title: On time evolution of quantum black holes

abstract:
  The time evolution of black holes involves both the canonical equations of
quantum gravity and the statistical mechanics of Hawking radiation, neither of
which contains a time variable. In order to introduce the time, we apply the
semiclassical approximation to the Hamiltonian constraint on the apparent
horizon and show that, when the backreaction is included, it suggests the
existence of a long-living remnant, similarly to what is obtained in the
microcanonical picture for the Hawking radiation.


title: Cosmological evolution in a brane-universe

abstract:
  The idea of extra-dimensions has recently gone through a renewal with the
hypothesis, suggested by recent developments in string theory, that ordinary
matter is confined to a sub-space, called brane, embedded in a higher
dimensional spacetime. I summarize here some consequences in cosmology of this
type of models. The most remarkable aspect is that the Friedmann laws, which
govern the expansion of the Universe, are modified. An important direction of
research is the study of cosmological perturbations and the possible signature
of extra-dimensions in cosmological observations.


title: Superfluid neutron stars

abstract:
  Neutron stars are believed to contain (neutron and proton) superfluids. I
will give a summary of a macroscopic description of the interior of neutron
stars, in a formulation which is general relativistic. I will also present
recent results on the oscillations of neutron stars, with superfluidity
explicitly taken into account, which leads in particular to the existence of a
new class of modes.


title: Subtle is the Gravity

abstract:
  In this lecture I build up the motivation for relativity and gravitation
based on general principles and common sense considerations which should fall
in the sphere of appreciation of a general reader. There is a novel way of
looking at things and understanding them in a more direct physical terms which
should be of interest to fellow relativists as well as physicists in general.


title: Many worlds in one

abstract:
  A generic prediction of inflation is that the thermalized region we inhabit
is spatially infinite. Thus, it contains an infinite number of regions of the
same size as our observable universe, which we shall denote as $\O$-regions. We
argue that the number of possible histories which may take place inside of an
$\O$-region, from the time of recombination up to the present time, is finite.
Hence, there are an infinite number of $\O$-regions with identical histories up
to the present, but which need not be identical in the future. Moreover, all
histories which are not forbidden by conservation laws will occur in a finite
fraction of all $\O$-regions. The ensemble of $\O$-regions is reminiscent of
the ensemble of universes in the many-world picture of quantum mechanics. An
important difference, however, is that other $\O$-regions are unquestionably
real.


title: Momentum Imparted by Gravitational Waves with Spherical Wavefronts

abstract:
  A different approach has been used to evaluate the momentum imparted by the
gravitational waves with spherical wavefronts. It is shown that the results
obtained for momentum coincide with those already available in the literature.


title:
Quantum noise in second generation, signal-recycled laser
  interferometric gravitational-wave detectors

abstract:
  It has long been thought that the sensitivity of laser interferometric
gravitational-wave detectors is limited by the free-mass standard quantum
limit, unless radical redesigns of the interferometers or modifications of
their input/output optics are introduced. Within a fully quantum-mechanical
approach we show that in a second-generation interferometer composed of arm
cavities and a signal recycling cavity, e.g., the LIGO-II configuration, (i)
quantum shot noise and quantum radiation-pressure-fluctuation noise are
dynamically correlated, (ii) the noise curve exhibits two resonant dips, (iii)
the Standard Quantum Limit can be beaten by a factor of 2, over a frequency
range \Delta f/f \sim 1, but at the price of increasing noise at lower
frequencies.


title:
Gravitational-wave dynamics and black-hole dynamics: second
  quasi-spherical approximation

abstract:
  Gravitational radiation with roughly spherical wavefronts, produced by
roughly spherical black holes or other astrophysical objects, is described by
an approximation scheme. The first quasi-spherical approximation, describing
radiation propagation on a background, is generalized to include additional
non-linear effects, due to the radiation itself. The gravitational radiation is
locally defined and admits an energy tensor, satisfying all standard local
energy conditions and entering the truncated Einstein equations as an effective
energy tensor. This second quasi-spherical approximation thereby includes
gravitational radiation reaction, such as the back-reaction on the black hole.
With respect to a canonical flow of time, the combined energy-momentum of the
matter and gravitational radiation is covariantly conserved. The corresponding
Noether charge is a local gravitational mass-energy. Energy conservation is
formulated as a local first law relating the gradient of the gravitational mass
to work and energy-supply terms, including the energy flux of the gravitational
radiation. Zeroth, first and second laws of black-hole dynamics are given,
involving a dynamic surface gravity. Local gravitational-wave dynamics is
described by a non-linear wave equation. In terms of a complex gravitational-
radiation potential, the energy tensor has a scalar-field form and the wave
equation is an Ernst equation, holding independently at each spherical angle.
The strain to be measured by a distant detector is simply defined.


title: Gravitational Collapse of a Radiating Shell

abstract:
  We study the collapse of a self-gravitating and radiating shell. Matter
constituting the shell is quantized and the construction is viewed as a
semiclassical model of possible black hole formation. It is shown that the
shell internal degrees of freedom are excited by the quantum non-adiabaticity
of the collapse and, consequently, on coupling them to a massless scalar field,
the collapsing matter emits a burst of coherent (thermal) radiation.


title: Numerical Relativity CM1-a and CM1-b sessions

abstract:
  Numerical Relativity is concerned with solving the Einstein equations, as
well as any field or matter equations on curved space-time, by means of
computer calculations. The methods developed for this purpose up to now, as
well as the addressed physical problems are getting more numerous every day.
This is a brief summary of the presentations which have been given during the
9th Marcel Grossman meeting, which took place in Rome, from 2nd to 8th of July
2000. Many different fields have been addressed, from pure numerics and applied
mathematics to neutron star properties and gravitational wave astronomy.


title: Exact Inflation Braneworlds

abstract:
  In Randall-Sundrum type braneworld cosmologies, the dynamical equations on
the three-brane differ from the general relativity equations by terms that
carry the effects of embedding and of the free gravitational field in the
five-dimensional bulk. In a FRW ansatze for the metric, we present two methods
for deriving inflationary solutions to the covariant non-linear dynamical
equations for the gravitational and matter fields on the brane. In the first
approach we examine the constraints on the dynamical relationship between the
cosmological scale factor and the scalar field driving self-interaction
potential, imposed by the weak energy condition. We then investigate
inflationary solutions obtained from a scalar field superpotential. Both these
techniques for solving the braneworld field equations are illustrated by flat
curvature models.


title: Cosmology and Local Physics

abstract:
  This article is dedicated to the memory of Dennis Sciama. It revisits a
series of issues to which he devoted much time and effort, regarding the
relationship between local physics and the large scale structure of the
universe - in particular, Olber's paradox, Mach's principle, and the various
arrows of time. Thus the focus is various ways in which local physics is
influenced by the universe itself.


title:
Using Markov chain Monte Carlo methods for estimating parameters with
  gravitational radiation data

abstract:
  We present a Bayesian approach to the problem of determining parameters for
coalescing binary systems observed with laser interferometric detectors. By
applying a Markov Chain Monte Carlo (MCMC) algorithm, specifically the Gibbs
sampler, we demonstrate the potential that MCMC techniques may hold for the
computation of posterior distributions of parameters of the binary system that
created the gravity radiation signal. We describe the use of the Gibbs sampler
method, and present examples whereby signals are detected and analyzed from
within noisy data.


title:
A nonlinear detection algorithm for periodic signals in gravitational
  wave detectors

abstract:
  We present an algorithm for the detection of periodic sources of
gravitational waves with interferometric detectors that is based on a special
symmetry of the problem: the contributions to the phase modulation of the
signal from the earth rotation are exactly equal and opposite at any two
instants of time separated by half a sidereal day; the corresponding is true
for the contributions from the earth orbital motion for half a sidereal year,
assuming a circular orbit. The addition of phases through multiplications of
the shifted time series gives a demodulated signal; specific attention is given
to the reduction of noise mixing resulting from these multiplications. We
discuss the statistics of this algorithm for all-sky searches (which include a
parameterization of the source spin-down), in particular its optimal
sensitivity as a function of required computational power. Two specific
examples of all-sky searches (broad-band and narrow-band) are explored
numerically, and their performances are compared with the stack-slide technique
(P. R. Brady, T. Creighton, Phys. Rev. D, 61, 082001).


title:
Spin-Polarised Cylinders and Torsion Balances to test Einstein-Cartan
  Gravity?

abstract:
  Spin-Polarised cylinders with and without axial magnetic fields are obtained
as particular families of solutions of Einstein-Cartan gravity (EC).The first
solution represents a spin-polarised cylinder in teleparallel gravity.The
second solution is a magnetized solution representing a spin-polarised cylinder
where the magnetic fields and spins are distributed along the infinite axis of
the cylinder.Altough it seems that the first solution is less realist than the
second it could be obtained by shielding the magnetic fields with a
superconductor.The second solution is computed by taking into account the
Ritter et al. experiment with the test spin-polarized mass to test spin
dependent forces.Ritter experiment deals with a test mass with $>10^{23}$ spin
polarized electrons which leads to a spin density of $10^{-4}gcm^{-1}s^{-1}$.


title:
B\"{a}cklund Transformations of Einstein's Field Equations for the
  Interior of a Uniformly Rotating Stationary Axisymmetric Perfect Fluid

abstract:
  Clairin's method of obtaining B\"{a}cklund transformations is applied to
Einstein's field equations for the interior of a uniformly rotating stationary
axisymmetric perfect fluid. It is shown that for arbitrary pressure $p$ and
mass density $\mu$ the method does not give non-trivial B\"{a}cklund
transformations, while if $\mu + 3p =0$ it gives the transformation of Ehlers.


title:
Electromagnetic wave propagation inside a material medium: an effective
  geometry interpretation

abstract:
  We present a method developed to deal with electromagnetic wave propagation
inside a material medium that reacts, in general, non-linearly to the field
strength. We work in the context of Maxwell' s theory in the low frequency
limit and obtain a geometrical representation of light paths for each case
presented. The isotropic case and artificial birefringence caused by an
external electric field are analyzed as an application of the formalism and the
effective geometry associated to the wave propagation is exhibited.


title: Hidden symmetry of the three-dimensional Einstein-Maxwell equations

abstract:
  It is shown how to generate three-dimensional Einstein-Maxwell fields from
known ones in the presence of a hypersurface-orthogonal non-null Killing vector
field. The continuous symmetry group is isomorphic to the Heisenberg group
including the Harrison-type transformation. The symmetry of the
Einstein-Maxwell-dilaton system is also studied and it is shown that there is
the $SL(2,{\bf R})$ transformation between the Maxwell and the dilaton fields.
This $SL(2,{\bf R})$ transformation is identified with the Geroch
transformation of the four-dimensional vacuum Einstein equation in terms of the
Ka{\l}uza-Klein mechanism.


