title:
Gauge invariant formalism for second order perturbations of
  Schwarzschild spacetimes

abstract:
  The ``close limit,'' a method based on perturbations of Schwarzschild
spacetime, has proved to be a very useful tool for finding approximate
solutions to models of black hole collisions. Calculations carried out with
second order perturbation theory have been shown to give the limits of
applicability of the method without the need for comparison with numerical
relativity results. Those second order calculations have been carried out in a
fixed coordinate gauge, a method that entails conceptual and computational
difficulties. Here we demonstrate a gauge invariant approach to such
calculations. For a specific set of models (requiring head on collisions and
quadrupole dominance of both the first and second order perturbations), we give
a self contained gauge invariant formalism. Specifically, we give (i) wave
equations and sources for first and second order gauge invariant wave
functions; (ii) the prescription for finding Cauchy data for those equations
from initial values of the first and second fundamental forms on an initial
hypersurface; (iii) the formula for computing the gravitational wave power from
the evolved first and second order wave functions.


title: Detection of the gravitomagnetic clock effect

abstract:
  The essence of the gravitomagnetic clock effect is properly defined showing
that its origin is in the topology of world lines with closed space
projections. It is shown that, in weak field approximation and for a
spherically symmetric central body, the loss of synchrony between two clocks
counter-rotating along a circular geodesic is proportional to the angular
momentum of the source of the gravitational field. Numerical estimates are
presented for objects within the solar system. The less unfavorable situation
is found around Jupiter.


title: Quantum Fields in an Expanding Universe

abstract:
  We extend our analysis for scalar fields in a Robertson-Walker metric to the
electromagnetic field and Dirac fields by the method of invariants. The issue
of the relation between conformal properties and particle production is
re-examined and it is verified that the electromagnetic and massless spinor
actions are conformal invariant, while the massless conformally coupled scalar
field is not. For the scalar field case it is pointed out that the violation of
conformal simmetry due to surface terms, although ininfluential for the
equation of motion, does lead to effects in the quantized theory.


title: A quantum holographic principle from decoherence

abstract:
  We present a fully quantum version of the holographic principle in terms of
quantum systems, subsystems, and their interactions. We use the concept of
environment induced decoherence to prove this principle. We discuss the
conditions under which the standard (semi-classical) holographic principle is
obtained from this quantum mechanical version.


title:
The Large Numbers Hypothesis: Outline of a self-similar
  quantum-cosmological Model

abstract:
  In 1919 A. Einstein suspected first that gravitational fields could play an
essential role in the structure of elementary particles. In 1937, P.A.M. Dirac
found a miraculous link between the properties of the visible Universe and
elementary particles. Both conjectures stayed alive through the following
decades but still no final theory could be derived to this issues. The herein
suggested fractal model of the Universe gives a consistent explanation to
Dirac's Large Numbers Hypothesis and combines the conjectures of Einstein and
Dirac.


title: Phases of Brans-Dicke cosmology(II):Matter from NS-NS sector

abstract:
  We study the cosmology of the Brans-Dicke(BD) theory coupled to perfect fluid
type matter. In our previous works, the case where matter is coming from the
Ramond-Ramond sector of the string theory was studied. Here, we study the case
where matter is coming from the NS-NS sector. Exact solutions are found and the
cosmology is classified according to the values of $\gamma$, the parameter of
the equation of state and $\omega$, Brans-Dicke parameter. We find taht, in
string frame, there are solutions without singularity for some ranges of
$\gamma$ and $\omega$. In Einstein frame, however, all solutions are singular.


title: Smearing of chaos in sandwich pp-waves

abstract:
  Recent results demonstrating the chaotic behavior of geodesics in
non-homogeneous vacuum pp-wave solutions are generalized. Here we concentrate
on motion in non-homogeneous sandwich pp-waves and show that chaos smears as
the duration of these gravitational waves is reduced. As the number of radial
bounces of any geodesic decreases, the outcome channels to infinity become
fuzzy, and thus the fractal structure of the initial conditions characterizing
chaos is cut at lower and lower levels. In the limit of impulsive waves, the
motion is fully non-chaotic. This is proved by presenting the geodesics in a
simple explicit form which permits a physical interpretation, and demonstrates
the focusing effect. It is shown that a circle of test particles is deformed by
the impulse into a family of closed hypotrochoidal curves in the transversal
plane. These are deformed in the longitudinal direction in such a way that a
specific closed caustic surface is formed.


title: Holographic Bound in Brans-Dicke Cosmology

abstract:
  We apply the holographic principle to the Brans-Dicke cosmology. We analyze
the holographic bound in both the Jordan and Einstein frames. The holographic
bound is satisfied for both the k=0 and k=-1 universe, but it is violated for
the k=1 matter dominated universe.


title: Kinetic Energy and the Equivalence Principle

abstract:
  According to the general theory of relativity, kinetic energy contributes to
gravitational mass. Surprisingly, the observational evidence for this
prediction does not seem to be discussed in the literature. I reanalyze
existing experimental data to test the equivalence principle for the kinetic
energy of atomic electrons, and show that fairly strong limits on possible
violations can be obtained. I discuss the relationship of this result to the
occasional claim that ``light falls with twice the acceleration of ordinary
matter.''


title: Conserved charges for gravity with locally AdS asymptotics

abstract:
  A new formula for the conserved charges in 3+1 gravity for spacetimes with
local AdS asymptotic geometry is proposed. It is shown that requiring the
action to have an extremum for this class of asymptotia sets the boundary term
that must be added to the Lagrangian as the Euler density with a fixed weight
factor. The resulting action gives rise to the mass and angular momentum as
Noether charges associated to the asymptotic Killing vectors without requiring
specification of a reference background in order to have a convergent
expression. A consequence of this definition is that any negative constant
curvature spacetime has vanishing Noether charges. These results remain valid
in the limit of vanishing cosmological constant.


title: A traversable wormhole

abstract:
  The paper has been withdrawn by the author, due to a fatal error. A horse
stumbles that has four legs.


title:
On the detectability of quantum spacetime foam with gravitational-wave
  interferometers

abstract:
  We discuss a recent provocative suggestion by Amelino-Camelia and others that
classical spacetime may break down into ``quantum foam'' on distance scales
many orders of magnitude larger than the Planck length, leading to effects
which could be detected using large gravitational wave interferometers. This
suggestion is based on a quantum uncertainty limit obtained by Wigner using a
quantum clock in a gedanken timing experiment. Wigner's limit, however, is
based on two unrealistic and unneccessary assumptions: that the clock is free
to move, and that it does not interact with the environment. Removing either of
these assumptions makes the uncertainty limit invalid, and removes the basis
for Amelino-Camelia's suggestion.


title:
Effective Action and Thermodynamics of Radiating Shells in General
  Relativity

abstract:
  An effective action is obtained for the area and mass aspect of a thin shell
of radiating self-gravitating matter. On following a mini-superspace approach,
the geometry of the embedding space-time is not dynamical but fixed to be
either Minkowski or Schwarzschild inside the shell and Vaidya in the external
space filled with radiation. The Euler-Lagrange equations of motion are
discussed and shown to entail the expected invariance of the effective
Lagrangian under time-reparametrization. They are equivalent to the usual
junction equations and suggest a macroscopic quasi-static thermodynamic
description.


title: Riemannian 2-D conical geometry of Heisenberg ferromagnets

abstract:
  An exact 2-dimensional conical Riemannian defect solution of 3-dimensional
Euclidean Einstein equations of stresses and defects representing a shear-free
Heisenberg ferromagnet is given.The system is equivalent to the Einstein
equations in vacuum.Geodesics of magnetic monopoles around the ferromagnet are
also investigated.


title: Darwin-Riemann problems in general relativity

abstract:
  A review is given of recent results about the computation of irrotational
Darwin-Riemann configurations in general relativity. Such configurations are
expected to represent fairly well the late stages of inspiralling binary
neutron stars.


title: The close limit of colliding black holes: an update

abstract:
  This is the writeup of the talk I gave at the Yukawa International Symposium
at Kyoto, Japan on June 29, 1999. The talk summarizes the present status of the
close limit approximation for colliding black holes.


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

abstract:
  Research Briefs:
  Does the GSL imply an entropy bound?, by Warren G. Anderson
  A lightweight review of middleweight black holes, by Ben Bromley
  The physics of isolated horizons, by Daniel Sudarsky
  LIGO project update, by Stan Whitcomb
  Meeting reports:
  Worskhop on initial value for binary black holes, by Carlos Lousto
  ITP Conference on strong gravitational fields, by Don Marolf
  Yukawa International Seminar, by John Friedman
  Minnowbrook symposium on the structure of space-time, by Kamesh Wali
  Black holes II and CCGRRA 8 by Jack Gegenberg and Gabor Kunstatter
  Hartlefest & 15th Pacific Coast Gravity Meeting by Simon Ross
  Second Capra workshop by Patrick Brady and Alan Wiseman
  Third Edoardo Amaldi Conference, by Gabriela Gonzalez
  Strings 99, by Thomas Thiemann


title: New methods in the theory of gauge fields

abstract:
  One of the fundamental problems of the theoretical physics is the search of
the axioms, which ought to be the basis for the one-valued construction of
Lagrangians of the relativistic fields. The creation of the gauge fields theory
was the great success in the solution of this problem. The gauge formalism
allowed to derive the total Lagrangians of the interacting fields from the
postulated Lagrangians of the noninteracting (free) fields. We offer to do
quite the reverse in consequence of what it is necessary to seek from the out
set the construction principles of the total Lagrangians. By the theory
construction we shall differ the wave-functions being the solutions of the
differential equations (``theoretical'' functions) from the wave-functions
which is constructed on the base of the experimental data possibly received by
a scattering of particles (``empiric'' functions). The ``empiric'' functions
are necessary only for the definition (it is possibly only approximately) of
the transition operators which will affect at the ``theoretical'' functions.
  This operators will be approximated the differential operators so, that the
generalized variance of the differentiable
  ``theoretical'' fields will be the minimal one.


title: The neutrinos, the gravitation and the gauge formalism

abstract:
  The detection and the research of the neutrinos background of
  Universe are the attractive problems. This problems do not seem the
unpromising one in the case of the high neutrinos density of Universe. It is
offered to use the low energy neutrinos background of Universe for the
explanation of the gravitational phenomena with the quantum position attracting
the Casimir's effect for this. As a result it can consider the normal matter
(not neutrinos) in the capasity of the
  Brownian particles by the help of which it can make the attempt to estimate
the statistic characteristics of the Universe neutrinos background.


