title: Non-linear numerical Schemes in General Relativity

abstract:
  This thesis describes the application of numerical techniques to solve
Einstein's field equations in three distinct cases. First we present the first
long-term stable second order convergent Cauchy characteristic matching code in
cylindrical symmetry including both gravitational degrees of freedom. Compared
with previous work we achieve a substantial simplification of the evolution
equations as well as the relations at the interface by factoring out the
z-Killing direction via the Geroch decomposition in both the Cauchy and the
characteristic region. In the second part we numerically solve the equations
for static and dynamic cosmic strings of infinite length coupled to gravity and
provide the first fully non-linear evolutions of cosmic strings in curved
spacetimes. The inclusion of null infinity as part of the numerical grid allows
us to apply suitable boundary conditions on the metric and the matter fields to
suppress unphysical divergent solutions. The code is used to study the
interaction between a Weber-Wheeler pulse of gravitational radiation with an
initially static string. In the final part of the thesis we probe a new
numerical approach for highly accurate evolutions of non-linear neutron star
oscillations in the case of radial oscillations of spherically symmetric stars.
For this purpose we view the evolution of the physical quantities as deviations
from a static equilibrium configuration and reformulate the equations in a
fully non-linear perturbative form. The high accuracy of the new scheme enables
us to study the non-linear coupling of eigenmodes over a wide range of initial
amplitudes.


title: Hilbert space structure of covariant loop quantum gravity

abstract:
  We investigate the Hilbert space in the Lorentz covariant approach to loop
quantum gravity. We restrict ourselves to the space where all area operators
are simultaneously diagonalizable, assuming that it exists. In this sector
quantum states are realized by a generalization of spin network states based on
Lorentz Wilson lines projected on irreducible representations of an SO(3)
subgroup. The problem of infinite dimensionality of the unitary Lorentz
representations is absent due to this projection. Nevertheless, the projection
preserves the Lorentz covariance of the Wilson lines so that the symmetry is
not broken. Under certain conditions the states can be thought as functions on
a homogeneous space. We define the inner product as an integral over this
space. With respect to this inner product the spin networks form an orthonormal
basis in the investigated sector. We argue that it is the only relevant part of
a larger state space arising in the approach. The problem of the
noncommutativity of the Lorentz connection is solved by restriction to the
simple representations. The resulting structure shows similarities with the
spin foam approach.


title: New Non-Separable Diagonal Cosmologies

abstract:
  We find all the perfect fluid G2 diagonal cosmologies with the property that
the quotient of the norms of the two orthogonal Killing vectors is constant
along each fluid world-line. We find four different families depending each one
on two or three arbitrary parameters which satisfy that the metric coefficients
are not separable functions. Some physical properties of these solutions
including energy conditions, kinematical quantities, Petrov type, the existence
and nature of the singularities and whether they contain
Friedman-Robertson-Walker cosmologies as particular cases are also included.


title:
String theory in a vertex operator representation: a simple model for
  testing loop quantum gravity

abstract:
  The loop quantum gravity technique is applied to the free bosonic string. A
Hilbert space similar to loop space in loop quantum gravity as well as
representations of diffeomorphism and hamiltonian constraints on it are
constructed. The string in this representation can be viewed as a set of
interacting relativistic particles each carrying a certain momentum. Two
different regularizations of the hamiltonian constraint are proposed. The first
of them is anomaly-free and give rise to interaction very similar to that of
two dimensional $\phi^4$-model. The second version of hamiltonian constraint is
similar to $\phi^3$-model and contains an anomaly. A possible relation of these
two models to the conventional quantization of the string based on Fock space
representation is discussed.


title: Maximum bounds on the surface redshift of anisotropic stars

abstract:
  It is shown that for realistic anisotropic star models the surface redshift
can not exceed the values 3.842 or 5.211 when the tangential pressure satisfies
the strong or the dominant energy condition respectively. Both values are
higher than 2, the bound in the perfect fluid case.


title: Initial data for fluid bodies in general relativity

abstract:
  We show that there exist asymptotically flat almost-smooth initial data for
Einstein-perfect fluid's equation that represent an isolated liquid-type body.
By liquid-type body we mean that the fluid energy density has compact support
and takes a strictly positive constant value at its boundary. By almost-smooth
we mean that all initial data fields are smooth everywhere on the initial
hypersurface except at the body boundary, where tangential derivatives of any
order are continuous at that boundary.
  PACS: 04.20.Ex, 04.40.Nr, 02.30.Jr


title: Interacting vector fields in Relativity without Relativity

abstract:
  Barbour, Foster and \'{O} Murchadha have recently developed a new framework,
called here {\it{the 3-space approach}}, for the formulation of classical
bosonic dynamics. Neither time nor a locally Minkowskian structure of spacetime
are presupposed. Both arise as emergent features of the world from
geodesic-type dynamics on a space of 3-dimensional metric--matter
configurations. In fact gravity, the universal light cone and Abelian gauge
theory minimally coupled to gravity all arise naturally through a single common
mechanism. It yields relativity -- and more -- without presupposing relativity.
This paper completes the recovery of the presently known bosonic sector within
the 3-space approach. We show, for a rather general ansatz, that 3-vector
fields can interact among themselves only as Yang--Mills fields minimally
coupled to gravity.


title: Free massive particles with total energy E < mc^2 in curved spacetimes

abstract:
  We analyze free elementary particles with rest mass $m$ and total energy $E <
m c^2$ in the Rindler wedge, outside Reissner-Nordstrom black holes and in the
spacetime of relativistic (and non-relativistic) stars, and use
Unruh-DeWitt-like detectors to calculate the associated particle detection rate
in each case. The (mean) particle position is identified with the spatial
average of the excitation probability of the detectors, which are supposed to
cover the whole space. Our results are shown to be in harmony with General
Relativity classical predictions. Eventually we reconcile our conclusions with
Earth-based experiments which are in good agreement with $E \geq m c^2$.


title: Classical gravitational spin-spin interaction

abstract:
  I obtain an exact, axially symmetric, stationary solution of Einstein's
equations for two massless spinning particles. The term representing the
spin-spin interaction agrees with recently published approximate work. The
spin-spin force appears to be proportional to the inverse fourth power of the
coordinate distance between the particles.


title:
Cosmological Vorticity Perturbations, Gravitomagnetism, and Mach's
  Principle

abstract:
  The axes of gyroscopes experimentally define non-rotating frames.
  But what physical cause governs the time-evolution of gyroscope axes?
  Starting from an unperturbed, spatially flat FRW cosmology, we consider
cosmological vorticity perturbations (i.e. vector perturbations, rotational
perturbations) at the linear level. We ask: Will cosmological rotational
perturbations drag the axis of a gyroscope relative to the directions
(geodesics) to galaxies beyond the rotational perturbation? We cast the laws of
Gravitomagnetism into a form showing clearly the close correspondence with the
laws of ordinary magnetism. Our results are: 1) The dragging of a gyroscope
axis by rotational perturbations beyond the $\dot{H}$ radius (H = Hubble
constant) is exponentially suppressed. 2) If the perturbation is a homogeneous
rotation inside a radius significantly larger than the $\dot{H}$ radius, then
the dragging of the gyroscope axis by the rotational perturbation is exact for
any equation of state for cosmological matter. 3) The time-evolution of a
gyroscope axis exactly follows a specific average of the matter inside the
$\dot{H}$ radius for any equation of state. In this precise sense Mach's
Principle follows from cosmology with Einstein Gravity.


title: Radiative Processes of the DeWitt-Takagi Detector

abstract:
  We examine the excitation of a uniformly accelerated DeWitt-Takagi detector
coupled quadratically to a Majorana-Dirac field. We obtain the transition
probability from the ground state of the detector and the vacuum state of the
field to an excited state with the emission of a Minkowski pair of quanta, in
terms of elementary processes of absorption and scattering of Rindler quanta
from the Fulling-Davies-Unruh thermal bath in the co-accelerated frame.


title:
Spherically Symmetric, Metrically Static, Isolated Systems in
  Quasi-Metric Gravity

abstract:
  The gravitational field exterior respectively interior to a spherically
symmetric, isolated body made of perfect fluid is examined within the
quasi-metric framework (QMF). It is required that the gravitational field is
"metrically static", meaning that it is static except for the effects of the
global cosmic expansion on the spatial geometry. Dynamical equations for the
gravitational field are set up and an exact solution is found for the exterior
part. Besides, equations of motion applying to inertial test particles moving
in the exterior gravitational field are set up. By construction, the
gravitational field of the system is not static with respect to the cosmic
expansion. This means that the radius of the source increases and that
distances between circular orbits of inertial test particles increase according
to the Hubble law. Moreover, it is shown that if this model of an expanding
gravitational field is taken to represent the gravitational field of the Sun
(or isolated planetary systems), this has no serious consequences for
observational aspects of planetary motion. On the contrary some observational
facts of the Earth-Moon system are naturally explained within the QMF. Finally,
the QMF predicts different secular increases for two different gravitational
coupling parameters. But such secular changes are neither present in the
Newtonian limit of the quasi-metric equations of motion nor in the Newtonian
limit of the quasi-metric field equations valid inside metrically static
sources. Thus standard interpretations of space experiments testing the secular
variation of G are explicitly theory-dependent and do not apply to the QMF.


title: Parity and Time Reversal in the Spin-Rotation Interaction

abstract:
  A recently reported discrepancy between experimental and theoretical values
of the muon's g-2 factor is interpreted as due to small violations of the
conservation of P and T in the spin-rotation coupling. The experiments place an
upper limit on these violations and on the weight change of spinning
gyroscopes.


title:
Scale Invariant Kaluza-Klein Theory and the Fate of the Gravitational
  Collapse

abstract:
  Pushing forward the similitudes between the gravitational collapse and the
expansion of the universe (in the reversed sense of time), it should be
expected that, during the collapse, eventually, a spacetime domain would be
reached where attained energy scales are very high. In consequence some of the
compactified extra dimensions may be decompactified and some presently broken
symmetries may be restored. A more fundamental theory (of which Einstein's
theory is a symmetry broken phase) is then expected to take account of further
description of the collapse. I propose a simple (classical) model for the
description of the late stages of the gravitational collapse: A non-Riemannian,
scale-invariant version of 5-dimensional Kaluza-Klein theory in which the
standard Riemann structure of the higher-dimensional manifold is replaced by a
Weyl-integrable one. A class of solutions, that generalize the "soliton" one by
Gross and Perry and Davidson and Owen, is found. This class contains both naked
singularities and wormhole solutions. On physical grounds it is argued that a
wormhole is the most reasonable destiny of the gravitational collapse.