title: Cosmological Evolution of Black Holes in Brans-Dicke Gravity

abstract:
  We consider a modified ``Swiss cheese'' model in Brans-Dicke theory, and use
it to discuss the evolution of black holes in an expanding universe. We define
the black hole radius by the Misner-Sharp mass and find their exact time
evolutions for dust and vacuum universes of all curvatures.


title: Bertotti-Robinson type solutions to Dilaton-Axion Gravity

abstract:
  We present a new solution to dilaton-axion gravity which looks like a
rotating Bertotti-Robinson (BR) Universe. It is supported by an homogeneous
Maxwell field and a linear axion and can be obtained as a near-horizon limit of
extremal rotating dilaton-axion black holes. It has the isometry $SL(2,R)\times
U(1)$ where U(1) is the remnant of the SO(3) symmetry of BR broken by rotation,
while $SL(2,R)$ corresponds to the $AdS_2$ sector which no longer factors out
of the full spacetime. Alternatively our solution can be obtained from the D=5
vacuum counterpart to the dyonic BR with equal electric and magnetic field
strengths. The derivation amounts to smearing it in D=6 and then reducing to
D=4 with dualization of one Kaluza-Klein two-form in D=5 to produce an axion.
Using a similar dualization procedure, the rotating BR solution is uplifted to
D=11 supergravity. We show that it breaks all supersymmetries of N=4
supergravity in D=4, and that its higher dimensional embeddings are not
supersymmetric either. But, hopefully it may provide a new arena for corformal
mechanics and holography. Applying a complex coordinate transformation we also
derive a BR solution endowed with a NUT parameter.


title:
Why hyperbolic theories of dissipation cannot be ignored: Comments on a
  paper by Kostadt and Liu

abstract:
  Contrary to what is asserted in a recent paper by Kostadt and Liu ("Causality
and stability of the relativistic diffusion equation"), experiments can tell
apart (and in fact do) hyperbolic theories from parabolic theories of
dissipation. It is stressed that the existence of a non--negligible relaxation
time does not imply for the system to be out of the hydrodynamic regime.


title: On free evolution of self gravitating, spherically symmetric waves

abstract:
  We perform a numerical free evolution of a selfgravitating, spherically
symmetric scalar field satisfying the wave equation. The evolution equations
can be written in a very simple form and are symmetric hyperbolic in
Eddington-Finkelstein coordinates. The simplicity of the system allow to
display and deal with the typical gauge instability present in these
coordinates. The numerical evolution is performed with a standard method of
lines fourth order in space and time. The time algorithm is Runge-Kutta while
the space discrete derivative is symmetric (non-dissipative). The constraints
are preserved under evolution (within numerical errors) and we are able to
reproduce several known results.


title:
Vacuum Solutions of Classical Gravity on Cyclic Groups from
  Noncommutative Geometry

abstract:
  Based on the observation that the moduli of a link variable on a cyclic group
modify Connes' distance on this group, we construct several action functionals
for this link variable within the framework of noncommutative geometry. After
solving the equations of motion, we find that one type of action gives
nontrivial vacuum solution for gravity on this cyclic group in a broad range of
coupling constants and that such solutions can be expressed with Chebyshev's
polynomials.


title: Gravitomagnetic Clock Effects in Black Hole Spacetimes

abstract:
  Gravitomagnetic clock effects for circularly rotating orbits in black hole
spacetimes are studied from a relative observer point of view, clarifying the
roles played by special observer families.


title: ''Homogeneous'' Gravitational Field in General Relativity ?

abstract:
  The gravitation field of the flat plate was investigated. It have been shown
that there exist the internal solution of Einstein equations sewed together
with external one, which described a ''homogeneous'' gravitational field.


title: Cyclotron damping and Faraday rotation of gravitational waves

abstract:
  We study the propagation of gravitational waves in a collisionless plasma
with an external magnetic field parallel to the direction of propagation. Due
to resonant interaction with the plasma particles the gravitational wave
experiences cyclotron damping or growth, the latter case being possible if the
distribution function for any of the particle species deviates from
thermodynamical equilibrium. Furthermore, we examine how the damping and
dispersion depends on temperature and on the ratio between the cyclotron- and
gravitational wave frequency. The presence of the magnetic field leads to
different dispersion relations for different polarizations, which in turn imply
Faraday rotation of gravitational waves.


title: Universes inside a $\Lambda$ black hole

abstract:
  We address the question of universes inside a $\Lambda$ black hole which is
described by a spherically symmetric globally regular solution to the Einstein
equations with a variable cosmological term $\Lambda_{\mu\nu}$, asymptotically
$\Lambda g_{\mu\nu}$ as $r\to 0$ with $\Lambda$ of the scale of symmetry
restoration. Global structure of spacetime contains an infinite sequence of
black and white holes, vacuum regular cores and asymptotically flat universes.
Regular core of a $\Lambda$ white hole models the initial stages of the
Universe evolution. In this model it starts from a nonsingular nonsimultaneous
big bang, which is followed by a Kasner-type anisotropic expansion. Creation of
a mass occurs mostly at the anisotropic stage of quick decay of the initial
vacuum energy. We estimate also the probability of quantum birth of baby
universes inside a $\Lambda$ black hole due to quantum instability of the de
Sitter vacuum.


title:
On the linear stability of solitons and hairy black holes with a
  negative cosmological constant: the odd-parity sector

abstract:
  Using a recently developed perturbation formalism based on curvature
quantities, we investigate the linear stability of black holes and solitons
with Yang-Mills hair and a negative cosmological constant. We show that those
solutions which have no linear instabilities under odd- and even- parity
spherically symmetric perturbations remain stable under odd-parity, linear,
non-spherically symmetric perturbations.


title: Stochastic semiclassical gravity and fluctuations during inflation

abstract:
  Stochastic semiclassical gravity is a theory for the interaction of gravity
with quantum matter fields which goes beyond the semiclassical limit. The
theory predicts stochastic fluctuations of the classical gravitational field
induced by the quantum fluctuations of the stress energy tensor of the matter
fields. Here we use an axiomatic approach to introduce the Einstein-Langevin
equations as the consistent set of dynamical equations for a first order
perturbative correction to semiclassical gravity and review their main
features. We then describe the application of the theory in a simple chaotic
inflationary model, where the fluctuations of the inflaton field induce
stochastic fluctuations in the gravitational field. The correlation functions
for these gravitational fluctuations lead to an almost Harrison-Zel'dovich
scale invariant spectrum at large scales, in agreement with the standard
theories for structure formation. A summary of recent results and other
applications of the theory is also given.


title: Spatially Homogeneous Dynamics: A Unified Picture

abstract:
  The Einstein equations for a perfect fluid spatially homogeneous spacetime
are studied in a unified manner by retaining the generality of certain
parameters whose discrete values correspond to the various Bianchi types of
spatial homogeneity. A parameter-dependent decomposition of the metric
variables adapted to the symmetry breaking effects of the nonabelian Bianchi
types on the "free dynamics" leads to a reduction of the equations of motion
for those variables to a 2-dimensional time-dependent Hamiltonian system
containing various time-dependent potentials which are explicitly described and
diagrammed. These potentials are extremely useful in deducing the gross
features of the evolution of the metric variables.


title: Energy and Momentum of a Class of Rotating Gravitational Waves

abstract:
  We calculate energy and momentum for a class of cylindrical rotating
gravitational waves using Einstein and Papapetrou's prescriptions. It is shown
that the results obtained are reduced to the special case of the cylindrical
gravitational waves already available in the literature.


title: Plunge waveforms from inspiralling binary black holes

abstract:
  We study the coalescence of non-spinning binary black holes from near the
innermost stable circular orbit down to the final single rotating black hole.
We use a technique that combines the full numerical approach to solve Einstein
equations, applied in the truly non-linear regime, and linearized perturbation
theory around the final distorted single black hole at later times. We compute
the plunge waveforms which present a non negligible signal lasting for $t\sim
100M$ showing early non-linear ringing, and we obtain estimates for the total
gravitational energy and angular momentum radiated.


title:
Coherent States for Canonical Quantum General Relativity and the
  Infinite Tensor Product Extension

abstract:
  We summarize a recently proposed concrete programme for investigating the
(semi)classical limit of canonical, Lorentzian, continuum quantum general
relativity in four spacetime dimensions. The analysis is based on a novel set
of coherent states labelled by graphs. These fit neatly together with an
Infinite Tensor Product (ITP) extension of the currently used Hilbert space.
The ITP construction enables us to give rigorous meaning to the infinite volume
(thermodynamic) limit of the theory which has been out of reach so far.


title:
Description of Supernova Data in Conformal Cosmology without
  Cosmological Constant

abstract:
  We consider cosmological consequences of a conformal invariant formulation of
Einstein's General Relativity where instead of the scale factor of the spatial
metrics in the action functional a massless scalar (dilaton) field occurs which
scales all masses including the Planck mass. Instead of the expansion of the
universe we get the Hoyle-Narlikar type of mass evolution, where the
temperature history of the universe is replaced by the mass history. We show
that this conformal invariant cosmological model gives a satisfactory
description of the new supernova Ia data for the effective magnitude - redshift
relation without a cosmological constant and make a prediction for the
high-redshift behavior which deviates from that of standard cosmology for
$z>1.7$.


title: Friedmann limits of rotating hypersurface-homogeneous dust models

abstract:
  The existence of Friedmann limits is systematically investigated for all the
hypersurface-homogeneous rotating dust models, presented in previous papers by
this author. Limiting transitions that involve a change of the Bianchi type are
included. Except for stationary models that obviously do not allow it, the
Friedmann limit expected for a given Bianchi type exists in all cases. Each of
the 3 Friedmann models has parents in the rotating class; the k = +1 model has
just one parent class, the other two each have several parent classes. The type
IX class is the one investigated in 1951 by Goedel. For each model, the
consecutive limits of zero rotation, zero tilt, zero shear and spatial isotropy
are explicitly calculated.


title:
Noncanonical quantization of gravity. II. Constraints and the physical
  Hilbert space

abstract:
  The program of quantizing the gravitational field with the help of affine
field variables is continued. For completeness, a review of the selection
criteria that singles out the affine fields, the alternative treatment of
constraints, and the choice of the initial (before imposition of the
constraints) ultralocal representation of the field operators is initially
presented. As analogous examples demonstrate, the introduction and enforcement
of the gravitational constraints will cause sufficient changes in the operator
representations so that all vestiges of the initial ultralocal field operator
representation disappear. To achieve this introduction and enforcement of the
constraints, a well characterized phase space functional integral
representation for the reproducing kernel of a suitably regularized physical
Hilbert space is developed and extensively analyzed.


