different coordinate representations of the Schwarzschild space-time. The
coordinate representations we consider do not possess a singularity at the
horizon unlike the standard Schwarzschild coordinate. However, the event
horizon manifests itself as a singularity in the expression for the
semiclassical action. This singularity is regularized by using the method of
complex paths and we find that Hawking radiation is recovered in these
coordinates indicating the covariance of Hawking radiation as far as these
coordinates are concerned.


title: Exact metric around a wiggly cosmic string

abstract:
  The exact metric around a wiggly cosmic string is found by modifying the
energy momentum-tensor of a straight infinitely thin cosmic string to include
an electric current along the symmetry axis.


title: Mother templates for gravitational wave chirps

abstract:
  Templates used in a search for binary black holes and neutron stars in
gravitational wave interferometer data will have to be computed on-line since
the computational storage and retrieval costs for the template bank are too
expensive. The conventional dimensionless variable $T=(c^3/Gm)t,$ where $m$ is
the total mass of a binary, in the time-domain and a not-so-conventional
velocity-like variable $v=(\pi Gm f)^{1/3}$ in the Fourier-domain, render the
phasing of the waves independent of the total mass of the system enabling the
construction of {\it mother templates} that depend only on the mass ratio of a
black hole binary. Use of such mother templates in a template bank will bring
about a reduction in computational costs up to a factor of 10 and a saving on
storage by a factor of 100.


title: Resource Letter on geometrical results for Embeddings and Branes

abstract:
  Due to the recent renewal in the interest for embedded surfaces we provide a
list of commented references of interest.


title: Evolution of perturbations in a domain wall cosmology

abstract:
  A fluid of domain walls has an effective equation of state $p_w = -
{2/3}\rho_w$. This equation of state is qualitativelly in agreement with the
supernova type Ia observations. We exploit a cosmological model where the
matter content is given by a dust fluid and a domain wall fluid. The process of
formation of galaxies is essentially preserved. On the other hand, the
behaviour of the density contrast in the ordinary fluid is highly altered when
domain walls begin to dominate the matter content of the Universe. This domain
wall phase occurs at relative recent era, and its possible consequences are
discussed, specially concerning the Sachs-Wolfe effect.


title: Angular momentum conservation law in Einstein-Cartan space-time

abstract:
  In the light of the local Lorentz transformations and the general Noether
theorem, a new formulate of the general covariant angular momentum conservation
law in Einstein-Cartan gravitation theory is obtained, which overcomes the
critical difficulty in the other formulates that the conservation law depended
on the coordinative choice.


title:
Auto-parallel equation as Euler-Lagrange's equation in spaces with
  affine connections and metrics

abstract:
  The auto-parallel equation over spaces with affine connections and metrics is
considered as a result of the application of the method of Lagrangians with
covariant derivatives (MLCD) on a given Lagrangian density.


title:
Naked Reissner-Nordstr\"{o}m Singularities and the Anomalous Magnetic
  Moment of the Electron Field

abstract:
  We study the problem of the quantization of the massive charged Dirac field
on a naked Reissner-Nordstr\"{o}m background. We show that the introduction of
an anomalous magnetic moment for the electron field allows a well--defined
quantum theory for the one-particle Dirac Hamiltonian, because no boundary
condition on the singularity is required. This means that would-be higher order
corrections can play an essential role in determining physics on the naked
Reissner-Nordstr\"{o}m background and that a non-perturbative approach is
required. Moreover, we show that bound states for the Dirac equation are
allowed. Various aspects of the physical picture emerging from our study are
also discussed, such as the possibility to obtain exotic atomic systems, the
formation of black holes by electronic capture and some interesting consistency
problems involving quantum gravity.


title: State sum models for quantum gravity

abstract:
  This paper reviews the construction of quantum field theory on a
4-dimensional spacetime by combinatorial methods, and discusses the recent
developments in the direction of a combinatorial construction of quantum
gravity.


title: Co-accelerated particles in the C-metric

abstract:
  With appropriately chosen parameters, the C-metric represents two uniformly
accelerated black holes moving in the opposite directions on the axis of the
axial symmetry (the z-axis). The acceleration is caused by nodal singularities
located on the z-axis.
  In the~present paper, geodesics in the~C-metric are examined. In general
there exist three types of timelike or null geodesics in the C-metric:
geodesics describing particles 1) falling under the black hole horizon;
2)crossing the acceleration horizon; and 3) orbiting around the z-axis and
co-accelerating with the black holes.
  Using an effective potential, it can be shown that there exist stable
timelike geodesics of the third type if the product of the parameters of the
C-metric, mA, is smaller than a certain critical value. Null geodesics of the
third type are always unstable. Special timelike and null geodesics of the
third type are also found in an analytical form.