title:
Tetrad Gravity: III) Asymptotic Poincare' Charges, the Physical
  Hamiltonian and Void Spacetimes

abstract:
  A discussion of asymptotic weak and strong Poincare' charges in metric
gravity is given to identify the proper Hamiltonian boundary conditions. The
asymptotic part of the lapse and shift functions is put equal to their
analogues on Minkowski hyperplanes. By adding Dirac's ten extra variables at
spatial infinity, metric gravity is extended to incorporate Dirac's ten extra
first class constraints (the new ten momenta equal to the weak Poincare'
charges) and this allows its deparametrization to parametrized Minkowski
theories restricted to spacelike hyperplanes. The absence of supertranslations
implies: i) boundary conditions identifying the family of
Christodoulou-Klainermann spacetimes; ii) the restriction of foliations to
those (Wigner-Sen-Witten hypersurfaces) corresponding to Wigner's hyperplanes
of Minkowski rest-frame instant form. These results are generalized to tetrad
gravity in the new formulation given in gr-qc/9807072, gr-qc/9807073. The
evolution in the parameter labelling the leaves of the foliation is generated
by the weak ADM energy. Some comments on the quantization in a completely fixed
special 3-orthogonal gauge are made.


title:
On the Stability of the Iterated Crank-Nicholson Method in Numerical
  Relativity

abstract:
  The iterated Crank-Nicholson method has become a popular algorithm in
numerical relativity. We show that one should carry out exactly two iterations
and no more. While the limit of an infinite number of iterations is the
standard Crank-Nicholson method, it can in fact be worse to do more than two
iterations, and it never helps. We explain how this paradoxical result arises.


title: Causal Structure of an Inflating Magnetic Monopole

abstract:
  We clarify the causal structure of an inflating magnetic monopole. The
spacetime diagram shows explicitly that this model is free from ``graceful
exit'' problem, while the monopole itself undergoes ``eternal inflation''. We
also discuss general nature of inflationary spacetimes.


title: Gravity on Finite Groups

abstract:
  Gravity theories are constructed on finite groups G. A self-consistent review
of the differential calculi on finite G is given, with some new developments.
The example of a bicovariant differential calculus on the nonabelian finite
group S_3 is treated in detail, and used to build a gravity-like field theory
on S_3.


title:
Stability and rotational mixing of modes in Newtonian and relativistic
  stars

abstract:
  Despite the recent excitement over the r-mode instability of rotating stars,
these modes are not yet well-understood for stellar models appropriate to
neutron stars - perfect fluid models in which both the equilibrium and
perturbed configurations obey the same one-parameter equation of state.
  In spherical stars of this kind, r-modes and g-modes form a degenerate
zero-frequency subspace. Rotation splits the degeneracy to zeroth order in the
star's angular velocity $\Omega$, and the resulting modes are generically
hybrids, whose limit as $\Omega\to 0$ is a stationary current with axial and
polar parts. Lindblom and Ipser have recently found these hybrid rotational
modes in an analytic study of the Maclaurin spheroids. This dissertation
studies them in Newtonian stars (both uniform density models and $n=1$
polytropes) and reports a first computation of the hybrid rotational modes of
relativistic stars.


title: Nonsingular static global string

abstract:
  A new solution for the spacetime outside the core of a U(1) static global
string has been presented which is nonsingular. This is the first example of a
nonsingular spacetime around a static global string.}}


title: Remarks on Cosmic Strings and Quantum Gravity

abstract:
  A quantum equivalence principle is formulated by means of a gravitational
phase operator which is an element of the Poincare group. This is applied to
the spinning cosmic string which suggests that it may, but not necessarily,
contain gravitational torsion. A new exact solution of the Einstein-
Cartan-Sciama-Kibble equations for the gravitational field with torsion is
obtained everywhere for a cosmic string with uniform energy density, spin
density and flux. The quantization condition for fluxoid due to London and
DeWitt is generalized to include the spin flux. A novel effect due to the
quantized gravitational field of the cosmic string on the wave function of a
particle outside the string is used to show that spacetime points are not
meaningful in quantum gravity.


title:
Towards a "pre-canonical" quantization of gravity without the space+time
  decomposition

abstract:
  Quantization of gravity is discussed in the context of field quantization
based on an analogue of canonical formalism (the De Donder-Weyl canonical
theory) which does not require the space+time decomposition. Using Horava's
(1991) De Donder-Weyl formulation of General Relativity we put forward a
covariant generalization of the Schr\"odinger equation for the wave function of
space-time and metric variables and a supplementary ``bootstrap condition''
which self-consistently incorporates the classical background space-time
geometry as a quantum average and closes the system of equations. Some open
questions for further research are outlined.


title: Duffin-Kemmer-Petiau equation in Riemannian space-times

abstract:
  In this work we analyze the generalization of Duffin-Kemmer-Petiau equation
to the case of Riemannian space-times and show that the usual results for
Klein-Gordon and Proca equations in Riemannian space-times can be fully
recovered when one selects, respectively, the spin 0 and 1 sectors of
Duffin-Kemmer-Petiau theory.


title: Quantization of Gravitational Waves and Squeezing

abstract:
  The question whether gravitational waves are quantised or not can in
principle be answered by the help of correlation measurements. If the
gravitational waves are quantised and they are generated by the change of the
background metrics then they can be in squeezed state.
  In a sqeezed state there is a correlation between the phase of the wave and
the quantum fluctuations. It is recommended to analyse the data to be obtained
by the gravitational detectors from the point of view of such correlations. An
explicit formula is derived for the squeezing parameter of the quantised
gravitational waves. The head on collision of two identical black holes is
analysed as a possible source of squeezed gravitational waves.


title:
Notes on covariant quantities in noninertial frames and invariance of
  radiation in classical and quantum field theory

abstract:
  A local observer can measure only the values of fields at the point of his
own position. By exploring the coordinate transformation between two Fermi
frames, it is shown that two observers, having the same instantaneous position
and velocity, will observe the same values of covariant fields at their common
instantaneous position, even if they have different instantaneous
accelerations. In particular, this implies that in classical physics the notion
of radiation is observer independent, contrary to the conclusion of some
existing papers. A "freely" falling charge in curved spacetime does not move
along a geodesic and therefore radiates. The essential feature of the Unruh
effect is the fact that it is based on a noninstantaneous measurement, which
may also be viewed as a source of effective noncovariance of measured
quantities. The particle concept in Minkowski spacetime is clarified. It is
argued that the particle concept in general spacetime does not depend on the
observer and that there exists a preferred coordinate frame with respect to
which the particle number should be defined.


title:
A Comment on the Degrees of Freedom in the Ashtekar Formulation for 2+1
  Gravity

abstract:
  We show that the recent claim that the 2+1 dimensional Ashtekar formulation
for General Relativity has a finite number of physical degrees of freedom is
not correct.


title: Polarizable-Vacuum (PV) representation of general relativity

abstract:
  Standard pedagogy treats topics in general relativity (GR) in terms of tensor
formulations in curved space-time. Although mathematically straightforward, the
curved space-time approach can seem abstruse to beginning students due to the
degree of mathematical sophistication required. As a heuristic tool to provide
insight into what is meant by a curved metric, we present a polarizable-vacuum
(PV) representation of GR derived from a model by Dicke and related to the
"TH-epsilon-mu" formalism used in comparative studies of gravitational
theories.


title:
A Modified Variational Principle in Relativistic Hydrodynamics. II.
  Variations of the vector field and the projection tensor in the general case
  and under definite assumptions

abstract:
  The purpose of the paper is to develop further a projection variational
approach in relativistic hydrodynamics. The approach, previously proposed in
[gr-qc/9908032], is based on the variation of the vector field and the
projection tensor (instead of the given metric tensor) and their first partial
derivatives. The previously proved property of non-commutativity of the
variation and the partial derivative in respect to the projection tensor has
been used to find all the variations. Subsequently, motivated by some analogy
with the well-known (3+1) ADM projection formalism, an assumption has been made
about a zero-covariant derivative of the projection tensor in respect to the
projection connection. The combination of the equations for the variations of
the projective tensor with covariant and contravariant indices has lead to the
derivation of an important and concisely written relation: the derivative of
the vector field length is equal to the ''twice'' projected along the vector
field initial Christoffell connection. The result is of interest due to the
following reasons: 1. It is a more general one and contains in itself a
well-known formulae in affine differential geometry for the so called
equiaffine connections (admitting covariantly conserved tensor fields), for
which the trace of the connection is equal to the gradient of the logarithm of
the vector field length. 2. The additional term is the projected (with the
projection tensor) initially given connection and accounts for the influence of
the reference system on the change of the vector field's length, measured in
this system. 3. The formulae has been obtained within the proposed formalism of
non-commuting variation and partial derivative.


title: The diffeomorphism algebra approach to quantum gravity

abstract:
  The representation theory of non-centrally extended Lie algebras of Noether
symmetries, including spacetime diffeomorphisms and reparametrizations of the
observer's trajectory, has recently been developped. It naturally solves some
long-standing problems in quantum gravity, e.g. the role of diffeomorphisms and
the causal structure, but some new questions also arise.


title:
Spinning Charged Solutions in 2+1 Dimensional Einstein-Maxwell-Dilaton
  Gravity

abstract:
  We report a new class of rotating charged solutions in 2+1 dimensions. These
solutions are obtained for Einstein-Maxwell gravity coupled to a dilaton field
with selfdual electromagnetic fields. The mass and the angular momentum of
these solutions computed at spatial infinity are finite. The class of solutions
considered here have naked singularities and are asymptotically flat.


title: Fractals and Scars on a Compact Octagon

abstract:
  A finite universe naturally supports chaotic classical motion. An ordered
fractal emerges from the chaotic dynamics which we characterize in full for a
compact 2-dimensional octagon. In the classical to quantum transition, the
underlying fractal can persist in the form of scars, ridges of enhanced
amplitude in the semiclassical wave function. Although the scarring is weak on
the octagon, we suggest possible subtle implications of fractals and scars in a
finite universe.