title:
Magnetic effects on the viscous boundary layer damping of the r-modes in
  neutron stars

abstract:
  This paper explores the effects that magnetic fields have on the viscous
boundary layers (VBLs) that can form in neutron stars at the crust-core
interface, and it investigates the VBL damping of the gravitational-radiation
driven r-mode instability. Approximate solutions to the magnetohydrodynamic
equations valid in the VBL are found for ordinary-fluid neutron stars. It is
shown that magnetic fields above 10^9 Gauss significantly change the structure
of the VBL, and that magnetic fields decrease the VBL damping time.
Furthermore, VBL damping completely suppresses the r-mode instability for B >=
10^{12} Gauss. Thus, magnetic fields will profoundly affect the VBL damping of
the r-mode instability in hot young pulsars (that are cool enough to have
formed a solid crust). One can speculate that magnetic fields can affect the
VBL damping of this instability in LMXBs and other cold old pulsars (if they
have sufficiently large internal fields).


title: Gravitational radiation from long gamma-ray bursts

abstract:
  Long gamma-ray bursts (GRBs) are probably powered by high-angular momentum
black hole-torus systems in suspended accretion. The torus will radiate
gravitational waves as non-axisymmetric instabilities develop. The luminosity
in gravitational-wave emissions is expected to compare favorably with the
observed isotropic equivalent luminosity in GRB-afterglow emissions. This
predicts that long GRBs are potentially the most powerful LIGO/VIRGO
burst-sources in the Universe. Their frequency-dynamics is characterized by a
horizontal branch in the $\dot{f}(f)-$diagram.


title:
Matters of Gravity, the newsletter of the APS Topical Group on
  Gravitation, Spring 2001

abstract:
  News:
  - APS Prize on gravitation, by Cliff Will
  - TGG elections, by David Garfinkle
  - We hear that... by Jorge Pullin
  Research Briefs:
  - Experimental Unruh radiation?, by Matt Visser
  - Why is the universe accelerating?, by Beverly Berger
  - The Lazarus Project, by Richard Price
  - LIGO locks its first detector!, by Stan Whitcomb
  - Progress on the nonlinear r-mode problem, by Keith Lockitch
  Conference reports:
  - Analog models of general relativity, by Matt Visser
  - Astrophysical Sources of Gravitational radiation by Joan Centrella
  - Numerical relativity at the 20th Texas meeting, by Pablo Laguna


title: Angular Noise in Gravitational Wave Detectors

abstract:
  Angular fluctuations of suspended mirrors in gravitational wave
interferometers are a source of noise both for the locking and the operation of
the detectors. We describe here some of the sources of these fluctuations and
methods for the estimation of their order of magnitude.


title:
Dissipation for Euler's Disk and a Desktop Demonstration of Coalescing
  Neutron Stars

abstract:
  I show that the recent calculation of Moffatt's regarding the viscous
dissipation of a spinning coin overlooked the importance of the finite width of
the viscous boundary layer. My new estimates are more in accord with that
observed. I also point out that the frequency ``chirp'' of the specially
designed toy ``Euler's Disk'' is similar to that expected during the last few
minutes of the life of a coalescing binary of two neutron stars. As such, this
toy is an excellent desktop demonstration for the expected phenomena.


title: Asymptotically Flat Initial Data with Prescribed Regularity at Infinity

abstract:
  We prove the existence of a large class of asymptotically flat initial data
with non-vanishing mass and angular momentum for which the metric and the
extrinsic curvature have asymptotic expansions at space-like infinity in terms
of powers of a radial coordinate.


title: Algebraic description of spacetime foam

abstract:
  A mathematical formalism for treating spacetime topology as a quantum
observable is provided. We describe spacetime foam entirely in algebraic terms.
To implement the correspondence principle we express the classical spacetime
manifold of general relativity and the commutative coordinates of its events by
means of appropriate limit constructions.


title:
On average properties of inhomogeneous fluids in general relativity II:
  perfect fluid cosmologies

abstract:
  For general relativistic spacetimes filled with an irrotational perfect fluid
a generalized form of Friedmann's equations governing the expansion factor of
spatially averaged portions of inhomogeneous cosmologies is derived. The
averaging problem for scalar quantities is condensed into the problem of
finding an `effective equation of state' including kinematical as well as
dynamical `backreaction' terms that measure the departure from a standard FLRW
cosmology. Applications of the averaged models are outlined including
radiation-dominated and scalar field cosmologies (inflationary and
dilaton/string cosmologies). In particular, the averaged equations show that
the averaged scalar curvature must generically change in the course of
structure formation, that an averaged inhomogeneous radiation cosmos does not
follow the evolution of the standard homogeneous-isotropic model, and that an
averaged inhomogeneous perfect fluid features kinematical `backreaction' terms
that, in some cases, act like a free scalar field source. The free scalar field
(dilaton) itself, modelled by a `stiff' fluid, is singled out as a special
inhomogeneous case where the averaged equations assume a simple form.


title: Note on Invariants of the Weyl Tensor

abstract:
  Algebraically special gravitational fields are described using algebraic and
differential invariants of the Weyl tensor. A type III invariant is also given
and calculated for Robinson-Trautman spaces.


title: 2d manifold-independent spinfoam theory

abstract:
  A number of background independent quantizations procedures have recently
been employed in 4d nonperturbative quantum gravity. We investigate and
illustrate these techniques and their relation in the context of a simple 2d
topological theory. We discuss canonical quantization, loop or spin network
states, path integral quantization over a discretization of the manifold, spin
foam formulation, as well as the fully background independent definition of the
theory using an auxiliary field theory on a group manifold. While several of
these techniques have already been applied to this theory by Witten, the last
one is novel: it allows us to give a precise meaning to the sum over
topologies, and to compute background-independent and, in fact,
"manifold-independent" transition amplitudes. These transition amplitudes play
the role of Wightman functions of the theory. They are physical observable
quantities, and the canonical structure of the theory can be reconstructed from
them via a C* algebraic GNS construction. We expect an analogous structure to
be relevant in 4d quantum gravity.


title: Notes on Black Hole Phase Transitions

abstract:
  In these notes we present a summary of existing ideas about phase transitions
of black hole spacetimes in semiclassical gravity and offer some thoughts on
three possible scenarios by which these transitions could take place. Our first
theme is ilustrated by a quantum atomic black hole system, generalizing to
finite-temperature a model originally offered by Bekenstein. In this
equilibrium atomic model, the black hole phase transition is realized as the
abrupt excitation of a high energy state, suggesting analogies with the study
of two-level atoms. Our second theme argues that the black hole system shares
similarities with the defect-mediated Kosterlitz-Thouless transition in
condensed matter. These similarities suggest that the black hole phase
transition may be more fully understood by focusing upon the dynamics of black
holes and white holes, the spacetime analogy of vortex and anti-vortex
topological defects. Finally we compare the black hole phase transition to
another transition driven by an exponentially increasing density of states, the
Hagedorn transition first found in hadron physics in the context of dual models
or the old string theory. In modern string theory, the Hagedorn transition is
linked by the Maldacena conjecture to the Hawking-Page black hole phase
transition in Anti-deSitter space, as observed by Witten. Understanding the
dynamics of the Hagedorn transition may thus yield insight into the dynamics of
the black hole phase transition. We argue that characteristics of the Hagedorn
transition are already contained within classical string systems where a
nonperturbative and dynamical analysis is possible.


title:
The Total Space-Time of a Point-Mass When the Cosmological Constant is
  Nonzero and Its Consequences for the Lake-Roeder Black Hole

abstract:
  Singularities associated with an incomplete space-time (S) are not
well-defined until a boundary is attached to it. Moreover, each boundary gives
rise to a different singularity structure for the resulting total space-time
(TST). Since S is compatible with a variety of boundaries, it therefore does
not represent a unique universe, but instead corresponds to a family of
universes, one for each possible boundary.
  It is shown that in the case of Weyl's space-time for a point-mass with
nonzero cosmological constant, the boundary which he attached is invalid, and
when the correct one is attached, the resulting TST is inextendible. This
implies that the Lake-Roeder black hole cannot be produced by gravitational
collapse.


title:
The Total Space-Time of a Point Charge and Its Consequences for Black
  Holes

abstract:
  Singularities associated with an incomplete space-time (S) are not uniquely
defined until a boundary is attached to it. [The resulting
space-time-with-boundary will be termed a "total" space-time (TST).] Since an
incomplete space-time is compatible with a variety of boundaries, it follows
that S does not represent a unique universe but instead corresponds to a family
of universes, one for each of the distinct TSTs. It is shown here that the
boundary attached to the Reissner-Nordstrom space-time for a point charge is
invalid for q^2 < m^2. When the correct boundary is used, the resulting TST is
inextendible. This implies that the Graves-Brill black hole cannot be produced
by gravitational collapse. The same is true of the Kruskal-Fronsdal black hole
for the point mass, and for those black holes which reduce to the latter for
special values of their parameters.


title: Black Holes: The Legacy of Hilbert's Error

abstract:
  The historical postulates for the point mass are shown to be satisfied by an
infinity of space-times, differing as to the limiting acceleration of a
radially approaching test particle. Taking this limit to be infinite gives
Schwarzschild's result, which for a point mass at x = y = z = 0 has C(0+) =
a^2, where a = 2m and C(r) denotes the coefficient of the angular terms in the
polar form of the metric. Hilbert's derivation used the variable r*
=[C(0+)]^1/2. For Hilbert, however, C was unknown, and thus could not be used
to determine r*(0). Instead he asserted, in effect, that r* = (x^2 + y^2 +
z^2)^1/2, which places the point mass at r* = 0. Unfortunately, this differs
from the value (a) obtained by substituting Schwarzschild's C into the
expression for r*(0), and since C(0+) is a scaler invariant, it follows that
Hilbert's assertion is invalid. Owing to this error, in each spatial section of
Hilbert's space-time, the boundary (r* = a) corresponding to r = 0 is no longer
a point, but a two-sphere. This renders his space-time analytically extendible,
and as shown by Kruskal and Fronsdal, its maximal extension contains a black
hole. Thus the Kruskal-Fronsdal black hole is merely an artifact of Hilbert's
error.