title: Black Hole Mass Formula Is a Vanishing Noether Charge

abstract:
  The Noether current and its variation relation with respect to diffeomorphism
invariance of gravitational theories have been derived from the horizontal
variation and vertical-horizontal bi-variation of the Lagrangian, respectively.
For Einstein's GR in the stationary, axisymmetric black holes, the mass formula
in vacuum can be derived from this Noether current although it definitely
vanishes. This indicates that the mass formula of black holes is a vanishing
Noether charge in this case. The first law of black hole thermodynamics can
also be derived from the variation relation of this vanishing Noether current.


title: On the Weak-Field Approximation in Generalized Scalar-Tensor Gravities

abstract:
  In the paper published in Phys. Lett. A245} (1998) 31, Barros and Romero
demonstrated that, in the weak-field approximation, solutions to the
Brans-Dicke equations are related to the solutions of General Relativity for
the same matter distributions. In the present work, we enphasize this result
and we extend it to for generalized scalar-tensor theories in which the
parameter $\omega$ is no longer a constant but an arbitrary function of the
(gravitational) scalar field.


title:
The Mixmaster Model as a Cosmological Framework and Aspects of its
  Quantum Dynamics

abstract:
  This paper provides a review of some recent issues on the Mixmaster dynamics
concerning the features of its stochasticity. After a description of the
geometrical structure characterizing the homogeneous cosmological models in the
Bianchi classification and the Belinsky-Khalatnikov-Lifshitz piecewise
representation of the types VIII and IX oscillatory regime, we face the
question regarding the time covariance of the resulting chaos as viewed in
terms of continuous Misner-Chitr\'e like variables. Finally we show how in the
statistical mechanics framework the Mixmaster chaos raises as semiclassical
limit of the quantum dynamics in the Planckian era.


title: Covariant Mixmaster Dynamics

abstract:
  We provide a Hamiltonian analysis of the Mixmaster Universe dynamics on the
base of a standard Arnowitt-Deser-Misner Hamiltonian approach, showing the
covariant nature of its chaotic behaviour with respect to the choice of any
time variable, from the point of view either of the dynamical systems theory,
either of the statistical mechanics one.


title: Polyhomogeneous expansions close to null and spatial infinity

abstract:
  A study of the linearised gravitational field (spin 2 zero-rest-mass field)
on a Minkowski background close to spatial infinity is done. To this purpose, a
certain representation of spatial infinity in which it is depicted as a
cylinder is used. A first analysis shows that the solutions generically develop
a particular type of logarithmic divergence at the sets where spatial infinity
touches null infinity. A regularity condition on the initial data can be
deduced from the analysis of some transport equations on the cylinder at
spatial infinity. It is given in terms of the linearised version of the Cotton
tensor and symmetrised higher order derivatives, and it ensures that the
solutions of the transport equations extend analytically to the sets where
spatial infinity touches null infinity. It is later shown that this regularity
condition together with the requirement of some particular degree of tangential
smoothness ensures logarithm-free expansions of the time development of the
linearised gravitational field close to spatial and null infinities.


title: Naked singularities in three-dimensions

abstract:
  We study an analytical solution to the Einstein's equations in
2+1-dimensions, representing the self-similar collapse of a circularly
symmetric, minimally coupled, massless, scalar field. Depending on the value of
certain parameters, this solution represents the formation of naked
singularities. Since our solution is asymptotically flat, these naked
singularities may be relevant for the weak cosmic censorship conjecture in
2+1-dimensions.


title: The 2m <= r property of spherically symmetric static spacetimes

abstract:
  We prove that all spherically symmetric static spacetimes which are both
regular at r=0 and satisfying the single energy condition rho + p_r + p_t >= 0
cannot contain any black hole region (equivalently, they must satisfy 2m/r <= 1
everywhere). This result holds even when the spacetime is allowed to contain a
finite number of matching hypersurfaces. This theorem generalizes a result by
Baumgarte and Rendall when the matter contents of the space-time is a perfect
fluid and also complements their results in the general non-isotropic case.


title:
Metric-Field Approach to Gravitation and the Problem of the Universe
  Acceleration

abstract:
  A metric-field approach to gravitation is presented. It is based on an idea
of dependency of space-time properties on measuring instruments. Some bimetric
equations that realize this idea are considered. They were tested by the binary
pulsar PSR1913+16. The spherically - symmetric solution of the equations has no
event horizon and no physical singularity in the center. The proper energy of a
point particle is finite. There can exist supermassive compact configurations
of degenerated Fermi-gas which can be identified with observed objects in
galactic centers. The problem of the Universe acceleration has a natural
explanation.


title: Mach's Principle and Spatial Scale-Invariance of Gravity

abstract:
  Gravity does not provide any scale for matter properties. We argue that this
is also the implication of Mach's hypothesis of the relativity of inertia. The
most general spacetime compatible with this property of gravity is that
admitting three, independent spatial homothetic Killing vectors generating an
arbitrary function of each one of the three spatial coordinates. The matter
properties for such a spacetime are (spatially) arbitrary and the matter
generating the spacetime admits {\it any} equation of state. This is also the
most general spacetime containing the weak gravity physics in its entirety.
This spacetime is machian in that it is {\em globally} degenerate for
anti-machian situations such as vacuum, a single matter particle etc. and,
hence, has no meaning in the absence of matter.


title:
Nonminimal coupling, equivalence principle and exact Foldy-Wouthuysen
  transformation

abstract:
  It is shown that the exact Foldy-Wouthuysen transformation for spin-0
particles on spacetimes described by the metrics $ds^2 = V^2 dt^2 - W^2 d
{\bf{x}}^2$, where $V=V({\bf{x}})$ and $W=W({\bf{x}})$, only exists if the
scalar field is nonminimally coupled to the Ricci scalar field with a coupling
constant equal to 1/6. The nonminimal coupling term, in turn, does not violate
the equivalence principle. As an application we obtain the nonrelativistic
Foldy-Wouthuysen Hamiltonian concerning the general solution to the linearized
field equations of higher-derivative gravity for a static pointlike source in
the Teyssandier gauge.


title: Baryogensis in fresh inflation

abstract:
  I study the possibility of baryogenesis can take place in fresh inflation. I
find that it is possible that violation of baryon number conservation can occur
during the period out-of-equilibrium in this scenario. Indeed, baryogenesis
could be possible before the thermal equilibrium is restored at the end of
fresh inflation.


title:
Time-Dependent Automorphism Inducing Diffeomorphisms, Open Algebras and
  the Generality of the Kantowski-Sachs Vacuum Geometry

abstract:
  Following the spirit of a previous work of ours, we investigate the group of
those General Coordinate Transformations (GCTs) which preserve manifest spatial
homogeneity. In contrast to the case of Bianchi Type Models we, here, permit an
isometry group of motions $G_{4}=SO(3)\otimes T_{r}$, where $T_{r}$ is the
translations group, along the radial direction, while SO(3) acts multiply
transitively on each hypersurface of simultaneity $\Sigma_{t}$. The basis
1-forms, can not be invariant under the action of the entire isometry group and
hence produce an Open Lie Algebra. In order for these GCTs to exist and have a
non trivial, well defined action, certain integrability conditions have to be
satisfied; their solutions, exhibiting the maximum expected ``gauge'' freedom,
can be used to simplify the generic, spatially homogeneous, line element. In
this way an alternative proof of the generality of the Kantowski-Sachs (KS)
vacuum is given, while its most general, manifestly homogeneous, form is
explicitly presented.


title:
Anisotropic quantum cosmological models: a discrepancy between
  many-worlds and dBB interpretations

abstract:
  In the isotropic quantum cosmological perfect fluid model, the initial
singularity can be avoided, while the classical behaviour is recovered
asymptotically. We verify if initial anisotropies can also be suppressed in a
quantum version of a classical anisotropic model where gravity is coupled to a
perfect fluid. Employing a Bianchi I cosmological model, we obtain a
"Schr\"odinger-like" equation where the matter variables play de role of time.
This equation has a hyperbolic signature. It can be explicitly solved and a
wave packet is constructed. The expectation value of the scale factor,
evaluated in the spirit of the many-worlds interpretation, reveals an isotropic
Universe. On the other hand, the bohmian trajectories indicate the existence of
anisotropies. This is an example where the Bohm-de Broglie and the many-worlds
interpretations are not equivalent. It is argued that this inequivalence is due
to the hyperbolic structure of the "Schr\"odinger-like" equation.


title: The Structure of the Big Bang from Higher-Dimensional Embeddings

abstract:
  We give relations for the embedding of spatially-flat
Friedmann-Robertson-Walker cosmological models of Einstein's theory in flat
manifolds of the type used in Kaluza-Klein theory. We present embedding
diagrams that depict different 4D universes as hypersurfaces in a higher
dimensional flat manifold. The morphology of the hypersurfaces is found to
depend on the equation of state of the matter. The hypersurfaces possess a
line-like curvature singularity infinitesimally close to the $t = 0^+$
3-surface, where $t$ is the time expired since the big bang. The family of
timelike comoving geodesics on any given hypersurface is found to have a
caustic on the singular line, which we conclude is the 5D position of the
point-like big bang.


title: Self-gravitating domain walls and the thin-wall limit

abstract:
  We analyse the distributional thin wall limit of self gravitating scalar
field configurations representing thick domain wall geometries. We show that
thick wall solutions can be generated by appropiate scaling of the thin wall
ones, and obtain an exact solution for a domain wall that interpolates between
AdS_4 asymptotic vacua and has a well-defined thin wall limit.Solutions
representing scalar field configurations obtained via the same scaling but that
do not have a thin wall limit are also presented.


title:
Bimetric Gravity Theory, Varying Speed of Light and the Dimming of
  Supernovae

abstract:
  In the bimetric scalar-tensor gravitational theory there are two frames
associated with the two metrics {\hat g}_{\mu\nu} and g_{\mu\nu}, which are
linked by the gradients of a scalar field \phi. The choice of a comoving frame
for the metric {\hat g}_{\mu\nu} or g_{\mu\nu} has fundamental consequences for
local observers in either metric spacetimes, while maintaining diffeomorphism
invariance. When the metric g_{\mu\nu} is chosen to be associated with comoving
coordinates, then the speed of light varies in the frame with the metric {\hat
g}_{\mu\nu}. Observers in this frame see the dimming of supernovae because of
the increase of the luminosity distance versus red shift, due to an increasing
speed of light in the early universe. Moreover, in this frame the scalar field
\phi describes a dark energy component in the Friedmann equation for the cosmic
scale without acceleration. If we choose {\hat g}_{\mu\nu} to be associated
with comoving coordinates, then an observer in the g_{\mu\nu} metric frame will
observe the universe to be accelerating and the supernovae will appear to be
farther away. The theory predicts that the gravitational constant G can vary in
spacetime, while the fine-structure constant \alpha=e^2/\hbar c does not vary.
The problem of cosmological horizons as viewed in the two frames is discussed.


