title: Generalized 2d dilaton gravity with matter fields

abstract:
  We extend the classical integrability of the CGHS model of 2d dilaton gravity
[1] to a larger class of models, allowing the gravitational part of the action
to depend more generally on the dilaton field and, simultaneously, adding
fermion- and U(1)-gauge-fields to the scalar matter. On the other hand we
provide the complete solution of the most general dilaton-dependent 2d gravity
action coupled to chiral fermions. The latter analysis is generalized to a
chiral fermion multiplet with a non-abelian gauge symmetry as well as to the
(anti-)self-dual sector df = *df (df = -*df) of a scalar field f.


title: Repulsive gravity in the very early Universe

abstract:
  I present two examples in which the curvature singularity of a
radiation-dominated Universe is regularized by (a) the repulsive effects of
spin interactions, and (b) the repulsive effects arising from a breaking of the
local gravitational gauge symmetry. In both cases the collapse of an initial,
asymptotically flat state is stopped, and the Universe bounces towards a state
of decelerated expansion. The emerging picture is typical of the pre-big bang
scenario, with the main difference that the string cosmology dilaton is
replaced by a classical radiation fluid, and the solutions are not
duality-invariant.


title:
On rotational excitations and axial deformations of BPS monopoles and
  Julia-Zee dyons

abstract:
  It is shown that Julia-Zee dyons do not admit slowly rotating excitations.
This is achieved by investigating the complete set of stationary excitations
which can give rise to non-vanishing angular momentum. The relevant zero modes
are parametrized in a gauge invariant way and analyzed by means of a harmonic
decomposition. Since general arguments show that the solutions to the
linearized Bogomol'nyi equations cannot contribute to the angular momentum, the
relevant modes are governed by a set of electric and a set of non self-dual
magnetic perturbation equations. The absence of axial dipole deformations is
also established.


title: Gamma-Ray Bursts and Quantum Cosmic Censorship

abstract:
  Gamma-ray bursts are believed to result from the coalescence of binary
neutron stars. However, the standard proposals for conversion of the
gravitational energy to thermal energy have difficulties. We show that if the
merger of the two neutron stars results in a naked singularity, instead of a
black hole, the ensuing quantum particle creation can provide the requisite
thermal energy in a straightforward way. The back-reaction of the created
particles can avoid the formation of the naked singularity predicted by the
classical theory. Hence cosmic censorship holds in the quantum theory, even if
it were to be violated in classical general relativity.


title:
The Singularity in Generic Gravitational Collapse Is Spacelike, Local,
  and Oscillatory

abstract:
  A longstanding conjecture by Belinskii, Khalatnikov, and Lifshitz that the
singularity in generic gravitational collapse is spacelike, local, and
oscillatory is explored analytically and numerically in spatially inhomogeneous
cosmological spacetimes. With a convenient choice of variables, it can be seen
analytically how nonlinear terms in Einstein's equations control the approach
to the singularity and cause oscillatory behavior. The analytic picture
requires the drastic assumption that each spatial point evolves toward the
singularity as an independent spatially homogeneous universe. In every case,
detailed numerical simulations of the full Einstein evolution equations support
this assumption.


title: Perturbations of Kerr-de Sitter Black Hole and Heun's Equations

abstract:
  It is well known that the perturbation equations of massless fields for the
Kerr-de Sitter geometry can be written in the form of separable equations. The
equations have five definite singularities so that the analysis has been
expected to be difficult. We show that these equations can be transformed to
Heun's equations, for which we are able to use known technique for the analysis
of the solutions. We reproduce results known previously for the Kerr geometry
and de Sitter geometry in the confluent limits of the Heun's functions. Our
analysis applies can be extended to Kerr-Newman-de Sitter geometry for massless
fields with spin 0 and 1/2.


title: The Generalized Thin-Sandwich Problem and its Local Solvability

abstract:
  We consider Einstein Gravity coupled to dynamical matter consisting of a
gauge field with any compact gauge group and minimally coupled scalar fields.
We investigate the conditions under which a free specification of a spatial
field configuration for the total system and its derivative with respect to
coordinate-time determines a solution to the field equations (generalized
thin-sandwich problem). Sufficient conditions for local solvability (in the
space of fields) are established.


title: Gravitational Collapse, Black Holes and Naked Singularities

abstract:
  This article gives an elementary review of gravitational collapse and the
cosmic censorship hypothesis. Known models of collapse resulting in the
formation of black holes and naked singularities are summarized. These models,
when taken together, suggest that the censorship hypothesis may not hold in
classical general relativity. The nature of the quantum processes that take
place near a naked singularity, and their possible implication for
observations, is briefly discussed.


title:
Can general-relativistic description of gravitation be considered
  complete?

abstract:
  The local galactic cluster, the Great attractor, embeds us in a dimensionless
gravitational potential of about - 3 x 10^{-5}. In the solar system this
potential is constant to about 1 part in 10^{11}. Consequently, planetary
orbits, which are determined by the gradient in the gravitational potential,
remain unaffected. However, this is not so for the recently introduced
flavor-oscillation clocks where the new redshift-inducing phases depend on the
gravitational potential itself. On these grounds, and by studying the
invariance properties of the gravitational phenomenon in the weak fields, we
argue that there exists an element of incompleteness in the
general-relativistic description of gravitation. An incompleteness-establishing
inequality is derived and an experiment is outlined to test the thesis
presented.


title: On Electrogravity Duality

abstract:
  By resolving the gravitational field into electric and magnetic parts, we
define an electrogravity duality transformation and discover an interesting
property of the field. Under the duality transformation a vacuum/flat spacetime
maps into the original spacetime with a topological defect of global
monopole/texture. The elctrogravity-duality is thus a topological defect
generating process. It turns out that all black hole solutions possess dual
solutions that imbibe a global monopole.


title:
Reply to `Comment on ``The influence of cosmological transitions on the
  evolution of density perturbations'' '

abstract:
  We reply to L.P. Grishchuk's comment (gr-qc/9801011) on our paper ``The
Influence of Cosmological Transitions on the Evolution of Density
Perturbations'' (Phys. Rev. D 57, 3302, 1998). We show that his points of
criticism are not correct.


title: 2D dilaton gravity made compact

abstract:
  We show that the equations of motion of two-dimensional dilaton gravity
conformally coupled to a scalar field can be reduced to a single non-linear
second-order partial differential equation when the coordinates are chosen to
coincide with the two scalar fields, the matter field $f$ and the dilaton
$\phi$, which are present in the theory. This result may help solve and
understand two- and higher-dimensional classical and quantum gravity.


title:
Naked singularity formation in the collapse of a spherical cloud of
  counterrotating particles

abstract:
  We investigate collapse of a spherical cloud of counter-rotating particles.
An explicit solution is given using an elliptic integral. If the specific
angular momentum $L(r)=O(r^2)$ at $r\to 0$, no central singularity occurs. With
$L(r)$ like that, there is a finite region around the center that bounces. On
the other hand, if the order of $L(r)$ is higher than that, a central
singularity occurs. In marginally bound collapse with $L(r)=4F(r)$, a naked
singularity occurs, where $F(r)$ is the Misner-Sharp mass. The solution for
this case is expressed by elementary functions. For $ 4 <L/F<\infty$ at
$r\to0$, there is a finite region around the center that bounces and a naked
singularity occurs. For $ 0 \le L/F< 4$ at $r\to0$, there is no such region.
The results suggests that rotation may play a crucial role on the final fate of
collapse.


title: Amplitude of superhorizon cosmological perturbations

abstract:
  We study the influence of reheating on super-horizon density perturbations
and gravitational waves. We correct wrong claims [L. P. Grishchuk Phys. Rev. D
50, 7154 (1994) and gr-qc/9801011] about the joining of perturbations at
cosmological transitions and about the quantization of cosmological
perturbations.


title:
Black holes and gravitational waves in concert - a probe of superstring
  cosmology

abstract:
  Two strands of observational gravitation, one the search for astrophysical
evidence of primordial black holes and the other the search for gravitational
waves, may combine to provide strong evidence in favour of cosmological models
based on superstring theory, the leading candidate for unifying gravity with
the other fundamental forces.


title: Classicality via hydrodynamics in quantum field theory

abstract:
  Motivated by the consistent histories approach to quantum mechanics, we
examine a simple model of hydrodynamic coarse-graining for a scalar field. It
consists in averaging the field over spatial regions of size L and constructing
the evolution equation for the coarse grained quantities, thus identifying
dissipation and noise.


title:
Wormholes, Gamma Ray Bursts and the Amount of Negative Mass in the
  Universe

abstract:
  In this essay, we assume that negative mass objects can exist in the
extragalactic space and analyze the consequences of their microlensing on light
from distant Active Galactic Nuclei. We find that such events have very similar
features to some observed Gamma Ray Bursts and use recent satellite data to set
an upper bound to the amount of negative mass in the universe.


title: Universe as a Phase Boundary in a Four-Dimensional Euclidean Space

abstract:
  It is proposed that space is a four-dimensional Euclidean space with
universal time. Originally this space was filled with a uniform substance,
pictured as a liquid, which at some time became supercooled. Our universe began
as a nucleation event initiating a liquid to solid transition. The universe we
inhabit and are directly aware of consists of only the three-dimensional
expanding phase boundary. Random energy transfers to the boundary from thermal
fluctuations in the adjacent bulk phases are interpreted by us as quantum
fluctuations. Fermionic matter is modeled as screw dislocations; gauge bosons
as phonons. Minkowski space emerges dynamically through redefining local time
to be proportional to the spatial coordinate perpendicular to the boundary.
Other features include a geometrical quantum gravitational theory, and an
explanation of quantum measurement.


title: A remark on Ma's "Cosmic gravitational background radiation"

abstract:
  The calculations of Guang-Wen Ma's recent Letter [Phys.Lett. A239, (1998)
209] contain an easily detectable error which makes his conclusions irrelevant.


title: Chaos in pp-wave spacetimes

abstract:
  We demonstrate chaotic behavior of timelike, null and spacelike geodesics in
non-homogeneous vacuum pp-wave solutions. This seems to be the first known
example of a chaotic motion in exact radiative spacetime.