title:
Solutions of Conformal Gravity with Dynamical Mass Generation in the
  Solar System

abstract:
  The field equations of Mannheim's theory of conformal gravity with dynamic
mass generation are solved numerically in the interior and exterior regions of
a model spherically symmetric sun with matched boundary conditions at the
surface. The model consists of a generic fermion field inside the sun, and a
scalar Higgs field in both the interior and exterior regions. From the
conformal geodesic equations it is shown how an asymptotic gradient in the
Higgs field causes an anomalous radial acceleration in qualitative agreement
with that observed on the Pioneer 10/11, Galileo, and Ulysses spacecraft. At
the same time the standard solar system tests of general relativity are
preserved within the limits of observation.


title: Quantum Mechanical Clock and Classical Relativistic Clock

abstract:
  A cyclic nature of quantum mechanical clock is discussed as ``quantization of
time." Quantum mechanical clock is seen to be equivalent to the relativistic
classical clock.


title: Conformally flat anisotropic spheres in general relativity

abstract:
  The condition for the vanishing of the Weyl tensor is integrated in the
spherically symmetric case. Then, the resulting expression is used to find new,
conformally flat, interior solutions to Einstein equations for locally
anisotropic fluids. The slow evolution of these models is contrasted with the
evolution of models with similar energy density or radial pressure distribution
but non-vanishing Weyl tensor, thereby bringing out the different role played
by the Weyl tensor, the local anisotropy of pressure and the inhomogeneity of
the energy density in the collapse of relativistic spheres.


title:
On the role of $\Lambda$-term in the evolution of Bianchi-I cosmological
  model with nonlinear spinor field

abstract:
  Self-consistent solutions to nonlinear spinor field equations in General
Relativity are studied for the case of Bianchi type-I space-time. It has been
shown that introduction of $\Lambda$-term in the Lagrangian generates
oscillations of the Bianchi type-I model.


title: 1/r - Potential Without Charge

abstract:
  In order to get geodesically complete Reissner - Nordstroem space - times, it
is necessary to identify pairs of singular points. This can be done in such a
way that "wormholes" are created which generate electric field lines without
any charge. Finally, it is shown that it is possible to glue these space -
times not in the singularities r=0, but at some r>0. The surface energy
generated by this gluing is exotic, but tends to zero in the limit r -> 0.


title: Scalar solitons in a 4-Dimensional curved space-time

abstract:
  There is a theorem known as a Virial theorem that restricts the possible
existence of non-trivial static solitary waves with scalar fields in a flat
space-time with 3 or more spatial dimensions. This raises the following
question: Does the analogous curved space-time version hold?. We investigate
the possibility of solitons in a 4-D curved space-time with a simple model
using numerical analysis. We found that there exists a static solution of the
proposed non linear wave equation. This proves that in curved space-time the
possibilities of solitonic solutions is enhanced relative to the flat
space-time case.


title:
Quantization of a generally covariant gauge system with two super
  Hamiltonian constraints

abstract:
  The Becci-Rouet-Stora-Tyutin (BRST) operator quantization of a
finite-dimensional gauge system featuring two quadratic super Hamiltonian and m
linear supermomentum constraints is studied as a model for quantizing generally
covariant gauge theories. The proposed model ``completely'' mimics the
constraint algebra of General Relativity. The Dirac constraint operators are
identified by realizing the BRST generator of the system as a Hermitian
nilpotent operator, and a physical inner product is introduced to complete a
consistent quantization procedure.


title: Stress Tensor Fluctuations and Passive Quantum Gravity

abstract:
  The quantum fluctuation of the stress tensor of a quantum field are
discussed, as are the resulting spacetime metric fluctuations. Passive quantum
gravity is an approximation in which gravity is not directly quantized, but
fluctuations of the spacetime geometry are driven by stress tensor
fluctuations. We discuss a decomposition of the stress tensor correlation
function into three parts, and consider the physical implications of each part.
The operational significance of metric fluctuations and the possible limits of
validity of semiclassical gravity are discussed.


title: Kasner-AdS spacetime and anisotropic brane-world cosmology

abstract:
  Anisotropic generalization of Randall and Sundrum brane-world model is
considered. A new class of exact solutions for brane and bulk geometry is
found; it is related to anisotropic Kasner solution. In view of this, the old
question of isotropy of initial conditions in cosmology rises once again in the
brane-world context.


title: Hamiltonian structure of 2+1 dimensional gravity

abstract:
  A summary is given of some results and perspectives of the hamiltonian ADM
approach to 2+1 dimensional gravity. After recalling the classical results for
closed universes in absence of matter we go over the the case in which matter
is present in the form of point spinless particles. Here the maximally slicing
gauge proves most effective by relating 2+1 dimensional gravity to the Riemann-
Hilbert problem. It is possible to solve the gravitational field in terms of
the particle degrees of freedom thus reaching a reduced dynamics which involves
only the particle positions and momenta. Such a dynamics is proven to be
hamiltonian and the hamiltonian is given by the boundary term in the
gravitational action. As an illustration the two body hamiltonian is used to
provide the canonical quantization of the two particle system.


title: Is Nature Generic?

abstract:
  An introductory guide to mathematical cosmology is given focusing on the
issue of the genericity of various important results which have been obtained
during the last thirty or so years. Some of the unsolved problems along with
certain new and potentially powerful methods which may be used for future
progress are also given from a unified perspective.


title: Evaporation of a two-dimensional charged black hole

abstract:
  We construct a dilatonic two-dimensional model of a charged black hole. The
classical solution is a static charged black hole, characterized by two
parameters, $m$ and $q$, representing the black hole's mass and charge. Then we
study the semiclassical effects, and calculate the evaporation rate of both $m$
and $q$, as a function of these two quantities. Analyzing this dynamical
system, we find two qualitatively different regimes, depending on the
electromagnetic coupling constant $g_{A}$. If the latter is greater than a
certain critical value, the charge-to-mass ratio decays to zero upon
evaporation. On the other hand, for $g_{A}$ smaller than the critical value,
the charge-to-mass ratio approaches a non-zero constant that depends on $g_{A}$
but not on the initial values of $m$ and $q$.


title: Strong field limit of black hole gravitational lensing

abstract:
  We give the formulation of the gravitational lensing theory in the strong
field limit for a Schwarzschild black hole as a counterpart to the weak field
approach. It is possible to expand the full black hole lens equation to work a
simple analytical theory that describes at a high accuracy degree the physics
in the strong field limit. In this way, we derive compact and reliable
mathematical formulae for the position of additional critical curves,
relativistic images and their magnification, arising in this limit.


title: Absence of Singularity in Loop Quantum Cosmology

abstract:
  It is shown that the cosmological singularity in isotropic minisuperspaces is
naturally removed by quantum geometry. Already at the kinematical level, this
is indicated by the fact that the inverse scale factor is represented by a
bounded operator even though the classical quantity diverges at the initial
singularity. The full demonstation comes from an analysis of quantum dynamics.
Because of quantum geometry, the quantum evolution occurs in discrete time
steps and does not break down when the volume becomes zero. Instead, space-time
can be extended to a branch preceding the classical singularity independently
of the matter coupled to the model. For large volume the correct semiclassical
behavior is obtained.


title: Axial-Vector Torsion and the Teleparallel Kerr Spacetime

abstract:
  In the context of the teleparallel equivalent of general relativity, we
obtain the tetrad and the torsion fields of the stationary axisymmetric Kerr
spacetime. It is shown that, in the slow rotation and weak field
approximations, the axial-vector torsion plays the role of the gravitomagnetic
component of the gravitational field, and is thus the responsible for the
Lense-Thirring effect.


title: Relativistic Lagrange Formulation

abstract:
  It is well-known that the equations for a simple fluid can be cast into what
is called their Lagrange formulation. We introduce a notion of a generalized
Lagrange formulation, which is applicable to a wide variety of systems of
partial differential equations. These include numerous systems of physical
interest, in particular, those for various material media in general
relativity. There is proved a key theorem, to the effect that, if the original
(Euler) system admits an initial-value formulation, then so does its
generalized Lagrange formulation.


title: Do gravitational waves carry energy-momentum and angular momentum?

abstract:
  In the paper we show that the real gravitational waves which have
$R_{iklm}\not= 0$ always carry energy-momentum and angular momentum. Our proof
uses canonical superenergy and supermomentum tensors for gravitational field.


title: BF gravity and the Immirzi parameter

abstract:
  We propose a novel BF-type formulation of real four-dimensional gravity,
which generalizes previous models. In particular, it allows for an arbitrary
Immirzi parameter. We also construct the analogue of the Urbantke metric for
this model.


title: A New Parametrization for Tetrad Gravity

abstract:
  A new version of tetrad gravity in globally hyperbolic, asymptotically flat
at spatial infinity spacetimes with Cauchy surfaces diffeomorphic to $R^3$ is
obtained by using a new parametrization of arbitrary cotetrads to define a set
of configurational variables to be used in the ADM metric action. Seven of the
fourteen first class constraints have the form of the vanishing of canonical
momenta. A comparison is made with other models of tetrad gravity and with the
ADM canonical formalism for metric gravity.


title: Critical Exponents For Schwarzschild-Kerr and BTZ Systems

abstract:
  Regarding the spin-up of Schwarzschild-Kerr and Banados-Teitelboim-Zanelli
systems as a symmetry breaking phase transition, critical exponents are
evaluated and compared with classical Landau predictions. We suggest a
definition of isothermal compressibity which is independent of spin direction.
We find identical exponents for both systems, and possible universality in the
phase transitions of these systems.


title: Dynamical Bar Instability in Relativistic Rotating Stars

abstract:
  We study by computational means the dynamical stability against bar-mode
deformation of rapidly and differentially rotating stars in a post-Newtonian
approximation of general relativity. We vary the compaction of the star $M/R$
(where $M$ is the gravitational mass and $R$ the equatorial circumferential
radius) between 0.01 and 0.05 to isolate the influence of relativistic
gravitation on the instability. For compactions in this moderate range, the
critical value of $\beta = T/W$ for the onset of the dynamical instability
(where $T$ is the rotational kinetic energy and W the gravitational binding
energy) slightly decreases from $\sim$ 0.26 to $\sim$ 0.25 with increasing
compaction for our choice of the differential rotational law. Combined with our
earlier findings based on simulations in full general relativity for stars with
higher compaction, we conclude that relativistic gravitation enhances the
dynamical bar-mode instability, i.e. the onset of instability sets in for
smaller values of $\beta$ in relativistic gravity than in Newtonian gravity. We
also find that once a triaxial structure forms after the bar-mode perturbation
saturates in dynamically unstable stars, the triaxial shape is maintained, at
least for several rotational periods. To check the reliability of our numerical
integrations, we verify that the general relativistic Kelvin-Helmholtz
circulation is well-conserved, in addition to rest-mass and total mass-energy,
linear and angular momentum. Conservation of circulation indicates that our
code is not seriously affected by numerical viscosity. We determine the
amplitude and frequency of the quasi-periodic gravitational waves emitted
during the bar formation process using the quadrupole formula.