title: Numerical Calculation of Conformally Smooth Hyperboloidal Data

abstract:
  This is the third paper in a series describing a numerical implementation of
the conformal Einstein equation. This paper describes a scheme to calculate
(three) dimensional data for the conformal field equations from a set of free
functions. The actual implementation depends on the topology of the spacetime.
We discuss the implementation and exemplary calculations for data leading to
spacetimes with one spherical null infinity (asymptotically Minkowski) and for
data leading to spacetimes with two toroidal null infinities (asymptotically
A3). We also outline the (technical) modifications of the implementation needed
to calculate data for spacetimes with two and more spherical null infinities
(asymptotically Schwarzschild and asymptotically multiple black holes).


title: Colliding Bubble Worlds

abstract:
  We consider a cosmological model in which our Universe is a spherically
symmetric bubble wall in 5-dimensional anti-de Sitter spacetime. We argue that
the bubble on which we live will undergo collisions with other similar bubbles
and estimate the spectrum of such collisions. The collision rate is found to be
independent of the age of our Universe. Collisions with small bubbles provide
an experimental signature of this scenario, while collisions with larger
bubbles would be catastrophic.


title: Chaos in Non-Abelian Gauge Fields, Gravity, and Cosmology

abstract:
  This talk describes the evolution of studies of chaos in Yang-Mills fields,
gravity, and cosmology. The main subject is a BKL regime near the singularity
$t=0$ and its survival in higher dimensions and in string theory. We also
describe the recent progress in the search for particle-like solutions of the
Einstein-Yang-Mills system (monopoles and dyons), colored black holes and the
problem of their stability.


title: An Introduction to Black Hole Evaporation

abstract:
  Classical black holes are defined by the property that things can go in, but
don't come out. However, Stephen Hawking calculated that black holes actually
radiate quantum mechanical particles. The two important ingredients that result
in back hole evaporation are (1) the spacetime geometry, in particular the
black hole horizon, and (2) the fact that the notion of a "particle" is not an
invariant concept in quantum field theory. These notes contain a step-by-step
presentation of Hawking's calculation. We review portions of quantum field
theory in curved spacetime and basic results about static black hole
geometries, so that the discussion is self-contained. Calculations are
presented for quantum particle production for an accelerated observer in flat
spacetime, a black hole which forms from gravitational collapse, an eternal
Schwarzschild black hole, and charged black holes in asymptotically deSitter
spacetimes. The presentation highlights the similarities in all these
calculations. Hawking radiation from black holes also points to a profound
connection between black hole dynamics and classical thermodynamics. A theory
of quantum gravity must predicting and explain black hole thermodynamics. We
briefly discuss these issues and point out a connection between black hole
evaportaion and the positive mass theorems in general relativity.


title:
On the motion of rotating bodies in field gravity theory and general
  relativity

abstract:
  On the basis of Lagrangian formalism of relativistic field theory
post-Newtonian equations of motion for a rotating body are derived in the frame
of Feynman's quantum field gravity theory (FGT) and compared with corresponding
geodesic equations in general relativity (GR). It is shown that in FGT the
trajectory of a rotating test body does not depend on a choice of a coordinate
system. The equation of translational motion of a gyroscope is applied to
description of laboratory experiments with free falling rotating bodies and
rotating bodies on a balance scale. Post-Newtonian relativistic effect of
periodical modulation of the orbital motion of a rotating body is discussed for
the case of planets of the solar system and for binary pulsars PSR B1913+16 and
PSR B1259-63. In the case of binary pulsars with known spin orientations this
effect gives a possibility to measure radiuses of neutron stars.


title:
Ricci Collineations of the Bianchi Types I and III, and Kantowski-Sachs
  Spacetimes

abstract:
  Ricci collineations of the Bianchi types I and III, and Kantowski-Sachs
space- times are classified according to their Ricci collineation vector (RCV)
field of the form (i)-(iv) one component of $\xi^a (x^b)$ is nonzero, (v)-(x)
two components of $\xi^a (x^b)$ are nonzero, and (xi)-(xiv) three components of
$\xi^a (x^b)$ are nonzero. Their relation with isometries of the space-times is
established. In case (v), when $det(R_{ab}) = 0$, some metrics are found under
the time transformation, in which some of these metrics are known, and the
other ones new. Finally, the family of contracted Ricci collineations (CRC) are
presented.


title:
The monodromy matrix method of solving an exterior boundary value
  problem for a given stationary axisymmetric perfect fluid solution

abstract:
  A procedure is described for matching a given stationary axisymmetric perfect
fluid solution to a not necessarily asymptotically flat vacuum exterior. Using
data on the zero pressure surface, the procedure yields the Ernst potential of
the matching vacuum metric on the symmetry axis. From this the full metric can
be constructed using a variety of well established procedures.


