title: Differentially rotating disks of dust

abstract:
  We present a three-parameter family of solutions to the stationary
axisymmetric Einstein equations that describe differentially rotating disks of
dust. They have been constructed by generalizing the Neugebauer-Meinel solution
of the problem of a rigidly rotating disk of dust. The solutions correspond to
disks with angular velocities depending monotonically on the radial coordinate;
both decreasing and increasing behaviour is exhibited. In general, the
solutions are related mathematically to Jacobi's inversion problem and can be
expressed in terms of Riemann theta functions. A particularly interesting
two-parameter subfamily represents Baecklund transformations to appropriate
seed solutions of the Weyl class.


title: The magnetic field of the relativistic stars in the 5D approach

abstract:
  It is well-known that the 5D equations without sources may be reduced to the
4D ones with sources, provided an appropriate definition for the
energy-momentum tensor of matter in terms of the extra part of the geometry.The
advantage consists on the naturally appearance of gravitational and
electromagnetic fields from this decomposition. With this ansatz an algorithm
is presented, which permits to express the physical parameters in terms of
gauge potentials and scalar field. An explicit form for the exterior magnetic
field of neutron star in terms of the scalar field and the gauge potentials is
deduced for a static, spherically-symmetric metric.


title:
The Interaction of Dirac Particles with Non-Abelian Gauge Fields and
  Gravity - Black Holes

abstract:
  We consider a static, spherically symmetric system of a Dirac particle in a
classical gravitational and SU(2) Yang-Mills field. We prove that the only
black-hole solutions of the corresponding Einstein-Dirac-Yang/Mills equations
are the Bartnik-McKinnon black-hole solutions of the SU(2) Einstein-Yang/Mills
equations; thus the spinors must vanish identically. This indicates that the
Dirac particles must either disappear into the black-hole or escape to
infinity.


title: Dilation Dark Matter in Vaidya-De-Sitter Spacetime

abstract:
  The exterior of a relativistic star can be modelated with the Vaidya
radiating metric. It is started from the generalized Vaidya metric that allows
a type II fluid and studied the conditions of generating new analytical
solutions of the Einstein's field equations. It is shown that the mass
parameter solution gives the classical de Sitter universe in the static case
and the extended de Sitter metric coupled with a dilation scalar field in the
time-dependent case. It is concluded that in the time-dependent case the
atmosphere of a relativistic star consists on an anisotropic string fluid
coupled with a dark matter null fluid and interpreted the scalar field as the
particle that produces the dark matter.


title: A Magnetic Mass Model within the General Relativity Framework

abstract:
  In this paper is presented a general-relativistic approach of cuasi-neutral
bodies endowed with magnetic field. Starting from the similarity of neutron
particles with neutron stars for which the general-relativistic framework is
imposed, this treatment is extended to neutrons. A class of interior solutions
is derived from the Einstein field equations for a spherically-symmetric
distribution of a perfect magneto-fluid in the magnetohydrodinamic
approximation and a magnetic mass model is proposed. The dependence of the
metric and of physical parameters on the magnetic field leads to the conclusion
that the mass is entirely magnetic in origin, which implies that the field
equations do not admit interior solutions if the source consist only on perfect
fluid.


title: Spin Foam Perturbation Theory

abstract:
  We study perturbation theory for spin foam models on triangulated manifolds.
Starting with any model of this sort, we consider an arbitrary perturbation of
the vertex amplitudes, and write the evolution operators of the perturbed model
as convergent power series in the coupling constant governing the perturbation.
The terms in the power series can be efficiently computed when the unperturbed
model is a topological quantum field theory. Moreover, in this case we can
explicitly sum the whole power series in the limit where the number of
top-dimensional simplices goes to infinity while the coupling constant is
suitably renormalized. This `dilute gas limit' gives spin foam models that are
triangulation-independent but not topological quantum field theories. However,
we show that models of this sort are rather trivial except in dimension 2.


title: Disclination in Lorentz Space-Time

abstract:
  The disclination in Lorentz space-time is studied in detail by means of
topological properties of $\phi $-mapping. It is found the space-time
disclination can be described in term of a Dirac spinor. The size of the
disclination, which is proved to be the difference of two sets of su(2)% -like
monopoles expressed by two mixed spinors, is quantized topologically in terms
of topological invariants$-$winding number. The projection of space-time
disclination density along an antisymmetric tensor field is characterized by
Brouwer degree and Hopf index.


title:
Equation of motion for relativistic compact binaries with the strong
  field point particle limit : Formulation, the first post-Newtonian and
  multipole terms

abstract:
  We derive the equation of motion for the relativistic compact binaries in the
post-Newtonian approximation taking explicitly their strong internal gravity
into account. For this purpose we adopt the method of the point particle limit
where the equation of motion is expressed in terms of the surface integrals. We
examine carefully the behavior of the surface integrals in the derivation. As a
result, we obtain the Einstein-Infeld-Hoffman equation of motion at the first
post-Newtonian (1PN) order, and a part of the 2PN order which depends on the
quadrupole moments and the spins of component stars. Hence, it is found that
the equation of motion in the post-Newtonian approximation is valid for the
compact binaries by a suitable definition of the mass, spin and quadrupole
moment.


title: Spin-torsion in Chaotic Inflation

abstract:
  The role of spin-torsion coupling to gravity is analyzed in the context of a
model of chaotic inflation. The system of equations constructed from the
Einstein-Cartan and inflaton field equations are studied and it is shown that
spin-torsion interactions are effective only at the very first e-folds of
inflation, becoming quickly negligible and, therefore, not affecting the
standard inflationary scenario nor the density perturbations spectrum
predictions.


title: An Explanation of the "Pioneer Effect" based on Quasi-Metric Relativity

abstract:
  According to the socalled "quasi-metric" framework developed elsewhere, the
cosmic expansion applies directly to gravitationally bound systems. This
prediction has a number of observable consequences, none of which are in
conflict with observation. In this paper we compare test particle motion in the
nonstatic gravitational field outside a spherically symmetric source (as
predicted by a quasi-metric theory of gravity) to test particle motion in the
Schwarzschild geometry. It is found that if one incorrectly uses the
Schwarzschild geometry (to the relevant accuracy) to represent the nonstatic
quasi-metric model, the largest errors result from the mismodelling of null
paths. One consequence of this is that using electromagnetic signals to track
the motion of a non-relativistic particle results in the illusion that the
particle is influenced by an anomalous force of size cH (where H is the Hubble
parameter) directed towards the observer. This result naturally explains the
apparently anomalous force acting on the Pioneer 10/11, Galileo and Ulysses
spacecraft as inferred from radiometric data.


title: Topology of the Universe

abstract:
  General relativity is unable to determine the topology of the Universe. We
propose to apply quantum approach. Quantization of dynamics of a test particle
is sensitive to the spacetime topology. Presented results for a particle in de
Sitter spacetimes favor a finite universe.


title: Nonminimal coupling and quintessence

abstract:
  Recent studies of Type Ia Supernovae with redshifts up to about $z~\laq~1$
reveal evidence for a cosmic acceleration in the expansion of the Universe. The
most straightforward explanation to account for this acceleration is a
cosmological constant dominating the recent history of our Universe; however, a
more interesting suggestion is to consider an evolving vacuum energy. Several
proposals have been put forward along these lines, most of them in the context
of General Relativity. In this work we analyse the conditions under which the
dynamics of a self-interacting Brans-Dicke field can account for this
accelerated expansion of the Universe. We show that accelerated expanding
solutions can be achieved with a quadratic self-coupling of the Brans-Dicke
field and a negative coupling constant $\omega$.


title:
Generation of Post-Newtonian Gravitational Radiation via Direct
  Integration of the Relaxed Einstein Equations

abstract:
  The completion of a network of advanced laser-interferometric
gravitational-wave observatories around 2001 will make possible the study of
the inspiral and coalescence of binary systems of compact objects (neutron
stars and black holes), using gravitational radiation. To extract useful
information from the waves, such as the masses and spins of the bodies,
theoretical general relativistic gravitational waveform templates of extremely
high accuracy will be needed for filtering the data, probably as accurate as
$O[(v/c)^6]$ beyond the predictions of the quadrupole formula. We summarize a
method, called DIRE, for Direct Integration of the Relaxed Einstein Equations,
which extends and improves an earlier framework due to Epstein and Wagoner, in
which Einstein's equations are recast as a flat spacetime wave equation with
source composed of matter confined to compact regions and gravitational
non-linearities extending to infinity. The new method is free of divergences or
undefined integrals, correctly predicts all gravitational wave ``tail'' effects
caused by backscatter of the outgoing radiation off the background curved
spacetime, and yields radiation that propagates asymptotically along true null
cones of the curved spacetime. The method also yields equations of motion
through $O[(v/c)^4]$, radiation-reaction terms at $O[(v/c)^5]$ and
$O[(v/c)^7]$, and gravitational waveforms and energy flux through $O[(v/c)^4]$,
in agreement with other approaches. We report on progress in evaluating the
$O[(v/c)^6]$ contributions.


title: The 5D-4D correspondence for the magnetic field

abstract:
  5D theory is an alternative model for understanding gravitational and
electromagnetic interactions together. In this work we used the correspondence
between 5D Einstein field equations with cosmological constant and the 4D
Einstein equations with sources. We started with the principal fiber bundle
P(M/F,U(1)) metric and studied the case when the gauge potential Aa corresponds
to the magnetic field: Aa =(0, 0, A3, 0). We identified the base-space with the
space-time of two models of universe: the Robertson-Walker - like model and the
Schwarzschild - like model. With this ansatz, we followed an algorithm that
permits to express the magnetic field in terms of the gauge potential Aa and
the scalar field F. This algorithm seems to work very well if the scalar field
is time dependent. When we analyzed its dependence on other coordinates, new
terms it comes out on the 5D field equations. We obtained the translation
between the effective 4D electromagnetic potential and the 5D gauge and scalar
fields.