title: TransPlanckian Particles and the Quantization of Time

abstract:
  Trans-Planckian particles are elementary particles accelerated such that
their energies surpass the Planck value. There are several reasons to believe
that trans-Planckian particles do not represent independent degrees of freedom
in Hilbert space, but they are controlled by the cis-Planckian particles. A way
to learn more about the mechanisms at work here, is to study black hole
horizons, starting from the scattering matrix Ansatz.
  By compactifying one of the three physical spacial dimensions, the scattering
matrix Ansatz can be exploited more efficiently than before. The algebra of
operators on a black hole horizon allows for a few distinct representations. It
is found that this horizon can be seen as being built up from string bits with
unit lengths, each of which being described by a representation of the SO(2,1)
Lorentz group. We then demonstrate how the holographic principle works for this
case, by constructing the operators corresponding to a field in space-time. The
parameter t turns out to be quantized in Planckian units, divided by the period
R of the compactified dimension.


title: The gravitational Vavilov-Cherenkov effect

abstract:
  In this essay we show that an uncharged black-hole moving superluminally in a
transparent dielectric medium violates Hawking's area theorem. The violation is
overcome through the emission of radiation. Since modes cannot emerge from the
black hole itself, this radiation must originate from a collective effect in
the medium, in complete analogy with the Vavilov-Cherenkov effect. However,
because the black-hole is uncharged, the emission mechanism must be different.
We discuss the physical origin of the effect and obtain a Newtonian estimative.
Then we obtain the appropriate equations in the relativistic case and show that
the field which is radiated away is a combination of gravitational and
electromagnetic degrees of freedom. Possible astrophysical relevance for the
detection of primordial black-holes and binary systems is discussed.


title: Relativistic and Non-relativistic Equations of Motion

abstract:
  It is shown that any second order dynamic equation on a configuration space
$X$ of non-relativistic time-dependent mechanics can be seen as a geodesic
equation with respect to some (non-linear) connection on the tangent bundle
$TX\to X$ of relativistic velocities. Using this fact, the relationship between
relativistic and non-relativistic equations of motion is studied.


title: Critical energy flux and mass in solvable theories of 2d dilaton gravity

abstract:
  In this paper we address the issue of determining the semiclassical threshold
for black hole formation in the context of a one-parameter family of theories
which continuously interpolates between the RST and BPP models. We find that
the results depend significantly on the initial static configuration of the
spacetime geometry before the influx of matter is turned on. In some cases
there is a critical energy density, given by the Hawking rate of evaporation,
as well as a critical mass $m_{cr}$ (eventually vanishing). In others there is
neither $m_{cr}$ nor a critical flux.


title: Proper Time Dynamics in General Relativity and Conformal Unified Theory

abstract:
  The paper is devoted to the description a measurable time-interval (``proper
time'') in the Hamiltonian version of general relativity with the Dirac-ADM
metric. To separate the dynamical parameter of evolution from the space metric
we use the Lichnerowicz conformally invariant variables. In terms of these
variables GR is equivalent to the conformally invariant
Penrose-Chernicov-Tagirov theory of a scalar field the role of which is played
by the scale factor multiplied on the Planck constant. Identification of this
scalar field with the modulus of the Higgs field in the standard model of
electroweak and strong interactions allows us to formulate an example of
conformally invariant unified theory where the vacuum averaging of the scalar
field is determined by cosmological integrals of motion of the Universe
evolution.


title: Dealing with the center and boundary problems in 1D Numerical Relativity

abstract:
  Instabilities in finite difference codes due to the singularity of spherical
coordinates at the center are studied. In typical Numerical Relativity
applications, standard regularization techniques by themselves do not ensure
long term stability. A proposal to remedy that problem is presented, which
takes advantage of redundant quantities introduced in recent hyperbolic
formulations of Einstein's evolution equations. The results are discussed
through the example case of a boson star, where a significant improvement in
the implementation of boundary conditions is also presented.


title: The stability of cosmological scaling solutions

abstract:
  We study the stability of cosmological scaling solutions within the class of
spatially homogeneous cosmological models with a perfect fluid subject to the
equation of state p_gamma=(gamma-1) rho_gamma (where gamma is a constant
satisfying 0 < gamma < 2) and a scalar field with an exponential potential. The
scaling solutions, which are spatially flat isotropic models in which the
scalar field energy density tracks that of the perfect fluid, are of physical
interest. For example, in these models a significant fraction of the current
energy density of the Universe may be contained in the scalar field whose
dynamical effects mimic cold dark matter. It is known that the scaling
solutions are late-time attractors (i.e., stable) in the subclass of flat
isotropic models. We find that the scaling solutions are stable (to shear and
curvature perturbations) in generic anisotropic Bianchi models when gamma <
2/3. However, when gamma > 2/3, and particularly for realistic matter with
gamma >= 1, the scaling solutions are unstable; essentially they are unstable
to curvature perturbations, although they are stable to shear perturbations. We
briefly discuss the physical consequences of these results.


title: An Implication of Ether Drift

abstract:
  The experimental results of the two-photon absorption(TPA) and
M\"{o}ssbauer-rotor(MR) for testing the isotropy of the speed of light are
explained in an ether drift model with a drift velocity of $\sim 10^{-3}c$.
Further tests of the ether drift assumption are suggested.


title: Quasi-Newtonian dust cosmologies

abstract:
  Exact dynamical equations for a generic dust matter source field in a
cosmological context are formulated with respect to a non-comoving
Newtonian-like timelike reference congruence and investigated for internal
consistency. On the basis of a lapse function $N$ (the relativistic
acceleration scalar potential) which evolves along the reference congruence
according to $\dot{N} = \alpha \Theta N$ ($\alpha = {const}$), we find that
consistency of the quasi-Newtonian dynamical equations is not attained at the
first derivative level. We then proceed to show that a self-consistent set can
be obtained by linearising the dynamical equations about a (non-comoving) FLRW
background. In this case, on properly accounting for the first-order momentum
density relating to the non-relativistic peculiar motion of the matter,
additional source terms arise in the evolution and constraint equations
describing small-amplitude energy density fluctuations that do not appear in
similar gravitational instability scenarios in the standard literature.


title:
Normal frames and the validity of the equivalence principle. III. The
  case along smooth maps with separable points of self-intersection

abstract:
  The equivalence principle is treated on a mathematically rigorous base on
sufficiently general subsets of a differentiable manifold. This is carried out
using the basis of derivations of the tensor algebra over that manifold.
Necessary and/or sufficient conditions of existence, uniqueness, and
holonomicity of these bases in which the components of the derivations of the
tensor algebra over it vanish on these subsets, are studied. The linear
connections are considered in this context. It is shown that the equivalence
principle is identically valid at any point, and along any path, in every
gravitational theory based on linear connections. On higher dimensional
submanifolds it may be valid only in certain exceptional cases.


title: Speed of light on rotating platforms

abstract:
  It is often taken for granted that on board a rotating disk it is possible to
operate a \QTR{it}{global}3+1 splitting of space-time, such that both lengths
and time intervals are \QTR{it}{uniquely} defined in terms of measurements
performed by real rods and real clocks at rest on the platform. This paper
shows that this assumption, although widespread and apparently trivial, leads
to an anisotropy of the velocity of two light beams travelling in opposite
directions along the rim of the disk; which in turn implies some recently
pointed out paradoxical consequences undermining the self-consistency of the
Special Theory of Relativity (SRT). A correct application of the SRT solves the
problem and recovers complete internal consistency for the theory. As an
immediate consequence, it is shown that the Sagnac effect only depends on the
non homogeneity of time on the platform and has nothing to do with any
anisotropy of the speed of light along the rim of the disk, contrary to an
incorrect but widely supported idea.


title: Classification of Inflationary Potentials

abstract:
  Brans-Dicke gravity is remarkable not only in that General Relativity and
Mach's Principle find a common enlarged scenario where they are mutually
consistent, but also in that it provides a very interesting quantum
cosmological model within the inflationary paradigm. The interplay between the
Brans-Dicke scalar $\Phi$ and the inflaton field $\sigma$ plays an important
r\^{o}le during the course of inflation, and although the dynamics as such is
governed by the potential, the onset and the end of inflation are determined by
the values of both fields jointly. The relative position of the beginning-- and
end-of-inflation curves (BoI and EoI respectively) is the most relevant factor
in determining the resulting quantum cosmological scenario. The classification
of potentials that is given in this paper is based on the criterion of whether
the BoI and EoI boundaries enclose a finite or infinite area in the
($\sigma$,$\Phi$) plane where inflation takes place. It is shown that this
qualitative classification distinguishes two classes of potentials that yield
very different cosmologies and it is argued that only those theories in which
BoI and EoI enclose a finite area in the ($\sigma$,$\Phi$) plane are compatible
with our observable universe.


title:
Local $\zeta$-function techniques vs point-splitting procedure: a few
  rigorous results

abstract:
  Some general properties of local $\zeta$-function procedures to renormalize
some quantities in $D$-dimensional (Euclidean) Quantum Field Theory in curved
background are rigorously discussed for positive scalar operators $-\Delta +
V(x)$ in general closed $D$-manifolds, and a few comments are given for
nonclosed manifolds too. A general comparison is carried out with respect to
the more known point-splitting procedure concerning the effective Lagrangian
and the field fluctuations. It is proven that, for $D>1$, the local
$\zeta$-function and point-splitting approaches lead essentially to the same
results apart from some differences in the subtraction procedure of the
Hadamard divergences. It is found that the $\zeta$ function procedure picks out
a particular term $w_0(x,y)$ in the Hadamard expansion. Also the presence of an
untrivial kernel of the operator $-\Delta +V(x)$ may produce some differences
between the two analyzed approaches. Finally, a formal identity concerning the
field fluctuations, used by physicists, is discussed and proven within the
local $\zeta$-function approach. This is done also to reply to recent criticism
against $\zeta$-function techniques.


title: Non-local gravitational effective action and particle production

abstract:
  We study the effective action for gravity obtained after the integration of
scalar matter fields, using the local momentum representation based on the
Riemann normal coordinates expansion. By considering this expansion around
different space-time points, we also compute the non-local terms together with
the more usual divergent ones. We discuss the applicability of our results to
the calculation of particle production rates in cosmological backgrounds and
compare this method with the traditional Bogolyubov transformations.


title: The gravitoelectromagnetic stress-energy tensor

abstract:
  We study the pseudo-local gravitoelectromagnetic stress-energy tensor for an
arbitrary gravitational field within the framework of general relativity. It is
shown that there exists a current of gravitational energy around a rotating
mass. This gravitational analog of the Poynting flux is evaluated for certain
classes of observers in the Kerr field.