title: Constraints and evolution in cosmology

abstract:
  We review some old and new results about strict and non strict hyperbolic
formulations of the Einstein equations.


title: On H. Friedrich's formulation of Einstein'equations with fluid sources

abstract:
  We establish a variant, which has the advantage of introducing only physical
characteristics, of the symmetric quasi linear first order system given by H.\
Friedrich for the evolution equations of gravitating fluid bodies in General
Relativity which can be important to solve realistic problems. We explicit the
conditions under which the system is hyperbolic and admits a well posed Cauchy
problem.


title: Scattering in Two Black Hole Moduli Space

abstract:
  In this work, we discuss the quantum mechanics on the moduli space consisting
of two maximally charged dilaton black holes. We study the quantum effects
resulting from the different structure of the moduli space geometry in the
scattering process.


title:
Gravitational Radiation from Post-Newtonian Sources and Inspiralling
  Compact Binaries

abstract:
  The article reviews the current status of a theoretical approach to the
problem of the emission of gravitational waves by isolated systems in the
context of general relativity. Part A of the article deals with general
post-Newtonian sources. The exterior field of the source is investigated by
means of a combination of analytic post-Minkowskian and multipolar
approximations. The physical observables in the far-zone of the source are
described by a specific set of radiative multipole moments. By matching the
exterior solution to the metric of the post-Newtonian source in the near-zone
we obtain the explicit expressions of the source multipole moments. The
relationships between the radiative and source moments involve many non-linear
multipole interactions, among them those associated with the tails (and
tails-of-tails) of gravitational waves. Part B of the article is devoted to the
application to compact binary systems. We present the equations of binary
motion, and the associated Lagrangian and Hamiltonian, at the third
post-Newtonian (3PN) order beyond the Newtonian acceleration. The
gravitational-wave energy flux, taking consistently into account the
relativistic corrections in the binary moments as well as the various tail
effects, is derived through 3.5PN order with respect to the quadrupole
formalism. The binary's orbital phase, whose prior knowledge is crucial for
searching and analyzing the signals from inspiralling compact binaries, is
deduced from an energy balance argument.


title: Spin Foam Models of Riemannian Quantum Gravity

abstract:
  Using numerical calculations, we compare three versions of the Barrett-Crane
model of 4-dimensional Riemannian quantum gravity. In the version with face and
edge amplitudes as described by De Pietri, Freidel, Krasnov, and Rovelli, we
show the partition function diverges very rapidly for many triangulated
4-manifolds. In the version with modified face and edge amplitudes due to Perez
and Rovelli, we show the partition function converges so rapidly that the sum
is dominated by spin foams where all the spins labelling faces are zero except
for small, widely separated islands of higher spin. We also describe a new
version which appears to have a convergent partition function without drastic
spin-zero dominance. Finally, after a general discussion of how to extract
physics from spin foam models, we discuss the implications of convergence or
divergence of the partition function for other aspects of a spin foam model.


title: On the SO(2,1) symmetry in General Relativity

abstract:
  The role of the SO(2,1) symmetry in General Relativity is analyzed.
Cosmological solutions of Einstein field equations invariant with respect to a
space-like Lie algebra G_r, with r between 3 and 6 and containing so(2,1) as a
subalgebra, are also classified.


title:
Gravitational radiation from collisions at the speed of light: a
  massless particle falling into a Schwarzschild black hole

abstract:
  We compute spectra, waveforms, angular distribution and total gravitational
energy of the gravitiational radiation emitted during the radial infall of a
massless particle into a Schwarzschild black hole. Our fully relativistic
approach shows that (i) less than 50% of the total energy radiated to infinity
is carried by quadrupole waves, (ii) the spectra is flat, and (iii) the zero
frequency limit agrees extremely well with a prediction by Smarr. This process
may be looked at as the limiting case of collisions between massive particles
traveling at nearly the speed of light, by identifying the energy $E$ of the
massless particle with $m_0 \gamma$, $m_0$ being the mass of the test particle
and $\gamma$ the Lorentz boost parameter. We comment on the implications for
the two black hole collision at nearly the speed of light process, where we
obtain a 13.3% wave generation efficiency, and compare our results with
previous results by D'Eath and Payne.


title: Holonomy invariance, orbital resonances, and kilohertz QPOs

abstract:
  Quantized orbital structures are typical for many aspects of classical
gravity (Newton's as well as Einstein's). The astronomical phenomenon of
orbital resonances is a well-known example. Recently, Rothman, Ellis and
Murugan (2001) discussed quantized orbital structures in the novel context of a
holonomy invariance of parallel transport in Schwarzschild geometry. We present
here yet another example of quantization of orbits, reflecting both orbital
resonances and holonomy invariance. This strong-gravity effect may already have
been directly observed as the puzzling kilohertz quasi-periodic oscillations
(QPOs) in the X-ray emission from a few accreting galactic black holes and
several neutron stars.


title: A causally connected superluminal Warp Drive spacetime

abstract:
  It will be shown that while horizons do not exist for warp drive spacetimes
traveling at subluminal velocities horizons begin to develop when a warp drive
spacetime reaches luminal velocities. However it will be shown that the control
region of a warp drive ship lie within the portion of the warped region that is
still causally connected to the ship even at superluminal velocities, therefore
allowing a ship to slow to subluminal velocities. Further it is shown that the
warped regions which are causally disconnected from a warp ship have no
correlation to the ship velocity.


title: Metric perturbations in Einstein-Cartan Cosmology

abstract:
  Metric perturbations the stability of solution of Einstein-Cartan cosmology
(ECC) are given. The first addresses the stability of solutions of
Einstein-Cartan (EC) cosmological model against Einstein static universe
background. In this solution we show that the metric is stable against
first-order perturbations and correspond to acoustic oscillations. The second
example deals with the stability of de Sitter metric also against first-order
perturbations. Torsion and shear are also computed in these cases. The
resultant perturbed anisotropic spacetime with torsion is only de Sitter along
one direction or is unperturbed along one direction and perturbed against the
other two. Cartan torsion contributes to the frequency of oscillations in the
model. Therefore gravitational waves could be triggered by the spin-torsion
scalar density .


title:
Can Reissner-Nordstr\"{o}m wormholes be considered for Spacetime Foam
  formation?

abstract:
  A simple model of spacetime foam, made by $N$ Reissner-Nordstr\"{o}m
wormholes with a magnetic and electric charge in a semiclassical approximation,
is taken under examination. The Casimir-like energy of the quantum fluctuation
of such a model is computed and compared with that one obtained with a foamy
space modeled by $N$ Schwarzschild wormholes. The comparison leads to the
conclusion that a foamy spacetime cannot be considered as a collection of $N$
Reissner-Nordstr\"{o}m wormholes but that such a collection can be taken as an
excited state of the foam.


title: Static, Self-Gravitating Elastic Bodies

abstract:
  There is proved an existence theorem, in the Newtonian theory, for static,
self-gravitating bodies composed of elastic material. The theorem covers the
case where these bodies are small, but allows them to have arbitrary shape.


title:
Thermodynamics and Kinetic Theory of Relativistic Gases in 2-D
  Cosmological Models

abstract:
  A kinetic theory of relativistic gases in a two-dimensional space is
developed in order to obtain the equilibrium distribution function and the
expressions for the fields of energy per particle, pressure, entropy per
particle and heat capacities in equilibrium. Furthermore, by using the method
of Chapman and Enskog for a kinetic model of the Boltzmann equation the
non-equilibrium energy-momentum tensor and the entropy production rate are
determined for a universe described by a two-dimensional Robertson-Walker
metric. The solutions of the gravitational field equations that consider the
non-equilibrium energy-momentum tensor - associated with the coefficient of
bulk viscosity - show that opposed to the four-dimensional case, the cosmic
scale factor attains a maximum value at a finite time decreasing to a "big
crunch" and that there exists a solution of the gravitational field equations
corresponding to a "false vacuum". The evolution of the fields of pressure,
energy density and entropy production rate with the time is also discussed.


title: Quantum Field Theory of Open Spin Networks and New Spin Foam Models

abstract:
  We describe how a spin-foam state sum model can be reformulated as a quantum
field theory of spin networks, such that the Feynman diagrams of that field
theory are the spin-foam amplitudes. In the case of open spin networks, we
obtain a new type of state-sum models, which we call the matter spin foam
models. In this type of state-sum models, one labels both the faces and the
edges of the dual two-complex for a manifold triangulation with the simple
objects from a tensor category. In the case of Lie groups, such a model
corresponds to a quantization of a theory whose fields are the principal bundle
connection and the sections of the associated vector bundles. We briefly
discuss the relevance of the matter spin foam models for quantum gravity and
for topological quantum field theories.


title: A cylindrically symmetric solution in Einstein-Maxwell-dilaton gravity

abstract:
  We consider the existence of Einstein-Maxwell-dilaton plus fluid system for
the case of stationary cylindrically symmetric spacetimes. An exact
inhomogeneous $ \epsilon$-order solution is found, where the parameter
$\epsilon$ parametrizes the non-minimally coupled electromagnetic field. Some
its physical attributes are investigated and a connection with already known
G\"odel-type solution is given. It is shown that the found solution also
survives in the string-inspired charged gravity framework. We find that a
magnetic field has positive influence on the chronology violation unlike the
dilaton influence.


title: Remarks on "singularities"

abstract:
  We present herewith certain thoughts on the important subject of nowadays
physics, pertaining to the so-called ``singularities'', that emanated from
looking at the theme in terms of ADG (: abstract differential geometry). Thus,
according to the latter perspective, we can involve ``singularities'' in our
arguments, while still employing fundamental differential-geometric notions
such as connections, curvature, metric and the like, retaining also the form of
standard important relations of the classical theory (e.g. Einstein and/or
Yang-Mills equations, in vacuum), even within that generalized context of ADG.
To wind up, we can extend (in point of fact, {calculate) over singularities
classical differential-geometric relations/equations, without altering their
forms and/or changing the standard arguments; the change concerns thus only the
way, we employ the usual differential geometry of smooth manifolds, so that the
base ``space'' acquires now quite a secondary role, not contributing at all (!)
to the differential-geometric technique/mechanism that we apply. Thus, the
latter by definition refers directly to the objects being involved--the objects
that ``live on that space'', which by themselves are not, of course, ipso facto
``singular''!