title: The Geometrical Generating of Gravity

abstract: the author considered it unmatured and withdraw it.


title:
Analysis of quantum evaporation process of black holes in the model of
  Expansive Nondecelerative Universe

abstract:
  In the model of Expansive Nondecelerative Universe, black hole cannot totally
evaporate via quantum evaporation process proposed by Hawking. In a limiting
case, an equilibrium of gravitation creation and black hole evaporation can be
reached keeping the surface of its horizon constant. This conclusion is in
accordance with the second law of thermodynamics.


title:
Model of Expansive Nondecelerativa Universe and unified approach to
  fundamental physical interactions

abstract:
  The contribution provides the backround of the model of Expansive
Nondecelerative Universe, rationalizes the introduction of Vaidya metrics
allowing thus to localize and quantify gravitational energy. A unifying
explanation of the fundamental physical interactions is accompanied by
demonstration of some consequences and predictions relating to cosmological
problems.


title: M{\o}ller Energy for the Kerr-Newman metric

abstract:
  The energy distribution in the Kerr-Newman space-time is computed using the
M{\o}ller energy-momentum complex. This agrees with the Komar mass for this
space-time obtained by Cohen and de Felice. These results support the
Cooperstock hypothesis.


title:
A Tolman-Bondi-Lemaitre Cell-Model for the Universe and Gravitational
  Collapse

abstract:
  A piecewise Tolman-Bondi-Lemaitre (TBL) cell-model for the universe
incorporating local collapsing and expanding inhomogeneities is presented here.
The cell-model is made up of TBL underdense and overdense spherical regions
surrounded by an intermediate region of TBL shells embedded in an expanding
universe. The cell-model generalizes the Friedmann as well as Einstein-Straus
swiss-cheese models and presents a number of advantages over other models, and
in particular the time evolution of the cosmological inhomogeneities is now
incorporated within the scheme. Important problem of gravitational collapse of
a massive dust cloud, such as a cluster of galaxies or even a massive star, in
such a cosmological background is examined. It is shown that the collapsing
local inhomogeneities in an expanding universe could result in either a black
hole, or a naked singularity, depending on the nature of the set of initial
data which consists of the matter distribution and the velocities of the
collapsing shells in the cloud at the initial epoch from which the collapse
commences.


title:
Statistical Mechanics of 2+1 Gravity From Riemann Zeta Function and
  Alexander Polynomial:Exact Results

abstract:
  In the recent publication (Journal of Geometry and Physics,33(2000)23-102) we
demonstrated that dynamics of 2+1 gravity can be described in terms of train
tracks. Train tracks were introduced by Thurston in connection with description
of dynamics of surface automorphisms. In this work we provide an example of
utilization of general formalism developed earlier. The complete exact solution
of the model problem describing equilibrium dynamics of train tracks on the
punctured torus is obtained. Being guided by similarities between the dynamics
of 2d liquid crystals and 2+1 gravity the partition function for gravity is
mapped into that for the Farey spin chain. The Farey spin chain partition
function, fortunately, is known exactly and has been thoroughly investigated
recently. Accordingly, the transition between the pseudo-Anosov and the
periodic dynamic regime (in Thurston's terminology) in the case of gravity is
being reinterpreted in terms of phase transitions in the Farey spin chain whose
partition function is just a ratio of two Riemann zeta functions. The mapping
into the spin chain is facilitated by recognition of a special role of the
Alexander polynomial for knots/links in study of dynamics of self
homeomorphisms of surfaces. At the end of paper, using some facts from the
theory of arithmetic hyperbolic 3-manifolds (initiated by Bianchi in 1892), we
develop systematic extension of the obtained results to noncompact Riemannian
surfaces of higher genus. Some of the obtained results are also useful for 3+1
gravity. In particular, using the theorem of Margulis, we provide new reasons
for the black hole existence in the Universe: black holes make our Universe
arithmetic. That is the discrete Lie groups of motion are arithmetic.


title: The phase of a quantum mechanical particle in curved spacetime

abstract:
  We investigate the quantum mechanical wave equations for free particles of
spin 0,1/2,1 in the background of an arbitrary static gravitational field in
order to explicitly determine if the phase of the wavefunction is $S/\hbar =
\int p_{\mu} dx^{\mu} / \hbar$, as is often quoted in the literature. We work
in isotropic coordinates where the wave equations have a simple managable form
and do not make a weak gravitational field approximation. We interpret these
wave equations in terms of a quantum mechanical particle moving in medium with
a spatially varying effective index of refraction. Due to the first order
spatial derivative structure of the Dirac equation in curved spacetime, only
the spin 1/2 particle has \textit{exactly} the quantum mechanical phase as
indicated above. The second order spatial derivative structure of the spin 0
and spin 1 wave equations yield the above phase only to lowest order in
$\hbar$. We develop a WKB approximation for the solution of the spin 0 and spin
1 wave equations and explore amplitude and phase corrections beyond the lowest
order in $\hbar$. For the spin 1/2 particle we calculate the phase appropriate
for neutrino flavor oscillations.