title: Conserved Quantities for Polyhomogeneous Space-Times

abstract:
  The existence of conserved quantities with a structure similar to the
Newman-Penrose quantities in a polyhomogeneous space-time is addressed. The
most general form for the initial data formally consistent with the
polyhomogeneous setting is found. The subsequent study is done for those
polyhomogeneous space-times where the leading term of the shear contains no
logarithmic terms. It is found that for these space-times the original NP
quantities cease to be constants, but it is still possible to construct a set
of other 10 quantities that are constant. From these quantities it is possible
to obtain as a particular case a conserved quantity found by Chrusciel et al.


title: The Quantum Stress-Tensor in Self-Similar Spherical Dust Collapse

abstract:
  We calculate the quantum stress tensor for a massless scalar field in the 2-d
self-similar spherical dust collapse model which admits a naked singularity. We
find that the outgoing radiation flux diverges on the Cauchy horizon. This may
have two consequences. The resultant back reaction may prevent the naked
singularity from forming, thus preserving cosmic censorship through quantum
effects. The divergent flux may lead to an observable signature differentiating
naked singularities from black holes in astrophysical observations.


title: Probing foamy spacetime with Variational Methods

abstract:
  A one-loop correction of the quasilocal energy in the Schwarzschild
background, with flat space as a reference metric, is performed by means of a
variational procedure in the Hamiltonian framework. We examine the graviton
sector in momentum space, in the lowest possible state. An application to the
black hole pair creation via the Casimir energy is presented. Implications on
the foam-like scenario are discussed.


title: Radiation from a Uniformly Accelerated Charge

abstract:
  The emission of radiation by a uniformly accelerated charge is analyzed.
According to the standard approach, a radiation is observed whenever there is a
relative acceleraion between the charge and the observer. Analyzing
difficulties that arose in the standard approach, we propose that a radaition
is created whenever a relative acceleration between the charge and its own
electric field exists. The electric field induced by a charge accelerated by an
external (nongravitational) force, is not accelerated with the charge. Hence
the electric field is curved in the instantanous rest frame of the accelerated
charge. This curvature gives rise to a stress force, and the work done to
overcome the stress force is the source of the energy carried by the radiation.
In this way, the "energy balance paradox" finds its solution.


title: Smooth sandwich gravitational waves

abstract:
  Gravitational waves which are smooth and contain two asymptotically flat
regions are constructed from the homogeneous pp-waves vacuum solution. Motion
of free test particles is calculated explicitly and the limit to an impulsive
wave is also considered.


title:
Three-dimensional simulations of distorted black holes. I. Comparison
  with axisymmetric results

abstract:
  We consider the numerical evolution of black hole initial data sets,
consisting of single black holes distorted by strong gravitational waves, with
a full 3D, nonlinear evolution code. These data sets mimic the late stages of
coalescing black holes. We compare various aspects of the evolution of
axisymmetric initial data sets, obtained with this 3D code, to results obtained
from a well established axisymmetric code. In both codes we examine and compare
the behavior of metric functions, apparent horizon properties, and waveforms,
and show that these dynamic black holes can be accurately evolved in 3D. In
particular we show that with present computational resources and techniques,
the process of excitation and ringdown of the black hole can be evolved, and
one can now extract accurately the gravitational waves emitted from the 3D
Cartesian metric functions, even when they carry away only a small fraction
($<< 1%$) of the rest mass energy of the system. Waveforms for both the
$\ell=2$ and the much more difficult $\ell=4$ and $\ell=6$ modes are computed
and compared with axisymmetric calculations. In addition to exploring the
physics of distorted black hole data sets, and showing the extent to which the
waves can be accurately extracted, these results also provide important
testbeds for all fully nonlinear numerical codes designed to evolve black hole
spacetimes in 3D, whether they use singularity avoiding slicings, apparent
horizon boundary conditions, or other evolution methods.


title:
Initial data for gravity coupled to scalar, electromagnetic and
  Yang-Mills fields

abstract:
  We give ansatze for solving classically the initial value constraints of
general relativity minimally coupled to a scalar field, electromagnetism or
Yang-Mills theory. The results include both time-symmetric and asymmetric data.
The time-asymmetric examples are used to test Penrose's cosmic censorship
inequality. We find that the inequality can be violated if only the weak energy
condition holds.


title: Instantons and unitarity in quantum cosmology with fixed four-volume

abstract:
  We find a number of complex solutions of the Einstein equations in the
so-called unimodular version of general relativity, and we interpret them as
saddle points yielding estimates of a gravitational path integral over a space
of almost everywhere Lorentzian metrics on a spacetime manifold with topology
of the "no-boundary" type. In this setting, the compatibility of the
no-boundary initial condition with the definability of the quantum measure
reduces reduces to the normalizability and unitary evolution of the no-boundary
wave function \psi. We consider the spacetime topologies R^4 and RP^4 # R^4
within a Taub minisuperspace model with spatial topology S^3, and the spacetime
topology R^2 x T^2 within a Bianchi type I minisuperspace model with spatial
topology T^3. In each case there exists exactly one complex saddle point (or
combination of saddle points) that yields a wave function compatible with
normalizability and unitary evolution. The existence of such saddle points
tends to bear out the suggestion that the unimodular theory is less divergent
than traditional Einstein gravity. In the Bianchi type I case, the
distinguished complex solution is approximately real and Lorentzian at late
times, and appears to describe an explosive expansion from zero size at T=0.
(In the Taub cases, in contrast, the only complex solution with nearly
Lorentzian late-time behavior yields a wave function that is normalizable but
evolves nonunitarily, with the total probability increasing exponentially in
the unimodular "time" in a manner that suggests a continuous creation of new
universes at zero volume.) The issue of the stability of these results upon the
inclusion of more degrees of freedom is raised.


title:
Stability under radiation reaction of circular equatorial orbits around
  Kerr black holes

abstract:
  We examine the evolution, under gravitational radiation reaction, of slightly
eccentric equatorial orbits of point particles around Kerr black holes. Our
method involves numerical integration of the Sasaki-Nakamura equation. It is
discovered that such orbits decrease in eccentricity throughout most of the
inspiral, until shortly before the innermost stable circular orbit (ISCO), when
a critical radius $r_{\text{crit}}$ is reached beyond which the inspiralling
orbits increase in eccentricity. It is shown that the number of orbits
remaining in this last (eccentricity increasing) phase of the inspiral is an
order of magnitude less for prograde orbits around rapidly spinning black holes
than for retrograde orbits. In the extreme limit of a Kerr black hole with spin
parameter $a=1$, this critical radius descends into the ``throat'' of the black
hole.


title: Addendum to Paper "Closed Spaces in Cosmology"

abstract:
  A few corrections and comments are made upon a previously published paper by
the author (Gen. Rel. Gravit. 24, 199 (1992)), on the subject of cosmological
models with compact spatial sections.


title: Flux Tube Solution in 5D Kaluza-Klein Theory

abstract:
  Spherically symmetric, vacuum solutions in 5D and 7D Kaluza-Klein theory are
obtained. These solutions are flux tubes with constant cross-sectional size,
located between (+) and (-) Kaluza-Klein's ``electrical'' and ``magnetic''
charges disposed respectively at $\pm\infty$ and filled by constant
Kaluza-Klein ``electrical'' and ``magnetic'' fields. These objects are
surprisingly similar to the flux tubes which forms between two monopoles in
Type-II superconductors and also the hypothesized color field flux tube that is
thought to form between two quarks in the QCD vacuum.


title: Path integral for the Hilbert-Palatini and Ashtekar gravity

abstract:
  To write down a path integral for the Ashtekar gravity one must solve three
fundamental problems. First, one must understand rules of complex contour
functional integration with holomorphic action. Second, one should find which
gauges are compatible with reality conditions. Third, one should evaluate the
Faddeev-Popov determinant produced by these conditions. In the present paper we
derive the BRST path integral for the Hilbert-Palatini gravity. We show, that
for certain class of gauge conditions this path integral can be re-written in
terms of the Ashtekar variables. Reality conditions define contours of
integration. For our class of gauges all ghost terms coincide with what one
could write naively just ignoring any Jacobian factors arising from the reality
conditions.


title: On Nonlinear $\sigma$-Models arizing in (Super-)Gravity

abstract:
  In a previous paper with Gibbons [CMP 120 (1987) 295] we derived a list of
three dimensional symmetric space $\sigma$-model obtained by dimensional
reduction of a class of four dimensional gravity theories with abelian gauge
fields and scalars. Here we give a detailed analysis of their group theoretical
structure leading to an abstract parametrization in terms of `triangular' group
elements. This allows for a uniform treatment of all these models. As an
interesting application we give a simple derivation of a `Quadratic Mass
Formula' for strictly stationary black holes.


title: Integrability in tetrad formalisms and conservation in cosmology

abstract:
  Integrability in general tetrad formalisms is reviewed, following and
clarifying work of Papapetrou and Edgar. The integrability conditions are
(combinations of) the Bianchi equations and their consequences. The
introduction of additional constraints is considered. Recent results on the
conservation of constraints in the 1+3 covariant formulation of cosmology are
shown to follow from the Bianchi equations


title: A New Approach to Black Hole Microstates

abstract:
  If one encodes the gravitational degrees of freedom in an orthonormal frame
field there is a very natural first order action one can write down (which in
four dimensions is known as the Goldberg action). In this essay we will show
that this action contains a boundary action for certain microscopic degrees of
freedom living at the horizon of a black hole, and argue that these degrees of
freedom hold great promise for explaining the microstates responsible for black
hole entropy, in any number of spacetime dimensions. This approach faces many
interesting challenges, both technical and conceptual.


title:
Hamiltonian Formulation and Exact Solutions of Bianchi type-I Model in
  Conformal Gravity

abstract:
  We develop a Hamiltonian formulation of Bianchi type-I cosmological model in
conformal gravity, i.e. the theory described by a Lagrangian which involves the
quadratic curvature invariant constructed from the Weyl tensor, in four
dimensions. We derive the explicit forms of the super-Hamiltonian and the
constraint expressing the conformal invariance of the theory, and we write down
the system of canonical equations. To seek out exact solutions to this system
we add extra constraints on the canonical variables and we go through a global
involution algorithm that possibly leads to the closure of the constraint
algebra. This enables us to extract all possible particular solutions that may
be written in closed analytical form. On the other hand, probing the local
analytical structure we show that the system does not possess the Painleve
property (presence of movable logarithms) and that it is therefore not
integrable. We stress that there is a very fruitful interplay of local
integrability-related methods such as the Painleve test and global techniques
such as the involution algorithm. Strictly speaking, we demonstrate that the
global involution algorithm has proven to be exhaustive in the search for exact
solutions. The conformal relationship of the solutions, or absence thereof,
with Einstein spaces is highlighted.