title:
Equations of motion of the mass centers in a scalar theory of
  gravitation: Expansion in the separation parameter

abstract:
  An asymptotic framework is defined for the small parameter eta which
quantifies a good separation between the extended bodies that make a weakly
gravitating system. This is introduced within an alternative scalar theory of
gravitation, though it may be defined similarly in other theories. This
framework allows one to truncate the translational equations of motion at any
well-defined order. Here, the post-Newtonian (PN) equations valid in the scalar
theory are truncated beyond the order eta^3. The PN approximation scheme used
is the asymptotic scheme, that expands all fields. To get the explicit form of
the equations of motion for the mass centers, the bodies are assumed spherical,
merely for calculating the PN corrections. It is found that, due to the use of
the asymptotic PN scheme, the internal structure of the bodies does play a role
in the equations of motion.


title: A six dimensional analysis of Maxwell's Field Equations

abstract:
  A framework based on an extension of Kaluza's original idea of using a five
dimensional space to unify gravity with electromagnetism is used to analyze
Maxwell\'{}s field equations. The extension consists in the use of a six
dimensional space in which all equations of electromagnetism may be obtained
using only Einstein's field equation. Two major advantages of this approach to
electromagnetism are discussed, a full symmetric derivation for the wave
equations for the potentials and a natural inclusion of magnetic monopoles
without using any argument based on singularities.


title: The orientability of spacetime

abstract:
  Contrary to established beliefs, spacetime may not be time-orientable. By
considering an experimental test of time orientability it is shown that a
failure of time-orientability of a spacetime region would be indistinguishable
from a particle antiparticle annihilation event.


title:
Spacetimes, electromagnetism and fluids (a revision of traditional
  concepts)

abstract:
  In this talk r-form fields in spacetimes of any dimension D are considered
(r<D). The weak-field Newtonian-type limit of Einstein's equations, in general,
with relativistic sources is studied in the static case yielding a revision of
the equivalence principle (intrinsically relativistic sources generate twice
stronger gravitational fields and hyperrelativistic sources, e.g., the stiff
matter, generate four times stronger fields than non-relativistic sources). It
is shown that analogues of electromagnetic field, strictly speaking, exist only
in even-dimensional spacetimes. In (2+1)-dimensional spacetime, the field
traditionally interpreted as "magnetic" turns out to be in fact a perfect
fluid, and "electric", a perverse fluid (this latter concept arises inevitably
in the r-form description of fluids for any D, and we consider here perverse
fluids in (3+1)-dimensional spacetime too). New exact solutions of
(2+1)-dimensional Einstein's equations with perfect and perverse fluids are
obtained, and it is shown that in this case there exists a vast family of
static solutions for non-coherent dust, in a sharp contrast to the
(3+1)-dimensional case. New general interpretation of the cosmological term in
D-dimensional Einstein's equations is given via the (D-1)-form field, and it is
shown that this field is as well responsible (as this is the case in 3+1
dimensions) for rotation of perfect fluids [(D-2)-form fields], thus the
"source" term in the corresponding field equations has to be interpreted as the
rotation term.


title: Accelerating black holes in anti-de Sitter universe

abstract:
  A physical interpretation of the C-metric with a negative cosmological
constant $\Lambda$ is suggested. Using a convenient coordinate system it is
demonstrated that this class of exact solutions of Einstein's equations
describes uniformly accelerating (possibly charged) black holes in anti-de
Sitter universe. Main differences from the analogous de Sitter case are
emphasised.


title: Building blocks of a black hole

abstract:
  What is the nature of the energy spectrum of a black hole ? The algebraic
approach to black hole quantization requires the horizon area eigenvalues to be
equally spaced. As stressed long ago by by Mukhanov, such eigenvalues must be
exponentially degenerate with respect to the area quantum number if one is to
understand black hole entropy as reflecting degeneracy of the observable
states. Here we construct the black hole states by means of a pair of "creation
operators" subject to a particular simple algebra, a slight generalization of
that for the harmonic oscillator. We then prove rigorously that the n-th area
eigenvalue is exactly 2 raised to the n-fold degenerate. Thus black hole
entropy qua logarithm of the number of states for fixed horizon area comes out
proportional to that area.


title: Lapse function for maximally sliced Brill-Lindquist initial data

abstract:
  For binary black holes the lapse function corresponding to the
Brill-Lindquist initial value solution for uncharged black holes is given in
analytic form under the maximal slicing condition. In the limiting case of very
small ratio of mass to separation between the black holes the surface defined
by the zero value of the lapse function coincides with the minimal surfaces
around the singularities.


title:
Stationary and Axisymmetric Perfect Fluids with one Conformal Killing
  Vector

abstract:
  We study the stationary and axisymmetric non-convective differentially
rotating perfect-fluid solutions of Einstein's field equations admitting one
conformal symmetry. We analyse the two inequivalent Lie algebras not
exhaustively considered in Mars and Senovilla, 1994, and show that the general
solution for each Lie algebra depends on one arbitrary function of one of the
coordinates while a set of three ordinary differential equations for four
unknowns remains to be solved. The conformal Killing vector of these solutions
is necessarily homothetic. We summarize in a table all the possible solutions
for all the allowed Lie algebras and also add a corrigendum to an erroneous
statement in the paper quated above concerning the differentially rotating
character of one of the solutions presented


title: What can we learn about neutron stars from gravity-wave observations?

abstract:
  In the next few years, the first detections of gravity-wave signals using
Earth-based interferometric detectors will begin to provide precious new
information about the structure and dynamics of compact bodies such as neutron
stars. The intrinsic weakness of gravity-wave signals requires a proactive
approach to modeling the prospective sources and anticipating the shape of the
signals that we seek to detect. Full-blown 3-D numerical simulations of the
sources are playing and will play an important role in planning the
gravity-wave data-analysis effort. I review some recent analytical and
numerical work on neutron stars as sources of gravity waves.


title: Thermal lensing in cryogenic sapphire substrates

abstract:
  We report the reduction of the thermal lensing in cryogenic sapphire mirrors,
which is planed to be used in the Large scale Cryogenic Gravitational wave
Telescope (LCGT) project. We measured three key parameters of sapphire
substrate for thermal lensing at cryogenic temperature. They are optical
absorption coefficient, thermal conductivity and temperature coefficient of
refractive index at cryogenic temperature. On basis of these measurements, we
estimated the shot noise sensitivity of the interferometer with thermal lensing
by using a wave-front tracing simulation. We found that thermal lensing in
cryogenic sapphire mirrors is negligible.


title: Creation of Spin-1/2 Particles in the Hyperboloid de Sitter Space-Time

abstract:
  In this work we solve Dirac equation by using the method of seperation of
variables. Then we analyzed the particle creation process. To compute the
density number of particles created Bogoliubov transformation technique is
used.


title: Effect of signature change in NGR

abstract:
  The field equations of the new general relativity (NGR) have been applied to
an absolute parallelism space having three unknown functions of the radial
coordinate. The field equations have been solved using two different schemes.
In the first scheme, we used the conventional procedure used in orthodox
general relativity. In the second scheme, we examined the effect of signature
change. The latter scheme gives a solution which is different from the
Schwarzschild one. In both methods we find solution of the field equations
under the same constraint imposed on the parameters of the theory. We also
calculated the energy associated with the solutions in the two cases using the
superpotential method. We found that the energetic content of one of the
solutions is different from that of the other. A comparison between the two
solutions obtained in the present work and a third one obtained by Hayashi and
Shirafuji (1979) shows that the change of the signature may give rise to new
physics.


title: Creation of the Nonconformal Scalar Particles in Nonstationary Metric

abstract:
  The nonconformal scalar field is considered in N-dimensional space-time with
metric which includes, in particular, the cases of nonhomogeneous spaces and
anisotropic spaces of Bianchi type-I. The modified Hamiltonian is constructed.
Under the diagonalization of it the energy of quasiparticles is equal to the
oscillator frequency of the wave equation. The density of particles created by
nonstationary metric is investigated. It is shown that the densities of
conformal and nonconformal particles created in Friedmann radiative-dominant
Universe coincide.


title: Absence of trapped surfaces and singularities in cylindrical collapse

abstract:
  The gravitational collapse of an infinite cylindrical thin shell of generic
matter in an otherwise empty spacetime is considered. We show that geometries
admitting two hypersurface orthogonal Killing vectors cannot contain trapped
surfaces in the vacuum portion of spacetime causally available to geodesic
timelike observers. At asymptotic future null infinity, however, congruences of
outgoing radial null geodesics become marginally trapped, due to convergence
induced by shear caused by the interaction of a transverse wave component with
the geodesics. The matter shell itself is shown to be always free of trapped
surfaces, for this class of geometries. Finally, two simplified matter models
are analytically examined. For one model, the weak energy condition is shown to
be a necessary condition for collapse to halt; for the second case, it is a
sufficient condition for collapse to be able to halt.


title: Rotating Dilaton Solutions in 2+1 Dimensions

abstract:
  We report a three parameter family of solutions for dilaton gravity in 2+1
dimensions with finite mass and finite angular momentum. These solutions are
obtained by a compactification of vacuum solutions in 3+1 dimensions with
cylindrical symmetry. One class of solutions corresponds to conical
singularities and the other leads to curvature singularities.


title:
Matters of Gravity, the newsletter of the APS Topical Group on
  Gravitation, Spring 2002

abstract:
  Community News:
  - Center for Gravitational Wave Physics, by Sam Finn
  - Perimeter Institute for Theoretical Physics, by Lee Smolin
  Research Briefs:
  - Detector and Data Developments within GEO 600, by Alicia Sintes
  - The Virtual Data Grid and LIGO, by Pat Brady and Manuela Campanelli
  - 1000 hours of data and first lock of the recycled TAMA300, by Seiji
Kawamura
  - LIGO Takes Some Data!, by Stan Whitcomb
  - Quantum gravity: progress from an unexpected direction, by Matt Visser
  Conference report:
  - Gravitational-wave phenomenology at PennState, by Nils Andersson


title: Density perturbations in warm inflation and COBE normalization

abstract:
  Starting from a gauge invariant treatment of perturbations an analytical
expression for the spectrum of long wavelength density perturbations in warm
inflation is derived. The adiabatic and entropy modes are exhibited explicitly.
As an application of the analytical results, we determined the observational
constraint for the dissipation term compatible with COBE observation of the
cosmic microwave radiation anisotropy for some specific models. In view of the
results the feasibility of warm inflation is discussed.


