abstract:
  For long black holes have been considered as endowed with a definite
temperature. Yet when the Schwarzschild black hole is treated as a canonical
ensemble three problems arise: incompatibility with the Hawking radiation,
divergence of the partition function, and a formally negative mean-square
fluctuation of the energy. We solve all three problems by considering the
Schwarzschild black hole as a grand canonical ensemble, with the Hamiltonian
(the ADM mass) and the horizon surface area, separately, as observable
parameters. The horizon area simulates the number of particles in statistical
mechanics since its spectrum is assumed to be discrete and equally spaced. We
obtain a logarithmic correction to the Bekenstein-Hawking entropy and a
Gaussian type distribution for the energy levels.


title: Local twistors and the conformal field equations

abstract:
  This note establishes the connection between Friedrich's conformal field
equations and the conformally invariant formalism of local twistors.


title: Mechanics of Isolated Horizons

abstract:
  A set of boundary conditions defining an undistorted, non-rotating isolated
horizon are specified in general relativity. A space-time representing a black
hole which is itself in equilibrium but whose exterior contains radiation
admits such a horizon. However, the definition is applicable in a more general
context, such as cosmological horizons. Physically motivated, (quasi-)local
definitions of the mass and surface gravity of an isolated horizon are
introduced and their properties analyzed. Although their definitions do not
refer to infinity, these quantities assume their standard values in the static
black hole solutions. Finally, using these definitions, the zeroth and first
laws of black hole mechanics are established for isolated horizons.


title:
Stationary Axisymmetric Solutions of the Einstein Equations with Rigidly
  Rotating Perfect Fluid and Nonlinear Charged Sources

abstract:
  A class of stationary rigidly rotating perfect fluid coupled with non-linear
electromagnetic fields was investigated. An exact solution of the Einstein
equations with sources for the Carter B(+) branch was found, for the equation
of state $3p + \epsilon = constant$. We use a structural function for the
Born-Infeld non-linear electrodynamics which is invariant under duality
rotations and a metric possessing a four- parameter group of motions. The
solution is of Petrov type D and the eigenvectors of the electromagnetic field
are aligned to the Debever-Penrose vectors.


title: Upper limits based on "loudest" events

abstract:
  This paper has been withdrawn due to a crucial error in combining the two
probability sectors represented in equations 13 and 14. Corrected, one can
recover, in the limit of no background, the results of Allen et al. The general
result that an analysis allowing for a background permits a substantial
improvement of the limit still holds, though the presentation in the
gr-qc/9907070 is flawed.


title: Space-time Structures from Critical Values in 2D Quantum Gravity

abstract:
  A model for 2D Quantum Gravity is constructed out of the Virasoro group. To
this end the quantization of the abstract Virasoro group is revisited. For the
critical values of the conformal anomaly c, some quantum operators (SL(2,R)
generators) lose their dynamical content (they are no longer conjugated
operators). The notion of space-time itself in 2D gravity then arises as
associated with this kinematical SL(2,R) symmetry. An ensemble of different
copies of AdS do co-exist in this model with different weights, depending on
their curvature (which is proportional to \hbar^{2}) and they are connected by
gravity operators. This model suggests that, in general, quantum diffemorphisms
should not be imposed as constraints to the theory, except for the classical
limit.


title: Static and Infalling Quasilocal Energy of Charged and Naked Black Holes

abstract:
  We extend the quasilocal formalism of Brown and York to include
electromagnetic and dilaton fields and also allow for spatial boundaries that
are not orthogonal to the foliation of the spacetime. The extension allows us
to study the quasilocal energy measured by observers who are moving around in a
spacetime. We show that the quasilocal energy transforms with respect to boosts
by Lorentz-type transformation laws. The resulting formalism can be used to
study spacetimes containing electric or magnetic charge but not both, a
restriction inherent in the formalism. The gauge dependence of the quasilocal
energy is discussed. We use the thin shell formalism of Israel to reinterpret
the quasilocal energy from an operational point of view and examine the
implications for the recently proposed AdS/CFT inspired intrinsic reference
terms. The distribution of energy around Reissner-Nordstr\"{o}m and naked black
holes is investigated as measured by both static and infalling observers. We
see that this proposed distribution matches a Newtonian intuition in the
appropriate limit. Finally the study of naked black holes reveals an alternate
characterization of this class of spacetimes in terms of the quasilocal
energies.