title: Chaos and Universality in the Dynamics of Inflationary Cosmologies

abstract:
  We describe a new statistical pattern in the chaotic dynamics of closed
inflationary cosmologies, associated with the partition of the Hamiltonian
rotational motion energy and hyperbolic motion energy pieces, in a linear
neighborhood of the saddle-center present in the phase space of the models. The
hyperbolic energy of orbits visiting a neighborhood of the saddle-center has a
random distribution with respect to the ensemble of initial conditions, but the
associated histograms define a statistical distribution law of the form $p(x) =
C x^{-\gamma}$, for almost the whole range of hyperbolic energies considered.
We present numerical evidence that $\gamma$ determines the dimension of the
fractal basin boundaries in the ensemble of initial conditions. This
distribution is universal in the sense that it does not depend on the
parameters of the models and is scale invariant. We discuss possible physical
consequences of this universality for the physics of inflation.tribution law of
the form $p(x) = C x^{-\gamma}$, for almost the whole range of hyperbolic
energies considered. We present numerical evidence that $\gamma$ determines the
dimension of the fractal basin boundaries in the ensemble of initial
conditions. This distribution is universal in the sense that it does not depend
on the parameters of the models and is scale invariant. We discuss possible
physical consequences of this universality for the physics of inflation.


title: Dynamics of magnetic Bianchi VI_0 cosmologies

abstract:
  Methods of dynamical systems analysis are used to show rigorously that the
presence of a magnetic field orthogonal to the two commuting Killing vector
fields in any spatially homogeneous Bianchi type VI_0 vacuum solution to
Einstein's equation changes the evolution toward the singularity from
convergent to oscillatory. In particular, it is shown that the alpha-limit set
(for time direction that puts the singularity in the past) of any of these
magnetic solutions contains at least two sequential Kasner points of the BKL
sequence and the orbit of the transition solution between them. One of the
Kasner points in the alpha-limit set is non-flat, which leads to the result
that each of these magnetic solutions has a curvature singularity.


title: A linearly Expanding Universe With Variable G and Lambda

abstract:
  We have studied a cosmological model with a cosmological term of the form
$\Lambda=3\alpha\fr{\dot R^2}{R^2}+\bt\fr{\ddot R}{R}+\fr{3\gamma}{R^2} \alpha,
\
  \bt \gamma$ are constants. The scale factor (R) is found to vary linearly
with time for both radiation and matter dominated epochs.
  The cosmological constant is found to decrease as $t^{-2}$ and the rate of
particle creation is smaller than the Steady State value.
  The model gives $\Omega^\Lambda=\fr{1}{3}$ and $\Omega^m=\fr{2}{3}$ in the
present era,
  $\Omega^\Lambda=\Omega^m=\fr{1}{2}$ in the radiation era.
  The present age of the universe $(\rm t_p$) is found to be $\rm t_p=H_p^{-1}$
, where $\rm H_p$ is the Hubble constant.
  The model is free from the main problems of the Standard Model. Since the
scale factor $\rm R\propto t$ during the entire evolution of the universe the
ratio of the cosmological constant at the Planck and present time is
$\rm\fr{\Lambda_{Pl}}{\Lambda_p}=10^{120}$.
  This decay law justifies why, today, the cosmological constant is exceedingly
small.


title: On the universality of low-energy string model

abstract:
  The low-energy (bosonic "heterotic") string theory is interpreted as a
universal limit of the Kaluza-Klein reduction when the dimension of an internal
space goes to infinity. We show that such an approach is helpful in obtaining
classical solutions of the string model. As a particular application, we obtain
new exact static solutions for the two-dimensional effective string model. They
turn out to be in agreement with the generalized no-hair conjecture, in
complete analogy with the four and higher dimensional Einstein theory of
gravity.


title:
Evolution of Dynamical Coupling in Scalar Tensor Theory from Noether
  Symmetry

abstract:
  We present the gravitational coupling function $\omega(\phi)$ in the vacuum
scalar-tensor theory as allowed by the Noether symmetry. We also obtain some
exact cosmological solutions in the spatially homogeneous and isotropic
background thereby showing that the attractor mechanism is not effective enough
to reduce the theory to Einstein theory. It is observed that, asymptotically,
the scalar tensor theory goes over to Einstein theory with finite value of
$\omega$. This work thus supports earlier works in this direction.


title: Quantum geometrodynamics of the Bianchi IX model in extended phase space

abstract:
  A way of constructing mathematically correct quantum geometrodynamics of a
closed universe is presented. The resulting theory appears to be
gauge-noninvariant and thus consistent with the observation conditions of a
closed universe, by that being considerably distinguished from the conventional
Wheeler - DeWitt one. For the Bianchi-IX cosmological model it is shown that a
normalizable wave function of the Universe depends on time, allows the standard
probability interpretation and satisfies a gauge-noninvariant dynamical
Schrodinger equation. The Wheeler - DeWitt quantum geometrodynamics is
represented by a singular, BRST-invariant solution to the Schrodinger equation
having no property of normalizability.


title:
On some geometric features of the Kramer interior solution for a
  rotating perfect fluid

abstract:
  Geometric features (including convexity properties) of an exact interior
gravitational field due to a self-gravitating axisymmetric body of perfect
fluid in stationary, rigid rotation are studied. In spite of the seemingly
non-Newtonian features of the bounding surface for some rotation rates, we
show, by means of a detailed analysis of the three-dimensional spatial
geodesics, that the standard Newtonian convexity properties do hold. A central
role is played by a family of geodesics that are introduced here, and provide a
generalization of the Newtonian straight lines parallel to the axis of
rotation.


title: On the extension of the Obukhov theorem in non-Riemannian gravity I

abstract:
  This is a first paper of a series in which we give some generalizations of
the Obukhov theorem in the Tucker-Wang approach to Metric- Affine gravity in
which we consider more general actions containing scalar and in general fields
which do not depend on the metric or connection.


title: A superradiance resonance cavity outside rapidly rotating black holes

abstract:
  We discuss the late-time behaviour of a dynamically perturbed Kerr black
hole. We present analytic results for near extreme Kerr black holes that show
that the large number of virtually undamped quasinormal modes that exist for
nonzero values of the azimuthal eigenvalue m combine in such a way that the
field oscillates with an amplitude that decays as 1/t at late times. This
prediction is verified using numerical time-evolutions of the Teukolsky
equation. We argue that the observed behaviour may be relevant for
astrophysical black holes, and that it can be understood in terms of the
presence of a ``superradiance resonance cavity'' immediately outside the black
hole.


title: Gravity waves from relativistic binaries

abstract:
  The stability of binary orbits can significantly shape the gravity wave
signal which future Earth-based interferometers hope to detect. The inner most
stable circular orbit has been of interest as it marks the transition from the
late inspiral to final plunge. We consider purely relativistic orbits beyond
the circular assumption. Homoclinic orbits are of particular importance to the
question of stability as they lie on the boundary between dynamical stability
and instability. We identify these, estimate their rate of energy loss to
gravity waves, and compute their gravitational waveforms.


title:
On certain global conformal invariants and 3-surface twistors of initial
  data sets

abstract:
  The Chern-Simons functionals built from various connections determined by the
initial data $h_{\mu\nu}$, $\chi_{\mu\nu}$ on a 3-manifold $\Sigma$ are
investigated. First it is shown that for asymptotically flat data sets the
logarithmic fall-off for $h_{\mu\nu}$ and $r\chi_{\mu\nu}$ is the necessary and
sufficient condition of the existence of these functionals. The functional
$Y_{k,l}$, built in the vector bundle corresponding to the irreducible
representation of SL(2,C) labelled by (k,l), is shown to be determined by the
Ashtekar-Chern-Simons functional and its complex conjugate. $Y_{k,l}$ is
conformally invariant precisely in the l=k (i.e. tensor) representations. An
unexpected connection with twistor theory is found: $Y_{k,k}$ can be written as
the Chern-Simons functional built from the 3-surface twistor connection, and
the not identically vanishing spinor parts of the 3-surface twistor curvature
are given by the variational derivatives of $Y_{k,k}$ with respect to
$h_{\mu\nu}$ and $\chi_{\mu\nu}$. The time derivative $\dot Y_{k,k}$ of
$Y_{k,k}$ is another conformal invariant of the initial data set, and for
vanishing $\dot Y_{k,k}$, in particular for all Petrov III and N spacetimes,
the Chern-Simons functional is a conformal invariant of the whole spacetime.


title: Loop Quantum Gravity on Non-Compact Spaces

abstract:
  We present a general procedure for constructing new Hilbert spaces for loop
quantum gravity on non-compact spatial manifolds. Given any fixed background
state representing a non-compact spatial geometry, we use the
Gel'fand-Naimark-Segal construction to obtain a representation of the algebra
of observables. The resulting Hilbert space can be interpreted as describing
fluctuation of compact support around this background state. We also give an
example of a state which approximates classical flat space and can be used as a
background state for our construction.


title: A General Treatment of Orbiting Gyroscope Precession

abstract:
  We review the derivation of the metric for a spinning body of any shape and
composition using linearized general relativity theory, and also obtain the
same metric using a transformation argument. The latter derivation makes it
clear that the linearized metric contains only the Eddington $\alpha$ and
$\gamma$ parameters, so no new parameter is involved in frame-dragging or
Lense-Thirring effects. We then calculate the precession of an orbiting
gyroscope in a general weak gravitational field, described by a Newtonian
potential (the gravito-electric field) and a vector potential (the
gravito-magnetic field). Next we make a multipole analysis of the potentials
and the precession equations, giving all of these in terms of the spherical
harmonics moments of the density distribution. The analysis is not limited to
an axially symmetric source, although the Earth, which is the main application,
is very nearly axisymmetric. Finally we analyze the precession in regard to the
Gravity Probe B (GP-B) experiment, and find that the effect of the Earth's
quadrupole moment (J_2) on the geodetic precession is large enough to be
measured by GP-B (a previously known result), but the effect on the
Lense-Thirring precession is somewhat beyond the expected GP-B accuracy.