title:
Perturbation theory for self-gravitating gauge fields I: The odd-parity
  sector

abstract:
  A gauge and coordinate invariant perturbation theory for self-gravitating
non-Abelian gauge fields is developed and used to analyze local uniqueness and
linear stability properties of non-Abelian equilibrium configurations. It is
shown that all admissible stationary odd-parity excitations of the static and
spherically symmetric Einstein-Yang-Mills soliton and black hole solutions have
total angular momentum number $\ell = 1$, and are characterized by
non-vanishing asymptotic flux integrals. Local uniqueness results with respect
to non-Abelian perturbations are also established for the Schwarzschild and the
Reissner-Nordstr\"om solutions, which, in addition, are shown to be linearly
stable under dynamical Einstein-Yang-Mills perturbations. Finally, unstable
modes with $\ell = 1$ are also excluded for the static and spherically
symmetric non-Abelian solitons and black holes.


title: A general worldline quantum inequality

abstract:
  Worldline quantum inequalities provide lower bounds on weighted averages of
the renormalised energy density of a quantum field along the worldline of an
observer. In the context of real, linear scalar field theory on an arbitrary
globally hyperbolic spacetime, we establish a worldline quantum inequality on
the normal ordered energy density, valid for arbitrary smooth timelike
trajectories of the observer, arbitrary smooth compactly supported weight
functions and arbitrary Hadamard quantum states. Normal ordering is performed
relative to an arbitrary choice of Hadamard reference state. The inequality
obtained generalises a previous result derived for static trajectories in a
static spacetime. The underlying argument is straightforward and is made
rigorous using the techniques of microlocal analysis. In particular, an
important role is played by the characterisation of Hadamard states in terms of
the microlocal spectral condition. We also give a compact form of our result
for stationary trajectories in a stationary spacetime.


title:
Generality of Singularity Avoidance in Superstring Theory: Anisotropic
  Case

abstract:
  In one-loop string effective action, we study a generality of non-singular
cosmological solutions found in the isotropic and homogeneous case. We discuss
Bianchi I and IX type spacetimes. We find that nonsingular solutions still
exist in Bianchi I model around nonsingular flat Friedmann solutions. On the
other hand, we cannot find any nonsingular solutions in Bianchi IX model.
Non-existence of nonsingular Bianchi IX universe may be consistent with the
analysis by Kawai, Sakagami and Soda, i.e. the tensor mode perturbations
against nonsingular flat Friedmann universe are unstable, because Bianchi IX
model can be regarded as a closed Friedmann universe with a single
gravitational wave. So based on these facts, we may conclude the nonsingular
universe is found in isotropic case is generally unstable, a singularity
avoidance may not work in the present model.


title:
On the Equivalence Principle and a Unified Description of Gravitation
  and Electromagnetism

abstract:
  We first investigate the form the General Relativity Theory would have taken
had the gravitational mass and the inertial mass of material objects been
different. We then extend this analysis to electromagnetism and postulate an
equivalence principle for the electromagnetic field. We argue that to each
particle with a different electric charge-to-mass ratio in superimposed
gravitational and electromagnetic fields there corresponds a spacetime manifold
whose metric tensor $g_{\mu\nu}$ describes the dynamical actions of gravitation
and electromagnetism. The electric field outside a charged sphere asserts
itself independently rather than contributing to the gravitational field. The
contribution of the electric field to the spacetime metric outside the charged
sphere is shown to be similar to the gravitational one in the Schwartzschild
metric but with a charge-to-mass ratio dependence of the test particle instead
of the Reissner - Nordstr\"om metric, resulting in a unified description of
gravitation and electromagnetism. We point out that there are existing
experiments whose results can be explained by the equivalence principle for the
electromagnetic field presented here. Additional experimental predictions of
the theory are mentioned.

categories: gr-qc astro-ph hep-ph math-ph math.MP quant-ph


title: Communication through an extra dimension

abstract:
  If our visible universe is considered a trapped shell in a five-dimensional
hyper-universe, all matter in it may be connected by superluminal signals
traveling through the fifth dimension. Events in the shell are still causal,
however, the propagation of signals proceeds at different velocities depending
on the fifth coordinate.


title: Signature of chaos in gravitational waves from a spinning particle

abstract:
  A spinning test particle around a Schwarzschild black hole shows a chaotic
behavior, if its spin is larger than a critical value. We discuss whether or
not some peculiar signature of chaos appears in the gravitational waves emitted
from such a system. Calculating the emitted gravitational waves by use of the
quadrupole formula, we find that the energy emission rate of gravitational
waves for a chaotic orbit is about 10 times larger than that for a circular
orbit, but the same enhancement is also obtained by a regular "elliptic" orbit.
A chaotic motion is not always enhance the energy emission rate maximally. As
for the energy spectra of the gravitational waves, we find some characteristic
feature for a chaotic orbit. It may tell us how to find out a chaotic behavior
of the system. Such a peculiar behavior, if it will be found, may also provide
us some additional informations to determine parameters of a system such as a
spin.


title: Entropy of gravitons produced in the early Universe

abstract:
  Gravitons produced from quantum vacuum fluctuations during an inflationary
stage in the early Universe have zero entropy as far as they reflect the time
evolution (squeezing) of a pure state, their large occupation number
notwithstanding. A non-zero entropy of the gravitons (classical gravitational
waves (GW) after decoherence) can be obtained through coarse graining. The
latter has to be physically justified {\it and} should not contradict
observational constraints. We propose two ways of coarse graining for which the
fixed temporal phase of each Fourier mode of the GW background still remains
observable: one based on quantum entanglement, and another one following from
the presence of a secondary GW background. The proposals are shown to be
mutually consistent. They lead to the result that the entropy of the primordial
GW background is significantly smaller than it was thought earlier. The
difference can be ascribed to the information about the regular (inflationary)
initial state of the Universe which is stored in this background and which
reveals itself, in particular, in the appearance of primordial peaks (acoustic
peaks in the case of scalar perturbations) in the multipole spectra of the CMB
temperature anisotropy and polarization.


title: Scalar GW detection with a hollow spherical antenna

abstract:
  We study the response and cross sections for the absorption of GW energy in a
Jordan-Brans-Dicke theory by a resonant mass detector shaped as a hollow
sphere.


title:
Late-time evolution of the Yang-Mills field in the spherically symmetric
  gravitational collapse

abstract:
  We investigate the late-time evolution of the Yang-Mills field in the
self-gravitating backgrounds: Schwarzschild and Reissner-Nordstr\"om
spacetimes. The late-time power-law tails develop in the three asymptotic
regions: the future timelike infinity, the future null infinity and the black
hole horizon. In these two backgrounds, however, the late-time evolution has
quantitative and qualitative differences. In the Schwarzschild black hole
background, the late-time tails of the Yang-Mills field are the same as those
of the neutral massless scalar field with multipole moment l=1. The late-time
evolution is dominated by the spacetime curvature. When the background is the
Reissner-Nordstr\"om black hole, the late-time tails have not only a smaller
power-law exponent, but also an oscillatory factor. The late-time evolution is
dominated by the self-interacting term of the Yang-Mills field. The cause
responsible for the differences is revealed.


title: Laws Governing Isolated Horizons: Inclusion of Dilaton Couplings

abstract:
  Mechanics of non-rotating black holes was recently generalized by replacing
the static event horizons used in standard treatments with `isolated horizons.'
This framework is extended to incorporate dilaton couplings. Since there can be
gravitational and matter radiation outside isolated horizons, now the
fundamental parameters of the horizon, used in mechanics, must be defined using
only the local structure of the horizon, without reference to infinity. This
task is accomplished and the zeroth and first laws are established. To
complement the previous work, the entire discussion is formulated tensorially,
without any reference to spinors.


title: Do stringy corrections stabilize coloured black holes?

abstract:
  We consider hairy black hole solutions of Einstein-Yang-Mills-Dilaton theory,
coupled to a Gauss-Bonnet curvature term, and we study their stability under
small, spacetime-dependent perturbations. We demonstrate that the stringy
corrections do not remove the sphaleronic instabilities of the coloured black
holes with the number of unstable modes being equal to the number of nodes of
the background gauge function. In the gravitational sector, and in the limit of
an infinitely large horizon, the coloured black holes are also found to be
unstable. Similar behaviour is exhibited by the magnetically charged black
holes while the bulk of the neutral black holes are proven to be stable under
small, gauge-dependent perturbations. Finally, the electrically charged black
holes are found to be characterized only by the existence of a gravitational
sector of perturbations. As in the case of neutral black holes, we demonstrate
that for the bulk of electrically charged black holes no unstable modes arise
in this sector.


title: Ermakov approach for Q=0 empty FRW minisuperspace oscillators

abstract:
  The Wheeler-DeWitt equation for empty FRW minisuperspace universes of
Hartle-Hawking factor ordering parameter Q=0 is mapped onto the dynamics of a
unit mass classical oscillator. The latter is studied by the classical Ermakov
invariant method. Angle quantities are presented in the same context


title:
Coherent state approach to quantum clock in a model where the
  Hamiltonian is a difference between two harmonic oscillators

abstract:
  In order to study the "problem of time", Rovelli proposed a model of a two
harmonic oscillator system where one of the oscillators can be thought of as a
'clock' for the other oscillator. In this paper we examine a model where the
Hamiltonian is a difference between two harmonic oscillators, and we consider
one of them which has the minus sign as a 'clock'. Klauder's projection
operator approach to generalized coherent states is used to define physical
states and operators. The resolution of unity is derived in terms of a gauge
invariant coordinate. We investigate the 'quantum clock' and show that the
evolution described by it is identical to the classical motion when the energy
becomes large.


title: Towards a regular type N vacuum gravitational field

abstract:
  An exact twisting type N vacuum solution is found. It has regular gauge and
curvature invariants and decays to flat spacetime for big retarded times.


title: Warm inflation with back - reaction: a stochastic approach

abstract:
  I study a stochastic approach for warm inflation considering back - reaction
of the metric with the fluctuations of matter field. This formalism takes into
account the local inhomogeneities fo the spacetime in a globally flat Friedmann
- Robertson - Walker metric. The stochastic equations for the fluctuations of
the matter field and the metric are obtained. Finally, the dynamics for the
amplitude of these fluctuations in a power - law expansion for the universe are
examined.


title: Dynamical Systems in Cosmology

abstract:
  Dynamical systems theory is especially well-suited for determining the
possible asymptotic states (at both early and late times) of cosmological
models, particularly when the governing equations are a finite system of
autonomous ordinary differential equations. We begin with a brief review of
dynamical systems theory. We then discuss cosmological models as dynamical
systems and point out the important role of self-similar models. We review the
asymptotic properties of spatially homogeneous perfect fluid models in general
relativity. We then discuss some results concerning scalar field models with an
exponential potential (both with and without barotropic matter). Finally, we
discuss some isotropic cosmological models derived from the string effective
action.