title:
Quantum Effects in the Presence of Expanding Semi-Transparent Spherical
  Mirrors

abstract:
  We study quantum effects in the presence of a spherical semi-transparent
mirror or a system of two concentric mirrors which expand with a constant
acceleration in a flat D-dimensional spacetime. Using the Euclidean approach,
we obtain expressions for fluctuations and the renormalized value of
stress-energy tensor for a scalar non-minimally coupled massless field.
Explicit expressions are obtained for the energy fluxes at the null infinity
generated by such mirrors in the physical spacetime and their properties are
discussed.


title: On The Vaidya Limit of the Tolman Model

abstract:
  We show that the only Tolman models which permit a Vaidya limit are those
having a dust distribution that is hollow - such as the self-similar case. Thus
the naked shell-focussing singularities found in Tolman models that are dense
through the origin have no Vaidya equivalent. This also casts light on the
nature of the Vaidya metric. We point out a hidden assumption in Lemos'
demonstration that the Vaidya metric is a null limit of the Tolman metric, and
in generalising his result, we find that a different transformation of
coordinates is required.


title:
Ricci Collineations for Non-Degenerate, Diagonal and Spherically
  Symmetric Ricci Tensors

abstract:
  The expression of the vector field generator of a Ricci Collineation for
diagonal, spherically symmetric and non-degenerate Ricci tensors is obtained.
The resulting expressions show that the time and radial first derivatives of
the components of the Ricci tensor can be used to classify the collineation,
leading to 64 families.
  Some examples illustrate how to obtain the collineation vector.


title: Inertia in the Structure of Space-Time

abstract:
  In Einstein's equation we suggest a geometrical object substituting the
tensor of energy of impulse and tension. The obtained equation, together with
the equation for external field, makes up the complete problem of mathematical
equations of gravitation, as well as those of inertia. Based on the example of
centrally symmetrical field those problems and their consequences are
discussed.


title: Quasilocal energy and naked black holes

abstract:
  We extend the Brown and York notion of quasilocal energy to include coupled
electromagnetic and dilaton fields and also allow for spatial boundaries that
are not orthogonal to the foliation of the spacetime. We investigate how the
quasilocal quantities measured by sets of observers transform with respect to
boosts. As a natural application of this work we investigate the naked black
holes of Horowitz and Ross calculating the quasilocal energies measured by
static versus infalling observers.


title:
SL(2,C) Gauge Theory of Gravitation and the Quantization of the
  Gravitational Field

abstract:
  A new approach to quantize the gravitational field is presented. It is based
on the observation that the quantum character of matter becomes more
significant as one gets closer to the big bang. As the metric loses its
meaning, it makes sense to consider Schrodinger's three generic types of
manifolds - unconnected differentiable, affinely connected, and metrically
connected - as a temporal sequence following the big bang. Hence one should
quantize the gravitational field on general differentiable manifolds or on
affinely connected manifolds. The SL(2,C) gauge theory of gravitation is
employed to explore this possibility. Within this framework, the quantization
itself may well be canonical.


title:
Linking a Minimal Theoretical Model of Scale Factor Evolution with
  Observational Universe Information

abstract:
  We study several approaches for constructing a minimal model of Universe
evolution by matching different stages of scale factor laws. We discuss the
continuity in the transitions among the stages and the time variables involved.
We develop a way to modelize these transitions without loss of observational
predictability. The key is the scale factor and its connection with minimal but
well stablished observational information (transition times and expansion
ratii). This construction is clearly useful in metric perturbations type
computations, but it can be applied in whatever subject dealing with a
cosmology involving different evolution stages.