title: Darwin-Riemann Problems in Newtonian Gravity

abstract:
  In this paper, we have reviewed the present status of the theory of
equilibrium configurations of compact binary star systems in Newtonian gravity.
Evolutionary processes of compact binary star systems due to gravitational wave
emission can be divided into three stages according to the time scales and
configurations. The evolution is quasi-stationary until a merging process
starts, since the time scale of the orbital change due to gravitational wave
emission is longer than the orbital period. In this stage, equilibrium
sequences can be applied to evolution of compact binary star systems. Along the
equilibrium sequences, there appear several critical states where some
instability sets in or configuration changes drastically. We have discussed
relations among these critical points and have stressed the importance of the
mass overflow as well as the dynamical instability of orbital motions.
Concerning the equilibrium sequences of binary star systems, we have summarized
classical results of incompressible ellipsoidal configurations. Recent results
of compressible binary star systems obtained by the ellipsoidal approximation
and by numerical computations have been shown and discussed. It is important to
note that numerical computational solutions to {\it exact equations} show that
compressibility may lead realistic neutron star binary systems to mass
overflows instead of dynamical disruptions for a wide range of parameters.


title: A Non-Classical Linear Xenomorph as a Model for Quantum Causal Space

abstract:
  A quantum picture of the causal structure of Minkowski space M is presented.
The mathematical model employed to this end is a non-classical version of the
classical topos {H} of real quaternion algebras used elsewhere to organize the
perceptions of spacetime events of a Boolean observer into M. Certain key
properties of this new quantum topos are highlighted by contrast against the
corresponding ones of its classical counterpart {H} modelling M and are seen to
accord with some key features of the algebraically quantized causal set
structure.


title: Strings in Kerr-Newmann Black Holes

abstract:
  We study the evolution of strings in the equatorial plane of a Kerr-Newmann
black hole. Writting the equations of motion and the constraints resulting from
Hamilton's principle, three classes of exact solutions are presented, for a
closed string, encircling the black hole. They all depend on two arbitrary
integration functions and two constants. A process of extracting energy is
examined for the case of one of the three families of solutions. This is the
analog of the Penrose process for the case of a particle.


title: Quasi-Normal Modes of Stars and Black Holes

abstract:
  Perturbations of stars and black holes have been one of the main topics of
relativistic astrophysics for the last few decades. They are of particular
importance today, because of their relevance to gravitational wave astronomy.
In this review we present the theory of quasi-normal modes of compact objects
from both the mathematical and astrophysical points of view. The discussion
includes perturbations of black holes (Schwarzschild, Reissner-Nordstr\"om,
Kerr and Kerr-Newman) and relativistic stars (non-rotating and
slowly-rotating). The properties of the various families of quasi-normal modes
are described, and numerical techniques for calculating quasi-normal modes
reviewed. The successes, as well as the limits, of perturbation theory are
presented, and its role in the emerging era of numerical relativity and
supercomputers is discussed.


title:
Brief Comments on ``The Shapiro Conjecture, Prompt or Delayed Collapse
  ?'' by Miller, Suen and Tobias

abstract:
  Recent numerical simulations address a conjecture by Shapiro that when two
neutron stars collide head-on from rest at infinity, sufficient thermal
pressure may be generated to support the hot remnant in quasi-static
equilibrium against collapse prior to neutrino cooling. The conjecture is meant
to apply even when the total remnant mass exceeds the maximum mass of a cold
neutron star. One set of simulations seems to corroborate the conjecture, while
another, involving higher mass progenitors each very close to the maximum mass,
does not. In both cases the total mass of the remnant exceeds the maximum mass.
We point out numerical subtleties in performing such simulations when the
progenitors are near the maximum mass; they can explain why the simulations
might have difficulty assessing the conjecture in such high-mass cases.


title: Vanishing Vierbein in Gauge Theories of Gravitation

abstract:
  We discuss the problem of a degenerate vierbein in the framework of gauge
theories of gravitation (thus including torsion). We discuss two examples:
Hanson-Regge gravitational instanton and Einstein-Rose bridge.We argue that a
region of space-time with vanishing vierbein but smooth principal connection
can be, in principle, detected by scattering experiments.


title: Statistical Entropy of BTZ Black Hole in Higher Curvature Gravity

abstract:
  For the BTZ black hole in the Einstein gravity, a statistical entropy has
been calculated to be equal to the Bekenstein-Hawking entropy. In this paper,
the statistical entropy of the BTZ black hole in the higher curvature gravity
is calculated and shown to be equal to the one derived by using the Noether
charge method. This suggests that the equivalence of the geometrical and
statistical entropies of the black hole is retained in the general
diffeomorphism invariant theories of gravity. A relation between the cosmic
censorship conjecture and the unitarity of the conformal field theory on the
boundary of AdS is also discussed.


title: Kruskal Dynamics For Radial Geodesics. I

abstract:
  The total spacetime manifold for a Schwarzschild black hole (BH) is described
by the Kruskal coordinates u=u(r,t) and v=v(r,t), where r and t are the
conventional Schwarzschild radial and time coordinates respectively. The
relationship between r and t for a test particle moving on a radial or
non-radial geodesic is well known. Similarly, the expression for the vacuum
Schwarzschild derivative for a geodesic, in terms of the constants of motion,
is well known. However, the same is not true for the Kruskal coordinates. Here,
we, first, explicitly obtain the value of the Kruskal coordinates on the Event
Horizon as a function of the constant of motion (E=energy per unit rest mass)
for a test particle on a radial geodesic by directly using the r-t relationship
as obtained by Chandrasekhar and also by Misner, Thorne and Wheeler. It is
found that u_H and v_H are finite for E <1. And then, we derive here the
expression for the Kruskal derivative for a radial geodesic in terms of the
constants of motion. In particular, it is seen that the value of |du/dv| (= 1)
is regular on the Event Horizon of the Black Hole. The regular nature of the
Kruskal derivative is in sharp contrast with the Schwarzschild derivative,
|dt/dr| =infty, at the Event Horizon.


title:
Consistent canonical quantization of general relativity in the space of
  Vassiliev knot invariants

abstract:
  We present a quantization of the Hamiltonian and diffeomorphism constraint of
canonical quantum gravity in the spin network representation. The novelty
consists in considering a space of wavefunctions based on the Vassiliev knot
invariants. The constraints are finite, well defined, and reproduce at the
level of quantum commutators the Poisson algebra of constraints of the
classical theory. A similar construction can be carried out in 2+1 dimensions
leading to the correct quantum theory.


title: Global monopole as dual-vacuum solution in Kaluza-Klein spacetime

abstract:
  By application of the duality transformation, which implies interchange of
active and passive electric parts of the Riemann curvature (equivalent to
interchange of Ricci and Einstein tensors) it is shown that the global monopole
solution in the Kaluza-Klein spacetime is dual to the corresponding vacuum
solution. Further we also obtain solution dual to flat space which would in
general describe a massive global monopole in 4-dimensional Euclidean space and
would have massless limit analogus to the 4-dimensional dual-flat solution.


title: An alternative method for calculating the energy of gravitational waves

abstract:
  In the expansive nondecelerative universe model, creation of matter occurs
due to which the Vaidya metrics is applied. This fact allows for localizing
gravitational energy and calculating the energy of gravitational waves using an
approach alternative to the well established procedure based on quadrupole
formula. Rationalization of the gradual increase in entropy of the Universe
using relation describing the total curvature of space-time is given too.


title: Gravoelectric-dual of the Kerr solution

abstract:
  By decomposing the Riemann curvature into electric and magnetic parts, we
define the gravoelectric duality transformation by interchange of active and
passive electric parts which amounts to interchange of the Ricci and Einstein
tensors. It turns out that the vacuum equation is duality-invariant. We obtain
solutions dual to the Kerr solution by writing an effective vacuum equation in
such a way that it still admits the Kerr solution but is not duality invariant.
The dual equation is then solved to obtain the dual-Kerr solution which can be
interpreted as the Kerr black hole sitting in a string dust universe.


title: Electromagnetic duality in general relativity

abstract:
  By resolving the Riemann curvature relative to a unit timelike vector into
electric and magnetic parts, we consider duality relations analogous to the
electromagnetic theory. It turns out that the duality symmetry of the Einstein
action implies the Einstein vacuum equation without the cosmological term. The
vacuum equation is invariant under interchange of active and passive electric
parts giving rise to the same vacuum solutions but the gravitational constant
changes sign. Further by modifying the equation it is possible to construct
interesting dual solutions to vacuum as well as to flat spacetimes.


title: Exact solutions for null fluid collapse in higher dimensions

abstract:
  A large family of inhomogeneous non-static spherically symmetric solutions of
the Einstein equation for null fluid in higher dimensions has been obtained. It
encompasses higher dimensional versions of many previously known solutions such
as Vaidya, charged Vaidya and Husain solutions and also some new solutions
representing global monopole or string dust. It turns out that physical
properties of the solutions carry over to higher dimensions.


title: Higher Dimensional Analogue of McVittie Solution

abstract:
  A generalization of the McVittie solution, representing spacetime of a mass
particle placed in (n+2) dimensional Robertson-Walker universe is reported.


title:
Gravitational waves, black holes and cosmic strings in cylindrical
  symmetry

abstract:
  Gravitational waves in cylindrically symmetric Einstein gravity are described
by an effective energy tensor with the same form as that of a massless Klein-
Gordon field, in terms of a gravitational potential generalizing the Newtonian
potential. Energy-momentum vectors for the gravitational waves and matter are
defined with respect to a canonical flow of time. The combined energy-momentum
is covariantly conserved, the corresponding charge being the modified Thorne
energy. Energy conservation is formulated as the first law expressing the
gradient of the energy as work and energy-supply terms, including the energy
flux of the gravitational waves. Projecting this equation along a trapping
horizon yields a first law of black-hole dynamics containing the expected term
involving area and surface gravity, where the dynamic surface gravity is
defined with respect to the canonical flow of time. A first law for dynamic
cosmic strings also follows. The Einstein equation is written as three wave
equations plus the first law, each with sources determined by the combined
energy tensor of the matter and gravitational waves.


title: Polydimensional Supersymmetric Principles

abstract:
  Systems of equations are invariant under "polydimensional transformations"
which reshuffle the geometry such that what is a line or a plane is dependent
upon the frame of reference. This leads us to propose an extension of Clifford
calculus in which each geometric element (vector, bivector) has its own
coordinate. A new classical action principle is proposed in which particles
take paths which minimize the distance traveled plus area swept out by the
spin. This leads to a solution of the 50 year old conundrum of `what is the
correct Lagrangian' in which to derive the Papapetrou equations of motion for
spinning particles in curved space (including torsion).
  Based on talk given at: 5th International Conference on Clifford Algebras and
their Applications in Mathematical Physics, Ixtapa-Zihuatanejo, Mexico, June
27-July 4, 1999.