title: Cosmological model in 5D: Stationarity, yes or no

abstract:
  The tired-light cosmology is considered in the framework of Kaluza-Klein
theory in 5D. The solution of the five-dimensional semi-classical Einstein
equations with nonzero five-dimensional energy-momentum tensor gives density of
matter in the Universe well conformed to the observations. Variation of the
light velocity and change of the rest energy and mass are interrelated.
Variation of the Planck constant and electron charge is determined from formula
for hydrogen spectral frequencies and observations of the fine-structure.
Physical constants variation presents as explanation of anomalous change of the
length of a received wave detected during radiometric analysis of Pioneer 10/11
spacecraft data. Contemporary measurements accuracy of the Microwave Cosmic
Background doesn't allow to determine tendency of its parameters change
permitting choice between stationary and expanding Universe's model.


title: The Einstein Equations on the 3-Brane World

abstract:
  We carefully investigate the gravitational equations of the brane world, in
which all the matter forces except gravity are confined on the 3-brane in a
5-dimensional spacetime with $Z_2$ symmetry.
  We derive the effective gravitational equations on the brane, which reduce to
the conventional Einstein equations in the low energy limit. {}From our general
argument we conclude that the first Randall & Sundrum-type theory (RS1)
[hep-ph/9905221] predicts that the brane with the negative tension is an
anti-gravity world and hence should be excluded from the physical point of
view. Their second-type theory (RS2) [hep-th/9906064] where the brane has the
positive tension provides the correct signature of gravity. In this latter
case, if the bulk spacetime is exactly anti-de Sitter, generically the matter
on the brane is required to be spatially homogeneous because of the Bianchi
identities. By allowing deviations from anti-de Sitter in the bulk, the
situation will be relaxed and the Bianchi identities give just the relation
between the Weyl tensor and the energy momentum tensor. In the present brane
world scenario, the effective Einstein equations cease to be valid during an
era when the cosmological constant on the brane is not well-defined, such as in
the case of the matter dominated by the potential energy of the scalar field.


title:
Bondi-type systems near space-like infinity and the calculation of the
  NP-constants

abstract:
  We relate Bondi systems near space-like infinity to another type of gauge
conditions. While the former are based on null infinity, the latter are defined
in terms of Einstein propagation, the conformal structure, and data on some
Cauchy hypersurface. For a certain class of time symmetric space-times we study
an expansion which allows us to determine the behavior of various fields
arising in Bondi systems in the region of space-time where null infinity
touches space-like infinity. The coefficients of these expansions can be read
off from the initial data. We obtain in particular expressions for the
constants discovered by Newman and Penrose (NP-constants) in terms of the
initial data. For this purpose we calculate a certain expansion up to 3rd
order.


title: Magnetohydrodynamics in the Inflationary Universe

abstract:
  Magnetohydrodynamic (MHD) waves are analysed in the early Universe, in the
inflationary era, assuming the Universe to be filled with a nonviscous fluid of
the Zel'dovich type ($p=\rho$) in a metric of the de Sitter form. A spatially
uniform, time dependent, magnetic field ${\bf B_0}$ is assumed to be present.
The Einstein equations are first solved to give the time dependence of the
scale factor, assuming that the matter density, but not the magnetic field,
contribute as source terms. The various modes are thereafter analysed; they
turn out to be essentially of the same kind as those encountered in
conventional nongravitational MHD, although the longitudinal magnetosonic wave
is not interpretable as a physical energy-transporting wave as the group
velocity becomes superluminal. We determine the phase speed of the various
modes; they turn out to be scale factor independent. The Alfv\'{e}n velocity of
the transverse magnetohydrodynamic wave becomes extremely small in the
inflationary era, showing that the wave is in practice 'frozen in'.


title: Loop Quantum Gravity and the Meaning of Diffeomorphism Invariance

abstract:
  This series of lectures gives a simple and self-contained introduction to the
non-perturbative and background independent loop approach of canonical quantum
gravity. The Hilbert space of kinematical quantum states is constructed and a
complete basis of spin network states is introduced. An application of the
formalism is provided by the spectral analysis of the area operator, which is
the quantum analogue of the classical area function. This leads to one of the
key results of loop quantum gravity: the derivation of the discreteness of the
geometry and the computation of the quanta of area. Finally, an outlock on a
possible covariant formulation of the theory is given leading to a "sum over
histories" approach, denoted as spin foam model. Throughout the whole lecture
great significance is attached to conceptual and interpretational issues. In
particular, special emphasis is given to the role played by the diffeomorphism
group and the notion of observability in general relativity.


title: Schwarzschild Atmospheric Processes: A Classical Path to the Quantum

abstract:
  We develop some classical descriptions for processes in the Schwarzschild
string atmosphere. These processes suggest relationships between macroscopic
and microscopic scales. The classical descriptions developed in this essay
highlight the fundamental quantum nature of the Schwarzschild atmospheric
processes.


title: A possible solution for the non-existence of time

abstract:
  A possible solution for the problem of non-existence of universal time is
given by utilizing Goedel's incompleteness theorem.


title: Linearized general relativity and the Lanczos potential

abstract:
  Recently, there has been a revival of interest in the Lanczos potential of
the Weyl conformal tensor. Previous work by Novello and Neto has been done with
the linearized Lanczos potential as a model of a spin-2 field, which depends on
a massless limit of the field. In this paper, we look at an action based on a
massless potential, and show that it is classically equivalent to the
linearized regime of general relativity, without reference to a massless limit.


title: Equation of motion in a scalar model of gravity

abstract:
  A scalar model of gravity is considered. We propose Lorentz invariant field
equation $\square f = k\eta_{ab}f_{,a}f_{,b}$. The aim of this model is to get,
approximately, Newton's law of gravity. It is shown that $f=-\frac
1k\ln(1-k\frac mr)$ is the unique spherical symmetric static solution of the
field equation. $f$ is taken to be the field of a particle at the origin,
having the mass $m$. The field of a particle moving with a constant velocity is
taken to be the appropriate Lorentz transformation of $f$. The field $F$ of $N$
particles moving on trajectories ${\psi_j(t)}$ is taken to be, to first order,
the superposition of the fields of the particles, where the instantaneous
Lorentz transformation of the fields pertaining to the $j$-th particle is
${\dot\psi_j(t)}$. When this field is inserted to the field equation the
outcome is singular at $({\psi_j(t)},t)$. The singular terms of the l.h.s. and
of the r.h.s. are both $O(R^{-2})$. The only way to reduce the singularity in
the field equation is by postulating Newton's law of force. It is hoped that
this model will be generalized to system of equations that are covariant under
general diffeomorphism.


title: Approximating Connections in Loop Quantum Gravity

abstract:
  We discuss the action of the configuration operators of loop quantum gravity.
In particular, we derive the generalised eigenbasis for the Wilson loop
operator and show that the transformation between this basis and the
spin-network basis is given by an expansion in terms of Chebyshev polynomials.
These results are used to construct states which approximate connections on the
background 3-manifold in an analogous way that the weave states reproduce area
and volumes of a given 3-metric. This should be necessary for the construction
of genuine semi-classical states that are peaked both in the configuration and
momentum variables.


title: Trautman-Bondi Mass for Scalar Field and Gravity

abstract:
  The energy at null infinity is presented with the help of a simple example of
a massless scalar field in Minkowski spacetime. It is also discussed for
Einstein gravity. In particular, various aspects of the loss of the energy in
the radiating regime are shown.


title:
Coulomb field of an accelerated charge: physical and mathematical
  aspects

abstract:
  The Maxwell field equations relative to a uniformly accelerated frame, and
the variational principle from which they are obtained, are formulated in terms
of the technique of geometrical gauge invariant potentials. They refer to the
transverse magnetic (TM) and the transeverse electric (TE) modes. This gauge
invariant "2+2" decomposition is used to see how the Coulomb field of a charge,
static in an accelerated frame, has properties that suggest features of
electromagnetism which are different from those in an inertial frame. In
particular, (1) an illustrative calculation shows that the Larmor radiation
reaction equals the electrostatic attraction between the accelerated charge and
the charge induced on the surface whose history is the event horizon, and (2) a
spectral decomposition of the Coulomb potential in the accelerated frame
suggests the possibility that the distortive effects of this charge on the
Rindler vacuum are akin to those of a charge on a crystal lattice.


title: Disc sources for Conformastationary metrics

abstract:
  Conformastationary metrics have been derived by Perjes and by Israel and
Wilson as source-free solutions of the Einstein-Maxwell equations. By analogy
with the conformastatic metrics which have charged dust sources it was assumed
that conformastationary metrics would be the external metrics of charged dust
in steady motion. However for axially symmetric conformastationary metrics we
show that, as well as moving dust, hoop tensions are always necessary to
balance the centrifugal forces induced by the motion. Exact examples of
conformastationary metrics with disk sources are worked out in full.
Generalisations to non-axially symmetric conformastationary metrics are
indicated.


title:
Entropy bound of a charged object and electrostatic self-energy in black
  holes

abstract:
  Without pretending to any rigour, we find a general expression of the
electrostatic self-energy in static black holes with spherical symmetry. We
determine the entropy bound of a charged object by assuming the existence of
thermodynamics for these black holes. By combining these two results, we show
that the entropy bound does not depend on the considered black hole.


title: Are we at the dawn of quantum-gravity phenomenology?

abstract:
  A handful of recent papers has been devoted to proposals of experiments
capable of testing some candidate quantum-gravity phenomena. These lecture
notes emphasize those aspects that are most relevant to the questions that come
to mind when one is exposed for the first time to these research developments:
How come theory and experiments are finally meeting in spite of all the gloomy
forecasts that pervade traditional reviews? Is this a case of theorists having
put forward more and more speculative ideas until a point was reached at which
conventional experiments could rule out the proposed phenomena? Or has there
been such a remarkable improvement in experimental techniques and ideas that we
are now capable of testing plausible candidate quantum-gravity phenomena? These
questions are analysed rather carefully for the recent proposals of
interferometry-based tests and tests using observations of gamma rays of
astrophysical origin. I also briefly discuss other proposed experiments
(including tests of quantum-gravity-induced decoherence using the neutral-kaon
system and accelerator tests of models with large extra dimensions). The
emerging picture suggests that we are finally starting the exploration of a
large class of plausible quantum-gravity effects. However, our chances to
obtain positive (discovery) experimental results depend crucially on the
magnitude of these effects. In most cases the level of sensitivity that the
relevant experiments should achieve within a few years corresponds to effects
suppressed only linearly by the Planck length.