title:
Gravity, Cosmology and Particle Physics without the Cosmological
  Constant Problem

abstract:
  This essay elucidates recent achievements of the "nongravitating vacuum
energy" (NGVE) theory" which has the feature that a shift of the Lagrangian
density by a constant does not affect dynamics. In the first order formalism, a
constraint appears that enforces the vanishing of the cosmological constant
\Lambda. Standard dynamics of gauge unified theories (including fermions) and
their SSB appear if a four index field strength condensate is present. At a
vacuum state there is exact balance to zero of the gauge fields condensate and
the original scalar fields potential. As a result it is possible to combine the
solution of the \Lambda problem with inflation and transition to a \Lambda =0
phase without fine tuning after a reheating period. The model opens new
possibilities for a solution of the hierarchy problem.


title:
Application of Colombeau's Generalized Functions to Cosmological Models
  with Signature Change

abstract:
  Colombeau's generalized functions are used to adapt the distributional
approach to singular hypersurfaces in general relativity with signature change.
Equations governing the dynamics of singular hypersurface is obtained and it is
shown that the stress-energy tensor of the surface can be non-vanishing.


title:
Quasi-normal modes of rotating relativistic stars - neutral modes for
  realistic equations of state

abstract:
  We compute zero-frequency (neutral) quasi-normal f-modes of fully
relativistic and rapidly rotating neutron stars, using several realistic
equations of state (EOSs) for neutron star matter. The zero-frequency modes
signal the onset of the gravitational radiation-driven instability. We find
that the l=m=2 (bar) f-mode is unstable for stars with gravitational mass as
low as 1.0 - 1.2 M_\odot, depending on the EOS. For 1.4 M_\odot neutron stars,
the bar mode becomes unstable at 83 % - 93 % of the maximum allowed rotation
rate. For a wide range of EOSs, the bar mode becomes unstable at a ratio of
rotational to gravitational energies T/W \sim 0.07-0.09 for 1.4 M_\odot stars
and T/W \sim 0.06 for maximum mass stars. This is to be contrasted with the
Newtonian value of T/W \sim 0.14. We construct the following empirical formula
for the critical value of T/W for the bar mode,
  (T/W)_2 = 0.115 - 0.048 M / M_{max}^{sph}, which is insensitive to the EOS to
within 4 - 6 %. This formula yields an estimate for the neutral mode sequence
of the bar mode as a function only of the star's mass, M, given the maximum
allowed mass, M_{max}^{sph}, of a nonrotating neutron star. The recent
discovery of the fast millisecond pulsar in the supernova remnant N157B,
supports the suggestion that a fraction of proto-neutron stars are born in a
supernova collapse with very large initial angular momentum. Thus, in a
fraction of newly born neutron stars the instability is a promising source of
continuous gravitational waves. It could also play a major role in the
rotational evolution (through the emission of angular momentum) of merged
binary neutron stars, if their post-merger angular momentum exceeds the maximum
allowed to form a Kerr black hole.


title:
A rigorous solution concept for geodesic and geodesic deviation
  equations in impulsive gravitational waves

abstract:
  The geodesic as well as the geodesic deviation equation for impulsive
gravitational waves involve highly singular products of distributions
$(\theta\de$, $\theta^2\de$, $\de^2$). A solution concept for these equations
based on embedding the distributional metric into the Colombeau algebra of
generalized functions is presented. Using a universal regularization procedure
we prove existence and uniqueness results and calculate the distributional
limits of these solutions explicitly. The obtained limits are regularization
independent and display the physically expected behavior.


title:
Scalar Field with Induced Nonlinearity: Regular Solutions and their
  Stability

abstract:
  Exact particle-like static, spherically and/or cylindrically symmetric
solutions to the equations of interacting scalar and electromagnetic field
system have been obtained within the scope of general relativity. In
particular, we considered Freedman-Robertson-Walker (FRW) space-time as an
external homogenous and isotropic gravitational field whereas the inhomogenous
and isotropic Universe is given by the G$\ddot o$del model. The solutions
obtained have been thoroughly studied for different types of interaction term.
It has been shown that in FRW space-time equations with different interaction
terms may have stable solutions while within the scope of G$\ddot o$del model
only the droplet-like configurations may be stable, if they are located in the
region where $g^{00}>0$.


title: Einstein-Podolski-Rosen Experiment from Noncommutative Quantum Gravity

abstract:
  It is shown that experiments of the Einstein-Podolski-Rosen type are the
natural consequence of the groupoid approach to noncommutative unification of
general relativity and quantum mechanics. The geometry of this model is
determined by the noncommutative algebra of complex valued, compactly supported
functions (with convolution as multiplication) on the groupoid G = E x D. In
the model considered in the present paper E is the total space of the frame
bundle over space-time, and D is the Lorentz group. Correlations of the EPR
type should be regarded as remnants of the totally non-local physics below the
Planck threshold which is modelled by a noncommutative geometry.


title: Black holes, brick walls and the Boulware state

abstract:
  The brick-wall model seeks to explain the Bekenstein-Hawking entropy as a
wall-contribution to the thermal energy of ambient quantum fields raised to the
Hawking temperature. Reservations have been expressed concerning the
self-consistency of this model. For example, it predicts large thermal energy
densities near the wall, producing a substantial mass-correction and,
presumably, a large gravitational back-reaction. We re-examine this model and
conclude that these reservations are unfounded once the ground state---the
Boulware state---is correctly identified. We argue that the brick-wall model
and the Gibbons-Hawking instanton (which ascribes a topological origin to the
Bekenstein-Hawking entropy) are mutually exclusive, alternative descriptions
(complementary in the sense of Bohr) of the same physics.


title:
Stable central structures in topologically nontrivial Anti-de Sitter
  spacetimes

abstract:
  We investigate stable central structures in multiply-connected, anti de
Sitter spacetimes with spherical, planar and hyperbolic geometries. We obtain
an exact solution for the pressure in terms of the radius when the density is
constant. We find that, apart from the usual simply-connected spherically
symmetric star with a well-behaved metric at $r=0$, the only solutions with
non-singular pressure and density have a wormhole topology. However these
wormhole solutions must be composed of matter which violates the weak energy
condition. Admitting this type of matter, we obtain a structure which is
maintained via a balance between its cohesive tension and its repulsive
negative matter density. If the tension is insufficiently large, this structure
can collapse to a black hole of negative mass.


title: Evolution of Distorted Black Holes: A Perturbative Approach

abstract:
  We consider a series of distorted black hole initial data sets, and develop
techniques to evolve them using the linearized equations of motion for the
gravitational wave perturbations on a Schwarzschild background. We apply this
to 2D and 3D distorted black hole spacetimes. In 2D, waveforms for different
modes of the radiation are presented, comparing full nonlinear evolutions for
different axisymmetric l-modes with perturbative evolutions. We show how
axisymmetric black hole codes solving the full, nonlinear Einstein equations
are capable of very accurate evolutions, and also how these techniques aid in
studying nonlinear effects. In 3D we show how the initial data for the
perturbation equations can be computed, and we compare with analytic solutions
given from a perturbative expansion of the initial value problem. In addition
to exploring the physics of these distorted black hole data sets, in particular
allowing an exploration of linear, nonlinear, and mode mixing effects, this
approach provides an important testbed for any fully nonlinear numerical code
designed to evolve black hole spacetimes in 2D or 3D.


title: Complex Instantons and Charged Rotating Black Hole Pair Creation

abstract:
  We consider the general process of pair-creation of charged rotating black
holes. We find that instantons which describe this process are necessarily
complex due to regularity requirements. However their associated probabilities
are real, and fully consistent with the interpretation that the entropy of a
charged rotating black hole is the logarithm of the number of its quantum
states.


title: Gravitational waves in a stringlike fluid cosmology

abstract:
  The coupling of a stringlike fluid with ordinary matter and gravity may lead
to a closed Universe with the dynamic of an open one. This can provide an
alternative solution for the age and horizon problems. A study of density
perturbations of the stringlike fluid indicates the existence of instabilities
in the small wavelength limit when it is employed a hydrodynamic approach.
Here, we extend this study to gravitational waves, where the hydrodynamical
approach plays a less important role, and we argue that traces of the existence
of this fluid must be present in the anisotropies of the cosmic background
radiation.


title: Initial data for superposed rotating black holes

abstract:
  The standard approach to initial data for both analytic and numerical
computations of black hole collisions has been to use conformally-flat initial
geometry. Among other advantages, this choice allows the simple superposition
of holes with arbitrary mass, location and spin. The conformally flat
restriction, however, is inappropriate to the study of Kerr holes, for which
the standard constant-time slice is not conformally flat. Here we point out
that for axisymmetric arrangements of rotating holes, a nonconformally flat
form of the 3-geometry can be chosen which allows fairly simple superposition
of Kerr holes with arbitrary mass and spin. We present initial data solutions
representing locally Kerr holes at large separation, and representing rotating
holes close enough so that outside a common horizon the spacetime geometry is a
perturbation of a single Kerr hole.