title: Exact solutions of charged wormhole

abstract:
  In this paper, the backreaction to the traversable Lorentzian wormhole
spacetime by the scalar field or electric charge is considered to find the
exact solutions. The charges play the role of the additional matter to the
static wormhole which is already constructed by the exotic matter. The
stability conditions for the wormhole with scalar field and electric charge are
found from the positiveness and flareness for the wormhole shape function.


title: Scattering problem of scalar wave in wormhole geometry

abstract:
  In this paper, we study the scattering problem of the scalar wave in the
traversable Lorentzian wormhole geometry. The potentials and Schr\"odinger-like
equations are found in cases of the static uncharged and the charged wormholes.
The differential scattering cross sections are determined by the phase shift of
the asymptotic wave function in low frequency limit. It is also found that the
cross section for charged wormhole is smaller than that for uncharged case by
the reduction of the throat size due to the charge effect.


title:
Exact relativistic treatment of stationary counter-rotating dust disks
  II: Axis, Disk and Limiting Cases

abstract:
  This is the second in a series of papers on the construction of explicit
solutions to the stationary axisymmetric Einstein equations which can be
interpreted as counter-rotating disks of dust. We discuss the class of
solutions to the Einstein equations for disks with constant angular velocity
and constant relative density which was constructed in the first part. The
metric for these spacetimes is given in terms of theta functions on a Riemann
surface of genus 2. We discuss the metric functions at the axis of symmetry and
the disk. Interesting limiting cases are the Newtonian limit, the static limit,
and the ultra-relativistic limit of the solution in which the central redshift
diverges.


title:
Explicit Derivation of the Fluctuation-Dissipation Relation of the
  Vacuum Noise in the N-dimensional de Sitter Spacetime

abstract:
  Motivated by a recent work by Terashima (Phys. Rev. D60 084001), we revisit
the fluctuation-dissipation (FD) relation between the dissipative coefficient
of a detector and the vacuum noise of fields in curved spacetime. In an
explicit manner we show that the dissipative coefficient obtained from
classical equations of motion of the detector and the scalar (or Dirac) field
satisfies the FD relation associated with the vacuum noise of the field, which
demonstrates that the Terashima's prescription works properly in the
$N$-dimensional de Sitter spacetime. This practice is useful not only to
reconfirm the validity of the use of the retarded Green function to evaluate
the dissipative coefficient from the classical equations of motion but also to
understand why the derivation works properly, which is discussed in connection
with previous investigations on the basis on the Kubo-Martin-Schwinger (KMS)
condition. Possible application to black hole spacetime is also briefly
discussed.


title: Hawking Radiation of Dirac Particles in a Variable-mass Kerr Black Hole

abstract:
  Hawking effect of Dirac particles in a variable-mass Kerr space-time is
investigated by using method of the generalized tortoise coordinate
transformation. The location and the temperature of event horizon of the
non-stationary Kerr black hole are derived. It is shown that the temperature
and the shape of event horizon depend not only on the time but also on the
polar angle. However, our results demonstrate that the Fermi-Dirac spectrum
displays a new spin-rotation effect which is absent from that of Bose-Einstein
distribution.


title: Bound and Radiation Fields in the Rindler Frame

abstract:
  The energy-momentum tensor of the Li\'enard-Wiechert field is split into
bound and emitted parts in the Rindler frame, by generalizing the reasoning of
Teitelboim applied in the inertial frame. Our analysis proceeds by invoking the
concept of ``energy'' defined with respect to the Killing vector field attached
to the frame. We obtain the radiation formula in the Rindler frame (the Rindler
version of the Larmor formula), and it is found that the radiation power is
proportional to the square of acceleration $\alpha^\mu$ of the charge relative
to the Rindler frame. This result leads us to split the Li\'enard-Wiechert
field into a part II', which is linear in $\alpha^\mu$, and a part I', which is
independent of $\alpha^\mu$. By using these, we split the energy-momentum
tensor into two parts. We find that these are properly interpreted as the
emitted and bound parts of the tensor in the Rindler frame. In our
identification of radiation, a charge radiates neither in the case that the
charge is fixed in the Rindler frame, nor in the case that the charge satisfies
the equation $\alpha^\mu=0$. We then investigate this equation. We consider
four gedanken experiments related to the observer dependence of the concept of
radiation.


title:
Exact relativistic treatment of stationary counter-rotating dust disks
  I: Boundary value problems and solutions

abstract:
  This is the first in a series of papers on the construction of explicit
solutions to the stationary axisymmetric Einstein equations which describe
counter-rotating disks of dust. These disks can serve as models for certain
galaxies and accretion disks in astrophysics. We review the Newtonian theory
for disks using Riemann-Hilbert methods which can be extended to some extent to
the relativistic case where they lead to modular functions on Riemann surfaces.
In the case of compact surfaces these are Korotkin's finite gap solutions which
we will discuss in this paper. On the axis we establish for general genus
relations between the metric functions and hence the multipoles which are
enforced by the underlying hyperelliptic Riemann surface. Generalizing these
results to the whole spacetime we are able in principle to study the classes of
boundary value problems which can be solved on a given Riemann surface. We
investigate the cases of genus 1 and 2 of the Riemann surface in detail and
construct the explicit solution for a family of disks with constant angular
velocity and constant relative energy density which was announced in a previous
Physical Review Letter.


title: Reconsidering Schwarzschild's original solution

abstract:
  We analyse the Schwarzschild solution in the context of the historical
development of its present use, and explain the invariant definition of a
singular surface at the Schwarzschild's radius, that can be applied to the
Kerr-Newman solution too.


title: Characteristic Evolution and Matching

abstract:
  I review the development of numerical evolution codes for general relativity
based upon the characteristic initial value problem. Progress is traced from
the early stage of 1D feasibility studies to current 3D black codes that
simulate binary black holes. A prime application of characteristic evolution is
Cauchy-characteristic matching, which is also reviewed.


title: Torsion Strings inside Static Black Holes in Teleparallel Gravity

abstract:
  Cosmic strings inside Schwarzschild black holes in teleparallel gravity are
considered.Torsion flux inside the black hole is compute like a torsion vortex
on a superfluid.Since some components of torsion are singular on Schwarzschild
horizon and others remain finite we compute a torsion invariant to decide
whether the torsion is singular and where torsion singularities located.It is
found out that as in the curvature case of Einstein's black hole the event
horizon is not a mere coordinate singularity for torsion although a true
torsion singularity is found at the center of the teleparallel black
hole.Torsion flux vanishes along the cosmic string itself.It is shown from
Cartan equation in differential forms that the spins inside the black hole are
polarized along the torsion string.Torsion string seems to be confined inside
the black hole.


title:
Hydrodynamics of an ultra-relativistic fluid in the flat anisotropic
  cosmological model

abstract:
  Motion of an ultra-relativistic perfect fluid in space-time with the Kasner
metrics is investigated by the Hamiltonian method. It is found that in the
limit of small times a tendency takes place to formation of strong
inhomogeneities in matter distribution. In the case of slow flows the effect of
non-stationary anisotropy on dynamics of sound waves and behaviour of frozen-in
vortices is considered. It is shown that hydrodynamics of slow vortices on the
static homogeneous background is equivalent to the usual Eulerian
incompressible hydrodynamics, but in the presence of an external non-stationary
strain velocity field.


title: Proper time and Minkowski structure on causal graphs

abstract:
  For causal graphs we propose a definition of proper time which for small
scales is based on the concept of volume, while for large scales the usual
definition of length is applied. The scale where the change from "volume" to
"length" occurs is related to the size of a dynamical clock and defines a
natural cut-off for this type of clock. By changing the cut-off volume we may
probe the geometry of the causal graph on different scales and therey define a
continuum limit. This provides an alternative to the standard coarse graining
procedures. For regular causal lattice (like e.g. the 2-dim. light-cone
lattice) this concept can be proven to lead to a Minkowski structure. An
illustrative example of this approach is provided by the breather solutions of
the Sine-Gordon model on a 2-dimensional light-cone lattice.


title:
A note on the Limits to Global Rotation from Teleparallel G\"{o}del
  Universe

abstract:
  A teleparallel G\"{o}del universe is shown to lead to a simple and natural
relation between Cartan torsion and the global rotation of the universe.This is
straightforward if one uses the formalism of Cartan's calculus of exterior
differential forms.It is possible to place a limit on the global rotation from
the knowledge of torsion and the converse is also true.The Obukhov recent limit
of $\frac{\omega}{H_{0}}=1$ leads to the well know value for cosmological
torsion of $10^{-17} cm^{-1}$.COBE constraints on the temperature anisotropy
allows us to obtain limits on the torsion fluctuation in G\"{o}del's universe.


title: A prescription for probabilities in eternal inflation

abstract:
  Some of the parameters we call ``constants of Nature'' may in fact be
variables related to the local values of some dynamical fields. During
inflation, these variables are randomized by quantum fluctuations. In cases
when the variable in question (call it $\chi$) takes values in a continuous
range, all thermalized regions in the universe are statistically equivalent,
and a gauge invariant procedure for calculating the probability distribution
for $\chi$ is known. This is the so-called ``spherical cutoff method''. In
order to find the probability distribution for $\chi$ it suffices to consider a
large spherical patch in a single thermalized region. Here, we generalize this
method to the case when the range of $\chi$ is discontinuous and there are
several different types of thermalized region. We first formulate a set of
requirements that any such generalization should satisfy, and then introduce a
prescription that meets all the requirements. We finally apply this
prescription to calculate the relative probability for different bubble
universes in the open inflation scenario.


title:
Remarks on the Bergmann-Thomsom Expression on Angular Momentum in
  General Relativity

abstract:
  Often it is asserted that only by using of the symmetric Landau-Lifschitz
energy-momentum complex one is able to formulate a conserved angular momentum
complex in General Relativity ({\bf GR}). Obviously, it is an uncorrect
statement. For example, years ago, Bergmann and Thomson have given other, very
useful expression on angular momentum. This expression is closely joined to the
non-symmetric, Einstein canonical energy-momentum complex. In the paper we
review the Bergmann-Thomson angular momentum complex and compare it with that
of given by Landau and Lifschitz.