title: Scattering map for two black holes

abstract:
  We study the motion of light in the gravitational field of two Schwarzschild
black holes, making the approximation that they are far apart, so that the
motion of light rays in the neighborhood of one black hole can be considered to
be the result of the action of each black hole separately. Using this
approximation, the dynamics is reduced to a 2-dimensional map, which we study
both numerically and analytically. The map is found to be chaotic, with a
fractal basin boundary separating the possible outcomes of the orbits (escape
or falling into one of the black holes). In the limit of large separation
distances, the basin boundary becomes a self-similar Cantor set, and we find
that the box-counting dimension decays slowly with the separation distance,
following a logarithmic decay law.


title:
The evolution of circular, non-equatorial orbits of Kerr black holes due
  to gravitational-wave emission

abstract:
  A major focus of much current research in gravitation theory is on
understanding how radiation reaction drives the evolution of a binary system,
particularly in the extreme mass ratio limit. Such research is of direct
relevance to gravitational-wave sources for space-based detectors (such as
LISA). We present here a study of the radiative evolution of circular (i.e.,
constant Boyer-Lindquist coordinate radius), non-equatorial Kerr black hole
orbits. Recent theorems have shown that, at least in an adiabatic evolution,
such orbits evolve from one circular configuration into another, changing only
their radius and inclination angle. This constrains the system's evolution in
such a way that the change in its Carter constant can be deduced from knowledge
of gravitational wave fluxes propagating to infinity and down the black hole's
horizon. Thus, in this particular case, a local radiation reaction force is not
needed. In accordance with post-Newtonian weak-field predictions, we find that
inclined orbits radiatively evolve to larger inclination angles (although the
post-Newtonian prediction overestimates the rate of this evolution in the
strong field by a factor $\lesssim 3$). We also find that the gravitational
waveforms emitted by these orbits are rather complicated, particularly when the
hole is rapidly spinning, as the radiation is influenced by many harmonics of
the orbital frequencies.


title: Gravitational Flux Tubes

abstract:
  By studying multidimensional Kaluza-Klein theories, or gravity plus U(1) or
SU(2) gauge fields it is shown that these theories possess similar flux tube
solutions. The gauge field which fills the tube geometry of these solutions
leads to a comparision with the flux tube structures in QCD. These solutions
also carry a ``magnetic'' charge, Q, which for the SU(2) Einstein-Yang-Mills
(EYM) system exhibits a dual relationship with the Yang-Mills gauge coupling,
g, ($Q=1/g$). As $Q \to 0$ or $Q \to \infty$, $g \to \infty$ or $g \to 0$
respectively. Thus within this classical EYM field theory we find solutions
which have features - flux tubes, magnetic charges, large value of the gauge
coupling - that are similar to the key ingredients of confinement in QCD.


title:
Hamilton-Jacobi approach to pre-big bang cosmology and the problem of
  initial conditions

abstract:
  The Hamilton-Jacobi equation for the string cosmology is solved using the
gradient expansion method. The zeroth order solution is taken to be the
standard pre-big bang model and the second order solution is found for the
dilaton and the three-metric. It indicates that corrections generated by
inhomogeneities of the seed metric are suppressed near the singularity and are
growing towards the asymptotic past, but corrections generated by the dilaton
inhomogeneities are growing near the singularity and are suppressed in the
past. Possible influences of initial metric inhomogeneities on the pre-big bang
superinflation are discussed.


title:
Dimensionless Constants of the Fundamental Physical Interactions viewed
  by the Model of Expansive Nondecelerative Universe

abstract:
  A profound relationship between the ENU (Expansive Nondecelerative Universe)
and dimensionless constants of the fundamental physical interactions is
presented. The contribution corrects the Dirac presumption on a time decrease
of the gravitational constant G and using simple relations it precises the
values of the vector bosons x and y.


title:
Proposed Experiments to Test the Unified Description of Gravitation and
  Electromagnetism through a Symmetric Metric

abstract:
  If gravitation and electromagnetism are both described in terms of a
symmetric metric tensor, then the deflection of an electron beam by a charged
sphere should be different from its deflection according to the
Reissner-Nordstr\"om solution of General Relativity. If such a unified
description is true, the equivalence principle for the electric field implies
that the photon has a nonzero effective electric charge-to-mass ratio and
should be redshifted in an electric field and be deflected in a magnetic field.
Experiments to test these predictions are proposed.


title: Generating rotating fields in general relativity

abstract:
  I present a new method to generate rotating solutions of the Einstein-Maxwell
equations from static solutions, give several examples of its application, and
discuss its general properties.


title: Minkowski Bessel modes

abstract:
  The global Minkowski Bessel (M-B) modes, whose explicit form allows the
identification and description of the condensed vacuum state resulting from the
operation of a pair of accelerated refrigerators, are introduced. They span the
representation space of the unitary representation of the Poincare group on 2-D
Lorentz space-time. Their three essential properties are: (1) they are
unitarily related to the familiar Minkowski plane waves; (2) they form a
unitary representation of the translation group on two dimensional Minkowski
spacetime. (3) they are eigenfunctions of Lorentz boosts around a given
reference event. In addition the global Minkowski Mellin modes are introduced.
They are the singular limit of the M-B modes. This limit corresponds to the
zero transverse momentum solutions to the zero rest mass wave equation.
  Also introduced are the four Rindler coordinate representatives of each
global mode. Their normalization and density of states are exhibited in a
(semi-infinite) accelerated frame with a finite bottom. In addition we exhibit
the asymptotic limit as this bottom approaches the event horizon and thereby
show how a mode sum approaches a mode integral as the frame becomes bottomless.


title: Quantum radiation from a partially reflecting moving mirror

abstract:
  We consider the quantum radiation from a partially reflecting moving mirror
for the massless scalar field in 1+1 Minkowski space. Partial reflectivity is
achieved by localizing a delta-type potential at the mirror's position. The
radiated flux is exactly obtained for arbitrary motions as an integral
functional of the mirror's past trajectory. Partial reflectivity corrections to
the perfect mirror result are discussed.


title: A new form of the Kerr solution

abstract:
  A new form of the Kerr solution is presented. The solution involves a time
coordinate which represents the local proper time for free-falling observers on
a set of simple trajectories. Many physical phenomena are particularly clear
when related to this time coordinate. The chosen coordinates also ensure that
the solution is well behaved at the horizon. The solution is well suited to the
tetrad formalism and a convenient null tetrad is presented. The Dirac
Hamiltonian in a Kerr background is also given and, for one choice of tetrad,
it takes on a simple, Hermitian form.


title: Dynamics and symmetries of a field partitioned by an accelerated frame

abstract:
  The canonical evolution and symmetry generators are exhibited for a
Klein-Gordon (K-G) system which has been partitioned by an accelerated
coordinate frame into a pair of subsystems. This partitioning of the K-G system
is conveyed to the canonical generators by the eigenfunction property of the
Minkowski Bessel (M-B) modes. In terms of the M-B degrees of freedom, which are
unitarily related to those of the Minkowski plane waves, a near complete
diagonalization of these generators can be realized.


title:
Interface of General Relativity, Quantum Physics and Statistical
  Mechanics: Some Recent Developments

abstract:
  The arena normally used in black holes thermodynamics was recently
generalized to incorporate a broad class of physically interesting situations.
The key idea is to replace the notion of stationary event horizons by that of
`isolated horizons.' Unlike event horizons, isolated horizons can be located in
a space-time quasi-locally. Furthermore, they need not be Killing horizons. In
particular, a space-time representing a black hole which is itself in
equilibrium, but whose exterior contains radiation, admits an isolated horizon.
In spite of this generality, the zeroth and first laws of black hole mechanics
extend to isolated horizons. Furthermore, by carrying out a systematic,
non-perturbative quantization, one can explore the quantum geometry of isolated
horizons and account for their entropy from statistical mechanical
considerations. After a general introduction to black hole thermodynamics as a
whole, these recent developments are briefly summarized.


title: Entropy Production and Cosmological Inflation

abstract:
  The notion of inflation (past or present) in standard cosmological models is
shown to be a consequence of a sufficiently high second law entropy production
from the internal heating of the universal expansion. The longitudinal viscous
internal heating of matter requires neither ``inflaton'' fields nor
``quintessence'' fields which in theory may induce a cosmological term into the
Einstein equations. The purely thermodynamic principles required to understand
inflation within the context of the standard general relativity equations will
be discussed in detail.


title: Loop Quantum Cosmology I: Kinematics

abstract:
  The framework of quantum symmetry reduction is applied to loop quantum
gravity with respect to transitively acting symmetry groups. This allows to
test loop quantum gravity in a large class of minisuperspaces and to
investigate its features - e.g. the discrete volume spectrum - in certain
cosmological regimes. Contrary to previous studies of quantum cosmology
(minisuperspace quantizations) the symmetry reduction is carried out not at the
classical level but on an auxiliary Hilbert space of the quantum theory before
solving the constraints. Therefore, kinematical properties like volume
quantization survive the symmetry reduction. In this first part the kinematical
framework, i.e. implementation of the quantum symmetry reduction and
quantization of Gauss and diffeomorphism constraints, is presented for Bianchi
class A models as well as locally rotationally symmetric and spatially
isotropic closed and flat models.


title: Loop Quantum Cosmology II: Volume Operators

abstract:
  Volume operators measuring the total volume of space in a loop quantum theory
of cosmological models are constructed. In the case of models with rotational
symmetry an investigation of the Higgs constraint imposed on the reduced
connection variables is necessary, a complete solution of which is given for
isotropic models; in this case the volume spectrum can be calculated
explicitly. It is observed that the stronger the symmetry conditions are the
smaller is the volume spectrum, which can be interpreted as level splitting due
to broken symmetries. Some implications for quantum cosmology are presented.