title:
Seismic gravity-gradient noise in interferometric gravitational-wave
  detectors

abstract:
  When ambient seismic waves pass near an interferometric gravitational-wave
detector, they induce density perturbations in the earth which produce
fluctuating gravitational forces on the interferometer's test masses. These
forces mimic a stochastic background of gravitational waves and thus constitute
noise. We compute this noise using the theory of multimode Rayleigh and Love
waves propagating in a layered medium that approximates the geological strata
at the LIGO sites. We characterize the noise by a transfer function $T(f)
\equiv \tilde x(f)/\tilde W(f)$ from the spectrum of direction averaged ground
motion $\tilde W(f)$ to the spectrum of test mass motion $\tilde x(f) = L\tilde
h(f)$ (where $L$ is the length of the interferometer's arms, and $\tilde h(f)$
is the spectrum of gravitational-wave noise). This paper's primary foci are (i)
a study of how $T(f)$ depends on the various seismic modes; (ii) an attempt to
estimate which modes are excited at the LIGO sites at quiet and noisy times;
and (iii) a corresponding estimate of the seismic gravity-gradient noise level.
At quiet times the noise is below the benchmark noise level of ``advanced LIGO
interferometers'' (although not by much near 10 Hz); it may significantly
exceed this level at noisy times. The lower edge of our quiet-time noise is a
limit beyond which there is little gain from further improvements in vibration
isolation and thermal noise, unless one also reduces seismic gravity-gradient
noise. Two methods of reduction are discussed: monitoring the earth's density
perturbations, computing their gravitational forces, and correcting the data
for those forces; and constructing narrow moats around the interferometers'
test masses to shield out the fundamental-mode Rayleigh waves, which we suspect
dominate at quiet times.


title: General relativistic corrections to the Sagnac effect

abstract:
  The difference in travel time of corotating and counter-rotating light waves
in the field of a central massive and spinning body is studied. The corrections
to the special relativistic formula are worked out in a Kerr field. Estimation
of numeric values for the Earth and satellites in orbit around it show that a
direct measurement is in the order of concrete possibilities.


title: U(N)-monopoles on Kerr black hole and its entropy

abstract:
  We describe U(N)-monopoles (N > 1) on Kerr black holes by the parameters of
the moduli space of holomorphic vector U(N)-bundles over two-sphere with the
help of the Grothendieck splitting theorem. For N = 2,3 we obtain this
description in an explicit form as well as the estimates for the corresponding
monopole masses. This gives a possibility to adduce some reasonings in favour
of existence of both a fine structure for Kerr black holes and the statistical
ensemble tied with it which might generate the Kerr black hole entropy.


title: Gravitational waves from coalescing binaries and Doppler experiments

abstract:
  Doppler tracking of interplanetary spacecraft provides the only method
presently available for broad-band searches of low frequency gravitational
waves. The instruments have a peak sensitivity around the reciprocal of the
round-trip light-time T of the radio link connecting the Earth to the
space-probe and therefore are particularly suitable to search for coalescing
binaries containing massive black holes in galactic nuclei. A number of Doppler
experiments -- the most recent involving the probes ULYSSES, GALILEO and MARS
OBSERVER -- have been carried out so far; moreover, in 2002-2004 the CASSINI
spacecraft will perform three 40 days data acquisition runs with expected
sensitivity about twenty times better than that achieved so far. Central aims
of this paper are: (i) to explore, as a function of the relevant instrumental
and astrophysical parameters, the Doppler output produced by in-spiral signals
-- sinusoids of increasing frequency and amplitude (the so-called chirp); (ii)
to identify the most important parameter regions where to concentrate intense
and dedicated data analysis; (iii) to analyze the all-sky and all-frequency
sensitivity of the CASSINI's experiments, with particular emphasis on possible
astrophysical targets, such as our Galactic Centre and the Virgo Cluster.


title:
Neutron star transition to strong-scalar-field state in tensor scalar
  gravity

abstract:
  Spherical neutron star models are studied within tensor-scalar theories of
gravity. Particularly, it is shown that, under some conditions on the second
derivative of the coupling function and on star's mass, for a given star there
exist two strong-scalar-field solutions as well as the usual weak-field one.
This last solution happens to be unstable and a star, becoming massive enough
to allow for all three solutions, evolves to reach one of the strong field
configurations. This transition is dynamically computed and it appears that the
star radiates away the difference in energy between both states (a few $10^{-3}
M_\odot c^2$) as gravitational radiation. Since part of the energy ($\sim
10^{-5} M_\odot c^2$) is injected into the star as kinetic energy, the velocity
of star's surface can reach up to $10^{-2} c$. The waveform of this monopolar
radiation is shown as well as the oscillations undergone by the star. These
oscillations are also studied within the slowly-rotating approximation, in
order to estimate an order of magnitude of the resulting quadrupolar radiation.


title: String Cosmology and Chaos

abstract:
  We investigate Bianchi type IX ''Mixmaster'' universes within the framework
of the low-energy tree-level effective action for string theory, which (when
the ''stringy'' 2-form axion potential vanishes) is formally the same as the
Brans-Dicke action with $\omega =-1$. We show that, unlike the case of general
relativity in vacuum, there is no Mixmaster chaos in these string cosmologies.
In the Einstein frame an infinite sequence of chaotic oscillations of the scale
factors on approach to the initial singularity is impossible, as it was in
general relativistic Mixmaster universes in the presence of stiff -fluid matter
(or a massless scalar field). A finite sequence of oscillations of the scale
factors approximated by Kasner metrics is possible, but it always ceases when
all expansion rates become positive. In the string frame the evolution through
Kasner epochs changes to a new form which reflects the duality symmetry of the
theory. Again, we show that chaotic oscillations must end after a finite time.
The need for duality symmetry appears to be incompatible with the presence of
chaotic behaviour as $t\to 0$. We obtain our results using the Hamiltonian
qualitative cosmological picture for Mixmaster models. We mention possible
relations of this picture to diffeomorphism-independent methods of measuring
chaos in general relativity. Finally, we discuss the effect of inhomogeneities
and higher dimensions on the possible emergence of chaos within the string
cosmology.


title: Relativistic models for Superconducting-Superfluid Mixtures

abstract:
  The material below the crust of a neutron star is understood to be
describable in terms of three principal independently moving constituents,
identifiable as neutrons, protons, and electrons, of which the first two are
believed to form mutually coupled bosonic condensates. The large scale
comportment of such a system will be that of a positively charged
superconducting superfluid in a negatively charged ``normal'' fluid background.
As a contribution to the development of the theory of such a system, the
present work shows how, subject to neglect of dissipative effects, it is
possible to set up an elegant category of simplified but fully relativistic
three-constituent superconducting superfluid models whose purpose is to provide
realistic approximations for cases in which a strictly conservative treatment
is sufficient. A "mesoscopic" model, describing the fluid between the vortices,
is constructed, as well as a "macroscopic" model taking into account the
average effect of quantised vortices.


title: Light-like Signals in General relativity and Cosmology

abstract:
  The modelling of light-like signals in General Relativity taking the form of
impulsive gravitational waves and light-like shells of matter is examined.
Systematic deductions from the Bianchi identities are made. These are based
upon Penrose's hierarchical classification of the geometry induced on the null
hypersurface history of the surface by its imbedding in the space-times to the
future and to the past of it. The signals are not confined to propagate in a
vacuum and thus their interaction with matter (a burst of radiation propagating
through a cosmic fluid, for example) is also studied. Results are accompanied
by illustrative examples using cosmological models, vacuum space-times, the de
sitter univers and Minkowskian space-time.


title: Gauge Theory of Gravity Requires Massive Torsion Field

abstract:
  One of the greatest unsolved issues of the physics of this century is to find
a quantum field theory of gravity. According to a vast amount of literature
unification of quantum field theory and gravitation requires a gauge theory of
gravity which includes torsion and an associated spin field. Various models
including either massive or massless torsion fields have been suggested. We
present arguments for a massive torsion field, where the probable rest mass of
the corresponding spin three gauge boson is the Planck mass.


title: Lens Spaces and Handlebodies in 3D Quantum Gravity

abstract:
  We calculate partition functions for lens spaces L_{p,q} up to p=8 and for
genus 1 and 2 handlebodies H_1, H_2 in the Turaev-Viro framework. These can be
interpreted as transition amplitudes in 3D quantum gravity. In the case of lens
spaces L_{p,q} these are vacuum-to-vacuum amplitudes $\O -> \O$, whereas for
the 1- and 2-handlebodies H_1, H_2 they represent genuinely topological
transition amplitudes $\O -> T^2$ and $\O -> T^2 # T^2$, respectively.


title: Planckian Scattering and Black Holes

abstract:
  Recently, 't Hooft's S-matrix for black hole evaporation, obtained from the
gravitational interactions between the in-falling particles and Hawking
radiation, has been generalised to include transverse effects. The action
describing the collision turned out to be a string theory action with an
antisymmetric tensor background. In this article we show that the model
reproduces both the correct longitudinal and transverse dynamics, even when one
goes beyond the eikonal approximation or particles collide at nonvanishing
incidence angles. It also gives the correct momentum tranfer that takes place
in the process. Including a curvature on the horizon provides the action with
an extra term, which can be interpreted as a dilaton contribution. The
amplitude of the scattering is seen to reproduce the Veneziano amplitude in a
certain limit, as in earlier work by 't Hooft. The theory resembles a
"holographic" field theory, in the sense that it only depends on the horizon
degrees of freedom, and the in- and out-Hilbert spaces are the same. The
operators representing the coordinates of in- and out-going particles are
non-commuting, and Heisenberg's uncertainty principle must be corrected by a
term proportional to the ratio of the ingoing momentum to the impact parameter,
times Newton's constant. Reducing to 2+1 dimensions, we find that the
coordinates satisfy an SO(2,1) algebra.


title: Nonlocal Equation of State in General Relativistic Radiating Spheres

abstract:
  We show that under particular circumstances a general relativistic
spherically symmetric bounded distribution of matter could satisfy a nonlocal
equation of state. This equation relates, at a given point, the components of
the corresponding energy momentum tensor not only as function at that point,
but as a functional throughout the enclosed configuration. We have found that
these types of dynamic bounded matter configurations, with constant
gravitational potentials at the surface, admit a Conformal Killing Vector and
fulfill the energy conditions for anisotropic imperfect fluids. We also present
several analytical and numerical models satisfying these equations of state
which collapse as reasonable radiating anisotropic spheres in general
relativity.


title: Some Connections between Quantum Tunneling and Inflation

abstract:
  The Wheeler-DeWitt equation in the minisuperspace approximation is studied in
four different models. Under certain circumstances each model leads to a
tunneling potential and under the same circumstances the classical version of
each model leads to inflation.


title: Head--on Collision of Two Unequal Mass Black Holes

abstract:
  We present results from the first fully nonlinear numerical calculations of
the head--on collision of two unequal mass black holes. Selected waveforms of
the most dominant l=2, 3 and 4 quasinormal modes are shown, as are the total
radiated energies and recoil velocities for a range of mass ratios and initial
separations. Our results validate the close and distant separation limit
perturbation studies, and suggest that the head--on collision scenario is not
likely to produce an astrophysically significant recoil effect.