title: Superenergy and Supermomentum of Goedel Universes

abstract:
  We review the canonical superenergy tensor and the canonical angular
supermomentum tensors in general relativity and calculate them for space-time
homogeneous G\"odel universes to show that both of these tensors do not, in
general, vanish. We consider both an original dust-filled pressureless acausal
G\"odel model of 1949 and a scalar-field-filled causal G\"odel model of Rebou\c
cas and Tiomno. For the acausal model, the non-vanishing components of
superenergy of matter are different from those of gravitation. The angular
supermomentum tensors of matter and gravitation do not vanish either which
simply reflects the fact that G\"odel universe rotates. However, the axial
(totally antisymmetric) and vectorial parts of supermomentum tensors vanish. It
is interesting that superenergetic quantities are {\it sensitive} to causality
in a way that superenergy density $_g S_{00}$ of gravitation in the acausal
model is {\it positive}, while superenergy density $_g S_{00}$ in the causal
model is {\it negative}. That means superenergetic quantities might serve as
criterion of causality in cosmology and prove useful.


title: Astrophysical limits on quantum gravity motivated birefringence

abstract:
  We obtain observational upper bounds on a class of quantum gravity related
birefringence effects, by analyzing the presence of linear polarization in the
optical and ultraviolet spectrum of some distant sources. In the notation of
Gambini and Pullin we find $\chi < 10^{-3}$.


title: Cosmic Strings and Closed Time-Like Curves in Teleparallel Gravity

abstract:
  Closed Time-like curves (CTC) in Cosmic strings in teleparallel $T_{4}$
gravity are forbidden.This result shown here in $T_{4}$ was shown by Soleng
(Phys.Rev.D49 (1994)1124) also to be valid in Einstein-Cartan (EC) gravity.Here
we show that in $T_{4}$ to allow for CTC we are also led to a lower bound on
the angular momentum of the cosmic string.This result is obtained by matching
the interior $T_{4}$ solution to a General Relativity (GR) vacuum solution.One
of the main differences of the present report and the one by Soleng is that
here the interior symmetric solution does not have necessary polarized spins
but only Cartan torsion in the spirit of teleparallelism.Torsion flux is
computed and it is show that the center of cylinder singularity corresponds to
a 2+1 spacetime rotating point particle in $T_{4}$.Therefore the possibility of
building time machines seems to be strongly constraint than in the case of EC
gravity.


title:
Spherically Symmetric Solutions of Gravitational Field Equations in
  Kalb-Ramond Background

abstract:
  Static spherically symmetric solution in a background spacetime with torsion
is derived explicitly. The torsion considered here is identified with the field
strength of a second rank antisymmetric tensor field namely the Kalb-Ramond
field and the proposed solution therefore has much significance in a string
inspired gravitational field theory.


title:
Exact relativistic treatment of stationary counter-rotating dust disks
  III. Physical Properties

abstract:
  This is the third in a series of papers on the construction of explicit
solutions to the stationary axisymmetric Einstein equations which can be
interpreted as counter-rotating disks of dust. We discuss the physical
properties of a class of solutions to the Einstein equations for disks with
constant angular velocity and constant relative density which was constructed
in the first part. The metric for these spacetimes is given in terms of theta
functions on a Riemann surface of genus 2. It is parameterized by two physical
parameters, the central redshift and the relative density of the two
counter-rotating streams in the disk. We discuss the dependence of the metric
on these parameters using a combination of analytical and numerical methods.
Interesting limiting cases are the Maclaurin disk in the Newtonian limit, the
static limit which gives a solution of the Morgan and Morgan class and the
limit of a disk without counter-rotation. We study the mass and the angular
momentum of the spacetime. At the disk we discuss the energy-momentum tensor,
i.e. the angular velocities of the dust streams and the energy density of the
disk. The solutions have ergospheres in strongly relativistic situations. The
ultrarelativistic limit of the solution in which the central redshift diverges
is discussed in detail: In the case of two counter-rotating dust components in
the disk, the solutions describe a disk with diverging central density but
finite mass. In the case of a disk made up of one component, the exterior of
the disks can be interpreted as the extreme Kerr solution.


title:
Finitary Spacetime Sheaves of Quantum Causal Sets: Curving Quantum
  Causality

abstract:
  A locally finite, causal and quantal substitute for a locally Minkowskian
principal fiber bundle $\cal{P}$ of modules of Cartan differential forms $\omg$
over a bounded region $X$ of a curved $C^{\infty}$-smooth differential manifold
spacetime $M$ with structure group ${\bf G}$ that of orthochronous Lorentz
transformations $L^{+}:=SO(1,3)^{\uparrow}$, is presented. ${\cal{P}}$ is the
structure on which classical Lorentzian gravity, regarded as a Yang-Mills type
of gauge theory of a $sl(2,\com)$-valued connection 1-form $\cal{A}$, is
usually formulated. The mathematical structure employed to model this
replacement of ${\cal{P}}$ is a principal finitary spacetime sheaf
$\vec{\cal{P}}_{n}$ of quantum causal sets $\amg_{n}$ with structure group
${\bf G}_{n}$, which is a finitary version of the group ${\bf G}$ of local
symmetries of General Relativity, and a finitary Lie algebra ${\bf
g}_{n}$-valued connection 1-form ${\cal{A}}_{n}$ on it, which is a section of
its sub-sheaf $\amg^{1}_{n}$. ${\cal{A}}_{n}$ is physically interpreted as the
dynamical field of a locally finite quantum causality, while its associated
curvature ${\cal{F}}_{n}$, as some sort of `finitary Lorentzian quantum
gravity.


title: A Ponzano-Regge model of Lorentzian 3-Dimensional gravity

abstract:
  We present the construction of the partition function of 3-dimensional
gravity in the Lorentzian regime as a state sum model over a triangulation.
This generalize the work of Ponzano and Regge to the case of Lorentzian
signature.


title: Relativistic Epicycles : another approach to geodesic deviations

abstract:
  We solve the geodesic deviation equations for the orbital motions in the
Schwarzschild metric which are close to a circular orbit. It turns out that in
this particular case the equations reduce to a linear system, which after
diagonalization describes just a collection of harmonic oscillators, with two
characteristic frequencies. The new geodesic obtained by adding this solution
to the circular one, describes not only the linear approximation of Kepler's
laws, but gives also the right value of the perihelion advance (in the limit of
almost circular orbits). We derive also the equations for higher-order
deviations and show how these equations lead to better approximations,
including the non-linear effects. The approximate orbital solutions are then
inserted into the quadrupole formula to estimate the gravitational radiation
from non-circular orbits.


title: Scattering of scalar waves by rotating black holes

abstract:
  We study the scattering of massless scalar waves by a Kerr black hole by
letting plane monochromatic waves impinge on the black hole. We calculate the
relevant scattering phase-shifts using the
  Pruefer phase-function method, which is computationally efficient and
reliable also for high frequencies and/or large values of the angular multipole
indices (l,m). We use the obtained phase-shifts and the partial-wave approach
to determine differential cross sections and deflection functions. Results for
off-axis scattering (waves incident along directions misaligned with the black
hole's rotation axis) are obtained for the first time. Inspection of the
off-axis deflection functions reveals the same scattering phenomena as in
Schwarzschild scattering. In particular, the cross sections are dominated by
the glory effect and the forward (Coulomb) divergence due to the long-range
nature of the gravitational field. In the rotating case the overall diffraction
pattern is ``frame-dragged'' and as a result the glory maximum is not observed
in the exact backward direction. We discuss the physical reason for this
behaviour, and explain it in terms of the distinction between prograde and
retrograde motion in the Kerr gravitational field. Finally, we also discuss the
possible influence of the so-called superradiance effect on the scattered
waves.


title: Spin and Rotation in General Relativity

abstract:
  Rapporteur's Introduction to the GT8 session of the Ninth Marcel Grossmann
Meeting (Rome, 2000); to appear in the Proceedings.


title:
The fate of classical tensor inhomogeneities in pre-big-bang string
  cosmology

abstract:
  In pre-big-bang string cosmology one uses a phase of dilaton-driven inflation
to stretch an initial (microscopic) spatial patch to the (much larger) size of
the big-bang fireball. We show that the dilaton-driven inflationary phase does
not naturally iron out the initial classical tensor inhomogeneities unless the
initial value of the string coupling is smaller than 10^(-35).


title: The Expanding Universe, Planetary Motion and the Pioneer 10/11 Anomaly

abstract:
  The effect of the expanding universe on planetary motion is considered to
first order in the Hubble constant H. Orbital elements are shown to be
unaffected, but there is a small change in the connection between planetary
proper time and coordinate time. This can produce an apparent anomalous
acceleration in velocities inferred from echo-ranging, but the effect is too
small by many orders of magnitude to account for the Pioneer 10/11 anomaly.


title: Gravitating Self-dual Chern-Simons Solitons

abstract:
  Self-dual solitons of Chern-Simons Higgs theory are examined in curved
spacetime. We derive duality transformation of the Einstein Chern-Simons Higgs
theory within path integral formalism and study various aspects of dual
formulation including derivation of Bogomolnyi type bound. We find all possible
rotationally-symmetric soliton configurations carrying magnetic flux and
angular momentum when underlying spatial manifolds of these objects comprise a
cone, a cylinder, and a two sphere.


title:
Machian Cosmological Solution in the Generalized Scalar-Tensor Theory of
  Gravitation

abstract:
  The Machian cosmological solution satisfying $\phi =O(\rho /\omega)$ is
discussed for the homogeneous and isotropic universe with a perfect fluid (with
negative pressure) in the generalized scalar-tensor theory of gravitation. We
propose $\omega (\phi)=\eta /(\xi -2)$ for the coupling function in the Machian
point of view. The parameter $\xi$ varies in time very slowly from $\xi =0$ to
$\xi =2$ because of the physical evolution of matter in the universe. When $\xi
\to 2$, the coupling function diverges to $-\infty$ and the scalar field $\phi$
converges to $G_{\infty}^{-1}$. The present mass density is precisely predicted
if the present time of the universe is given. We obtain $\rho_{0}=1.6\times
10^{-29} g.cm^{-3}$ for $t_{0}=1.5\times 10^{10} yr$. The universe shows the
slowly decelerating expansion for the time-varying coupling function.


title: Understanding singularities in Cartan's and NSF geometric structures

abstract:
  In this work we establish a relationship between Cartan's geometric approach
to third order ODEs and the 3-dim Null Surface Formulation (NSF). We then
generalize both constructions to allow for caustics and singularities that
necessarily arise in these formalisms.