title:
Long-range acceleration induced by a scalar field external to gravity
  and the indication from Pioneer 10/11, Galileo and Ulysses Data

abstract:
  We suggest an explanation of the "Pioneer effect" based on the interaction of
the spacecraft with a long-range scalar field, $\phi$. The scalar field under
consideration is external to gravity, coupled to the ordinary matter and
undergoes obedience to the weak equivalence principle. In the weak fields limit
it result a long-range acceleration $a_{P}$, asymptotically constant within the
region of the solar system hitherto crossed by the spacecraft.


title: Paired Accelerated Frames

abstract:
  The geometrical and quantum mechanical basis for Davies' and Unruh's
acceleration temperature is traced to a type of quantum mechanical
(``achronal'') spin. Its existence and definition are based on pairs of
causally disjoint accelerated frames. For bosons the expected spin vector of
monochromatic particles is given by the ``Planckian power'' and the ``r.m.s.
thermal fluctuation'' spectra. Under spacetime translation the spin direction
precesses around that ``Planckian'' vector. By exhibiting the conserved
achronal spin four-current, we extend the identification of achronal spin from
single quanta to multiparticle systems. Total achronal spin conservation is
also shown to hold, even in the presence of quadratic interactions.


title: Acceleration-induced carrier of the imprints of gravitation

abstract:
  We exhibit a purely quantum mechanical carrier of the imprints of gravitation
by identifying for a relativistic charge a property which (i) is independent of
its mass and (ii) expresses the Poincare invariance of spacetime in the absence
of gravitation.
  This carrier is a Klein-Gordon-equation-determined vector field given by the
``Planckian power'' and the ``r.m.s. thermal fluctuation'' spectra. The
imprints themselves are deviations away from this vector field.


title: Nature of singularities in gravitational collapse

abstract:
  We discuss several aspects of cosmic censorship hypothesis. There is evidence
both in favor and against the hypothesis. On one hand one can prove that cosmic
censorship holds in several special cases and on the other hand there is a
number of special solutions of Einstein equations in which it is violated. One
way to resolve cosmic censorship problem is to test it observationally. We
point out to several possibilities of such tests using present and future
instruments.


title:
Gravitational Collapse of Perfect Fluid in N-Dimensional Spherically
  Symmetric Spacetimes

abstract:
  The Riemann, Ricci and Einstein tensors for N-dimensional spherically
symmetric spacetimes in various systems of coordinates are studied, and the
general metric for conformally flat spacetimes is given. As an application, all
the Friedmann-Robertson-Walker-like solutions for a perfect fluid with an
equation of state $p = k \rho$ are found. Then, these solutions are used to
model the gravitational collapse of a compact ball, by first cutting them along
a timelike hypersurface and then joining them with asymptotically flat Vaidya
solutions. It is found that when the collapse has continuous self-similarity,
the formation of black holes always starts with zero mass, and when the
collapse has no such symmetry, the formation of black holes always starts with
a finite non-zero mass.


title: Why do we live in a Riemannian space time ?

abstract:
  We start from the pure Einstein-Hilbert action in Metric Affine Gravity, with
the orthonormal metric. We get an effective Levi-Civita Dilaton gravity theory
in which the Dilaton field is related to the scaling of the gravitational
coupling. When the Weyl symmetry is broken the resulting Einstein-Hilbert term
is equivalent to the Levi-Civita one, using the projective invariance of the
model, the non-metricity and torsion may be removed, so that we get a theory
perfectly equivalent to general relativity. This may explain why low energy
gravity is described by a Riemannian connection.


title: A Calculation on the Self-field of a Point Charge and the Unruh Effect

abstract:
  Within the context of quantum field theory in curved spacetimes, Hacyan and
Sarmiento defined the vacuum stress-energy tensor with respect to the
accelerated observer. They calculated it for uniform acceleration and circular
motion, and derived that the rotating observer perceives a flux. Mane related
the flux to synchrotron radiation. In order to investigate the relation between
the vacuum stress and bremsstrahlung, we estimate the stress-energy tensor of
the electromagnetic field generated by a point charge, at the position of the
charge. We use the retarded field as a self-field of the point charge.
Therefore the tensor diverges if we evaluate it as it is. Hence we remove the
divergent contributions by using the expansion of the tensor in powers of the
distance from the point charge. Finally, we take an average for the angular
dependence of the expansion. We calculate it for the case of uniform
acceleration and circular motion, and it is found that the order of the vacuum
stress multiplied by $\pi\alpha$ ($\alpha=e^2/\hbar c$ is the fine structure
constant) is equal to that of the self-stress. In the Appendix, we give another
trial approach with a similar result.


title: Scalar-Tensor Gravity Theory For Dynamical Light Velocity

abstract:
  A gravity theory is developed with the metric ${\hat g}_{\mu\nu}=
{g}_{\mu\nu}+B\partial_\mu\phi\partial_\nu\phi$. In the present universe the
additional contribution from the scalar field in the metric ${\hat g}_{\mu\nu}$
can generate an acceleration in the expansion of the universe, without negative
pressure and with a zero cosmological constant. In this theory, gravitational
waves will propagate at a different speed from non-gravitational waves. It is
suggested that gravitational wave experiments could test this observational
signature.


title: Rotating Boson Star with Large Self-interaction in (2+1) dimensions

abstract:
  Solutions for rotating boson stars in (2+1) dimensional gravity with a
negative cosmological constant are obtained numerically. The mass, particle
number, and radius of the (2+1) dimensional rotating boson star are shown.
Consequently we find the region where the stable boson star can exist.


title: Pair of accelerated frames: a perfect interferometer

abstract:
  The four Rindler quadrants of a pair of oppositely accelerated frames are
identified as a (Lorentzian) Mach-Zehnder interferometer. The Rindler frequency
dependence of the interference process is expressed by means of a (Lorentzian)
differential cross section. The Rindler frequencies of the waves in the two
acccelerated frames can be measured directly by means of a simple inertially
moving detector.


title: Covariant description for superfluids in gravitational fields

abstract:
  In this paper we develop a formalism to describe a superfluid in a
gravitational background. This formalism is based on a covariant generalization
of the field description for a superconductor in terms of a U(1) spontaneous
symmetry breaking. We study the stability of the solutions for a vortexless
fluid and the force acting on vortices in the fluid, which is a generalization
of the well-known flat space-time Magnus force. To clarify the development we
include the explicit discussion of two particular cases, one of them of
astrophysical interest.


title: The Angular Resolution of Space-Based Gravitational Wave Detectors

abstract:
  Proposed space-based gravitational wave antennas involve satellites arrayed
either in an equilateral triangle around the earth in the ecliptic plane (the
ecliptic-plane option) or in an equilateral triangle orbiting the sun in such a
way that the plane of the triangle is tilted at 60 degrees relative to the
ecliptic (the precessing-plane option). In this paper, we explore the angular
resolution of these two classes of detectors for two kinds of sources
(essentially monochromatic compact binaries and coalescing massive-black-hole
binaries) using time-domain expressions for the gravitational waveform that are
accurate to 4/2 PN order. Our results display an interesting effect not
previously reported in the literature, and underline the importance of
including the higher-order PN terms in the waveform when predicting the angular
resolution of ecliptic-plane detector arrays.


title: Toward gravitational wave detection

abstract:
  An overview of some tools and techniques being developed for data
conditioning (regression of instrumental and environmental artifacts from the
data channel), detector design evaluation (modeling the science ``reach'' of
alternative detector designs and configurations), noise simulations for mock
data challenges and analysis system validation, and analyses for the detection
of gravitational radiation from gamma-ray burst sources.


title: Quantum evolution in spacetime foam

abstract:
  In this work, I review some aspects concerning the evolution of quantum
low-energy fields in a foamlike spacetime, with involved topology at the Planck
scale but with a smooth metric structure at large length scales, as follows.
Quantum gravitational fluctuations may induce a minimum length thus introducing
an additional source of uncertainty in physics. The existence of this
resolution limit casts doubts on the metric structure of spacetime at the
Planck scale and opens a doorway to nontrivial topologies, which may dominate
Planck scale physics. This foamlike structure of spacetime may show up in
low-energy physics through loss of quantum coherence and mode-dependent energy
shifts, for instance, which might be observable. Spacetime foam introduces
nonlocal interactions that can be modeled by a quantum bath, and low-energy
fields evolve according to a master equation that displays such effects.
Similar laws are also obtained for quantum mechanical systems evolving
according to good real clocks, although the underlying Hamiltonian structure in
this case establishes serious differences among both scenarios. Contents.---
Quantum fluctuations of the gravitational field; Spacetime foam; Loss of
quantum coherence; Quantum bath; Low-energy effective evolution; Real clocks;
Conclusions.


title: Schlesinger system, Einstein equations and hyperelliptic curves

abstract:
  We review recent developments in the method of algebro-geometric integration
of integrable systems related to deformations of algebraic curves. In
particular, we discuss the theta-functional solutions of Schlesinger system,
Ernst equation and self-dual SU(2)-invariant Einstein equations.


title: Free-Field Realization of D-dimensional Cylindrical Gravitational Waves

abstract:
  We find two-dimensional free-field variables for D-dimensional general
relativity on spacetimes with D-2 commuting spacelike Killing vector fields and
non-compact spatial sections for D>4. We show that there is a canonical
transformation which maps the corresponding two-dimensional dilaton gravity
theory into a two-dimensional diffeomorphism invariant theory of the free-field
variables. We also show that the spacetime metric components can be expressed
as asymptotic series in negative powers of the dilaton, with coefficients which
can be determined in terms of the free fields.


title: Quantum Holonomies in (2+1)-Dimensional Gravity

abstract:
  We describe an approach to the quantisation of (2+1)-dimensional gravity with
topology R x T^2 and negative cosmological constant, which uses two quantum
holonomy matrices satisfying a q-commutation relation. Solutions of diagonal
and upper-triangular form are constructed, which in the latter case exhibit
additional, non-trivial internal relations for each holonomy matrix.
Representations are constructed and a group of transformations - a
quasi-modular group - which preserves this structure, is presented.