title: Domain Walls in Kaluza-Klein spacetime

abstract:
  Three families of exact solutions of Einstein field equations are found. Each
family contains three parameters. Two of these families represent thick domain
walls in a five dimensional Kaluza-Klein spacetime. The dynamical behaviour of
our models is briefly discussed. The spacetime in all the cases is found to be
reflection symmetric with respect to the wall.


title: Vorticity affects the stability of neutron stars

abstract:
  The spin rate \Omega of neutron stars at a given temperature T is constrained
by the interplay between gravitational-radiation instabilities and viscous
damping. Navier-Stokes theory has been used to calculate the viscous damping
timescales and produce a stability curve for r-modes in the (\Omega,T) plane.
In Navier-Stokes theory, viscosity is independent of vorticity, but kinetic
theory predicts a coupling of vorticity to the shear viscosity. We calculate
this coupling and show that it can in principle significantly modify the
stability diagram at lower temperatures. As a result, colder stars can remain
stable at higher spin rates.


title:
Soliton Solutions with Real Poles in the Alekseev formulation of the
  Inverse-Scattering method

abstract:
  A new approach to the inverse-scattering technique of Alekseev is presented
which permits real-pole soliton solutions of the Ernst equations to be
considered. This is achieved by adopting distinct real poles in the scattering
matrix and its inverse. For the case in which the electromagnetic field
vanishes, some explicit solutions are given using a Minkowski seed metric. The
relation with the corresponding soliton solutions that can be constructed using
the Belinskii-Zakharov inverse-scattering technique is determined.


title: Introduction to causal sets: an alternate view of spacetime structure

abstract:
  This paper provides a thorough introduction to the causal set hypothesis
aimed at students, and other interested persons, with some knowledge of general
relativity and nonrelativistic quantum mechanics. I elucidate the arguments for
why the causal set structure might be the appropriate structure for a theory of
quantum gravity. The logical and formal development of a causal set theory as
well as a few illuminating examples are also provided.


title:
Quasi-stationary binary inspiral II: Radiation-balanced boundary
  conditions

abstract:
  The quasi-stationary method for black hole binary inspiral is an
approximation for studying strong field effects while suppressing radiation
reaction. In this paper we use a nonlinear scalar field toy model (i) to
explain the underlying method of approximating binary motion by periodic orbits
with radiation; (ii) to show how the fields in such a model are found by the
solution of a boundary value problem; (iii) to demonstrate how a good
approximation to the outgoing radiation can be found by finding fields with a
balance of ingoing and outgoing radiation (a generalization of standing waves).


title:
Superconducting Cosmic Strings that Connected a Charged Black Hole and
  Considered as Hair of Black Hole

abstract:
  This paper describes that the superconducting cosmic strings can be connected
to an electrically charged black hole, and can be considerd as the hair of
black hole. What the no-hair theorems show is that a large amount of
information is lost when a body collapses to form a black hole. In addition,
the no-hair theorem has not been proved for the Yang-Mills field. This paper
proves and claims that the superconducting cosmic strings can be connected to
an electrically charged hole when the current inside these strings and black
holes approaches the critical value. Because, this state is the final state of
the gravitational collapse, and the event horizon would be destroyed in this
state. Therefore, these strings should be considered as hair of the charged
black holes, and may be titled as BHCS (Black Hole Connected Strings). This
means that at least the charged black holes have the hair. Thus, the no-hair
theorem is not applicable for the charged black holes in the state of the
critical current.


title:
Spikes in Cosmic Crystallography II: Topological Signature of Compact
  Flat Universes

abstract:
  We study the topological signature of euclidean isometries in pair
separations histograms (PSH) and elucidate some unsettled issues regarding
distance correlations between cosmic sources in cosmic crystallography.
Reducing the noise of individual PSH's using mean pair separations histograms
we show how to distinguish between topological and statistical spikes. We
report results of simulations that evince that topological spikes are not
enough to distinguish between manifolds with the same set of Clifford
translations in their covering groups, and that they are not the only signature
of topology in PSH's corresponding to euclidean small universes. We also show
how to evince the topological signature due to non-translational isometries.


title: Quantum gravity corrections to neutrino propagation

abstract:
  Massive spin-1/2 fields are studied in the framework of loop quantum gravity
by considering a state approximating, at a length scale $\cal L$ much greater
than Planck length $\ell_P=1.2\times 10^{-33}$cm, a spin-1/2 field in flat
spacetime. The discrete structure of spacetime at $\ell_P$ yields corrections
to the field propagation at scale $\cal L$. Next, Neutrino Bursts (${\bar
p}\approx 10^5$GeV) accompaning Gamma Ray Bursts that have travelled
cosmological distances, $L\approx 10^{10}$l.y., are considered. The dominant
correction is helicity independent and leads to a time delay w.r.t. the speed
of light, $c$, of order $({\bar p} \ell_P) L/c\approx 10^4$s. To next order in
${\bar p} \ell_P$ the correction has the form of the Gambini and Pullin effect
for photons. Its contribution to time delay is comparable to that caused by the
mass term. Finally, a dependence $L_{\rm os}^{-1} \propto {\bar p}^2 \ell_P$ is
found for a two-flavour neutrino oscillation length.


title: Sensitivity curves for spaceborne gravitational wave interferometers

abstract:
  To determine whether particular sources of gravitational radiation will be
detectable by a specific gravitational wave detector, it is necessary to know
the sensitivity limits of the instrument. These instrumental sensitivities are
often depicted (after averaging over source position and polarization) by
graphing the minimal values of the gravitational wave amplitude detectable by
the instrument versus the frequency of the gravitational wave. This paper
describes in detail how to compute such a sensitivity curve given a set of
specifications for a spaceborne laser interferometer gravitational wave
observatory. Minor errors in the prior literature are corrected, and the first
(mostly) analytic calculation of the gravitational wave transfer function is
presented. Example sensitivity curve calculations are presented for the
proposed LISA interferometer. We find that previous treatments of LISA have
underestimated its sensitivity by a factor of $\sqrt{3}$.


title: Propagation of light in non-inertial reference frames

abstract:
  It is shown that the complete description of the propagation of light in a
gravitational field and in non-inertial reference frames in general requires an
average coordinate and an average proper velocity of light. The need for an
average coordinate velocity of light in non-inertial frames is demonstrated by
considering the propagation of two vertical light rays in the Einstein elevator
(in addition to the horizontal ray originally discussed by Einstein). As an
average proper velocity of light is implicitly used in the Shapiro time delay
(as shown in the Appendix) it is explicitly derived and it is shown that for a
round trip of a light signal between two points in a gravitational field the
Shapiro time delay not only depends on which point it is measured at, but in
the case of a parallel gravitational field it is not always a delay effect. The
propagation of light in rotating frames (the Sagnac effect) is also discussed
and an expression for the coordinate velocity of light is derived. The use of
this coordinate velocity naturally explains why an observer on a rotating disk
finds that two light signals emitted from a point on the rim of the disk and
propagating in opposite directions along the rim do not arrive simultaneously
at the same point.


title:
Generalized Kerr Schild metrics and the gravitational field of a
  massless particle on the horizon

abstract:
  We investigate the structure of the gravitational field generated by a
massless particle moving on the horizon of an arbitrary (stationary) black
hole. This is done by employing the generalized Kerr-Schild class where we take
the null generators of the horizon as the geodetic null vector-field and a
scalar function which is concentrated on the horizon.


title: Automatic cross-talk removal from multi-channel data

abstract:
  A technique is described for removing interference from a signal of interest
("channel 1") which is one of a set of N time-domain instrumental signals
("channels 1 to N"). We assume that channel 1 is a linear combination of "true"
signal plus noise, and that the "true" signal is not correlated with the noise.
We also assume that part of this noise is produced, in a poorly-understood way,
by the environment, and that the environment is monitored by channels 2 to N.
Finally, we assume that the contribution of channel n to channel 1 is described
by an (unknown!) linear transfer function R_n(t-t'). Our technique estimates
the R_i and provides a way to subtract the environmental contamination from
channel 1, giving an estimate of the "true" signal which minimizes its
variance. It also provides some insights into how the environment is
contaminating the signal of interest. The method is illustrated with data from
a prototype interferometric gravitational-wave detector, in which the channel
of interest (differential displacement) is heavily contaminated by
environmental noise (magnetic and seismic noise) and laser frequency noise but
where the coupling between these signals is not known in advance.


title: R-Modes in Superfluid Neutron Stars

abstract:
  The analogs of r-modes in superfluid neutron stars are studied here. These
modes, which are governed primarily by the Coriolis force, are identical to
their ordinary-fluid counterparts at the lowest order in the small
angular-velocity expansion used here. The equations that determine the next
order terms are derived and solved numerically for fairly realistic superfluid
neutron-star models. The damping of these modes by superfluid ``mutual
friction'' (which vanishes at the lowest order in this expansion) is found to
have a characteristic time-scale of about 10^4 s for the m=2 r-mode in a
``typical'' superfluid neutron-star model. This time-scale is far too long to
allow mutual friction to suppress the recently discovered gravitational
radiation driven instability in the r-modes. However, the strength of the
mutual friction damping depends very sensitively on the details of the
neutron-star core superfluid. A small fraction of the presently acceptable
range of superfluid models have characteristic mutual friction damping times
that are short enough (i.e. shorter than about 5 s) to suppress the
gravitational radiation driven instability completely.


title: Probing Models of Quantum Space-Time Foam

abstract:
  We review the possibility that quantum fluctuations in the structure of
space-time at the Planck scale might be subject to experimental probes. We
study the effects of space-time foam in an approach inspired by string theory,
in which solitonic D-brane excitations are taken into account when considering
the ground state. We model the properties of this medium by analyzing the
recoil of a D particle which is induced by the scattering of a closed-string
state. We find that this recoil causes an energy-dependent perturbation of the
background metric, which in turn induces an energy-dependent refractive index
in vacuo, and stochastic fluctuations of the light cone. We show how distant
astrophysical sources such as Gamma-Ray Bursters (GRBs) may be used to test
this possibility, making an illustrative analysis of GRBs whose redshifts have
been measured. Within this framework, we also discuss the propagation of
massive particles and the possible appearance of cosmological vacuum energy
that relaxes towards zero. We also discuss D-brane recoil in models with
`large' extra dimensions.