title: The mathematical role of time and space-time in classical physics

abstract:
  We use Padoa's principle of independence of primitive symbols in axiomatic
systems in order to discuss the mathematical role of time and space-time in
some classical physical theories. We show that time is eliminable in Newtonian
mechanics and that space-time is also dispensable in Hamiltonian mechanics,
Maxwell's electromagnetic theory, the Dirac electron, classical gauge fields,
and general relativity.


title: Finitary Spacetime Sheaves

abstract:
  The notion of finitary spacetime sheaves is introduced based on locally
finite approximations of the continuous topology of a bounded region of a
spacetime manifold. Finitary spacetime sheaves are seen to be sound
mathematical models of approximations of continuous spacetime observables.


title:
Quantum backreaction of massive fields and self-consistent semiclassical
  extreme black holes and acceleration horizons

abstract:
  We consider the effect of backreaction of quantized massive fields on the
metric of extreme black holes (EBH). We find the analytical approximate
expression for the stress-energy tensor for a scalar (with an arbitrary
coupling), spinor and vector fields near an event horizon. We show that,
independent of a concrete type of EBH, the energy measured by a freely falling
observer is finite on the horizon, so that quantum backreaction is consistent
with the existence of EBH. For the Reissner-Nordstrom EBH with a total mass
M_{tot} and charge Q we show that for all cases of physical interest M_{tot}<
Q. We also discuss different types of quantum-corrected Bertotti-Robinson
spacetimes, find for them exact self-consistent solutions and consider
situations in which tiny quantum corrections lead to the qualitative change of
the classical geometry and topology. In all cases one should start not from a
classical background with further adding quantum corrections but from the
quantum-corrected self-consistent geometries from the very beginning.


title: Quantum Field Theory of Spin Networks

abstract:
  We study the transition amplitudes in state-sum models of quantum gravity in
D=2,3,4 spacetime dimensions by using the field theory over a Lie group
formulation. By promoting the group theory Fourier modes into creation and
annihilation operators we construct a Fock space for the quantum field theory
whose Feynman diagrams give the transition amplitudes. By making products of
the Fourier modes we construct operators and states representing the spin
networks associated to triangulations of spatial boundaries of a triangulated
spacetime manifold. The corresponding spin network amplitudes give the
state-sum amplitudes for triangulated manifolds with boundaries. We also show
that one can introduce a discrete time evolution operator, where the time is
given by the number of D-simplices in the triangulation, or equivalently by the
number of the vertices in the Feynman diagram. The corresponding transition
amplitude is a finite sum of Feynman diagrams, and in this way one avoids the
problem of infinite amplitudes caused by summing over all possible
triangulations.


title: Zero temperature black holes in semiclassical gravity

abstract:
  The semiclassical Einstein equations are solved to first order in $\epsilon =
\hbar/M^2$ for the case of an extreme or nearly extreme Reissner-Nordstr\"{o}m
black hole perturbed by the vacuum stress-energy of quantized free fields. It
is shown that, for realistic fields of spin 0, 1/2, or 1, any zero temperature
black hole solution to the equations must have an event horizon at $r_h < |Q|$,
with $Q$ the charge of the black hole. It is further shown that no black hole
solutions with $r_h < |Q|$ can be obtained by solving the semiclassical
Einstein equations perturbatively.


title:
Gravitational fields with a non Abelian bidimensional Lie algebra of
  symmetries

abstract:
  Vacuum gravitational fields invariant for a bidimensional non Abelian Lie
algebra of Killing fields, are explicitly described. They are parameterized
either by solutions of a transcendental equation (the tortoise equation) or by
solutions of a linear second order differential equation on the plane.
Gravitational fields determined via the tortoise equation, are invariant for a
3-dimensional Lie algebra of Killing fields with bidimensional leaves. Global
gravitational fields out of local ones are also constructed.


title: Interaction of gravitational waves with an elastic solid medium

abstract:
  Contents. 1. Introduction. 2. Kinematics of a Material Medium: Material
Representation. 3. Kinematics of a Material Medium: Convected Differentials. 4.
Kinematics of a Perfect Elastic Medium. 5. Small Gravitational Perturbations of
an Elastic Medium.


title: Implications of the r-mode instability of rotating relativistic stars

abstract:
  Several recent surprises appear dramatically to have improved the likelihood
that the spin of rapidly rotating, newly formed neutron stars (and, possibly,
of old stars spun up by accretion) is limited by a nonaxisymmetric instability
driven by gravitational waves. Except for the earliest part of the spin-down,
the axial l=m=2 mode (an r-mode) dominates the instability, and the emitted
waves may be observable by detectors with the sensitivity of LIGO II. A review
of these hopeful results is followed by a discussion of constraints on the
instability set by dissipative mechanisms, including viscosity, nonlinear
saturation, and energy loss to a magnetic field driven by differential
rotation.


title: Does the charge of a body reduce its gravitational field?

abstract:
  One can get the impression from the Reissner-Nordstrom solution of Einstein's
equations that the charge of a body reduces its gravitational field. This looks
surprising since the energy of the electrostatic field surrounding a charged
body, must contribute positively, as an additional, "electromagnetic mass", to
the gravitational field produced by the body. We resolve this puzzle by showing
that the mass M in the Reissner-Nordstrom solution is not the "bare mass" of
the body, but its "renormalized mass". I. e. M, in addition to the bare mass,
includes the total electromagnetic mass of the body. But at finite distances
from the body only a part of the electromagnetic mass contributes to the
gravitational field. That is why the gravity of a charged body is determined by
the quantity smaller than M.


title: The Early Universe as a Quantum Growing Network

abstract:
  We consider a quantum gravity register that is a particular quantum memory
register which grows with time, and whose qubits are pixels of area of quantum
de Sitter horizons. At each time step, the vacuum state of this quantum
register grows because of the uncertainty in quantum information induced by the
vacuum quantum fluctuations. The resulting virtual states, (responsible for the
speed up of growth, i.e., inflation), are operated on by quantum logic gates
and transformed into qubits. The model of quantum growing network (QGN)
described here is exactly solvable, and (apart from its cosmological
implications), can be regarded as the first attempt toward a future model for
the quantum World-Wide Web. We also show that the bound on the speed of
computation, the bound on clock precision, and the holographic bound, are
saturated by the QGN.


title:
Varying Cosmological Constant and the Machian Solution in the
  Generalized Scalar-Tensor Theory

abstract:
  The cosmological constant $(1/2)\lambda_{1}\phi_{, \mu}\phi ^{, \mu}/\phi
^{2}$ is introduced to the generalized scalar-tensor theory of gravitation with
the coupling function $\omega (\phi)=\eta /(\xi -2)$ and the Machian
cosmological solution satisfying $\phi =O(\rho /\omega)$ is discussed for the
homogeneous and isotropic universe with a perfect fluid (with negative
pressure). We require the closed model and the negative coupling function for
the attractive gravitational force. The constraint $% \omega (\phi)<-3/2$ for
$0\leqq \xi <2$ leads to $\eta >3$. If $\lambda_{1}<0$ and $0\leqq -\eta
/\lambda_{1}<2$, the universe shows the slowly accelerating expansion. The
coupling function diverges to $-\infty $ and the scalar field $\phi $ converges
to $G_{\infty}^{-1}$ when $\xi \to 2$ ($t\to +\infty $). The cosmological
constant decays in proportion to $t^{-2}$. Thus the Machian cosmological model
approaches to the Friedmann universe in general relativity with $\ddot{a}=0$,
$\lambda =0$, and $p=-\rho /3$ as $t\to +\infty $. General relativity is
locally valid enough at present.


title: An alternative to quintessence

abstract:
  We consider a FRW cosmological model with an exotic fluid known as Chaplygin
gas. We show that the resulting evolution of the universe is not in
disagreement with the current observation of cosmic acceleration. The model
predict an increasing value for the effective cosmological constant.


title: An Improved Exact Riemann Solver for Relativistic Hydrodynamics

abstract:
  A Riemann problem with prescribed initial conditions will produce one of
three possible wave patterns corresponding to the propagation of the different
discontinuities that will be produced once the system is allowed to relax. In
general, when solving the Riemann problem numerically, the determination of the
specific wave pattern produced is obtained through some initial guess which can
be successively discarded or improved. We here discuss a new procedure,
suitable for implementation in an exact Riemann solver in one dimension, which
removes the initial ambiguity in the wave pattern. In particular we focus our
attention on the relativistic velocity jump between the two initial states and
use this to determine, through some analytic conditions, the wave pattern
produced by the decay of the initial discontinuity. The exact Riemann problem
is then solved by means of calculating the root of a nonlinear equation.
Interestingly, in the case of two rarefaction waves, this root can even be
found analytically. Our procedure is straightforward to implement numerically
and improves the efficiency of numerical codes based on exact Riemann solvers.


title:
A detector of small harmonic displacements based on two coupled
  microwave cavities

abstract:
  The design and test of a detector of small harmonic displacements is
presented. The detector is based on the principle of the parametric conversion
of power between the resonant modes of two superconducting coupled microwave
cavities. The work is based on the original ideas of Bernard, Pegoraro, Picasso
and Radicati, who, in 1978, suggested that superconducting coupled cavities
could be used as sensitive detectors of gravitational waves, and on the work of
Reece, Reiner and Melissinos, who, {in 1984}, built a detector of this kind.
They showed that an harmonic modulation of the cavity length l produced an
energy transfer between two modes of the cavity, provided that the frequency of
the modulation was equal to the frequency difference of the two modes. They
achieved a sensitivity to fractional deformations of dl/l~10^{-17} Hz^{-1/2}.
We repeated the Reece, Reiner and Melissinos experiment, and with an improved
experimental configuration and better cavity quality, increased the sensitivity
to dl/l~10^{-20} Hz^{-1/2}. In this paper the basic principles of the device
are discussed and the experimental technique is explained in detail. Possible
future developments, aiming at gravitational waves detection, are also
outlined.


title:
On the dual interpretation of zero-curvature Friedmann-Robertson-Walker
  models

abstract:
  Two possible interpretations of FRW cosmologies (perfect fluid or dissipative
fluid)are considered as consecutive phases of the system. Necessary conditions
are found, for the transition from perfect fluid to dissipative regime to
occur, bringing out the conspicuous role played by a particular state of the
system (the ''critical point '').