title:
Numerical Evolution in time of curvature perturbations in Kerr black
  holes

abstract:
  This paper reviews the basic features of the theory of curvature
perturbations in Kerr spacetime, which is customarily written in terms of gauge
invariant components of the Weyl tensor which satisfy a perturbation equation
known as the Teukolsky equation. I will describe how to evolve generic
perturbations about the Kerr metric and the separable form of the wave
solutions that one obtains, and the relation of the Teukolsky function to the
energy of gravitational waves emitted by the black hole. A discussion of a
numerical scheme to evolve perturbations as a function of time and some
preliminary results of our research project implementing it for matter sources
falling into the black hole is included.


title:
Classical and quantum evolution of non-isentropic hot singular layers in
  finite-temperature general relativity

abstract:
  The spherically symmetric layer of matter is considered within the frameworks
of general relativity. We perform generalization of the already known theory
for the case of nonconstant surface entropy and finite temperature. We also
propose the minisuperspace model to determine the behaviour of temperature
field and perform the Wheeler-DeWitt quantization.


title: Scalar mesostatic field with regard for gravitational effects

abstract:
  (Foreword by translator.) The aim of present translation is to clarify the
historically important question who was the pioneer in obtaining of exact
static solutions of Einstein equations minimally coupled with scalar field.
Usually, people cite the works by Janis, Newman, Winicour (Phys. Rev. Lett. 20
(1968) 878) and others authors whereas it is clear that JNW rediscovered (in
other coordinates) the Fisher's solution which was obtained 20 years before, in
1947. Regrettably, up to now I continue to meet many papers (even very fresh
ones) whose authors evidently do not know about the Fisher's work, so I try to
remove this gap by virtue of present translation and putting it into the LANL
e-print archive. (Original Abstract.) It is considered the scalar mesostatic
field of a point source with the regard for spacetime curvature caused by this
field. For the field with $\mass = 0$ the exact solution of Einstein equations
was obtained. It was demonstrated that at small distance from a source the
gravitational effects are so large that they cause the significant changes in
behavior of meson field. In particular, the total energy of static field
diverges logarithmically.


title:
Canonical quantum gravity in the Vassiliev invariants arena: I.
  Kinematical structure

abstract:
  We generalize the idea of Vassiliev invariants to the spin network context,
with the aim of using these invariants as a kinematical arena for a canonical
quantization of gravity. This paper presents a detailed construction of these
invariants (both ambient and regular isotopic) requiring a significant
elaboration based on the use of Chern-Simons perturbation theory which extends
the work of Kauffman, Martin and Witten to four-valent networks. We show that
this space of knot invariants has the crucial property -from the point of view
of the quantization of gravity- of being loop differentiable in the sense of
distributions. This allows the definition of diffeomorphism and Hamiltonian
constraints. We show that the invariants are annihilated by the diffeomorphism
constraint. In a companion paper we elaborate on the definition of a
Hamiltonian constraint, discuss the constraint algebra, and show that the
construction leads to a consistent theory of canonical quantum gravity.


title:
Canonical quantum gravity in the Vassiliev invariants arena: II.
  Constraints, habitats and consistency of the constraint algebra

abstract:
  In a companion paper we introduced a kinematical arena for the discussion of
the constraints of canonical quantum gravity in the spin network representation
based on Vassiliev invariants. In this paper we introduce the Hamiltonian
constraint, extend the space of states to non-diffeomorphism invariant
``habitats'' and check that the off-shell quantum constraint commutator algebra
reproduces the classical Poisson algebra of constraints of general relativity
without anomalies. One can therefore consider the resulting set of constraints
and space of states as a consistent theory of canonical quantum gravity.


title:
On the Possibility of Building a Black Hole for Electrons in the
  Laboratory

abstract:
  We point out in this work that if our recently proposed unified description
of gravitation and electromagnetism through a symmetric metric tensor is true,
then building in the laboratory black holes for electrons with radii r_E\ge
0.5m in air and with much smaller radii in a vacuum should be possible.


title:
GRLite and GRTensorJ: Graphical user interfaces to the computer algebra
  system GRTensorII

abstract:
  GRLite and GRTensorJ are first and second generation graphical user
interfaces to the computer algebra system GRTensorII. Current development
centers on GRTensorJ, which provides fully customizable symbolic procedures
that reduce many complex calculations to "elementary functions". Although still
in development, GRTensorJ, which is now available (free of charge) over the
internet, is sufficiently advanced to be of interest to researchers in general
relativity and related fields.

categories: gr-qc astro-ph cond-mat.mtrl-sci physics.comp-ph


title: On the Levi-Civita solutions with cosmological constant

abstract:
  The main properties of the Levi-Civita solutions with the cosmological
constant are studied. In particular, it is found that some of the solutions
need to be extended beyond certain hypersurfaces in order to have geodesically
complete spacetimes. Some extensions are considered and found to give rise to
black hole structure but with plane symmetry. All the spacetimes that are not
geodesically complete are Petrov type D, while in general the spacetimes are
Petrov type I.


title: Spectral Methods for Numerical Relativity. The Initial Data Problem

abstract:
  Numerical relativity has traditionally been pursued via finite differencing.
Here we explore pseudospectral collocation (PSC) as an alternative to finite
differencing, focusing particularly on the solution of the Hamiltonian
constraint (an elliptic partial differential equation) for a black hole
spacetime with angular momentum and for a black hole spacetime superposed with
gravitational radiation. In PSC, an approximate solution, generally expressed
as a sum over a set of orthogonal basis functions (e.g., Chebyshev
polynomials), is substituted into the exact system of equations and the
residual minimized. For systems with analytic solutions the approximate
solutions converge upon the exact solution exponentially as the number of basis
functions is increased. Consequently, PSC has a high computational efficiency:
for solutions of even modest accuracy we find that PSC is substantially more
efficient, as measured by either execution time or memory required, than finite
differencing; furthermore, these savings increase rapidly with increasing
accuracy. The solution provided by PSC is an analytic function given
everywhere; consequently, no interpolation operators need to be defined to
determine the function values at intermediate points and no special
arrangements need to be made to evaluate the solution or its derivatives on the
boundaries. Since the practice of numerical relativity by finite differencing
has been, and continues to be, hampered by both high computational resource
demands and the difficulty of formulating acceptable finite difference
alternatives to the analytic boundary conditions, PSC should be further pursued
as an alternative way of formulating the computational problem of finding
numerical solutions to the field equations of general relativity.


title: The Relativistic Transformation to Rotating Frames

abstract:
  We present a critical review of the relativistic rotation transformation of
Trocheris and Takeno. A new transformation is proposed which is free from the
drawbacks of the former. Some applications are presented.


title:
Paired accelerated arames: The perfect interferometer with everywhere
  smooth wave amplitudes

abstract:
  Rindler's acceleration-induced partitioning of spacetime leads to a
nature-given interferometer. It accomodates quantum mechanical and wave
mechanical processes in spacetime which in (Euclidean) optics correspond to
wave processes in a ``Mach-Zehnder'' interferometer: amplitude splitting,
reflection, and interference. These processes are described in terms of
amplitudes which behave smoothly across the event horizons of all four Rindler
sectors. In this context there arises quite naturally a complete set of
orthonormal wave packet histories, one of whose key properties is their
"explosivity index". In the limit of low index values the wave packets trace
out fuzzy world lines. By contrast, in the asymptotic limit of high index
values, there are no world lines, not even fuzzy ones. Instead, the wave packet
histories are those of entities with non-trivial internal collapse and
explosion dynamics. Their details are described by the wave processes in the
above-mentioned Mach-Zehnder interferometer. Each one of them is a double slit
interference process. These wave processes are applied to elucidate the
amplification of waves in an accelerated inhomogeneous dielectric. Also
discussed are the properties and relationships among the transition amplitudes
of an accelerated finite-time detector.


title:
Nonlinear and Perturbative Evolution of Distorted Black Holes. II.
  Odd-parity Modes

abstract:
  We compare the fully nonlinear and perturbative evolution of nonrotating
black holes with odd-parity distortions utilizing the perturbative results to
interpret the nonlinear results. This introduction of the second polarization
(odd-parity) mode of the system, and the systematic use of combined techniques
brings us closer to the goal of studying more complicated systems like
distorted, rotating black holes, such as those formed in the final inspiral
stage of two black holes. The nonlinear evolutions are performed with the 3D
parallel code for Numerical Relativity, {Cactus}, and an independent
axisymmetric code, {Magor}. The linearized calculation is performed in two
ways: (a) We treat the system as a metric perturbation on Schwarzschild, using
the Regge-Wheeler equation to obtain the waveforms produced. (b) We treat the
system as a curvature perturbation of a Kerr black hole (but here restricted to
the case of vanishing rotation parameter a) and evolve it with the Teukolsky
equation The comparisons of the waveforms obtained show an excellent agreement
in all cases.


title:
Geometry and topology of two kinds of extreme
  Reissner-Nordstr$\ddot{o}$m-anti-de Sitter black holes

abstract:
  Different geometrical and topological properties have been shown for two
kinds of extreme Reissner-Nordstr$\ddot{o}$m-anti-de Sitter black holes. The
relationship between the geometrical properties and the intrinsic
thermodynamical properties has been made explicit.


title: Quantum Mechanical Carrier of the Imprints of Gravitation

abstract:
  We exhibit a purely quantum mechanical carrier of the imprints of gravitation
by identifying for a relativistic system a property which (i) is independent of
its mass and (ii) expresses the Poincare invariance of spacetime in the absence
of gravitation. This carrier consists of the phase and amplitude correlations
of waves in oppositely accelerating frames. These correlations are expressed as
a Klein-Gordon-equation-determined vector field whose components are the
``Planckian power'' and the ``r.m.s. thermal fluctuation'' spectra. The
imprints themselves are deviations away from this vector field.


title:
Integrability of the Minimal Strain Equations for the Lapse and Shift in
  3+1 Numerical Relativity

abstract:
  Brady, Creighton and Thorne have argued that, in numerical relativity
simulations of the inspiral of binary black holes, if one uses lapse and shift
functions satisfying the ``minimal strain equations'' (MSE), then the
coordinates might be kept co-rotating, the metric components would then evolve
on the very slow inspiral timescale, and the computational demands would thus
be far smaller than for more conventional slicing choices. In this paper, we
derive simple, testable criteria for the MSE to be strongly elliptic, thereby
guaranteeing the existence and uniqueness of the solution to the Dirichlet
boundary value problem. We show that these criteria are satisfied in a test-bed
metric for inspiraling binaries, and we argue that they should be satisfied
quite generally for inspiraling binaries. If the local existence and uniqueness
that we have proved holds globally, then, for appropriate boundary values, the
solution of the MSE exhibited by Brady et. al. (which tracks the inspiral and
keeps the metric evolving slowly) will be the unique solution and thus should
be reproduced by (sufficiently accurate and stable) numerical integrations.