title: Charged Dilatonic Black Holes: String frame vs Einstein frame

abstract:
  The descriptions of Reissner-Nordstroem and Kerr-Newman dilatonic black holes
in the Einstein frame are compared to those in the string frame. We describe
various physical measurements in the two frames and show which experiments can
distinguish between the two frames. In particular we discuss the gyromagnetic
ratios of black holes, the decay law via Hawking radiation and the propagation
of light on black hole backgrounds.


title:
Testing the Boundary Conditions of General Relativity Near the Earth-Sun
  Saddle Point

abstract:
  We suggest that a satellite with a stable atomic clock on board be sent
through the Earth-Sun gravitational saddle point to experimentally determine
whether Nature prefers static solutions of the field equations of General
Relativity, such as the standard Schwarzschild solution, or whether Nature
prefers equivalent non-static solutions. This is a test of the boundary
conditions of General Relativity rather than of the field equations. The
fractional difference in clock rates between the two possibilities is a part in
a hundred million. This is a large and easily measurable effect.


title: Can Quantum-Corrected BTZ Black Hole Anti-Evaporate?

abstract:
  Kaluza-Klein reduction of 3D gravity with minimal scalars leads to 2D
dilaton-Maxwell gravity with dilaton coupled scalars. Evaluating the one-loop
effective action for dilaton coupled scalars in large $N$ and s-wave
approximation we apply it to study quantum evolution of BTZ black hole. It is
shown that quantum-corrected BTZ BH may evaporate or else anti-evaporate
similarly to 4D Nariai BH as is observed by Bousso and Hawking. Instable higher
modes in the spectrum indicate also the possibility of proliferation of BTZ BH.


title: Comment on the Herzlich's proof of the Penrose inequality

abstract:
  Recently Herzlich proved a Penrose-like inequality with a coefficient being a
kind of a Sobolev constant. We show that this constant tends to zero for
charged black holes approaching maximal Reissner-Nordstroem solutions. The
method proposed by Herzlich is not appropriate for charged matter with nonzero
global charge.


title:
Black Hole Spectroscopy: Determining Waveforms from 3D Excited Black
  Holes

abstract:
  We present the first results for Cauchy nonlinear evolution of 3D,
nonaxisymmetric distorted black holes. We focus on the extraction and
verification of 3D waveforms determined by numerical relativity. We show that
the black hole evolution can be accurately followed through the ringdown
period, and comparing with a recently developed perturbative evolution
technique, we show that many waveforms in the black hole spectrum of modes,
such as l=2 and l=4, including weakly excited nonaxisymmetric modes with m not
zero, can be accurately evolved and extracted from the full nonlinear numerical
evolution. We also identify new physics contained in higher modes, due to
nonlinear effects. The implications for simulations related to gravitational
wave astronomy are discussed.


title: Compact Einstein-Weyl four-dimensional manifolds

abstract:
  We look for four dimensional Einstein-Weyl spaces equipped with a regular
Bianchi metric. Using the explicit 4-parameters expression of the distance
obtained in a previous work for non-conformally-Einstein Einstein-Weyl
structures, we show that only four 1-parameter families of regular metrics
exist on orientable manifolds : they are all of Bianchi $IX$ type and
conformally K\"ahler ; moreover, in agreement with general results, they have a
positive definite conformal scalar curvature. In a Gauduchon's gauge, they are
compact and we obtain their topological invariants. Finally, we compare our
results to the general analyses of Madsen, Pedersen, Poon and Swann : our
simpler parametrisation allows us to correct some of their assertions.


title: Extremely Charged Static Dust Distributions in General Relativity

abstract:
  Conformo static charged dust distributions are investigated in the framework
of General Relativity. Einstein's equations reduce to a nonlinear version of
Poisson's equations and Maxwell's eqations imply the equaltiy of the charge and
mass densities. An interior solution to the extreme Reissner-Nordstrom metric
is given. Dust distributions concentrated on regular surfaces are discussed and
a complete solution is given for a spherical thin shell.


title: Physics and cosmology in an inhomogeneous Universe

abstract:
  Examples are presented of applications of the Lema\^{i}tre - Tolman model to
problems of astrophysics and gravitation theory. They are: 1. Inferring the
spatial distribution of matter by interpretation of observations; 2.
Interaction of inhomogeneities in matter distribution with the CMB radiation;
3. Evolution of voids; 4. Singularities; 5. Influence of electromagnetic field
on gravitational collapse. This review is meant to demonstrate that the theory
is already well-prepared to meet the challenges posed by an inhomogeneous
Universe.


title: Exact Solutions for Boson-Fermion Stars in (2+1) dimensions

abstract:
  We solve Einstein equations coupled to a complex scalar field with infinitely
large self-interaction, degenerate fermions, and a negative cosmological
constant in $(2+1)$ dimensions. Exact solutions for static boson-fermion stars
are found when circular symmetry is assumed. We find that the minimum binding
energy of boson-fermion star takes a negative value if the value of the
cosmological constant is sufficiently small.


title:
Quantum Theory of Geometry III: Non-commutativity of Riemannian
  Structures

abstract:
  The basic framework for a systematic construction of a quantum theory of
Riemannian geometry was introduced recently. The quantum versions of Riemannian
structures --such as triad and area operators-- exhibit a non-commutativity. At
first sight, this feature is surprising because it implies that the framework
does not admit a triad representation. To better understand this property and
to reconcile it with intuition, we analyze its origin in detail. In particular,
a careful study of the underlying phase space is made and the feature is traced
back to the classical theory; there is no anomaly associated with quantization.
We also indicate why the uncertainties associated with this non-commutativity
become negligible in the semi-classical regime.


title: Scalar perturbations in deflationary cosmological models

abstract:
  We consider scalar perturbations of energy--density for a class of
cosmological models where an early phase of accelerated expansion evolves,
without any fine--tuning for graceful exit, towards the standard Friedman eras
of observed universe. The geometric procedure which generates such models
agrees with results for string cosmology since it works if dynamics is
dominated by a primordial fluid of extended massive objects. The main result is
that characteristic scales of cosmological interest, connected with the
extension of such early objects, are selected.}


title: The effective cosmological constant in higher order gravity theories

abstract:
  An effective time--dependent cosmological constant can be recovered for
higher--order theories of gravity by extending to these ones the no--hair
conjecture. The results are applied to some specific cosmological models.


title: Gas of wormholes: a possible ground state of Quantum Gravity

abstract:
  In order to gain insight into the possible Ground State of Quantized
Einstein's Gravity, we have derived a variational calculation of the energy of
the quantum gravitational field in an open space, as measured by an asymptotic
observer living in an asymptotically flat space-time. We find that for Quantum
Gravity (QG) it is energetically favourable to perform its quantum fluctuations
not upon flat space-time but around a ``gas'' of wormholes of mass m_p, the
Planck mass (m_p ~= 10^{19}GeV) and average distance l_p, the Planck length
a_p(a_p ~= 10^{-33}cm). As a result, assuming such configuration to be a good
approximation to the true Ground State of Quantum Gravity, space-time, the
arena of physical reality, turns out to be well described by Wheeler's quantum
foam and adequately modeled by a space-time lattice with lattice constant l_p,
the Planck lattice.


title:
Covariant cosmological perturbation dynamics in the inflationary
  universe

abstract:
  The linear cosmological perturbation theory of almost homogeneous and
isotropic perfect fluid and scalar field universes is reconsidered and formally
simplified. Using the existence of a covariant conserved quantity on large
perturbation scales, a closed integral expression for comoving energy density
perturbations is obtained for arbitrary equations of state. On this basis we
establish a simple relation between fluid energy density perturbations at
`reentry' into the horizon and the corresponding scalar field quantities at the
first Hubble scale crossing during an early de Sitter phase of a standard
inflationary scenario.


title:
Spherically Symmetric Solution for Torsion and the Dirac equation in 5D
  spacetime

abstract:
  Torsion in a 5D spacetime is considered. In this case gravitation is defined
by the 5D metric and the torsion. It is conjectured that torsion is connected
with a spinor field. In this case Dirac's equation becomes the nonlinear
Heisenberg equation. It is shown that this equation has a discrete spectrum of
solutions with each solution being regular on the whole space and having finite
energy. Every solution is concentrated on the Planck region and hence we can
say that torsion should play an important role in quantum gravity in the
formation of bubbles of spacetime foam. On the basis of the algebraic relation
between torsion and the classical spinor field in Einstein-Cartan gravity the
geometrical interpretation of the spinor field is considered as ``the square
root'' of torsion.


title: Thermal properties of spacetime foam

abstract:
  Spacetime foam can be modeled in terms of nonlocal effective interactions in
a classical nonfluctuating background. Then, the density matrix for the
low-energy fields evolves, in the weak-coupling approximation, according to a
master equation that contains a diffusion term. Furthermore, it is argued that
spacetime foam behaves as a quantum thermal field that, apart from inducing
loss of coherence, gives rise to effects such as gravitational Lamb and Stark
shifts as well as quantum damping in the evolution of the low-energy
observables. These effects can be, at least in principle, experimentally
tested.


title: Self-Similarity in General Relativity \endtitle

abstract:
  The different kinds of self-similarity in general relativity are discussed,
with special emphasis on similarity of the ``first'' kind, corresponding to
spacetimes admitting a homothetic vector. We then survey the various classes of
self-similar solutions to Einstein's field equations and the different
mathematical approaches used in studying them. We focus mainly on spatially
homogenous and spherically symmetric self-similar solutions, emphasizing their
possible roles as asymptotic states for more general models. Perfect fluid
spherically symmetric similarity solutions have recently been completely
classified, and we discuss various astrophysical and cosmological applications
of such solutions. Finally we consider more general types of self-similar
models.


title: Averaged Energy Conditions in 4D Evaporating Black Hole Backgrounds

abstract:
  Using Visser's semi-analytical model for the stress-energy tensor
corresponding to the conformally coupled massless scalar field in the Unruh
vacuum, we examine, by explicitly evaluating the relevant integrals over
half-complete geodesics, the averaged weak (AWEC) and averaged null (ANEC)
energy conditions along with Ford-Roman quantum inequality-type restrictions on
negative energy in the context of four dimensional evaporating black hole
backgrounds. We find that in all cases where the averaged energy conditions
fail, there exist quantum inequality bounds on the magnitude and duration of
negative energy densities.