title: Aspects of Cosmological Relativity

abstract:
  We review cosmological relativity, a new special theory of relativity that
was recently developed for cosmology, and discuss in detail some of its
aspects.


title:
Conformal symmetry, anomaly and effective action for metric-scalar
  gravity with torsion

abstract:
  We consider some aspects of conformal symmetry in a metric-scalar-torsion
system. It is shown that, for some special choice of the action, torsion acts
as a compensating field and the full theory is conformally equivalent to
General Relativity on classical level. Due to the introduction of torsion, this
equivalence can be provided for the positively-defined gravitational and scalar
actions. One-loop divergences arising from the scalar loop are calculated and
both the consequent anomaly and the anomaly-induced effective action are
derived.


title: Projections and covariant divergency of energy-momentun tensors

abstract:
  The invariant projections of the energy-momentum tensors of Lagrangian
densities for tensor fields over differentiable manifolds with contravariant
and covariant affine connections and metrics [$(\bar{L}_n,g)$-spaces] are found
by the use of an non-null (non-isotropic) contravariant vector field and its
corresponding projective metrics. The notions of rest mass density, momentum
density, energy current density and stress tensor are introduced as
generalizations of these notions from the relativistic continuum media
mechanics. The energy-momentum tensors are represented by means of the
introduced notions and the corresponding identities are found. The notion of
covariant differential operator along a contravariant tensor field is
introduced. On its basis, as a special case, the notion of contravariant metric
differential operator is proposed. The properties of the operators are
considered. By the use of these operators the notion of covariant divergency of
a mixed tensor field is determined. The covariant divergency of tensor fields
of second rank of the types 1 and 2 is found. Invariant representations of the
covariant divergency of the energy-momentum tensor are obtained by means of the
projective metrics of a contravariant non-isotropic (non-null) vector field and
the corresponding rest mass density, momentum density, and energy flux density.
An invariant representation of the first Noether identity is found as well as
relations between the covariant divergencies of the different energy-momentum
tensors and their structures determining covariant local conserved quantities.


title: Influence of scalar fields on the approach to a cosmological singularity

abstract:
  The method of consistent potentials is used to explain how a minimally
coupled (classical) scalar field can suppress Mixmaster oscillations in the
approach to the singularity of generic cosmological spacetimes.


title: Black Holes, Bandwidths and Beethoven

abstract:
  It is usually believed that a function whose Fourier spectrum is bounded can
vary at most as fast as its highest frequency component. This is in fact not
the case, as Aharonov, Berry and others drastically demonstrated with explicit
counter examples, so-called superoscillations. It has been claimed that even
the recording of an entire Beethoven symphony can occur as part of a signal
with 1Hz bandwidth. Bandlimited functions also occur as ultraviolet regularized
fields. Their superoscillations have been suggested, for example, to resolve
the transplanckian frequencies problem of black hole radiation.
  Here, we give an exact proof for generic superoscillations. Namely, we show
that for every fixed bandwidth there exist functions which pass through any
finite number of arbitrarily prespecified points. Further, we show that, in
spite of the presence of superoscillations, the behavior of bandlimited
functions can be characterized reliably, namely through an uncertainty
relation. This also generalizes to time-varying bandwidths. In QFT, we identify
the bandwidth as the in general spatially variable finite local density of
degrees of freedom of ultraviolet regularized fields.

categories: gr-qc hep-th math.FA physics.data-an quant-ph


title:
Late-time decay of gravitational and electromagnetic perturbations along
  the event horizon

abstract:
  We study analytically, via the Newman-Penrose formalism, the late-time decay
of linear electromagnetic and gravitational perturbations along the event
horizon (EH) of black holes. We first analyze in detail the case of a
Schwarzschild black hole. Using a straightforward local analysis near the EH,
we show that, generically, the ``ingoing'' ($s>0$) component of the perturbing
field dies off along the EH more rapidly than its ``outgoing'' ($s<0$)
counterpart. Thus, while along $r=const>2M$ lines both components of the
perturbation admit the well-known $t^{-2l-3}$ decay rate, one finds that along
the EH the $s<0$ component dies off in advanced-time $v$ as $v^{-2l-3}$,
whereas the $s>0$ component dies off as $v^{-2l-4}$. We then describe the
extension of this analysis to a Kerr black hole. We conclude that for axially
symmetric modes the situation is analogous to the Schwarzschild case. However,
for non-axially symmetric modes both $s>0$ and $s<0$ fields decay at the same
rate (unlike in the Schwarzschild case).