title: Scale Invariant Cosmology

abstract:
  An attempt is made here to extend to the microscopic domain the scale
invariant character of gravitation - which amounts to consider expansion as
applying to any physical scale. Surprisingly, this hypothesis does not prevent
the redshift from being obtained. It leads to strong restrictions concerning
the choice between the presently available cosmological models and to new
considerations about the notion of time. Moreover, there is no horizon problem
and resorting to inflation is not necessary.


title: Aberration and the Speed of Gravity

abstract:
  The observed absence of gravitational aberration requires that ``Newtonian''
gravity propagate at a speed $c_g>2\times10^{10}c$. By evaluating the
gravitational effect of an accelerating mass, I show that aberration in general
relativity is almost exactly canceled by velocity-dependent interactions,
permitting $c_g=c$. This cancellation is dictated by conservation laws and the
quadrupole nature of gravitational radiation.


title: Energy Production in the Formation of a Finite Thickness Cosmic String

abstract:
  The classical electromagnetic modes outside a long, straight, superconducting
cosmic string are calculated, assuming the string to be surrounded by a
superconducting cylindric surface of radius R. Thereafter, by use of a
Bogoliubov-type argument, the electromagnetic energy W produced per unit length
in the lowest two modes is calculated when the string is formed "suddenly". The
essential new element in the present analysis as compared with prior work of
Parker [Phys. Rev. Lett. {\bf 59}, 1369 (1987)] and Brevik and Toverud [Phys.
Rev. D {\bf 51}, 691 (1995)], is that the radius {\it a} of the string is
assumed finite, thus necessitating Neumann functions to be included in the
fundamental modes. We find that the theory is changed significantly: W is now
strongly concentrated in the lowest mode $(m,s)=(0,1)$, whereas the
proportionality $W \propto (G\mu /t)^2$ that is characteristic for zero-width
strings is found in the next mode (1,1). Here G is the gravitational constant,
$\mu$ the string mass per unit length, and t the GUT time.


title:
3+1 description of silent universes: a uniqueness result for the Petrov
  type I vacuum case

abstract:
  Silent universes are studied using a ``3+1'' decomposition of the field
equations in order to make progress in proving a recent conjecture that the
only silent universes of Petrov type I are spatially homogeneous Bianchi I
models. The infinite set of constraints are written in a geometrically clear
form as an infinite set of Codacci tensors on the initial hypersurface. In
particular, we show that the initial data set for silent universes is
``non-contorted'' and therefore (Beig and Szabados, 1997) isometrically
embeddable in a conformally flat spacetime. We prove, by making use of
algebraic computing programs, that the conjecture holds in the simpler case
when the spacetime is vacuum. This result points to confirming the validity of
the conjecture in the general case. Moreover, it provides an invariant
characterization of the Kasner metric directly in terms of the Weyl tensor. A
physical interpretation of this uniqueness result is briefly discussed.


title:
Quadrupole interaction of relativistic quantum particle with external
  fields

abstract:
  We consider the motion of a spinning relativistic particle with an arbitrary
value of spin in external electromagnetic and gravitational fields, to first
order in the external field. We use the noncovariant description of spin. An
explicit expression is obtained for the interaction of second order in spin.
The value of the quadrupole moment is found for which this interaction
decreases when the energy grows.


title: Waves and uniformity of space-times

abstract:
  Undulatory field functions represent a real wave only if there exists a class
of infinite reference systems for which an identical wave is described by the
same functional forms.


title:
Limiting sensitivity of superconductive LC - circuit placed in weak
  gravitational wave

abstract:
  It is demonstrated that the sensitivity of a superconductive LC - circuit
placed in a weak gravitational wave is limited by two factors. One is the
quantization of the magnetic flux through the circuit, the second one is the
fraction of the elementary charge (effect Laughlin - Stormer - Tsui).
Application to a possibility of using a superconductive LC - circuit as a weak
gravitational waves detector is discussed.


title: The Apparent Fractal Conjecture

abstract:
  This short communication advances the hypothesis that the observed fractal
structure of large-scale distribution of galaxies is due to a geometrical
effect, which arises when observational quantities relevant for the
characterization of a cosmological fractal structure are calculated along the
past light cone. If this hypothesis proves, even partially, correct, most, if
not all, objections raised against fractals in cosmology may be solved. For
instance, under this view the standard cosmology has zero average density, as
predicted by an infinite fractal structure, with, at the same time, the
cosmological principle remaining valid. The theoretical results which suggest
this conjecture are reviewed, as well as possible ways of checking its
validity.


title: Generalized De Sitter Space

abstract:
  This paper deals with some two-parameter solutions to the spherically
symmetric, vacuum Einstein equations which, we argue, are more general than de
Sitter solution. The global structure of one such spacetimes and its extension
to the multiply connected case have also been investigated. By using a
six-dimensional Minkowskian embedding as its maximal extension, we check that
the thermal properties of the considered solution in such an embedding space
are the same as those derived by the usual Euclidean method. The stability of
the generalized de Sitter space containing a black hole has been investigated
as well by introducing perturbations of the Ginsparg-Perry type in first order
approximation. It has been obtained that such a space perdures against the
effects of these perturbations.


title: Does a dynamical system lose energy by emitting gravitational waves?

abstract:
  We note that Eddington's radiation damping calculation of a spinning rod
fails to account for the complete mass integral as given by Tolman. The missing
stress contributions precisely cancel the standard rate given by the
'quadrupole formula'. This indicates that while the usual 'kinetic' term can
properly account for dynamical changes in the source, the actual mass is
conserved. Hence gravity waves are not carriers of energy in vacuum. This
supports the hypothesis that energy including the gravitational contribution is
confined to regions of non-vanishing energy-momentum tensor $T_{ik}$.
  PACS numbers: 04.20.Cv, 04.30.-w


title: The Wahlquist metric cannot describe an isolated rotating body

abstract:
  It is proven that the Wahlquist perfect fluid space-time cannot be smoothly
joined to an exterior asymptotically flat vacuum region. The proof uses a power
series expansion in the angular velocity, to a precision of the second order.
In this approximation, the Wahlquist metric is a special case of the rotating
Whittaker space-time. The exterior vacuum domain is treated in a like manner.
We compute the conditions of matching at the possible boundary surface in both
the interior and the vacuum domain. The conditions for matching the induced
metrics and the extrinsic curvatures are mutually contradictory.


title:
Perturbations of the metric induced by back - reaction in the warm
  inflation scenario

abstract:
  A second-order expansion for the quantum fluctuations of the matter field was
considered in the framemork of the warm inflation scenario. The friction and
Hubble parameters were expanded by means of a semiclassical approach. The
fluctuations of the Hubble parameter generates fluctuations of the metric.
These metric fluctuations produce an effective term of curvature. The power
spectrum for the metric fluctuations can be calculated on the infrared sector.


title: Geometric models of (d+1)-dimensional relativistic rotating oscillators

abstract:
  Geometric models of quantum relativistic rotating oscillators in arbitrary
dimensions are defined on backgrounds with deformed anti-de Sitter metrics. It
is shown that these models are analytically solvable, deriving the formulas of
the energy levels and corresponding normalized energy eigenfunctions. An
important property is that all these models have the same nonrelativistic
limit, namely the usual harmonic oscillator.


title:
The normalized energy eigenspinors of the Dirac field on anti-de Sitter
  spacetime

abstract:
  It is shown how can be derived the normalized energy eigenspinors of the free
Dirac field on anti-de Sitter spacetime, by using a Cartesian tetrad gauge
where the separation of spherical variables can be done like in special
relativity.


title:
Some Possible Roles for Topos Theory in Quantum Theory and Quantum
  Gravity

abstract:
  We discuss some ways in which topos theory (a branch of category theory) can
be applied to interpretative problems in quantum theory and quantum gravity. In
Section 1, we introduce these problems. In Section 2, we introduce topos
theory, especially the idea of a topos of presheaves. In Section 3, we discuss
several possible applications of topos theory to the problems in Section 1. In
Section 4, we draw some conclusions.


title: Decoherence and quantum mechanics in a gravitational field

abstract:
  Quantum mechanical interference of wave functions leads to some difficulties
if a probability density is considered as a source of gravity. We show that an
introduction of a quantum energy-momentum tensor as a source term in Einstein
equations can be consistent with general relativity if the gravitational waves
are quantized.


title:
The reduced phase space of spherically symmetric Einstein-Maxwell theory
  including a cosmological constant

abstract:
  We extend here the canonical treatment of spherically symmetric (quantum)
gravity to the most simple matter coupling, namely spherically symmetric
Maxwell theory with or without a cosmological constant. The quantization is
based on the reduced phase space which is coordinatized by the mass and the
electric charge as well as their canonically conjugate momenta, whose
geometrical interpretation is explored. The dimension of the reduced phase
space depends on the topology chosen, quite similar to the case of pure (2+1)
gravity. We investigate several conceptual and technical details that might be
of interest for full (3+1) gravity. We use the new canonical variables
introduced by Ashtekar, which simplifies the analysis tremendously.


title:
Generalized boundary conditions for general relativity for the
  asymptotically flat case in terms of Ashtekar's variables

abstract:
  There is a gap that has been left open since the formulation of general
relativity in terms of Ashtekar's new variables namely the treatment of
asymptotically flat field configurations that are general enough to be able to
define the generators of the Lorentz subgroup of the asymptotical Poincar\'e
group. While such a formulation already exists for the old geometrodynamical
variables, up to now only the generators of the translation subgroup could be
defined because the function spaces of the fields considered earlier are taken
too special. The transcription of the framework from the ADM variables to
Ashtekar's variables turns out not to be straightforward due to the a priori
freedom to choose the internal SO(3) frame at spatial infinity and due to the
fact that the non-trivial reality conditions of the Ashtekar framework reenter
the stage when imposing suitable boundary conditions on the fields and the
Lagrange multipliers.


title: Complete quantization of a diffeomorphism invariant field theory

abstract:
  In order to test the canonical quantization programme for general relativity
we introduce a reduced model for a real sector of complexified Ashtekar gravity
which captures important properties of the full theory. While it does not
correspond to a subset of Einstein's gravity it has the advantage that the
programme of canonical quantization can be carried out completely and
explicitly, both, via the reduced phase space approach or along the lines of
the algebraic quantization programme. This model stands in close correspondence
to the frequently treated cylindrically symmetric waves. In contrast to other
models that have been looked at up to now in terms of the new variables the
reduced phase space is infinite dimensional while the scalar constraint is
genuinely bilinear in the momenta. The infinite number of Dirac observables can
be expressed in compact and explicit form in terms of the original phase space
variables. They turn out, as expected, to be non-local and form naturally a set
of countable cardinality.