title:
Can the local stress-energy conservation laws be derived solely from
  field equations?

abstract:
  According to a recent suggestion [1], the energy--momentum tensor for
gravitating fields can be computed through a suitable rearrangement of the
matter field equations, without relying on the variational definition. We show
that the property observed by Accioly et al. in [1] is the consequence of a
general identity, which follows from the covariance of the matter Lagrangian in
much the same way as (generalized) Bianchi identities follow from the
covariance of the purely gravitational Lagrangian. However, we also show that
only in particular cases can this identity be used to obtain the actual form of
the stress-energy tensor, while in general the method leads to ambiguities and
possibly to wrong results. Moreover, in nontrivial cases the computations turn
out to be more difficult than the standard variational technique.


title:
Physically Realistic Solutions to the Ernst Equation on Hyperelliptic
  Riemann Surfaces

abstract:
  We show that the class of hyperelliptic solutions to the Ernst equation (the
stationary axisymmetric Einstein equations in vacuum) previously discovered by
Korotkin and Neugebauer and Meinel can be derived via Riemann-Hilbert
techniques. The present paper extends the discussion of the physical properties
of these solutions that was begun in a Physical Review Letter, and supplies
complete proofs. We identify a physically interesting subclass where the Ernst
potential is everywhere regular except at a closed surface which might be
identified with the surface of a body of revolution. The corresponding
spacetimes are asymptotically flat and equatorially symmetric. This suggests
that they could describe the exterior of an isolated body, for instance a
relativistic star or a galaxy. Within this class, one has the freedom to
specify a real function and a set of complex parameters which can possibly be
used to solve certain boundary value problems for the Ernst equation. The
solutions can have ergoregions, a Minkowskian limit and an ultrarelativistic
limit where the metric approaches the extreme Kerr solution. We give explicit
formulae for the potential on the axis and in the equatorial plane where the
expressions simplify. Special attention is paid to the simplest non-static
solutions (which are of genus two) to which the rigidly rotating dust disk
belongs.


title: Scale invariance and critical gravitational collapse

abstract:
  We examine ways to write the Choptuik critical solution as the evolution of
scale invariant variables. It is shown that a system of scale invariant
variables proposed by one of the authors does not evolve periodically in the
Choptuik critical solution. We find a different system, based on maximal
slicing. This system does evolve periodically, and may generalize to the case
of axisymmetry or of no symmetry at all.


title:
Dominance of a Dynamical Measure and Disappearance of the Cosmological
  Constant

abstract:
  We consider an action which consists of two terms: the first S_{1}=\int
L_{1}\Phi d^{4}x and the second S_{2}=\int L_{2}\sqrt{-g}d^{4}x where \Phi is a
measure which has to be determined dynamically. S_{1} satisfies the requirement
that the transformation L_{1}\to L_{1}+const does not effect equations of
motion. In the first order formalism, a constraint appears which allows to
solve \chi =\Phi/\sqrt{-g}. Then, in a true vacuum state (TVS), \chi\to\infty
and in the conformal Einstein frame no singularities are present, the energy
density of TVS is zero without fine tuning of any scalar potential in S_{1} or
S_{2}. When considering only a linear potential for a scalar field \phi in
S_{1}, the continuous symmetry \phi\to\phi+const is respected. Surprisingly, in
this case SSB takes place while no massless ("Goldstone") boson appears.


title:
On the propagation of electromagnetic radiation in the field of a plane
  gravitational wave

abstract:
  The propagation of free electromagnetic radiation in the field of a plane
gravitational wave is investigated. A solution is found one order of
approximation beyond the limit of geometrical optics in both
transverse--traceless (TT) gauge and Fermi Normal Coordinate (FNC) system. The
results are applied to the study of polarization perturbations. Two
experimental schemes are investigated in order to verify the possibility to
observe these perturbations, but it is found that the effects are exceedingly
small.


title: On the global visibility of singularity in quasi-spherical collapse

abstract:
  We analyze here the issue of local versus the global visibility of a
singularity that forms in gravitational collapse of a dust cloud, which has
important implications for the weak and strong versions of the cosmic
censorship hypothesis. We find conditions as to when a singularity will be only
locally naked, rather than being globally visible, thus preseving the weak
censorship hypothesis. The conditions for formation of a black hole or naked
singularity in the Szekeres quasi-spherical collapse models are worked out. The
causal behaviour of the singularity curve is studied by examining the outgoing
radial null geodesics, and the final outcome of collapse is related to the
nature of the regular initial data specified on an initial hypersurface from
which the collapse evolves. An interesting feature that emerges is the
singularity in Szekeres spacetimes can be ``directionally naked''.


title: Cosmological Pair Production of Charged and Rotating Black Holes

abstract:
  We investigate the general process of black hole pair creation in a
cosmological background, considering the creation of charged and rotating black
holes. We motivate the use of Kerr-Newmann-deSitter solutions to investigate
this process, showing how they arise from more general C-metric type solutions
that describe a pair of general black holes accelerating away from each other
in a cosmological background. All possible KNdS-type spacetimes are classified
and we examine whether they may be considered to be in full thermodynamic
equilibrium. Instantons that mediate the creation of these space-times are
constructed and we see that they are necessarily complex due to regularity
requirements. Thus we argue that instantons need not always be real Euclidean
solutions to the Einstein equations. Finally, we calculate the actions of these
instantons and find that the standard action functional must be modified to
correctly take into account the effects of the rotation. The resultant
probabilities for the creation of the space-times are found to be real and
consistent with the interpretation that the entropy of a charged and rotating
black hole is the logarithm of the number of its quantum states.


title: Non-Local Boundary Conditions in Euclidean Quantum Gravity

abstract:
  Non-local boundary conditions for Euclidean quantum gravity are proposed,
consisting of an integro-differential boundary operator acting on metric
perturbations. In this case, the operator P on metric perturbations is of
Laplace type, subject to non-local boundary conditions; by contrast, its
adjoint is the sum of a Laplacian and of a singular Green operator, subject to
local boundary conditions. Self-adjointness of the boundary-value problem is
correctly formulated by looking at Dirichlet-type and Neumann-type realizations
of the operator P, following recent results in the literature. The set of
non-local boundary conditions for perturbative modes of the gravitational field
is written in general form on the Euclidean four-ball. For a particular choice
of the non-local boundary operator, explicit formulae for the boundary-value
problem are obtained in terms of a finite number of unknown functions, but
subject to some consistency conditions. Among the related issues, the problem
arises of whether non-local symmetries exist in Euclidean quantum gravity.


title: Four approaches to quantization of the relativistic particle

abstract:
  The connection between four different approaches to quantization of the
relativistic particle is studied: reduced phase space quantization, Dirac
quantization, BRST quantization, and (BRST)-Fock quantization are each carried
out. The connection to the BFV path integral in phase space is provided. In
particular, it is concluded that that the full range of the lapse should be
used in such path integrals. The relationship between all these approaches is
established.


title: Perturbative analysis of generalized Einstein's theories

abstract:
  The hypothesis that the energy-momentum tensor of ordinary matter is not
conserved separately, leads to a non-adiabatic expansion and, in many cases, to
an Universe older than usual. This may provide a solution for the entropy and
age problems of the Standard Cosmological Model. We consider two different
theories of this type, and we perform a perturbative analysis, leading to
analytical expressions for the evolution of gravitational waves, rotational
modes and density perturbations. One of these theories exhibits satisfactory
properties at this level, while the other one should be discarded.


title: An Octonionic Geometric (Balanced) state Sum Model

abstract:
  We propose a new 4D state sum model, related to the balanced model, which is
constructed using the octonions, or equivalently, triality. An effective
continuum physical theory constructed from this model coupled to the balanced
model would have a non-vanishing cosmological constant, chiral asymmetry, and a
gauge group related to the octonions.


title: The Genuine Cosmic Rosetta

abstract:
  Reexamination of general relativistic experimental results shows the universe
is governed by Einstein's static-spacetime general relativity instead of
Friedmann-Lemaitre expanding-spacetime general relativity. The absence of
expansion redshifts in a static-spacetime universe suggests a reevaluation of
the present cosmology is needed.


title: Is the principle of equivalence a principle?

abstract:
  The work argues the principle of equivalence to be a theorem and not a
principle (in a sense of an axiom). It contains a detailed analysis of the
concepts of normal and inertial frame of reference. The equivalence principle
is proved to be valid (at every point and along every path) in any
gravitational theory based on linear connections. Possible generalizations of
the equivalence principle are pointed out.


title:
Solar-System Experiments and Saa's Model of Gravity with Propagating
  Torsion

abstract:
  It's shown that Saa's model of gravity with propagating torsion is
inconsistent with basic solar-system gravitational experiments.


title: Negative Energy Density States for the Dirac Field in Flat Spacetime

abstract:
  Negative energy densities in the Dirac field produced by state vectors that
are the superposition of two single particle electron states are examined. I
show that for such states the energy density of the field is not bounded from
below and that the quantum inequalities derived for scalar fields are
satisfied. I also show that it is not possible to produce negative energy
densities in a scalar field using state vectors that are arbitrary
superpositions of single particle states.


title: Initial Conditions in String Cosmology

abstract:
  We take a critical look at a recent conjecture concerning the past attractor
in the pre-big-bang scenario. We argue that the Milne universe is unlikely to
be a general past attractor for such models and support this with a number of
examples.


title: The Coherence of Primordial Fluctuations Produced During Inflation

abstract:
  The behaviour of quantum metric perturbations produced during inflation is
considered at the stage after the second Hubble radius crossing. It is shown
that the classical correlation between amplitude and momentum of a perturbation
mode, previously shown to emerge in the course of an effective
quantum-to-classical transition, is maintained for a sufficiently long time,
and we present the explicit form in which it takes place using the Wigner
function. We further show with a simple diffraction experiment that quantum
interference, non-expressible in terms of a classical stochastic description of
the perturbations, is essentially suppressed. Rescattering of the perturbations
leads to a comparatively slow decay of this correlation and to a complete
stochastization of the system.


title: On the Phase-Space Volume of Primordial Cosmological Perturbations

abstract:
  We show how to determine the typical phase space volume $\Gamma$ for
primordial gravitational waves produced during an inflationary stage, which is
invariant under squeezing. An expression for $\Gamma$ is found in the long
wavelength regime. The quasi-classical entropy of a pure vacuum initial state
defined as the logarithm of $\Gamma$ modulo a constant remains zero in spite of
the generation of fluctuations (creation of real gravitons).