title: Matching Condition on the Event Horizon and the Holography Principle

abstract:
  It is shown that the event horizon of 4D black hole or $ds^2 = 0$ surfaces of
multidimensional wormhole-like solutions reduce the amount of information
necessary for determining the whole spacetime and hence satisfy the Holography
principle. This leads to the fact that by matching two metrics on a $ds^2 = 0$
surface (an event horizon for 4D black holes) we can match only the metric
components but not their derivatives. For example, this allows us to obtain a
composite wormhole inserting a 5D wormhole-like flux tube between two
Reissner-Nordstr\"om black holes and matching them on the event horizon. Using
the Holography principle, the entropy of a black hole from the algorithm theory
is obtained.


title:
Description of Charged Scalar System by means of General Relativit y
  Approach

abstract:
  The K\"ahler metric which has been constructed by present author is used in
this paper to find an exact solution of Einstein equations with energy-momentum
tensor of special type. The type of $T_{ij}$ admits in particular to use it as
energy-momentum tensor of charged scalar field and in case of such system the
field function is determined.


title: Global Solutions in Gravity. Lorentzian signature

abstract:
  The constructive method of conformal blocks is developed for the construction
of global solutions for two-dimensional metrics having one Killing vector. The
method is proved to yeild a smooth universal covering space with a smooth
pseudo-Riemannian metric. The Schwarzschild,
  Reisner--Nordstrom solutions, extremal black hole, dilaton black hole, and
constant curvature surfaces are considered as examples.


title: Gravitational Waves: Just Plane Symmetry

abstract:
  We present some remarkable properties of the symmetry group for gravitational
plane waves. Our main observation is that metrics with plane wave symmetry
satisfy every system of generally covariant vacuum field equations except the
Einstein equations. The proof uses the homothety admitted by metrics with plane
wave symmetry and the scaling behavior of generally covariant field equations.
We also discuss a mini-superspace description of spacetimes with plane wave
symmetry.


title: Entanglement/Brick-wall entropies correspondence

abstract:
  There have been many attempts to understand the statistical origin of
black-hole entropy. Among them, entanglement entropy and the brick wall model
are strong candidates. In this paper we show a relation between entanglement
entropy and the brick wall model: the brick wall model seeks the maximal value
of the entanglement entropy. In other words, the entanglement approach reduces
to the brick wall model when we seek the maximal entanglement entropy .


title:
Monople and dyon solutions in the Einstein Yang-Mills theory in
  asymptotically AdS space

abstract:
  Regular monopole and dyon solutions to the SU(2) Einstein Yang-Mills
equations in asymptotically anti-de Sitter space are discussed. A class of
monopole solutions are shown to be stable against spherically symmetric linear
perturbations.


title: Newman-Janis method and rotating dilaton-axion black hole

abstract:
  It's shown that the rotating dilaton-axion black hole solution can be
obtained from GGHS static charged dilaton black hole solution via Newman-Janis
method.


title: On the Perturbative Solutions of Bohmian Quantum Gravity

abstract:
  In this paper we have solved the Bohmian equations of quantum gravity,
perturbatively. Solutions up to second order are derived explicitly, but in
principle the method can be used in any order. Some consequences of the
solution are disscused.


title:
Newtonian and Post-Newtonian approximations of the k = 0 Friedmann
  Robertson Walker Cosmology

abstract:
  In a previous paper we derived a post-Newtonian approximation to cosmology
which, in contrast to former Newtonian and post-Newtonian cosmological
theories, has a well-posed initial value problem. In this paper, this new
post-Newtonian theory is compared with the fully general relativistic theory,
in the context of the k = 0 Friedmann Robertson Walker cosmologies. It is found
that the post-Newtonian theory reproduces the results of its general
relativistic counterpart, whilst the Newtonian theory does not.