title: Reduced models for quantum gravity

abstract:
  The preceding talks given at this conference have dealt mainly with general
ideas for, main problems of and techniques for the task of quantizing gravity
canonically. Since one of the major motivations to arrange for this meeting was
that it should serve as a beginner's introduction to canonical quantum gravity,
we regard it as important to demonstrate the usefulness of the formalism by
means of applying it to simplified models of quantum gravity, here formulated
in terms of Ashtekar's new variables. From the various, completely solvable,
models that have been discussed in the literature we choose those that we
consider as most suitable for our pedagogical reasons, namely 2+1 gravity and
the spherically symmetric model. The former model arises from a dimensional,
the latter from a Killing reduction of full 3+1 gravity. While 2+1 gravity is
usually treated in terms of closed topologies without boundary of the initial
data hypersurface, the toplogy for the spherically symmetric system is chosen
to be asymptotically flat. Finally, 2+1 gravity is more suitably quantized
using the loop representation while spherically symmetric gravity is easier to
quantize via the self-dual representation. Accordingly, both types of
reductions, both types of topologies and both types of representations that are
mainly employed in the literature in the context of the new variables come into
practice. What makes the discussion especially clear is the fact that for both
models the reduced phase space turns out to be finitely dimensional.


title:
Reduced Phase Space Quantization of spherically symmetric
  Einstein-Maxwell-Theory including a cosmological constant

abstract:
  We present here the canonical treatment of spherically symmetric (quantum)
gravity coupled to spherically symmetric Maxwell theory with or without a
cosmological constant. The quantization is based on the reduced phase space
which is coordinatized by the mass and the electric charge as well as their
canonically conjugate momenta, whose geometrical interpretation is explored.
The dimension of the reduced phase space depends on the topology chosen, quite
similar to the case of pure (2+1) gravity. We also compare the reduced phase
space quantization to the algebraic quantization. Altogether, we observe that
the present model serves as an interesting testing ground for full (3+1)
gravity. We use the new canonical variables introduced by Ashtekar which
simplifies the analysis tremendously.


title:
Canonical quantization of a minisuperspace model for gravity using
  self-dual variables

abstract:
  The present article summarizes the work of the papers \cite{1} dealing with
the quantization of pure gravity and gravity coupled to a Maxwell field and a
cosmological constant in presence of spherical symmetry. The class of models
presented is intended as an interesting testing ground for the quantization of
full 3+1 gravity. We are working in Ashtekar's self-dual representation.


title: Is the brick-wall model unstable for a rotating background?

abstract:
  The stability of the brick wall model is analyzed in a rotating background.
It is shown that in the Kerr background without horizon but with an inner
boundary a scalar field has complex-frequency modes and that, however, the
imaginary part of the complex frequency can be small enough compared with the
Hawking temperature if the inner boundary is sufficiently close to the horizon,
say at a proper altitude of Planck scale. Hence, the time scale of the
instability due to the complex frequencies is much longer than the relaxation
time scale of the thermal state with the Hawking temperature. Since ambient
fields should settle in the thermal state in the latter time scale, the
instability is not so catastrophic. Thus, the brick wall model is well defined
even in a rotating background if the inner boundary is sufficiently close to
the horizon.


title: Limited Frequency Range Observations of Cosmological Point Sources

abstract:
  This paper advances a general proposal for testing non-standard cosmological
models by means of observational relations of cosmological point sources in
some specific waveband, and their use in the context of the data provided by
the galaxy redshift surveys, but for any cosmological metric. By starting from
the general theory for observations in relativistic cosmology the equations for
colour, K-correction, and number counts of cosmological point sources are
discussed in the context of curved spacetimes. The number counts equation is
also written in terms of the selection and luminosity functions, which provides
a relativistic generalization of its Euclidean version. Since these observables
were not derived in the framework of any specific cosmology, they are valid for
any cosmological model. The hypotheses used in such derivation are reviewed,
together with some difficulties for the practical use of those observables.


title: Total Energy of the Bianchi Type I Universes

abstract:
  Using the symmetric energy-momentum complexes of Landau and Lifshitz,
Papapetrou, and Weinberg we obtain the energy of the universe in anisotropic
Bianchi type I cosmological models . The energy (due to matter plus field) is
found to be zero and this agrees with a previous result of Banerjee and Sen who
investigated this problem using the Einstein energy-momentum complex. Our
result supports the importance of the energy-momentum complexes and contradicts
the prevailing ``folklore'' that different energy-momentum complexes could give
different and hence unacceptable energy distribution in a given space-time. The
result that the total energy of the universe in these models is zero supports
the viewpoint of Tryon. Rosen computed the total energy of the closed
homogeneous isotropic universe and found that to be zero, which agrees with the
studies of Tryon.


title: Inertial Effects on Neutrino Oscillations

abstract:
  The inertial effects on neutrino oscillations induced by the acceleration and
angular velocity of a reference frame are calculated. Such effects have been
analyzed in the framework of the solar and atmospheric neutrino problem.


title: Generalized Uncertainty Principle from Quantum Geometry

abstract:
  The generalized uncertainty principle of string theory is derived in the
framework of
  Quantum Geometry by taking into account the existence of an upper limit on
the acceleration of massive particles.


title: Dirac Equation in Kerr Geometry

abstract:
  We are familiar with Dirac equation in flat space by which we can investigate
the behaviour of half-integral spin particle. With the introduction of general
relativistic effects the form of the Dirac equation will be modified. For the
cases of different background geometry like Kerr, Schwarzschild etc. the
corresponding form of the Dirac equation as well as the solution will be
different. In 1972, Teukolsky wrote the Dirac equation in Kerr geometry.
Chandrasekhar separated it into radial and angular parts in 1976. Later
Chakrabarti solved the angular equation in 1984. In 1999 Mukhopadhyay and
Chakrabarti have solved the radial Dirac equation in Kerr geometry in a
spatially complete manner. In this review we will discuss these developments
systematically and present some solutions.


title: On the response of gravitational antennas to dilatonic waves

abstract:
  It is pointed out that the coupling of macroscopic test masses to the
gravi-dilaton background of string theory is non geodesic, in general, and
cannot be parametrized by a Brans-Dicke model of scalar-tensor gravity. The
response of gravitational antennas to dilatonic waves should be analyzed
through a generalized equation of geodesic deviation, taking into account the
possible direct coupling of the background to the (composition-dependent)
dilatonic charge of the antenna.


title: On signature transition in Robertson-Walker cosmologies

abstract:
  We analyse a classical model of gravitation coupled to a self interacting
scalar field. We show that, within the context of this model for
Robertson-Walker cosmologies, there exist solutions in the spatially non-flat
cases exhibiting transitions from a Euclidean to a Lorentzian spacetime. We
then discuss the conditions under which these signature changing solutions to
Einstein's field equations exist. In particular, we find that an upper bound
for the cosmological constant exists and that close to the signature changing
hypersurface, both the scale factor and the scalar field have to be constant.
Moreover we find that the signature changing solutions do not exist when the
scalar field is massless.


title: Dilatonic, Current-Carrying Cosmic String

abstract:
  We study the implications of a scalar-tensorial gravity for the metric of an
isolated self-gravitating superconducting cosmic string. These modifications
are induced by an arbitrary coupling of a massless scalar field to the usual
tensorial field in the gravitational Lagrangian. We derive the metric in the
weak-field approximation and we analyse the behaviour of light in this
spacetime. We end with some discussions.


title:
Collision of 1.4 $M_{\odot}$ Neutron Stars: Dynamical or
  Quasi-Equilibrium?

abstract:
  Shapiro put forth a conjecture stating that neutron stars in head-on
collisions (infalling from infinity) will not collapse to black holes before
neutrino cooling, independent of the mass of the neutron stars. In a previous
paper we carried out a numerical simulation showing a counter example based on
1.4 $M_{\odot}$ neutron stars, and provided an analysis explaining why
Shapiro's argument was not applicable for this case. A recent paper by Shapiro
put forth an argument suggesting that numerical simulations of the 1.4
$M_{\odot}$ collisions could not disprove the conjecture with the accuracy that
is presently attainable. We show in this paper that this argument is not
applicable for the same reason that the Shapiro conjecture is not applicable to
the 1.4 $M_{\odot}$ neutron star collision, namely, the collision is too
dynamical to be treated by quasi-equilibrium arguments.


title:
On the Salecker-Wigner limit and the use of interferometers in
  space-time-foam studies

abstract:
  The recent paper gr-qc/9909017 criticizes the limit on the measurability of
distances that was derived by Salecker and Wigner in the 1950s. If justified,
this criticism would have important implications for all the recent studies
that have used in various ways the celebrated Salecker-Wigner result, but I
show here that the analysis reported in gr-qc/9909017 is incorrect. Whereas
Salecker and Wigner sought an operative definition of distances suitable for
the Planck regime, the analysis in gr-qc/9909017 relies on several assumptions
that appear to be natural in the context of most present-day experiments but
are not even meaningful in the Planck regime. Moreover, contrary to the claim
made in gr-qc/9909017, a relevant quantum uncertainty which is used in the
Salecker-Wigner derivation cannot be truly eliminated; unsurprisingly, it can
only be traded for another comparable contribution to the total uncertainty in
the measurement. I also comment on the role played by the Salecker-Wigner limit
in my recent proposal of interferometry-based tests of quantum properties of
space-time, which was incorrectly described in gr-qc/9909017. In particular, I
emphasize that, as discussed in detail in gr-qc/9903080, only some of the
quantum-gravity ideas that can be probed with modern interferometers are
motivated by the Salecker-Wigner limit. The bulk of the insight we can expect
from such interferometric studies concerns the properties of "foamy" models of
space-time, which are intrinsically interesting independently of the
Salecker-Wigner limit.


title:
The fate of Reissner-Nortstr\"{o}m black hole in the
  Einstein-Yang-Mills-Higgs system

abstract:
  We study about an evaporating process of black holes in SO(3)
Einstein-Yang-Mills-Higgs system. We consider a massless scalar field which
couple neither with the Yang-Mills field nor with the Higgs field surrounding
the black hole. We discuss differences in evaporating rate between a monopole
black hole and a Reissner-Nortstr\"{o}m (RN) black hole.