title:
Self force on a scalar charge in the spacetime of a stationary,
  axisymmetric black hole

abstract:
  We study the self force acting on a particle endowed with scalar charge,
which is held static (with respect to an undragged, static observer at
infinity) outside a stationary, axially-symmetric black hole. We find that the
acceleration due to the self force is in the same direction as the black hole's
spin, and diverges when the particle approaches the outer boundary of the black
hole's ergosphere. This acceleration diverges more rapidly approaching the
ergosphere's boundary than the particle's acceleration in the absence of the
self force. At the leading order this self force is a (post)$^2$-Newtonian
effect. For scalar charges with high charge-to-mass ratio, the acceleration due
to the self force starts dominating over the regular acceleration already far
from the black hole. The self force is proportional to the rate at which the
black hole's rotational energy is dissipated. This self force is local (i.e.,
only the Abraham-Lorentz-Dirac force and the local coupling to Ricci curvature
contribute to it). The non-local, tail part of the self force is zero.


title:
Dark matter an effect of gravitation permeability of material in Jordan,
  Brance - Dicke theory

abstract:
  Analyzing the static spherically symmetric and rotating ellipsoid solutions
in the Newtonian limit of Jordan, Brance - Dicke theory we find the following.
In empty space scalar-tensor theories have trivial solution of field equation
with constant scalar potential (efficient value of gravitation constant). In
this case no celestial-mechanical experiments to reveal a difference between
scalar-tensor theories and Einstein theory is not presented possible. However,
scalar field, inside the matter, has characteristics like gravitation
permeability of material similar electromagnetic permeability of material in
Maxwell theories of electromagnetism. Investigation of obtained exact solutions
for given functions of a matter distributions in the Newtonian limit of Jordan,
Brance - Dicke theory show the efficient value of gravitation constant depends
on density of matter, sizes and form of object, as well as on the value of
theories coupling constant. That for example led to weakening gravitation force
in the central regions of a Galaxies. This assumption constitutes the way to
explain observed rotation curves of Galaxies without using cold dark matter.


title: Renormalization of Gravity and Gravitational Waves

abstract:
  Strictly respecting the Einstein equations and supposing space-time is a
medium, we derive the deformation of this medium by gravity. We derive the
deformation in case of infinite plane, Robertson-Walker manifold, Schwarzschild
manifold and gravitational waves. Some singularities are removed or changed. We
call this procedure renormalization of gravity. We show that some results
following from the classical gravity must be modified.


title: Gravitational waveforms with controlled accuracy

abstract:
  A partially first-order form of the characteristic formulation is introduced
to control the accuracy in the computation of gravitational waveforms produced
by highly distorted single black hole spacetimes. Our approach is to reduce the
system of equations to first-order differential form on the angular
derivatives, while retaining the proven radial and time integration schemes of
the standard characteristic formulation. This results in significantly improved
accuracy over the standard mixed-order approach in the extremely nonlinear
post-merger regime of binary black hole collisions.


title: Oscillatory null singularity inside realistic spinning black holes

abstract:
  We calculate the asymptotic behavior of the curvature scalar $(Riemann)^2$
near the null weak singularity at the inner horizon of a generic spinning black
hole, and show that this scalar oscillates infinite number of times while
diverging. The dominant parallelly-propagated Riemann components oscillate in a
similar manner. This oscillatory behavior, which is in a remarkable contrast to
the monotonic mass-inflation singularity in spherical charged black holes, is
caused by the dragging of inertial frames due to the black- hole's spin.


title:
Scalar Field as Dark Matter and Machian Cosmological Solution in the
  Generalized Scalar-Tensor Theory of Gravitation

abstract:
  The Machian cosmological solution satisfying $\phi =O(\rho /\omega)$ in the
generalized scalar-tensor theory of gravitation with the varying cosmological
constant is summarized. The scalar field $\phi $ with the exponential potential
is introduced as dark matter and the barotropic evolution of matter in the
universe is discussed. As the universe expands, the coefficient $\gamma $ of
the equation of state approaches to -1/3 and the coupling function $\omega
(\phi)$ diverges to $-\infty $.


title:
Casimir energy in a small volume multiply connected static hyperbolic
  pre-inflationary Universe

abstract:
  A few years ago, Cornish, Spergel and Starkman (CSS), suggested that a
multiply connected ``small'' Universe could allow for classical chaotic mixing
as a pre-inflationary homogenization process. The smaller the volume, the more
important the process. Also, a smaller Universe has a greater probability of
being spontaneously created. Previously DeWitt, Hart and Isham (DHI) calculated
the Casimir energy for static multiply connected flat space-times. Due to the
interest in small volume hyperbolic Universes (e.g. CSS), we generalize the DHI
calculation by making a a numerical investigation of the Casimir energy for a
conformally coupled, massive scalar field in a static Universe, whose spatial
sections are the Weeks manifold, the smallest Universe of negative curvature
known. In spite of being a numerical calculation, our result is in fact exact.
It is shown that there is spontaneous vacuum excitation of low multipolar
components.


title: On closed rotating worlds

abstract:
  A new solution for the stationary closed world with rigid rotation is
obtained for the spinning fluid source. It is found that the spin and vorticity
are locally balanced. This model qualitatively shows that the local rotation of
the cosmological matter can be indeed related to the global cosmic vorticity,
provided the total angular momentum of the closed world is vanishing.


title: On the derivation of the spacetime metric from linear electrodynamics

abstract:
  In the framework of metric-free electrodynamics, we start with a {\em linear}
spacetime relation between the excitation 2-form $H = ({\cal D}, {\cal H})$ and
the field strength 2-form $F = ({E,B})$. This linear relation is constrained by
the so-called closure relation. We solve this system algebraically and extend a
previous analysis such as to include also singular solutions. Using the
recently derived fourth order {\em Fresnel} equation describing the propagation
of electromagnetic waves in a general {\em linear} medium, we find that for all
solutions the fourth order surface reduces to a light cone. Therefrom we derive
the corresponding metric up to a conformal factor.


title: Conserved currents for general teleparallel models

abstract:
  The obstruction for the existence of an energy momentum tensor for the
gravitational field is connected with differential-geometric features of the
Riemannian manifold. It has not to be valid for alternative geometrical
structures. In this article a general 3-parameter class of teleparallel models
is considered. The field equation turns out to have a form completely similar
to the Maxwell field equation $d*\F^a=\T^a$. By applying the Noether procedure,
the source 3-form $\T^a$ is shown to be connected with the diffeomorphism
invariance of the Lagrangian. Thus the source of the coframe field is
interpreted as the total conserved energy-momentum current of the system. A
reduction of the conserved current to the Noether current and the Noether
charge for the coframe field is provided. An energy-momentum tensor for the
coframe field is defined in a diffeomorphism invariant and a translational
covariant way. The total energy-momentum current of a system is conserved. Thus
a redistribution of the energy-momentum current between material and coframe
(gravity) field is possible in principle, unlike as in GR. The energy-momentum
tensor is calculated for various teleparallel models: the pure Yang-Mills type
model, the anti-Yang-Mills type model and the generalized teleparallel
equivalent of GR. The latter case can serve as a very close alternative to the
GR description of gravity.


title: Coalescence of Two Spinning Black Holes: An Effective One-Body Approach

abstract:
  We generalize to the case of spinning black holes a recently introduced
``effective one-body'' approach to the general relativistic dynamics of binary
systems. The combination of the effective one-body approach, and of a Pad\'e
definition of some crucial effective radial functions, is shown to define a
dynamics with much improved post-Newtonian convergence properties, even for
black hole separations of the order of $6 GM / c^2$. We discuss the approximate
existence of a two-parameter family of ``spherical orbits'' (with constant
radius), and, of a corresponding one-parameter family of ``last stable
spherical orbits'' (LSSO). These orbits are of special interest for forthcoming
LIGO/VIRGO/GEO gravitational wave observations. It is argued that for most (but
not all) of the parameter space of two spinning holes the effective one-body
approach gives a reliable analytical tool for describing the dynamics of the
last orbits before coalescence. This tool predicts, in a quantitative way, how
certain spin orientations increase the binding energy of the LSSO. This leads
to a detection bias, in LIGO/VIRGO/GEO observations, favouring spinning black
hole systems, and makes it urgent to complete the conservative effective
one-body dynamics given here by adding (resummed) radiation reaction effects,
and by constructing gravitational waveform templates that include spin effects.
Finally, our approach predicts that the spin of the final hole formed by the
coalescence of two arbitrarily spinning holes never approaches extremality.


title: Critical Phenomena Associated with Boson Stars

abstract:
  We present a brief synopsis of related work (gr-qc/0007039), describing a
study of black hole threshold phenomena for a self-gravitating, massive complex
scalar field in spherical symmetry. We construct Type I critical solutions
dynamically by tuning a one-parameter family of initial data consisting of a
boson star and a massless real scalar field, and numerically evolving this
data. The resulting critical solutions appear to correspond to boson stars on
the unstable branch, as we show via comparisons between our simulations and
perturbation theory. For low-mass critical solutions, we find small ``halos''
of matter in the tails of the solutions, and these distort the profiles which
otherwise agree with unstable boson stars. These halos seem to be artifacts of
the collisions between the original boson stars and the massless fields, and do
not appear to belong to the true critical solutions. From this study, it
appears that unstable boson stars are unstable to dispersal (``explosion'') in
addition to black hole formation. Given the similarities in macroscopic
stability between boson stars and neutron stars, we suggest that similar
phenomena could occur in models of neutron stars.


title:
On the energy-momentum current of the electromagnetic field in a
  pre-metric axiomatic approach. I

abstract:
  We complete a metric-free axiomatic framework for electrodynamics by
introducing the appropriate energy-momentum current Sigma of the
electromagnetic field. We start from the Lorentz force density and motivate the
form of Sigma. Then we postulate it (fourth axiom) and discuss its properties.
In particular, it is found that Sigma is traceless and invariant under an
electric-magnetic reciprocity transformation. By using the Maxwell-Lorentz
spacetime relation (fifth axiom), Sigma is also shown to be symmetric, that is,
it has 9 independent components


title: A simple quantum cosmology

abstract:
  A simple and surprisingly realistic model of the origin of the universe can
be developed using the Friedmann equation from general relativity, elementary
quantum mechanics, and the experimental values of h, c, G and the proton mass.
The model assumes there are N space dimensions (with N > 6) and the potential
constraining the radius r of the invisible N -3 compact dimensions varies as
r^4. In this model, the universe has zero total energy and is created from
nothing. There is no initial singularity. If space-time is eleven dimensional,
as required by M theory, the scalar field corresponding to the size of the
compact dimensions inflates the universe by about 26 orders of magnitude (60
e-folds). If the Hubble constant is 65 km/sec Mpc, the energy density of the
scalar field after inflation results in Omega-sub-Lambda = 0.68, in agreement
with recent astrophysical observations.