title:
Galerkin Method in the Gravitational Collapse: a Dynamical System
  Approach

abstract:
  We study the general dynamics of the spherically symmetric gravitational
collapse of a massless scalar field. We apply the Galerkin projection method to
transform a system of partial differential equations into a set of ordinary
differential equations for modal coefficients, after a convenient truncation
procedure, largely applied to problems of turbulence. In the present case, we
have generated a finite dynamical system that reproduces the essential features
of the dynamics of the gravitational collapse, even for a lower order of
truncation. Each initial condition in the space of modal coefficients
corresponds to a well definite spatial distribution of scalar field. Numerical
experiments with the dynamical system show that depending on the strength of
the scalar field packet, the formation of black-holes or the dispersion of the
scalar field leaving behind flat spacetime are the two main outcomes. We also
found numerical evidence that between both asymptotic states, there is a
critical solution represented by a limit cycle in the modal space with period
$\Delta u \approx 3.55$.


title: Homoclinic chaos in the dynamics of a general Bianchi IX model

abstract:
  The dynamics of a general Bianchi IX model with three scale factors is
examined. The matter content of the model is assumed to be comoving dust plus a
positive cosmological constant. The model presents a critical point of
saddle-center-center type in the finite region of phase space. This critical
point engenders in the phase space dynamics the topology of stable and unstable
four dimensional tubes $R \times S^3$, where $R$ is a saddle direction and
$S^3$ is the manifold of unstable periodic orbits in the center-center sector.
A general characteristic of the dynamical flow is an oscillatory mode about
orbits of an invariant plane of the dynamics which contains the critical point
and a Friedmann-Robertson-Walker (FRW) singularity. We show that a pair of
tubes (one stable, one unstable) emerging from the neighborhood of the critical
point towards the FRW singularity have homoclinic transversal crossings. The
homoclinic intersection manifold has topology $R \times S^2$ and is constituted
of homoclinic orbits which are bi-asymptotic to the $S^3$ center-center
manifold. This is an invariant signature of chaos in the model, and produces
chaotic sets in phase space. The model also presents an asymptotic DeSitter
attractor at infinity and initial conditions sets are shown to have fractal
basin boundaries connected to the escape into the DeSitter configuration
(escape into inflation), characterizing the critical point as a chaotic
scatterer.


title:
Explicit Gravitational Radiation in Hyperbolic Systems for Numerical
  Relativity

abstract:
  A method for studying the causal structure of space-time evolution systems is
presented. This method, based on a generalization of the well known Riemann
problem, provides intrinsic results which can be interpreted from the
geometrical point of view. A one-parameter family of hyperbolic evolution
systems is presented and the physical relevance of their characteristic speeds
and eigenfields is discussed. The two degrees of freedom corresponding to
gravitational radiation are identified in an intrinsic way, independent of the
space coordinate system. A covariant interpretation of these degrees of freedom
is provided in terms of the geometry of the wave fronts. The requirement of a
consistent geometrical interpretation of the gravitational radiation degrees of
freedom is used to solve the ordering ambiguity that arises when obtaining
first order evolution systems from the second order field equations. This
achievement provides a benchmark which can be used to check both the existing
and future first order hyperbolic formalisms for Numerical Relativity.


title: Relational Relativity

abstract:
  According to a simple model of inertia a Machianized theory of special and
general relativity named as relational relativity is presented.


title: Dynamics of electromagnetic waves in Kerr geometry

abstract:
  Here we are interested to study the spin-1 particle i.e., electro-magnetic
wave in curved space-time, say around black hole. After separating the
equations into radial and angular parts, writing them according to the black
hole geometry, say, Kerr black hole we solve them analytically. Finally we
produce complete solution of the spin-1 particles around a rotating black hole
namely in Kerr geometry. Obviously there is coupling between spin of the
electro-magnetic wave and that of black hole when particles propagate in that
space-time. So the solution will be depending on that coupling strength. This
solution may be useful to study different other problems where the analytical
results are needed. Also the results may be useful in some astrophysical
contexts.


title:
Relativistic gravitational collapse in non-comoving coordinates: The
  post-quasistatic approximation

abstract:
  A general, iterative, method for the description of evolving self-gravitating
relativistic spheres is presented. Modeling is achieved by the introduction of
an ansatz, whose rationale becomes intelligible and finds full justification
within the context of a suitable definition of the post--quasistatic
approximation. As examples of application of the method we discuss three
models, in the adiabatic case.


title:
New Charged Dilaton Solutions in 2+1 Dimensions and Solutions with
  Cylindrical Symmetry in 3+1 Dimensions

abstract:
  We report a new family of solutions to Einstein-Maxwell-dilaton gravity in
2+1 dimensions and Einstein-Maxwell gravity with cylindrical symmetry in 3+1
dimensions. A set of static charged solutions in 2+1 dimensions are obtained by
a compactification of charged solutions in 3+1 dimensions with cylindrical
symmetry. These solutions contain naked singularities for certain values of the
parameters considered. New rotating charged solutions in 2+1 dimensions and 3+1
dimensions are generated treating the static charged solutions as seed metrics
and performing $SL(2;R)$ transformations.


title: Gauge Invariance with Mass: Higher Spins in Cosmological Spaces

abstract:
  I review recent work on massive higher (s>1) spins in constant curvature
(deSitter) spaces. Some of the novel properties that emerge are: partial
masslessness and new local gauge invariances, unitarily forbidden ranges of
mass, correlation between fermions/bosons and nagative/positive cosmological
constant Lambda and finally the consistency requirement that in the limit of
infinite spin towers, Lambda must tend to zero.


title: Acceleration-Induced Nonlocality: Uniqueness of the Kernel

abstract:
  We consider the problem of uniqueness of the kernel in the nonlocal theory of
accelerated observers. In a recent work, we showed that the convolution kernel
is ruled out as it can lead to divergences for nonuniform accelerated motion.
Here we determine the general form of bounded continuous kernels and use
observational data regarding spin-rotation coupling to argue that the kinetic
kernel given by $K(\tau ,\tau')=k(\tau')$ is the only physically acceptable
solution.


title: Numerical Relativity: Status and Prospects

abstract:
  We are entering an era where the numerical construction of generic spacetimes
is becoming a reality. The use of computer simulations, in principle, allows us
to solve Einstein equations in their full generality and unravel important
messages so far hidden in the theory. Despite the problems still found in
present applications, significant progress is being achieved in a number of
areas where simulations are on the verge of providing useful physical
information. This article reviews recent progress made in the field, paying
particular attention to black hole spacetimes and discuss open problems and
prospects for the future.


title: Singularity-free Cosmological Solutions with Non-rotating Perfect Fluids

abstract:
  The paper establishes the result that solutions of the type described in the
title of the article are only those that have been already presented in the
literature. The procedure adopted in the paper is somewhat novel - while the
usual practice is to display an exact solution and then to examine whether it
is singularity free, the present paper discovers the conditions which a
singularity free solution of the desired type must satistfy. There is no
attempt to obtain exact solutions. Simply, the conditions that were ad-hoc
introduced in the deduction of singularity free solutions are here shown to
follow from the requirement of non-singularity.


title: The Interaction of Gravity with Other Fields

abstract:
  We consider the interaction of gravity, as expressed by Einstein's Equations
of General Relativity, to other force fields. We describe some recent results,
discussing both the mathematics, and the physical interpretations. These
results concern both elementary particles, as well as cosmological models.
(This paper describes joint work variously done with with F. Finster, N.
Kamran, B. Temple, and S.-T. Yau.)


title:
Can the notion of a homogeneous gravitational field be transferred from
  classical mechanics to the Relativistic Theory of Gravity ?

abstract:
  The generalization of the concept of homogeneous gravitational field from
Classical Mechanics was considered in the framework of Einstein's General
Relativity by Bogorodskii. In this paper, I look for such a generalization in
the framework of the Relativistic Theory of Gravitation. There exist a
substantial difference between the solutions in these two theories.
Unfortunately, the solution obtained according to the Relativistic Theory of
Gravitation can't be accepted because it doesn't fulfill the Causality
Principle in this theory. So, it remains open in RTG the problem of finding a
generalization of the classical concept of homogeneous gravitational field.


title: Wormholes supported by pure ghost radiation

abstract:
  Traversible wormhole space-times are found as static, spherically symmetric
solutions to the Einstein equations with ingoing and outgoing pure ghost
radiation, i.e. pure radiation with negative energy density. Switching off the
radiation causes the wormhole to collapse to a Schwarzschild black hole.


title: G_2 Perfect-Fluid Cosmologies with a proper conformal Killing vector

abstract:
  We study the Einstein field equations for spacetimes admitting a maximal
two-dimensional abelian group of isometries acting orthogonally transitively on
spacelike surfaces and, in addition, with at least one conformal Killing
vector. The three-dimensional conformal group is restricted to the case when
the two-dimensional abelian isometry subalgebra is an ideal and it is also
assumed to act on non-null hypersurfaces (both, spacelike and timelike cases
are studied). We consider both, diagonal and non-diagonal metrics and find all
the perfect-fluid solutions under these assumptions (except those already
known). We find four families of solutions, each one containing arbitrary
parameters for which no differential equations remain to be integrated. We
write the line-elements in a simplified form and perform a detailed study for
each of these solutions, giving the kinematical quantities of the fluid
velocity vector, the energy-density and pressure, values of the parameters for
which the energy conditions are fulfilled everywhere, the Petrov type, the
singularities in the spacetimes and the Friedmann-Lemaitre-Robertson-Walker
metrics contained in each family.


title: Embedding of the Brane into Six Dimensions

abstract:
  Embedding of the brane metric into Euclidean (2+4)-space is found. Brane
geometry can be visualized as the surface of the hyper-sphere in six dimensions
which 'radius' is governed by the cosmological constant. Minkowski space in
this picture is lied on the intersection of this surface with the plane formed
by the extra space-like and time-like coordinates.