title:
Non spherical sources of strong gravitational fields out of hydrostatic
  equilibrium

abstract:
  We describe the departure from equilibrium of matter distributions
representing sources for a class of Weyl metric. It is shown that, for
extremely high gravitational fields, slight deviations from spherical symmetry
may enhance the stability of the system weakening thereby its tendency to a
catastrophic collapse. For critical values of surface gravitational potential,
in contrast with the exactly spherically symmetric case, the speed of entering
the collapse regime decreases substantially, at least for specific cases.


title:
Self-adjoint wave equations for dynamical perturbations of
  self-gravitating fields

abstract:
  It is shown that the dynamical evolution of linear perturbations on a static
space-time is governed by a constrained wave equation for the extrinsic
curvature tensor. The spatial part of the wave operator is manifestly elliptic
and self-adjoint. In contrast to metric formulations, the curvature-based
approach to gravitational perturbation theory generalizes in a natural way to
self-gravitating matter fields. It is also demonstrated how to obtain symmetric
pulsation equations for self-gravitating non-Abelian gauge fields, Higgs fields
and perfect fluids. For vacuum fluctuations on a vacuum space-time, the
Regge-Wheeler and Zerilli equations are rederived.


title: M{\o}ller energy of the nonstatic spherically symmetric metrics

abstract:
  The energy distribution in the most general nonstatic spherically symmetric
space-time is obtained using M{\o}ller's energy-momentum complex. This result
is compared with the energy expression obtained by using the energy-momentum
complex of Einstein. Some examples of energy distributions in different
prescriptions are discussed.


title: From Now to Timelike Infinity on a Finite Grid

abstract:
  We use the conformal approach to numerical relativity to evolve hyperboloidal
gravitational wave data without any symmetry assumptions. Although our grid is
finite in space and time, we cover the whole future of the initial data in our
calculation, including future null and future timelike infinity.


title: A List of References on Spacetime Splitting and Gravitoelectromagnetism

abstract:
  Revised version to be published in the Proceedings of the Encuentros
Relativistas Espa\~noles, September, 2000 [ http://hades.eis.uva.es/EREs2000 ]


title:
New family of inhomogeneous $\gamma$-law cosmologies: example of
  gravitational waves in a homogeneous $p=\varrho/3$ background

abstract:
  We present an explicit three-parameter class of $p=\gamma \varrho$,
($-1/3\leq\gamma<1$), cosmological models admitting a two-dimensional group
$G_{2}$ of isometries acting on spacelike surfaces. The family is self-similar
in the sense that it has a further homothetic vector field and it contains
subfamilies of both (previously unknown) tilted and non-tilted Bianchi models
with that equation of state. This is the first algebraically general class of
solutions of this kind including dust inhomogeneous solutions. The whole class
presents a universal spacelike big-bang singularity in the finite past. More
interestingly, the case $p=\varrho /3$ constitutes a new two-parameter
inhomogeneous subfamily which can be viewed as a Bianchi V background with a
gravitational wave travelling orthogonally to the surfaces of transitivity of
the $G_{2}$ group. This wave generates the {\it inhomogeneity} of the spacetime
and is related to the sound waves {\it tilting} the perfect fluid. It seems to
be the first explicit exact example of a gravitational wave travelling along a
homogeneous background that has a realistic equation of state $p=\varrho /3$.


title:
Generalized Hubble law, violation of the cosmological principle and
  Supernovae

abstract:
  The acceleration of the cosmic expansion has been discovered as a consequence
of redshift Supernovae data. In the usual way, this cosmic acceleration is
explained by the presence of a positive cosmological constant or quantum vacuum
energy, in the background of standard Friedmann models. Recently, looking for
an alternative explanation, I have considered an inhomogeneous barotropic
spherically symmetric spacetime. Obviously, in this inhomogeneous model the
philosophical cosmological principle is not verified. Within this framework,
the kinematical acceleration of the cosmic fluid or, equivalently, the
inhomogeneity of matter, is just the responsible of the SNe Ia measured cosmic
acceleration. Moreover, this model gives rise to a generalized Hubble law with
two anisotropic terms (dipole acceleration and quadrupole shear), besides the
expansion one. The dipole term of this generalized Hubble law could explain, in
a cosmological setting, the observed large scale flow of matter, without to
have recourse to peculiar velocity-type newtonian models which assume a Doppler
dipole.