title:
Invariance of the distributional curvature of the cone under smooth
  diffeomorphisms

abstract:
  An explicit calculation is carried out to show that the distributional
curvature of a 2-cone, calculated by Clarke et al. (1996), using Colombeau's
new generalised functions is invariant under non-linear $C^\infty$ coordinate
transformations.


title: Size Gap for Zero Temperature Black Holes in Semiclassical Gravity

abstract:
  We show that a gap exists in the allowed sizes of all zero temperature static
spherically symmetric black holes in semiclassical gravity when only
conformally invariant fields are present. The result holds for both charged and
uncharged black holes. By size we mean the proper area of the event horizon.
The range of sizes that do not occur depends on the numbers and types of
quantized fields that are present. We also derive some general properties that
both zero and nonzero temperature black holes have in all classical and
semiclassical metric theories of gravity.


title: On spontaneous scalarization

abstract:
  We study in the physical frame the phenomenon of spontaneous scalarization
that occurs in scalar-tensor theories of gravity for compact objects. We
discuss the fact that the phenomenon occurs exactly in the regime where the
Newtonian analysis indicates it should not. Finally we discuss the way the
phenomenon depends on the equation of state used to describe the nuclear
matter.


title: Maintaining a Wormhole with a Scalar Field

abstract:
  It is well known that it takes matter that violates the averaged weak energy
condition to hold the throat of a wormhole open. The production of such
``exotic'' matter is usually discussed within the context of quantum field
theory. In this paper I show that it is possible to produce the exotic matter
required to hold a wormhole open classically. This is accomplished by coupling
a scalar field to matter that satisfies the weak energy condition. The
energy-momentum tensor of the scalar field and the matter separately satisfy
the weak energy condition, but there exists an interaction energy-momentum
tensor that does not. It is this interaction energy-momentum tensor that allows
the wormhole to be maintained.


title: A rigidity result on the ideal boundary structure of smooth space-times

abstract:
  Following a survey of the abstract boundary definition of Scott and Szekeres,
a rigidity result is proved for the smooth case, showing that the topological
structure of the regular part of this boundary in invariantly defined.


title: Weighing the string mass with the COBE data

abstract:
  In the context of the pre-big bang scenario the large-scale CMB anisotropy
can be seeded by a primordial background of very light (or massless) axion
fluctuations. In that case the slope of the temperature anisotropy spectrum,
allowed by present observations, defines an allowed range of values for the
string mass scale. Conversely, from the theoretical expected value of the
string scale we can predict the slope of the anisotropy spectrum. In both cases
there is a remarkable agreement between observations and theoretical
expectations.


title: Geometrical features of (4+d) gravity

abstract:
  We obtain the vacuum spherical symmetric solutions for the gravitational
sector of a (4+d)-dimensional Kaluza-Klein theory. In the various regions of
parameter space, the solutions can describe either naked singularities or
black-holes or wormholes. We also derive, by performing a conformal rescaling,
the corresponding picture in the four-dimensional space-time.


title: Ermakov approach for empty FRW minisuperspace oscillators

abstract:
  The formal Ermakov approach for empty FRW minisuperspace cosmological models
of arbitrary Hartle-Hawking factor ordering and the corresponding squeezing
features are briefly discussed as a possible means of describing cosmological
evolution


title: Nonlinear electrodynamics and FRW cosmology

abstract:
  Maxwell electrodynamics, considered as a source of the classical Einstein
field equations, leads to the singular isotropic Friedmann solutions. We show
that this singular behavior does not occur for a class of nonlinear
generalizations of the electromagnetic theory. A mathematical toy model is
proposed for which the analytical nonsingular extension of FRW solutions is
obtained.


title:
Gravitational waves from inspiraling compact binaries: Second
  post-Newtonian waveforms as search templates II

abstract:
  We present further evidence that the second post-Newtonian (pN) approximation
to the gravitational waves emitted by inspiraling compact binaries is
sufficient for the detection of these systems. This is established by comparing
the 2-pN wave forms to signals calculated from black hole perturbation theory.
Results are presented for different detector noise curves. We also discuss the
validity of this type of analysis.


title:
Quasi-Local Energy Conservation Law Derived From The Einstein's
  Equations

abstract:
  The quasi-local energy conservation law is derived from the vacuum Einstein's
equations on the timelike boundary surface in the canonical (2,2)-formalism of
general relativity. The quasi-local energy and energy flux integral agree with
the standard results in the asymptotically flat limit and in spherically
symmetric spacetimes.


title: Loop quantum gravity and quanta of space: a primer

abstract:
  We present a straightforward and self-contained introduction to the basics of
the loop approach to quantum gravity, and a derivation of what is arguably its
key result, namely the spectral analysis of the area operator. We also discuss
the arguments supporting the physical prediction following this result: that
physical geometrical quantities are quantized in a non-trivial, computable,
fashion. These results are not new; we present them here in a simple form that
avoids the many non-essential complications of the first derivations.


title: Exact Solutions in Locally Anisotropic Gravity and Strings

abstract:
  In this Report we outline some basic results on generalized
Finsler--Kaluza--Klein gravity and locally anisotropic strings. There are
investigated exact solutions for locally anisotropic
Friedmann--Robertson--Walker universes and three dimensional and string black
holes with generic anisotropy.


title: Negative Energy Densities and the Limit of Classical Space-Time

abstract:
  Although negative energy densities are predicted by relativistic quantum
field theories, I present an argument that an "operational" positivity still
holds: the energy in a region, plus the energy of an isolated device which
traps or measures that energy, must be positive. If we assume Einstein's field
equation, this means the local geometry of a negative energy-density region
cannot be measured by the trajectories of test particles.
  So far, all attempts to design thought-experiments to verify a classical
local geometry in the negative energy-density region have failed. It seems we
must impute a quantum character to such a space-time regime.


title: Gravitational Waves from The Newtonian plus H\'enon-Heiles System

abstract:
  In this work we analyze the emission of gravitational waves from a
gravitational system described by a Newtonian term plus a H\'enon-Heiles term.
The main concern is to analyze how the inclusion of the Newtonian term changes
the emission of gravitational waves, considering its emission in the chaotic
and regular regime.


title:
Quantum Fields in Curved Spacetime: Quantum-Gravitational Nonlocality
  and Conservation of Particle Numbers

abstract:
  We argue that the conventional quantum field theory in curved spacetime has a
grave drawback: The canonical commutation relations for quantum fields and
conjugate momenta do not hold. Thus the conventional theory should be denounced
and the related results revised. A Hamiltonian version of the canonical
formalism for a free scalar quantum field is advanced, and the fundamentals of
an appropriate theory are constructed. The principal characteristic feature of
the theory is quantum-gravitational nonlocality: The Schroedinger field
operator at time t depends on the metric at t in the whole 3-space.
Applications to cosmology and black holes are given, the results being in
complete agreement with those of general relativity for particles in curved
spacetime. A model of the universe is advanced, which is an extension of the
Friedmann universe; it lifts the problem of missing dark matter. A fundamental
and shocking result is the following: There is no particle creation in the case
of a free quantum field in curved spacetime; in particular, neither the
expanding universe nor black holes create particles.


title: Space Time Quantization and the Big Bang

abstract:
  A recent cosmological model is recapitulated which deduces the correct mass,
radius and age of the universe as also the Hubble constant and other well known
apparently coincidental relations. It also predicts an ever expanding
accelerating universe as is confirmed by latest supernovae observations.
Finally the Big Bang model is recovered as a suitable limiting case.


title: Singularity-free cosmological solutions in quadratic gravity

abstract:
  We study a general field theory of a scalar field coupled to gravity through
a quadratic Gauss-Bonnet term $\xi(\phi) R^2_{GB}$. The coupling function has
the form $\xi(\phi)=\phi^n$, where $n$ is a positive integer. In the absence of
the Gauss-Bonnet term, the cosmological solutions for an empty universe and a
universe dominated by the energy-momentum tensor of a scalar field are always
characterized by the occurrence of a true cosmological singularity. By
employing analytical and numerical methods, we show that, in the presence of
the quadratic Gauss-Bonnet term, for the dual case of even $n$, the set of
solutions of the classical equations of motion in a curved FRW background
includes singularity-free cosmological solutions. The singular solutions are
shown to be confined in a part of the phase space of the theory allowing the
non-singular solutions to fill the rest of the space. We conjecture that the
same theory with a general coupling function that satisfies certain criteria
may lead to non-singular cosmological solutions.


title: On Spinor Representations in the Weyl Gauge Theory

abstract:
  A spinor current-source is found in the Weyl non-Abelian gauge theory which
does not contain the abstract gauge space. It is shown that the searched spinor
representation can be constructed in the space of external differential forms
and it is a 16-component quantity for which a gauge-invariant Lagrangian is
determined. The connexion between the Weyl non-Abelian gauge potential and the
Cartan torsion field and the problem of a possible manifestation of the
considered interactions are considered.


title: The Synergy between Numerical and Perturbative Approaches to Black Holes

abstract:
  I describe approaches to the study of black hole spacetimes via numerical
relativity. After a brief review of the basic formalisms and techniques used in
numerical black hole simulations, I discuss a series of calculations from
axisymmetry to full 3D that can be seen as stepping stones to simulations of
the full 3D coalescence of two black holes. In particular, I emphasize the
interplay between perturbation theory and numerical simulation that build both
confidence in present results and tools to aid and to interpret results of
future simulations of black hole coalescence.


title: Numerical Relativity: Towards Simulations of 3D Black Hole Coalescence

abstract:
  I review recent developments in numerical relativity, focussing on progress
made in 3D black hole evolution. Progress in development of black hole initial
data, apparent horizon boundary conditions, adaptive mesh refinement, and
characteristic evolution is highlighted, as well as full 3D simulations of
colliding and distorted black holes. For true 3D distorted holes, with Cauchy
evolution techniques, it is now possible to extract highly accurate,
nonaxisymmetric waveforms from fully nonlinear simulations, which are verified
by comparison to pertubration theory, and with characteristic techniques
extremely long term evolutions of 3D black holes are now possible. I also
discuss a new code designed for 3D numerical relativity, called Cactus, that
will be made public.