title:
The Electrogravitational Field of an Electrically Charged Mass Point and
  the Causality Principle in RTG

abstract:
  In this paper, I determine the electrogravitational field produced by a
charged mass point according to the Relativistic Theory of Gravitation. The
Causality Principle in the Relativistic Theory of Gravitation will play a very
important part in finding this field. The analytical form and the domain of
definition, i.e the gravitational radius of the obtained solution, differ from
that given by Einstein's General Relativity Theory.


title: The detection of Gravitational Waves

abstract:
  This chapter is concerned with the question: how do gravitational waves (GWs)
interact with their detectors? It is intended to be a theory review of the
fundamental concepts involved in interferometric and acoustic (Weber bar) GW
antennas. In particular, the type of signal the GW deposits in the detector in
each case will be assessed, as well as its intensity and deconvolution. Brief
reference will also be made to detector sensitivity characterisation, including
very summary data on current state of the art GW detectors.


title:
Generalized Chaplygin Gas, Accelerated Expansion and Dark Energy-Matter
  Unification

abstract:
  We consider the scenario emerging from the dynamics of a generalized
$d$-brane in a $(d+1, 1)$ spacetime. The equation of state describing this
system is given in terms of the energy density, $\rho$, and pressure, $p$, by
the relationship $p = - A/\rho^{\alpha}$, where $A$ is a positive constant and
$0 < \alpha \le 1$. We discuss the conditions under which homogeneity arises
and show that this equation of state describes the evolution of a universe
evolving from a phase dominated by non-relativistic matter to a phase dominated
by a cosmological constant via an intermediate period where the effective
equation of state is given by $p = \alpha \rho$.


title:
Slowly, rotating non-stationary, fluid solutions of Einstein's equations
  and their match to Kerr empty space-time

abstract:
  A general class of solutions of Einstein's equation for a slowly rotating
fluid source, with supporting internal pressure, is matched using Lichnerowicz
junction conditions, to the Kerr metric up to and including first order terms
in angular speed parameter. It is shown that the match applies to any
previously known non-rotating fluid source made to rotate slowly for which a
zero pressure boundary surface exists. The method is applied to the dust source
of Robertson-Walker and in outline to an interior solution due to McVittie
describing gravitational collapse. The applicability of the method to
additional examples is transparent. The differential angular velocity of the
rotating systems is determined and the induced rotation of local inertial frame
is exhibited.


title: Cosmology of the Jackiw-Teitelboim model

abstract:
  We investigate the cosmology of the two-dimensional Jackiw-Teitelboim model.
Since the matter coupling is not defined uniquely, we consider two possible
choices. The dilaton field plays an important role in the discussion of the
properties of the solutions. In particular, the possibility of universes having
a finite initial size emerges.


title: Nature of singularities in anisotropic string cosmology

abstract:
  We study nature of singularities in anisotropic string-inspired cosmological
models in the presence of a Gauss-Bonnet term. We analyze two string gravity
models-- dilaton-driven and modulus-driven cases-- in the Bianchi type-I
background without an axion field. In both scenarios singularities can be
classified in two ways- the determinant singularity where the main determinant
of the system vanishes and the ordinary singularity where at least one of the
anisotropic expansion rates of the Universe diverges. In the dilaton case,
either of these singularities inevitably appears during the evolution of the
system. In the modulus case, nonsingular cosmological solutions exist both in
asymptotic past and future with determinant $D=+\infty$ and D=2, respectively.
In both scenarios nonsingular trajectories in either future or past typically
meet the determinant singularity in past/future when the solutions are
singular, apart from the exceptional case where the sign of the time-derivative
of dilaton is negative. This implies that the determinant singularity may play
a crucial role to lead to singular solutions in an anisotropic background.


title: Axial Magnetostatics of a Ring Current in a Kerr Field

abstract:
  The electromagnetic fields generated by a ring current around a Kerr black
hole have been found. The acceleration of a charged particle by a force
electric field along the rotation axis is investigated in the constructed
model, as applied to the astrophysics of quasars.


title: Kasner-like behaviour for subcritical Einstein-matter systems

abstract:
  Confirming previous heuristic analyses \`a la Belinskii-Khalatnikov-Lifshitz,
it is rigorously proven that certain ``subcritical'' Einstein-matter systems
exhibit a monotone, generalized Kasner behaviour in the vicinity of a spacelike
singularity. The D-dimensional coupled Einstein-dilaton-p-form system is
subcritical if the dilaton couplings of the p-forms belong to some dimension
dependent open neighbourhood of zero, while pure gravity is subcritical if D is
greater than or equal to 11. Our proof relies, like the recent theorem dealing
with the (always subcritical) Einstein-dilaton system, on the use of Fuchsian
techniques, which enable one to construct local, analytic solutions to the full
set of equations of motion. The solutions constructed are ``general'' in the
sense that they depend on the maximal expected number of free functions.


title:
Hawking Radiation of Dirac Particles in an Arbitrarily Accelerating
  Kinnersley Black Hole

abstract:
  Quantum thermal effect of Dirac particles in an arbitrarily accelerating
Kinnersley black hole is investigated by using the method of generalized
tortoise coordinate transformation. Both the location and the temperature of
the event horizon depend on the advanced time and the angles. The Hawking
thermal radiation spectrum of Dirac particles contains a new term which
represents the interaction between particles with spin and black holes with
acceleration. This spin-acceleration coupling effect is absent from the thermal
radiation spectrum of scalar particles.


title: Background of gravitational waves from pre-galactic black hole formation

abstract:
  We study the generation of a gravitational wave (GW) background produced from
a population of core-collapse supernovae, which form black holes in scenarios
of structure formation of the Universe. We obtain, for example, that a
pre-galactic population of black holes, formed at redshifts $z\simeq 30-10$,
could generate a stochastic GW background with a maximum amplitude of $h_{\rm
BG}\simeq 10^{-24}$ in the frequency band $\nu_{\rm obs}\simeq 30-470 {\rm Hz}$
(considering a maximum efficiency of generation of GWs, namely, $\epsilon_{\rm
GW}=7\times 10^{-4}$). In particular, we discuss what astrophysical information
could be obtained from a positive, or even a negative, detection of such a GW
background produced in scenarios such as those studied here. One of them is the
possibility of obtaining the initial and final redshifts of the emission period
from the observed spectrum of GWs.


title: The Early Universe Odyssey With Gravitational Waves

abstract:
  This contribution summarizes some recent work on gravitational-wave astronomy
and, especially, on the generation and detection of relic gravitational waves.
We begin with a brief discussion of astrophysical sources of gravitational
waves that are likely to be detected first by the coming in operation laser
interferometers, such as GEO, LIGO, VIRGO. Then, we proceed to relic
gravitational waves emphasizing their quantum-mechanical origin and the
inevitability of their existence. Combining the theory with available
observations, we discuss the prospects of direct detection of relic
gravitational waves. A considerable part of the paper is devoted to comparison
of relic gravitational waves with the density perturbations of
quantum-mechanical origin. It is shown how the phenomenon of squeezing of
quantum-mechanically generated cosmological perturbations manifests itself in
the periodic structures of the metric power spectra and in the oscillatory
behaviour of the CMBR multipoles $C_l$ as a function of $l$. The cosmological
importance of the theoretically calculated (statistical) dipole moment $C_1$ is
stressed. The paper contains also some comments on the damage to
gravitational-wave research inflicted by the "standard inflationary result". We
conclude with the (now common) remarks on the great scientific importance of
the continuing effort to observe relic gravitational waves, directly or
indirectly.


title:
Classical Boundary-value Problem in Riemannian Quantum Gravity and
  Self-dual Taub-NUT-(anti)de Sitter Geometries

abstract:
  The classical boundary-value problem of the Einstein field equations is
studied with an arbitrary cosmological constant, in the case of a compact
($S^{3}$) boundary given a biaxial Bianchi-IX positive-definite three-metric,
specified by two radii $(a,b).$ For the simplest, four-ball, topology of the
manifold with this boundary, the regular classical solutions are found within
the family of Taub-NUT-(anti)de Sitter metrics with self-dual Weyl curvature.
For arbitrary choice of positive radii $(a,b),$ we find that there are three
solutions for the infilling geometry of this type. We obtain exact solutions
for them and for their Euclidean actions. The case of negative cosmological
constant is investigated further. For reasonable squashing of the three-sphere,
all three infilling solutions have real-valued actions which possess a ``cusp
catastrophe'' structure with a non-self-intersecting ``catastrophe manifold''
implying that the dominant contribution comes from the unique real
positive-definite solution on the ball. The positive-definite solution exists
even for larger deformations of the three-sphere, as long as a certain
inequality between $a$ and $b$ holds. The action of this solution is
proportional to $-a^{3}$ for large $a (\sim b)$ and hence larger radii are
favoured. The same boundary-value problem with more complicated interior
topology containing a ``bolt'' is investigated in a forthcoming paper.


title:
Basic Principles of 4D Dilatonic Gravity and Some of Their Consequences
  for Cosmology, Astrophysics and Cosmological Constant Problem

abstract:
  We present a class of simple scalar-tensor models of gravity with one scalar
field (dilaton $\Phi$) and only one unknown function (cosmological potential
$U(\Phi)$). These models might be considered as a stringy inspired ones with
broken SUSY. They have the following basic properties: 1) Positive dilaton
mass, $m_\Phi$, and positive cosmological constant $\Lambda$, define two
extremely different scales. The models under consideration are consistent with
the known experimental facts if $m_\Phi > 10^{-3} eV$ and
$\Lambda=\Lambda^{obs}\sim 10^{-56} cm^{-2}$. 2) Einstein week equivalence
principle is strictly satisfied and extended to scalar-tensor theories of
gravity using a novel form of principle of "constancy of fundamental
constants". 3) The dilaton plays simultaneously role of inflation field and
quintessence field and yields a sequential hyper-inflation with graceful exit
to asymptotic de Sitter space-time which is an attractor, and is approached as
$\exp(-\sqrt{3\Lambda^{obs}} ct/2)$. The time duration of inflation is $\Delta
t_{infl} \sim m_\Phi^{-1}$. 4) Ultra-high frequency ($\omega_\Phi \sim m_\Phi$)
dilatonic oscillations take place in asymptotic regime. 5) No fine tuning. (The
Robertson-Walker solutions of general type have the above properties.) 6) A
novel adjustment mechanism for cosmological constant problem seems to be
possible: the huge value of cosmological constant in the stringy frame is
re-scaled to its observed value by dilaton after transition to phenomenological
frame.