title: Higher-Derivative Quantum Cosmology

abstract:
  The quantum cosmology of a higher-derivative derivative gravity theory
arising from the heterotic string effective action is reviewed. A new type of
Wheeler-DeWitt equation is obtained when the dilaton is coupled to the
quadratic curvature terms. Techniques for solving the Wheeler-DeWitt equation
with appropriate boundary conditions shall be described, and implications for
semiclassical theories of inflationary cosmology will be outlined.


title: A novel approach to particle production in an uniform electric field

abstract:
  We outline a different method of describing scalar field particle production
in a uniform electric field. In the standard approach, the (analytically
continued) harmonic oscillator paradigm is important in describing particle
production. However, there is another gauge in which the particle production
process has striking similarities with the one used to describe Hawking
radiation in black holes. The gauge we use to describe the electric field in is
the lightcone gauge, so named because the mode functions for a scalar field are
found to be singular on the lightcone. We use these modes in evaluating the
effective Lagrangian using the proper time technique. The key feature of this
analysis is that these modes can be explicitly "normalized" by using the
criterion that they reduce to the usual flat space modes in the limit of the
electric field tending to zero. We find that the proper time kernel is not the
same as the analytically continued oscillator kernel though the effective
Lagrangian is the standard result as it should be. We also consider an example
of a confined electric field system using the lightcone gauge modes. Our
analysis indicates that the Bogolubov coefficients, in taking the limit to the
uniform electric field case, are multiplied by energy dependent boundary
factors that have not been taken into account before.


title: Underlying Field Structure of Matter

abstract:
  Intrinsic unfication of quantum theory and general relativity based on the
underlying quantum dynamics of fundamental field has been proposed.


title:
Two Coupled Superconducting Cavities as a Gravitational Wave Detector:
  First Experimental Results

abstract:
  First experimental results of a feasibility study of a gravitational wave
detector based on two coupled superconducting cavities are presented. Basic
physical principles underlying the detector behaviour and sensitivity limits
are discussed. The detector layout is described in detail and its rf properties
are showed. The limit sensitivity to small harmonic displacements at the
detection frequency (around 1 MHz) is showed. The system performance as a
potential g.w. detector is discussed and future developments are foreseen.


title:
Relativistic Conservation Laws on Curved Backgrounds and the Theory of
  Cosmological Perturbations

abstract:
  We first consider the Lagrangian formulation of general relativity for
perturbations with respect to a background spacetime. We show that by combining
Noether's method with Belinfante's "symmetrization'' procedure we obtain
conserved vectors that are independent of any divergence added to the perturbed
Hilbert Lagrangian. We also show that the corresponding perturbed energy-
momentum tensor is symmetrical and divergenceless but only on backgrounds that
are "Einstein spaces" in the sense of A.Z. Petrov. de Sitter or anti-de Sitter
and Einstein "spacetimes" are Einstein spaces but in general
Friedmann-Robertson -Walker spacetimes are not. Each conserved vector is a
divergence of an anti- symmetric tensor, a "superpotential". We find
superpotentials which are a generalization of Papapetrou's superpotential and
are rigorously linear, even for large perturbations, in terms of the inverse
metric density components and their first order derivatives. The
superpotentials give correct globally conserved quantities at spatial infinity.
They resemble Abbott and Deser's superpotential, but give correctly the
Bondi-Sachs total four-momentum at null infinity. Next we calculate conserved
vectors and superpotentials for perturbations of a Friedmann-Robertson-Walker
background associated with its 15 conformal Killing vectors given in a
convenient form. The integral of each conserved vector in a finite volume V at
a given conformal time is equal to a surface integral on the boundary of V of
the superpotential. For given boundary conditions each such integral is part of
a flux whose total through a closed hypersurface is equal to zero. For given
boundary conditions on V, the integral can be considered as an "integral
constraint" on data in the volume...


title: Vierbein walls in condensed matter

abstract:
  The effective field, which plays the part of the vierbein in general
relativity, can have topologically stable surfaces, vierbein domain walls,
where the effective contravariant metric is degenerate. We consider vierbein
walls separating domains with the flat space-time which are not causally
connected at the classical level. Possibility of the quantum mechanical
connection between the domains is discussed.


title: Development of a Double Pendulum for Gravitational Wave Detectors

abstract:
  Seismic noise will be the dominant source of noise at low frequencies for
ground based gravitational wave detectors, such as LIGO now under construction.
Future interferometers installed at LIGO plan to use at least a double pendulum
suspension for the test masses to help filter the seismic noise. We are
constructing an apparatus to use as a test bed for double pendulum design. Some
of the tests we plan to conduct include: dynamic ranges of actuators, and how
to split control between the intermediate mass and lower test mass;
measurements of seismic transfer functions; measurements of actuator and
mechanical cross couplings; and measurements of the noise from sensors and
actuators. All these properties will be studied as a function of mechanical
design of the double pendulum.


title: Gauge - invariant fluctuations of the metric in stochastic inflation

abstract:
  I derive the stochastic equation for the perturbations of the metric for a
gauge - invariant energy - momemtum - tensor (EMT) in stochastic inflation. A
quantization for the field that describes the gauge - invariant perturbations
for the metric is developed. In a power - law expansion for the universe the
amplitude for these perturbations on a background metric could be very
important in the infrared sector.


title: Effective noise in stochastic description of inflation

abstract:
  Stochastic description of inflationary spacetimes emulates the growth of
vacuum fluctuations by an effective stochastic ``noise field'' which drives the
dynamics of the volume-smoothed inflaton. We investigate statistical properties
of this field and find its correlator to be a function of distance measured in
units of the smoothing length. Our results apply for a wide class of smoothing
window functions and are different from previous calculations by Starobinsky
and others who used a sharp momentum cutoff. We also discuss the applicability
of some approximate noise descriptions to simulations of stochastic inflation.


title: Quintessence inhomogeneous cosmology

abstract:
  The Einstein-Klein-Gordon field equations are solved in a inhomogeneous
shear-free universe containing a material fluid, a self-interacting scalar
field, a variable cosmological term, and a heat flux. A quintessence-dominated
scenario arises with a power-law accelerated expansion compatible with the
currently observed homogeneous universe.


title: Remarks on the Charged, Magnetized Tomimatsu-Sato $\delta=2$ Solution

abstract:
  The full metric describing a charged, magnetized generalization of the
Tomimatsu-Sato (TS) $\delta=2$ solution is presented in a concise explicit
form. We use it to investigate some physical properties of the solution; in
particular, we point out the existence of naked ring singularities in the
hyperextreme TS metrics, the fact previously overlooked by the researchers, and
we also demonstrate that the ring singularities can be eliminated by
sufficiently strong magnetic fields in the subextreme case, while in the
hyperextreme case the magnetic field can move singularities to the equatorial
plane.


title: The global existence problem in general relativity

abstract:
  We survey some known facts and open questions concerning the global
properties of 3+1 dimensional spacetimes containing a compact Cauchy surface.
We consider spacetimes with an $\ell$-dimensional Lie algebra of space-like
Killing fields. For each $\ell \leq 3$, we give some basic results and
conjectures on global existence and cosmic censorship.


title: Matching characteristic codes: exploiting two directions

abstract:
  Combining incoming and outgoing characteristic formulations can provide
numerical relativists with a natural implementation of Einstein's equations
that better exploits the causal properties of the spacetime and gives access to
both null infinity and the interior region simultaneously (assuming the
foliation is free of caustics and crossovers). We discuss how this combination
can be performed and illustrate its behavior in the Einstein-Klein-Gordon field
in 1D.


title: Gravitational wave astronomy

abstract:
  The first decade of the new millenium should see the first direct detections
of gravitational waves. This will be a milestone for fundamental physics and it
will open the new observational science of gravitational wave astronomy. But
gravitational waves already play an important role in the modeling of
astrophysical systems. I review here the present state of gravitational
radiation theory in relativity and astrophysics, and I then look at the
development of detector sensitivity over the next decade, both on the ground
(such as LIGO) and in space (LISA). I review the sources of gravitational waves
that are likely to play an important role in observations by first- and
second-generation interferometers, including the astrophysical information that
will come from these observations. The review covers some 10 decades of
gravitational wave frequency, from the high-frequency normal modes of neutron
stars down to the lowest frequencies observable from space. The discussion of
sources includes recent developments regarding binary black holes, spinning
neutron stars, and the stochastic background.


title: The Principle of Equivalence and Electromagnetism

abstract:
  The problem of unification of Gravitation and Electromagnetism in four
dimensions; some new ideas involving mixtures of commuting and anti-commuting
co-ordinates. Maxwell's equations are extracted in terms of the curvature of
the anti-commuting component of space-time. The profound difference in the size
of the coupling constants of the two forces is interpreted in terms of the
degree of expansion of the two kinds of space-time with evolution of the
universe. Uncertainty in the quantum realm is interpreted in terms of an
unmeasurable component of anti-commuting space-time.


title: Black Holes of a Minimal Size in String Gravity

abstract:
  A lower limit for a neutral black hole size is obtained in the frames of the
string gravity model with the second order curvature correction. It is shown
that this effect remains when the third order curvature correction is also
taken into account and argued that such restriction does exist in all
perturbative orders of curvature expansions.


title: A Minimal Model for Dilatonic Gravity

abstract:
  We study a new minimal scalar-tensor model of gravity with Brans-Dicke factor
$\omega(\Phi)\equiv 0$ and cosmological factor $\Pi(\Phi)$. The constraints on
$\Pi(\Phi)$ from known gravitational experiments are derived. We show that
almost any time evolution of the scale factor in a homogeneous isotropic
Universe can be obtained via properly chosen $\Pi(\Phi)$ and discuss the
general properties of models of this type.


title: Boson stars with generic self-interactions

abstract:
  We study boson star configurations with generic, but not non-topological,
self-interaction terms, i.e. we do not restrict ourselves just to consider the
standard $\lambda |\psi|^4$ interaction but more general
U(1)-symmetry-preserving profiles. We find that when compared with the usual
potential, similar results for masses and number of particles appear. However,
changes are of order of few percent of the star masses. We explore the
stability properties of the configurations, that we analyze using catastrophe
theory. We also study possible observational outputs: gravitational redshifts,
rotation curves of accreted particles, and lensing phenomena, and compare with
the usual case.