title: Quantum Cosmology

abstract:
  We comment on two issues in quantum cosmology, in the context of the
Wheeler-De Witt equation and wave function of the Universe: (i) arrow of time
and interpretation of the wave function in the classically allowed regions;
(ii) stability of an approximation of the Born-Oppenheimer type in classically
forbidden regions of the scale factor.


title: Neutrino Oscillations in Brans-Dicke Theory of Gravity

abstract:
  Flavor oscillations of neutrinos are analyzed in the framework of Brans-Dicke
theory of gravity. We find a shift of quantum mechanical phase of neutrino
proportional to $G_N\Delta m^2$ and depending on the parameter $\omega$.
Consequences on atmospheric, solar and astrophysical neutrinos are discussed.


title:
A Robust Test for Detecting Non-Stationarity in Data from Gravitational
  Wave Detectors

abstract:
  It is difficult to choose detection thresholds for tests of non-stationarity
that assume {\em a priori} a noise model if the data is statistically
uncharacterized to begin with. This is a potentially serious problem when an
automated analysis is required, as would be the case for the huge data sets
that large interferometric gravitational wave detectors will produce. A
solution is proposed in the form of a {\em robust} time-frequency test for
detecting non-stationarity whose threshold for a specified false alarm rate is
almost independent of the statistical nature of the ambient stationary noise.
The efficiency of this test in detecting bursts is compared with that of an
ideal test that requires prior information about both the statistical
distribution of the noise and also the frequency band of the burst. When
supplemented with an approximate knowledge of the burst duration, this test can
detect, at the same false alarm rate and detection probability, bursts that are
about 3 times larger in amplitude than those that the ideal test can detect.
Apart from being robust, this test has properties which make it suitable as an
online monitor of stationarity.


title: Comment on Ricci Collineations for type B warped space-times

abstract:
  We present two counterexamples to the paper by Carot et al. in Gen. Rel.
Grav. 1997, 29, 1223 and show that the results obtained are correct but not
general.


title: The structure of the extreme Schwarzschild-de Sitter space-time

abstract:
  The extreme Schwarzschild-de Sitter space-time is a spherically symmetric
solution of Einstein's equations with a cosmological constant Lambda and mass
parameter m>0 which is characterized by the condition that 9 Lambda m^2=1. The
global structure of this space-time is here analyzed in detail. Conformal and
embedding diagrams are constructed, and synchronous coordinates which are
suitable for a discussion of the cosmic no-hair conjecture are presented. The
permitted geodesic motions are also analyzed. By a careful investigation of the
geodesics and the equations of geodesic deviation, it is shown that specific
families of observers escape from falling into the singularity and approach
nonsingular asymptotic regions which are represented by special "points" in the
complete conformal diagram. The redshift of signals emitted by particles which
fall into the singularity, as detected by those observers which escape, is also
calculated.


title: The Einstein-Dirac-Maxwell Equations - Black Hole Solutions

abstract:
  In this summary article, we review and discuss the non-existence of
stationary black hole solutions for the Einstein-Dirac-Maxwell equations.


title: New Gauge Conditions in General Relativity: What Can We Learn from Them?

abstract:
  The construction of conformally invariant gauge conditions for Maxwell and
Einstein theories on a manifold M is found to involve two basic ingredients.
First, covariant derivatives of a linear gauge (e.g. Lorenz or de Donder),
completely contracted with the tensor field representing the metric on the
vector bundle of the theory. Second, the addition of a compensating term,
obtained by covariant differentiation of a suitable tensor field built from the
geometric data of the problem. If the manifold M is endowed with an
m-dimensional positive-definite metric g, the existence theorem for such a
gauge in gravitational theory can be proved. If the metric g is Lorentzian,
which corresponds to general relativity, some technical steps are harder, but
one has again to solve integral equations on curved space-time to be able to
impose such gauges.


title: Relativistic Scalar Gravity: A Laboratory for Numerical Relativity

abstract:
  We present here a relativistic theory of gravity in which the spacetime
metric is derived from a single scalar field $\Phi$. The field equation,
derived from a simple variational principle, is a non-linear flat-space
four-dimensional wave equation which is particularly suited for numerical
evolution. We demonstrate that while this theory does not generate results
which are exactly identical quantitatively to those of general relativity (GR),
many of the qualitative features of the full GR theory are reproduced to a
reasonable approximation. The advantage of this formulation lies in the fact
that 3D numerical grids can be numerically evolved in minutes or hours instead
of the days and weeks required by GR, thus drastically reducing the development
time of new relativistic hydrodynamical codes. Scalar gravity therefore serves
as a meaningful testbed for the development of larger routines destined for use
under the full theory of general relativity.


title: Getting Ready for GEO600 Data

abstract:
  Data of good quality is expected from a number of gravitational wave
detectors within the next two years. One of these, GEO600, has special
capabilities, such as narrow-band operation. I describe here the preparations
that are currently being made for the analysis of GEO600 data.


title:
Morse index and causal continuity. A criterion for topology change in
  quantum gravity

abstract:
  Studies in 1+1 dimensions suggest that causally discontinuous topology
changing spacetimes are suppressed in quantum gravity. Borde and Sorkin have
conjectured that causal discontinuities are associated precisely with index 1
or n-1 Morse points in topology changing spacetimes built from Morse functions.
We establish a weaker form of this conjecture. Namely, if a Morse function f on
a compact cobordism has critical points of index 1 or n-1, then all the Morse
geometries associated with f are causally discontinuous, while if f has no
critical points of index 1 or n-1, then there exist associated Morse geometries
which are causally continuous.


title: Killing-Yano tensors, non-standard supersymmetries and an index theorem

abstract:
  The existence of Killing-Yano tensors on space-times can be probed by
spinning particles. Specifically, Dirac particles possess new fermionic
constants of motion corresponding to non-standard supersymmetries on the
particle worldline. A geometrical duality connects space-times with
Killing-Yano structure, but without torsion, to other space-times with
Killing-Yano structure and torsion. A relation between the indices of the Dirac
operators on the dual space-times allows to express the index on the space-time
with torsion in terms of that of the space-time without torsion.


title: Theory of Everything

abstract:
  This is a set of 25 articles, developed starting from the Relativistic Theory
of Quantum Gravity (first article). Together they form the Theory of
Everything.


title: Entropy and the cosmological constant: a spacetime-foam approach

abstract:
  A simple model of spacetime foam, made by N wormholes in a semiclassical
approximation, is taken under examination. The Casimir-like energy of the
quantum fluctuation of such a model and its probability of being realized are
computed. Implications on the Bekenstein-Hawking entropy and the cosmological
constant are considered.


title: Deformation of relativistic magnetized stars

abstract:
  We formulate deformation of relativistic stars due to the magnetic stress,
considering the magnetic fields to be perturbations from spherical stars. The
ellipticity for the dipole magnetic field is calculated for some stellar
models. We have found that the ellipticity becomes large with increase of a
relativistic factor for the models with the same energy ratio of the magnetic
energy to the gravitational energy.


title: Quadratic Lagrangians and Topology in Gauge Theory Gravity

abstract:
  We consider topological contributions to the action integral in a gauge
theory formulation of gravity. Two topological invariants are found and are
shown to arise from the scalar and pseudoscalar parts of a single integral.
Neither of these action integrals contribute to the classical field equations.
An identity is found for the invariants that is valid for non-symmetric Riemann
tensors, generalizing the usual GR expression for the topological invariants.
The link with Yang-Mills instantons in Euclidean gravity is also explored. Ten
independent quadratic terms are constructed from the Riemann tensor, and the
topological invariants reduce these to eight possible independent terms for a
quadratic Lagrangian. The resulting field equations for the parity
non-violating terms are presented. Our derivations of these results are
considerably simpler that those found in the literature.


title: Gravity Waves, Chaos, and Spinning Compact Binaries

abstract:
  Spinning compact binaries are shown to be chaotic in the Post-Newtonian
expansion of the two body system. Chaos by definition is the extreme
sensitivity to initial conditions and a consequent inability to predict the
outcome of the evolution. As a result, the spinning pair will have
unpredictable gravitational waveforms during coalescence. This poses a
challenge to future gravity wave observatories which rely on a match between
the data and a theoretical template.


title: Primary scalar hair in dilatonic theories with modulus fields

abstract:
  We study the general spherical symmetric solutions of dilaton-modulus gravity
non-minimally coupled to a Maxwell field, using methods from the theory of
dynamical systems. We show that the solutions can be classified by the mass,
the electric charge, and a third parameter which we argue can be related to a
scalar charge. The global properties of the solutions are discussed.


title:
A numeric solution for metric-affine gravity and Einstein's
  gravitational theory with Proca matter

abstract:
  A special case of metric-affine gauge theory of gravity (MAG) is equivalent
to general relativity with Proca matter as source. We study in detail a
corresponding numeric solution of the Reissner-Nordstr"om type. It is static,
spherically symmetric, and of electric type. In particular, this solution has
no horizon, so it has a naked singularity as its origin.


title: On the metric operator for quantum cylindrical waves

abstract:
  Every (1 polarization) cylindrical wave solution of vacuum general relativity
is completely determined by a corresponding axisymmetric solution to the free
scalar wave equation on an auxilliary 2+1 dimensional flat spacetime. The
physical metric at radius R is determined by the energy, $\gamma (R)$, of the
scalar field in a box (in the flat spacetime) of radius R. In a recent work,
among other important results, Ashtekar and Pierri have introduced a strategy
to study the quantum geometry in this system, through a regularized quantum
counterpart of $\gamma (R)$. We show that this regularized object is a densely
defined symmetric operator, thereby correcting an error in their proof of this
result. We argue that it admits a self adjoint extension and show that the
operator, unlike its classical counterpart, is not positive.


title: Spherical Harmonic Decomposition on a Cubic Grid

abstract:
  A method is described by which a function defined on a cubic grid (as from a
finite difference solution of a partial differential equation) can be resolved
into spherical harmonic components at some fixed radius. This has applications
to the treatment of boundary conditions imposed at radii larger than the size
of the grid, following Abrahams, Rezzola, Rupright et al.(gr-qc/9709082}. In
the method described here, the interpolation of the grid data to the
integration 2-sphere is combined in the same step as the integrations to
extract the spherical harmonic amplitudes, which become sums over grid points.
Coordinates adapted to the integration sphere are not needed.