title: On the M{\o}ller Energy-Momentum Complex of the Melvin Magnetic Universe

abstract:
  We use the M{\o}ller energy-momentum complex to calculate the energy of the
Melvin magnetic universe. The energy distribution depends on the magnetic
field.


title:
Five-Dimensional Unification of the Cosmological Constant and the Photon
  Mass

abstract:
  Using a non-Riemannian geometry that is adapted to the 4+1 decomposition of
space-time in Kaluza-Klein theory, the translational part of the connection
form is related to the electromagnetic vector potential and a Stueckelberg
scalar. The consideration of a five-dimensional gravitational action functional
that shares the symmetries of the chosen geometry leads to a unification of the
four-dimensional cosmological term and a mass term for the vector potential.


title: Isotropic Loop Quantum Cosmology

abstract:
  Isotropic models in loop quantum cosmology allow explicit calculations,
thanks largely to a completely known volume spectrum, which is exploited in
order to write down the evolution equation in a discrete internal time. Because
of genuinely quantum geometrical effects the classical singularity is absent in
those models in the sense that the evolution does not break down there,
contrary to the classical situation where space-time is inextendible. This
effect is generic and does not depend on matter violating energy conditions,
but it does depend on the factor ordering of the Hamiltonian constraint.
Furthermore, it is shown that loop quantum cosmology reproduces standard
quantum cosmology and hence (e.g., via WKB approximation) to classical behavior
in the large volume regime where the discreteness of space is insignificant.
Finally, an explicit solution to the Euclidean vacuum constraint is discussed
which is the unique solution with semiclassical behavior representing quantum
Euclidean space.


title:
Thermodynamics and/of Horizons: A Comparison of Schwarzschild,RINDLER
  and desitter Spacetimes

abstract:
  The notions of temperature, entropy and `evaporation', usually associated
with spacetimes with horizons, are analyzed using general approach and the
following results, applicable to different spacetimes, are obtained at one go.
(i) The concept of temperature associated with the horizon is derived in a
unified manner and is shown to arise from purely kinematic considerations. (ii)
QFT near any horizon is mapped to a conformal field theory without introducing
concepts from string theory. (iii) For spherically symmetric spacetimes (in
D=1+3) with a horizon at r=l, the partition function has the generic form
$Z\propto \exp[S-\beta E]$, where $S= (1/4) 4\pi l^2$ and $|E|=(l/2)$. This
analysis reproduces the conventional result for the blackhole spacetimes and
provides a simple and consistent interpretation of entropy and energy for
deSitter spacetime. (iv) For the Rindler spacetime the entropy per unit
transverse area turns out to be (1/4) while the energy is zero. (v) In the case
of a Schwarzschild black hole there exist quantum states (like Unruh vacuum)
which are not invariant under time reversal and can describe blackhole
evaporation. There also exist quantum states (like Hartle-Hawking vacuum) in
which temperature is well-defined but there is no flow of radiation to
infinity. In the case of deSitter universe or Rindler patch in flat spacetime,
one usually uses quantum states analogous to Hartle-Hawking vacuum and obtains
a temperature without the corresponding notion of evaporation. It is, however,
possible to construct the analogues of Unruh vacuum state in the other cases as
well. Associating an entropy or a radiating vacuum state with a general horizon
raises conceptual issues which are briefly discussed.


title:
A note on the foundation of relativistic mechanics. II: Covariant
  hamiltonian general relativity

abstract:
  I illustrate a simple hamiltonian formulation of general relativity, derived
from the work of Esposito, Gionti and Stornaiolo, which is manifestly 4d
generally covariant and is defined over a finite dimensional space. The
spacetime coordinates drop out of the formalism, reflecting the fact that they
are not related to observability. The formulation can be interpreted in terms
of Toller's reference system transformations, and provides a physical
interpretation for the spinnetwork to spinnetwork transition amplitudes
computable in principle in loop quantum gravity and in the spin foam models.


title:
Entropy and energy of a class of spacetimes with horizon: a general
  derivation

abstract:
  Euclidean continuation of several Lorentzian spacetimes with horizons
requires treating the Euclidean time coordinate to be periodic with some period
$\beta$.
  Such spacetimes (Schwarzschild, deSitter,Rindler .....) allow a temperature
$T=\beta^{-1}$ to be associated with the horizon. I construct a canonical
ensemble of a subclass of such spacetimes with a fixed value for $\beta$ and
evaluate the partition function $Z(\beta)$. For spherically symmetric
spacetimes with a horizon at r=a, the partition function has the generic form
$Z\propto \exp[S-\beta E]$, where $S= (1/4) 4\pi a^2$ and $|E|=(a/2)$. Both S
and E are determined entirely by the properties of the metric near the horizon.
This analysis reproduces the conventional result for the blackhole spacetimes
and provides a simple and consistent interpretation of entropy and energy for
deSitter spacetime. For the Rindler spacetime the entropy per unit transverse
area turns out to be (1/4) while the energy is zero. The implications are
discussed.


title:
The non-existence of a Lanczos potential for the Weyl curvature tensor
  in dimensions n>=7

abstract:
  In this paper it is shown that a Lanczos potential for the Weyl curvature
tensor does not exist for all spaces of dimension $n\geq 7$.


title: On the linear and weak-field limits of scalar-tensor theories of gravity

abstract:
  The linear approximation of scalar-tensor theories of gravity is obtained in
the physical (Jordan) frame under the 4+0 (covariant) and 3+1 formalisms. Then
the weak-field limit is analyzed and the conditions leading to significant
deviations of the $1/r^{2}$ Newton's law of gravitation are discussed. Finally,
the scalarization effects induced by these theories in extended objects are
confronted within the weak-field limit.


title: FRW cosmologies between chaos and integrability

abstract:
  A recent paper by Castagnino, Giacomini and Lara concludes that there is no
chaos in a conformally coupled closed Friedmann-Robertson-Walker universe,
which is in apparent contradiction with previous works. We point out that
although nonchaotic the quoted system is nonintegrable.


title:
Constraints on the Cosmological Parameters in the Relativistic Theory of
  Gravitation

abstract:
  The causality principle imposes the constraints on the cosmological
parameters in the relativistic theory of gravitation. As a result, X-matter
causes the quite definite cosmological scenario with the alternate acceleration
and deceleration and the final recollapse


title:
Circular Holonomy, Clock Effects and Gravitoelectromagnetism: Still
  Going Around in Circles After All These Years

abstract:
  The historical origins of Fermi-Walker transport and Fermi coordinates and
the construction of Fermi-Walker transported frames in black hole spacetimes
are reviewed. For geodesics this transport reduces to parallel transport and
these frames can be explicitly constructed using a Killing-Yano tensor as shown
by Marck. For accelerated or geodesic circular orbits in such spacetimes, both
parallel and Fermi-Walker transported frames can be given, and allow one to
study circular holonomy and related clock and spin transport effects. In
particular the total angle of rotation that a spin vector undergoes around a
closed loop can be expressed in a factored form, where each factor is due to a
different relativistic effect, in contrast with the usual sum of terms
decomposition. Finally the Thomas precession frequency is shown to be a special
case of the simple relationship between the parallel transport and Fermi-Walker
transport frequencies for stationary circular orbits.


title: Self-force via a Green's function decomposition

abstract:
  The gravitational field of a particle of small mass \mu moving through curved
spacetime is naturally decomposed into two parts each of which satisfies the
perturbed Einstein equations through O(\mu). One part is an inhomogeneous field
which, near the particle, looks like the \mu/r field distorted by the local
Riemann tensor; it does not depend on the behavior of the source in either the
infinite past or future. The other part is a homogeneous field and includes the
``tail term''; it completely determines the self force effects of the particle
interacting with its own gravitational field, including radiation reaction.
Self force effects for scalar, electromagnetic and gravitational fields are all
described in this manner.


title: Axially symmetric Einstein-Straus models

abstract:
  The existence of static and axially symmetric regions in a Friedman-Lemaitre
cosmology is investigated under the only assumption that the cosmic time and
the static time match properly on the boundary hypersurface. It turns out that
the most general form for the static region is a two-sphere with arbitrarily
changing radius which moves along the axis of symmetry in a determined way. The
geometry of the interior region is completely determined in terms of background
objects. When any of the most widely used energy-momentum contents for the
interior region is imposed, both the interior geometry and the shape of the
static region must become exactly spherically symmetric. This shows that the
Einstein-Straus model, which is the generally accepted answer for the null
influence of the cosmic expansion on the local physics, is not a robust model
and it is rather an exceptional and isolated situation. Hence, its suitability
for solving the interplay between cosmic expansion and local physics is
doubtful and more adequate models should be investigated.


title:
Comment on ``Singularity-free Cosmological Solutions with Non-rotating
  Perfect Fluids''

abstract:
  A theorem stated by Raychaudhuri which claims that the only physical
non-singular cosmological models are comprised in the Ruiz-Senovilla family is
shown to be incorrect. An explicit counterexample is provided and the failure
of the argument leading to the theorem is explicitly pointed out.


title: Cosmological Equations for a Thick Brane

abstract:
  Generalized Friedmann equations governing the cosmological evolution inside a
thick brane embedded in a five-dimensional Anti-de Sitter spacetime are
derived. These equations are written in terms of four-dimensional effective
brane quantities obtained by integrating, along the fifth dimension, over the
brane thickness. In the case of a Randall-Sundrum type cosmology, different
limits of these effective quantities are considered yielding cosmological
equations which interpolate between the thin brane limit (governed by
unconventional brane cosmology), and the opposite limit of an ``infinite''
brane thickness corresponding to the familiar Kaluza-Klein approach. In the
more restrictive case of a Minkowski bulk, it is shown that no effective
four-dimensional reduction is possible in the regimes where the brane thickness
is not small enough.


title: Celestial mechanics in Kerr spacetime

abstract:
  The dynamical parameters conventionally used to specify the orbit of a test
particle in Kerr spacetime are the energy $E$, the axial component of the
angular momentum, $L_{z}$, and Carter's constant $Q$. These parameters are
obtained by solving the Hamilton-Jacobi equation for the dynamical problem of
geodesic motion. Employing the action-angle variable formalism, on the other
hand, yields a different set of constants of motion, namely, the fundamental
frequencies $\omega_{r}$, $\omega_{\theta}$ and $\omega_{\phi}$ associated with
the radial, polar and azimuthal components of orbital motion. These
frequencies, naturally, determine the time scales of orbital motion and,
furthermore, the instantaneous gravitational wave spectrum in the adiabatic
approximation. In this article, it is shown that the fundamental frequencies
are geometric invariants and explicit formulas in terms of quadratures are
derived. The numerical evaluation of these formulas in the case of a rapidly
rotating black hole illustrates the behaviour of the fundamental frequencies as
orbital parameters such as the semi-latus rectum $p$, the eccentricity $e$ or
the inclination parameter $\theta_{-}$ are varied. The limiting cases of
circular, equatorial and Keplerian motion are investigated as well and it is
shown that known results are recovered from the general formulas.