title: Chaos in FRW cosmology with gently sloping scalar field potentials

abstract:
  The chaotic behavior in FRW cosmology with a scalar field is studied for
scalar field potentials less steep than quadratic. We describe a transition to
much stronger chaos for appropriate parameters of such potentials. The range of
parameters which allows this transition is specified. The influence of ordinary
matter on the chaotic properties of this model is also discussed.


title:
Calculating the self force in Schwarzschild spacetime by mode-sum
  regularization

abstract:
  We outline a method for calculating the self force (the "radiation reaction
force") acting on a scalar particle in a strong field orbit in a Schwarzschild
spacetime. In this method, the contribution to the self force associated with
each multipole mode of the particle's field is calculated separately, and the
sum over modes is then evaluated, subject to a certain regularization
procedure. We present some explicit results concerning the implementation of
the calculation scheme for a static particle, and also for a uniform circular
motion, on the Schwarzschild background.


title: Clifford Algebra Approach to Superenergy Tensors

abstract:
  Senovilla has recently defined an algebraic construction of a superenergy
tensor T{A} from any arbitrary tensor A, by structuring it as an r-fold form.
This superenergy tensor satisfies automatically the dominant superenergy
property. We present a more compact definition using the r-direct product
Clifford algebra r-Cl(p,q). This form for the superenergy tensors allows to
obtain an easy proof of the dominant superenergy property valid for any
dimension.


title: Self force on static charges in Schwarzschild spacetime

abstract:
  We study the self forces acting on static scalar and electric test charges in
the spacetime of a Schwarzschild black hole. The analysis is based on a direct,
local calculation of the self forces via mode decomposition, and on two
independent regularization procedures: A spatially-extended particle model
method, and on a mode-sum regularization prescription. In all cases we find
excellent agreement with the known exact results.


title: The Effect of Higher-Order Curvature Terms on String Quantum Cosmology

abstract:
  Several new results regarding the quantum cosmology of the quadratic gravity
theory derived from the heterotic string effective action are presented. After
describing techniques for solving the Wheeler-De Witt equation with appropriate
boundary conditions, it is shown that this quantum cosmological model may be
compared with semiclassical theories of inflationary cosmology. In particular,
it should be possible to compute corrections to the standard inflationary model
perturbatively about a stable exponentially expanding classical background.


title: Inertial Control of the VIRGO Superattenuator

abstract:
  The VIRGO superattenuator (SA) is effective in depressing the seismic noise
below the thermal noise level above 4 Hz. On the other hand, the residual
mirror motion associated to the SA normal modes can saturate the dynamics of
the interferometer locking system. This motion is reduced implementing a
wideband (DC-5 Hz) multidimensional control (the so called inertial damping)
which makes use of both accelerometers and position sensors and of a DSP
system. Feedback forces are exerted by coil-magnet actuators on the top of the
inverted pendulum. The inertial damping is successful in reducing the mirror
motion within the requirements. The results are presented.


title:
Monodromy Transform Approach to Solution of Some Field Equations in
  General Relativity and String Theory

abstract:
  A monodromy transform approach, presented in this communication, provides a
general base for solution of space-time symmetry reductions of Einstein
equations in all known integrable cases, which include vacuum, electrovacuum,
massless Weyl spinor field and stiff matter fluid, as well as some string
theory induced gravity models. It was found a special finite set of functional
parameters, defined as the monodromy data for the fundamental solution of
associated spectral problem. Similarly to the scattering data in the inverse
scattering transform, these monodromy data can be used for characterization of
any local solution of the field equations. A "direct" and "inverse" problems of
such monodromy transform admit unambiguous solutions. For the linear singular
integral equation with a scalar (i.e. non-matrix) kernel, which solves the
inverse problem of this monodromy transform, an equivalent regularization -- a
Fredholm linear integral equation of the second kind is constrcuted in several
convenient forms. For arbitrary choice of the monodromy data a simple iterative
method leads to an effective construction of the solution in terms of
homogeneously convergent functional series.


title:
Regular Black Hole in General Relativity Coupled to Nonlinear
  Electrodynamics

abstract:
  The first regular exact black hole solution in General Relativity is
presented. The source is a nonlinear electrodynamic field satisfying the weak
energy condition, which in the limit of weak field becomes the Maxwell field.
The solution corresponds to a charged black hole with |q| \leq 2 s_c m \approx
0.6 m, having the metric, the curvature invariants, and the electric field
regular everywhere.


title: Revised Relativistic Hydrodynamical Model for Neutron-Star Binaries

abstract:
  We report on numerical results from a revised hydrodynamic simulation of
binary neutron-star orbits near merger. We find that the correction recently
identified by Flanagan significantly reduces but does not eliminate the
neutron-star compression effect. Although results of the revised simulations
show that the compression is reduced for a given total orbital angular
momentum, the inner most stable circular orbit moves to closer separation
distances. At these closer orbits significant compression and even collapse is
still possible prior to merger for a sufficiently soft EOS. The reduced
compression in the corrected simulation is consistent with other recent studies
of rigid irrotational binaries in quasiequilibrium in which the compression
effect is observed to be small. Another significant effect of this correction
is that the derived binary orbital frequencies are now in closer agreement with
post-Newtonian expectations.


title: On Spin-driven inflation from fields in General Relativity and COBE data

abstract:
  Obukhov spin-driven inflation in General Relativity is extended to include
inflaton fields.A de Sitter phase solution is obtained and new slow-rolling
conditions for the spin potential are obtained.The spin potential reduces to
Obukhov result at the present epoch of the Universe where the spin density is
low with comparison to the Early Universe spin densities.A relation betwenn the
spin density energy and the temperature fluctuation can be obtained which allow
us to determine the spin density energy in terms of the COBE data for
temperature fluctuations.


title: A Topological Signature in Cosmic Topology

abstract:
  Two procedures for obtaining (extracting and constructing) the topological
signature of any multiply connected Robertson-Walker (RW) universe are
presented. It is shown through computer-aided simulations that both approaches
give rise to the same topological signature for a multiply connected flat RW
universe. The strength of these approaches is illustrated by extracting the
topological signatures of a flat ($k=0$), an elliptic ($k=1$), and a hyperbolic
($k=-1$) multiply connected RW universes. We also show how separated
contributions of the covering isometries add up to form the topological
signature of a RW flat universe. There emerges from our theoretical results and
simulations that the topological signature arises (in the mean) even when there
are just a few images for each object. It is also shown that the mean pair
separation histogram technique works, and that it is a suitable approach for
studying the topological signatures of RW universes as well as the role of
non-translational isometries.


title: Test compatible metrics and 2-branes

abstract:
  We propose a sufficient condition for a general spherical symmetric static
metric to be compatible with classical tests of gravity. A 1-parametric class
of such metrics are constructed.
  The Schwarzschild metric as well as the Yilmaz-Rosen metric are in this
class.
  By computing the scalar curvature we show that the non-Schwarzschild metrics
can be interpreted as close 2-branes.
  All the manifolds endowed the described metrics contain in a class of
pseudo-Riemannian manifolds with a scalar curvature of a fixed sign.


title: Complex Geometry of Nature and General Relativity

abstract:
  An attempt is made of giving a self-contained introduction to holomorphic
ideas in general relativity, following work over the last thirty years by
several authors. The main topics are complex manifolds, spinor and twistor
methods, heaven spaces.


title: Spontaneous Scalarization and Boson Stars

abstract:
  We study spontaneous scalarization in Scalar-Tensor boson stars. We find that
scalarization does not occur in stars whose bosons have no self-interaction. We
introduce a quartic self-interaction term into the boson Lagrangian and show
that when this term is large, scalarization does occur. Strong self-interaction
leads to a large value of the compactness (or sensitivity) of the boson star, a
necessary condition for scalarization to occur, and we derive an analytical
expression for computing the sensitivity of a boson star in Brans-Dicke theory
from its mass and particle number. Next we comment on how one can use the
sensitivity of a star in any Scalar-Tensor theory to determine how its mass
changes when it undergoes gravitational evolution. Finally, in the Appendix, we
derive the most general form of the boson wavefunction that minimises the
energy of the star when the bosons carry a U(1) charge.


title: Entropy, Gravitation, and Thermodynamics

abstract:
  The relationship between the intrinsic motion of gravity, light, and time is
explored in terms of the principles of entropy, causality, energy, and symmetry
conservation. A conceptual mechanism for gravity and the gravitational
connection between quantum mechanics and relativity is explored. A "concept
equation" is given for the gravitational annihilation of space and the
extraction of a metrically equivalent temporal residue. The relationship of
gravity to the other forces is discussed, including the reason for the weakness
of gravity.


title:
On Wigner's clock and the detectability of spacetime foam with
  gravitational-wave interferometers

abstract:
  A recent paper (gr-qc/9909017) criticizes our work on the structure of
spacetime foam. Its authors argue that the quantum uncertainty limit for the
position of the quantum clock in a gedanken timing experiment, obtained by
Wigner and used by us, is based on unrealistic assumptions. Here we point out
some flaws in their argument. We also discuss their other comments and some
other issues related to our work, including a simple connection to the
holographic principle. We see no reason to change our cautious optimism on the
detectability of spacetime foam with future refinements of modern
gravitational-wave interferometers like LIGO/VIRGO and LISA.


title: Gravitational-Recoil Effects on Fermion Propagation in Space-Time Foam

abstract:
  Motivated by the possible experimental opportunities to test quantum gravity
via its effects on high-energy neutrinos propagating through space-time foam,
we discuss how to incorporate spin structures in our D-brane description of
gravitational recoil effects in vacuo. We also point to an interesting
analogous condensed-matter system. We use a suitable supersymmetrization of the
Born-Infeld action for excited D-brane gravitational backgrounds to argue that
energetic fermions may travel slower than the low-energy velocity of light:
\delta c / c \sim -E/M. It has been suggested that Gamma-Ray Bursters may emit
pulses of neutrinos at energies approaching 10^{19} eV: these would be
observable only if M \gsim 10^{27} GeV.