title: Radiating spherical collapse with heat flow

abstract:
  We present here a simple model of radiative gravitational collapse with
radial heat flux which describes qualitatively the stages close to the
formation of a superdense cold star. Starting with a static general solution
for a cold star, the model can generate solutions for the earlier evolutionary
stages. The temporal evolution of the model is specified by solving the
junction conditions appropriate for radiating gravitational collapse.


title: Algebraic Rainich theory and antisymmetrisation in higher dimensions

abstract:
  The classical Rainich(-Misner-Wheeler) theory gives necessary and sufficient
conditions on an energy-momentum tensor $T$ to be that of a Maxwell field (a
2-form) in four dimensions. Via Einstein's equations these conditions can be
expressed in terms of the Ricci tensor, thus providing conditions on a
spacetime geometry for it to be an Einstein-Maxwell spacetime. One of the
conditions is that $T^2$ is proportional to the metric, and it has previously
been shown in arbitrary dimension that any tensor satisfying this condition is
a superenergy tensor of a simple $p$-form. Here we examine algebraic Rainich
conditions for general $p$-forms in higher dimensions and their relations to
identities by antisymmetrisation. Using antisymmetrisation techniques we find
new identities for superenergy tensors of these general (non-simple) forms, and
we also prove in some cases the converse; that the identities are sufficient to
determine the form. As an example we obtain the complete generalisation of the
classical Rainich theory to five dimensions.


title:
The Singularity Threshold of the Nonlinear Sigma Model Using 3D Adaptive
  Mesh Refinement

abstract:
  Numerical solutions to the nonlinear sigma model (NLSM), a wave map from 3+1
Minkowski space to S^3, are computed in three spatial dimensions (3D) using
adaptive mesh refinement (AMR). For initial data with compact support the model
is known to have two regimes, one in which regular initial data forms a
singularity and another in which the energy is dispersed to infinity. The
transition between these regimes has been shown in spherical symmetry to
demonstrate threshold behavior similar to that between black hole formation and
dispersal in gravitating theories. Here, I generalize the result by removing
the assumption of spherical symmetry. The evolutions suggest that the
spherically symmetric critical solution remains an intermediate attractor
separating the two end states.


title: Detectability of Cosmic Topology in Flat Universes

abstract:
  Recent observations seem to indicate that we live in a universe whose spatial
sections are nearly or exactly flat. Motivated by this we study the problem of
observational detection of the topology of universes with flat spatial
sections. We first give a complete description of the diffeomorphic
classification of compact flat 3-manifolds, and derive the expressions for the
injectivity radii, and for the volume of each class of Euclidean 3-manifolds.
There emerges from our calculations the undetectability conditions for each
(topological) class of flat universes. To illustrate the detectability of flat
topologies we construct toy models by using an assumption by Bernshtein and
Shvartsman which permits to establish a relation between topological typical
lengths to the dynamics of flat models.


title: Gravitational waves and cosmic magnetism; a cosmological approach

abstract:
  We present the formalism for the covariant treatment of gravitational
radiation in a magnetized environment and discuss the implications of the field
for gravity waves in the cosmological context. Our geometrical approach brings
to the fore the tension properties of the magnetic force lines and reveals
their intricate interconnection to the spatial geometry of a magnetised
spacetime. We show how the generic anisotropy of the field can act as a source
of gravitational wave perturbations and how, depending on the spatial curvature
distortion, the magnetic tension can boost or suppress waves passing through a
magnetized region.


title: A multidomain spectral method for solving elliptic equations

abstract:
  We present a new solver for coupled nonlinear elliptic partial differential
equations (PDEs). The solver is based on pseudo-spectral collocation with
domain decomposition and can handle one- to three-dimensional problems. It has
three distinct features. First, the combined problem of solving the PDE,
satisfying the boundary conditions, and matching between different subdomains
is cast into one set of equations readily accessible to standard linear and
nonlinear solvers. Second, touching as well as overlapping subdomains are
supported; both rectangular blocks with Chebyshev basis functions as well as
spherical shells with an expansion in spherical harmonics are implemented.
Third, the code is very flexible: The domain decomposition as well as the
distribution of collocation points in each domain can be chosen at run time,
and the solver is easily adaptable to new PDEs. The code has been used to solve
the equations of the initial value problem of general relativity and should be
useful in many other problems. We compare the new method to finite difference
codes and find it superior in both runtime and accuracy, at least for the
smooth problems considered here.


title: General Covariance and the "Problem of Time" in a Discrete Cosmology

abstract:
  Identifying an appropriate set of ``observables'' is a nontrivial task for
most approaches to quantum gravity. We describe how it may be accomplished in
the context of a recently proposed family of stochastic (but classical)
dynamical laws for causal sets. The underlying idea should work equally well in
the quantum case.


title: At the interface of quantum and gravitational realms

abstract:
  In this talk I review a series of recent conceptual developments at the
interface of the quantum and gravitational realms. Wherever possible, I comment
on the possibility to probe the interface experimentally. It is concluded that
the underlying spacetime for a quantum theory of gravity must be
non-commutative, that wave-particle duality suffers significant modification at
the Planck scale, and that the latter forbids probing spacetime below Planck
length. Furthermore, study of quantum test particles in classical and quantum
sources of gravity puts forward theoretical challenges and new experimental
possibilities. It is suggested that existing technology may allow to probe
gravitationally-modified wave particle duality in the laboratory.


title:
De-Sitter Type of Cosmological Model in n-Dimensional Space-Time-Mass
  (STM) Theory of Gravitation

abstract:
  Exact solution are obtained for a homogeneous spacially isotropic
cosmological model in a matter free space with or without cosmological consant
for a n-dimensional Kaluza-Klein type of metric in the rest mass varying theory
of gravity proposed by Wesson[1983]. The behavior of the model is discussed.


title: Stroboscopic Variation Measurement

abstract:
  A new procedure of the linear position measurement which allows to obtain
sensitivity better than the Standard Quantum Limit and close to the Energetic
Quantum Limit is proposed and analyzed in details. Proposed method is based on
the principles of stroboscopic quantum measurement and variation quantum
measurement and allows to avoid main disadvantages of both these procedures.
This method can be considered as a good candidate for use as a local position
meter in the ``intracavity'' topologies of the laser gravitational-wave
antennae.


title: Flux Limiter Methods in 3D Numerical Relativity

abstract:
  New numerical methods have been applied in relativity to obtain a numerical
evolution of Einstein equations much more robust and stable. Starting from 3+1
formalism and with the evolution equations written as a FOFCH (first-order flux
conservative hyperbolic) system, advanced numerical methods from CFD
(Computational Fluid Dynamics) have been successfully applied. A flux limiter
mechanism has been implemented in order to deal with steep gradients like the
ones usually associated with black hole spacetimes. As a test bed, the method
has been applied to 3D metrics describing propagation of nonlinear gauge waves.
Results are compared with the ones obtained with standard methods, showing a
great increase in both robustness and stability of the numerical algorithm.


title:
The family of regular interiors for non-rotating black holes with $T^0_0
  = T^1_1$

abstract:
  We find the general solution for the spacetimes describing the interior of
static black holes with an equation of state of the type $ T^0_0 = T^1_1 $ ($T$
being the stress-energy tensor). This form is the one expected from taking into
account different quantum effects associated with strong gravitational fields.
We recover all the particular examples found in the literature. We remark that
all the solutions found follow the natural scheme of an interior core linked
smoothly with the exterior solution by a transient region. We also discuss
their local energy properties and give the main ideas involved in a possible
generalization of the scheme, in order to include other realistic types of
sources.


title: New nonabelian solutions in D=4, N=4 gauged supergravity

abstract:
  In this paper we look for static, purely magnetic, nonabelian solutions with
unusual topology in the context of N=4 Freedman-Schwarz supergravity in four
dimensions.Two new exact solutions satisfying first order Bogomol'nyi equations
are discussed.The main characteristics of the general solutions are presented
and differences with respect to the spherically symmetric case are studied. We
argue that all solutions present naked singularities.


title: Entropic issues in contemporary cosmology

abstract:
  Penrose [1] has emphasized how the initial big bang singularity requires a
special low entropy state. We address how recent brane cosmological schemes
address this problem and whether they offer any apparent resolution. Pushing
the start time back to $t=-\infty$ or utilizing maximally symmetric AdS spaces
simply exacerbates or transfers the problem.
  Because the entropy of de Sitter space is $S\leq 1/\Lambda$, using the
present acceleration of the universe as a low energy $(\Lambda\sim 10^{-120}$)
inflationary stage, as in cyclic ekpyrotic models, produces a gravitational
heat death after one cycle. Only higher energy driven inflation, together with
a suitable, quantum gravity holography style, restriction on {\em ab initio}
degrees of freedom, gives a suitable low entropy initial state. We question the
suggestion that a high energy inflationary stage could be naturally reentered
by Poincare recurrence within a finite causal region of an accelerating
universe.
  We further give a heuristic argument that so-called eternal inflation is not
consistent with the 2nd law of thermodynamics within a causal patch.


title:
Numerical stability of a new conformal-traceless 3+1 formulation of the
  Einstein equation

abstract:
  There is strong evidence indicating that the particular form used to recast
the Einstein equation as a 3+1 set of evolution equations has a fundamental
impact on the stability properties of numerical evolutions involving black
holes and/or neutron stars. Presently, the longest lived evolutions have been
obtained using a parametrized hyperbolic system developed by Kidder, Scheel and
Teukolsky or a conformal-traceless system introduced by Baumgarte, Shapiro,
Shibata and Nakamura. We present a new conformal-traceless system. While this
new system has some elements in common with the
Baumgarte-Shapiro-Shibata-Nakamura system, it differs in both the type of
conformal transformations and how the non-linear terms involving the extrinsic
curvature are handled. We show results from 3D numerical evolutions of a
single, non-rotating black hole in which we demonstrate that this new system
yields a significant improvement in the life-time of the simulations.