title:
Conformal derivative and conformal transports over spaces with an affine
  connection and metrics

abstract:
  Transports preserving the angle between two contravariant vector fields but
changing their lengths proportional to their own lengths are introduced as
`conformal' transports and investigated over spaces with one affine connection
and metric. They are more general than the Fermi-Walker transports. In an
analogous way as in the case of Fermi-Walker transports a conformal covariant
differential operator and its conformal derivative are defined and considered
over spaces with one affine connection and metric. Different special types of
conformal transports are determined inducing also Fermi-Walker transports for
orthogonal vector fields as special cases. Conditions under which the length of
a non-null contravariant vector field could swing as a homogeneous harmonic
oscillator are established. The results obtained regardless of any concrete
field (gravitational) theory could have direct applications in such types of
theories. PACS numbers: 04.90.+e; 04.50.+h; 12.10.Gq; 02.40.Vh


title: Radiative Tail of Realistic Rotating Gravitational Collapse

abstract:
  An astrophysically realistic model of wave dynamics in black-hole spacetimes
must involve a non-spherical background geometry with angular momentum. We
consider the evolution of gravitational (and electromagnetic) perturbations in
rotating Kerr spacetimes. We show that a rotating Kerr black hole becomes
`bald' slower than the corresponding spherically-symmetric Schwarzschild black
hole. Moreover, our results turn over the traditional belief (which has been
widely accepted during the last three decades) that the late-time tail of
gravitational collapse is universal. In particular, we show that different
fields have different decaying rates. Our results are also of importance both
to the study of the no-hair conjecture and the mass-inflation scenario
(stability of Cauchy horizons).


title:
Polyhomogeneity and zero-rest-mass fields with applications to
  Newman-Penrose constants

abstract:
  A discussion of polyhomogeneity (asymptotic expansions in terms of $1/r$ and
$\ln r$) for zero-rest-mass fields and gravity and its relation with the
Newman-Penrose (NP) constants is given. It is shown that for spin-$s$
zero-rest-mass fields propagating on Minkowski spacetime, the logarithmic terms
in the asymptotic expansion appear naturally if the field does not obey the
``Peeling theorem''. The terms that give rise to the slower fall-off admit a
natural interpretation in terms of advanced field. The connection between such
fields and the NP constants is also discussed. The case when the background
spacetime is curved and polyhomogeneous (in general) is considered. The free
fields have to be polyhomogeneous, but the logarithmic terms due to the
connection appear at higher powers of $1/r$. In the case of gravity, it is
shown that it is possible to define a new auxiliary field, regular at null
infinity, and containing some relevant information on the asymptotic behaviour
of the spacetime. This auxiliary zero-rest-mass field ``evaluated at future
infinity ($i^+$)'' yields the logarithmic NP constants.


title: Implementing fully relativistic hydrodynamics in three dimensions

abstract:
  We report on our numerical implementation of fully relativistic hydrodynamics
coupled to Einstein's field equations in three spatial dimensions. We briefly
review several steps in our code development, including our recasting of
Einstein's equations and several tests which demonstrate its advantages for
numerical integrations. We outline our implementation of relativistic
hydrodynamics, and present numerical results for the evolution of both stable
and unstable Oppenheimer-Volkov equilibrium stars, which represent a very
promising first test of our code.


title: Einstein's Equations and Equivalent Hyperbolic Dynamical Systems

abstract:
  We discuss several explicitly causal hyperbolic formulations of Einstein's
dynamical 3+1 equations in a coherent way, emphasizing throughout the
fundamental role of the ``slicing function,'' $\alpha$---the quantity that
relates the lapse $N$ to the determinant of the spatial metric $\bar{g}$
through $N = \bar{g}^{1/2} \alpha$. The slicing function allows us to
demonstrate explicitly that every foliation of spacetime by spatial time-slices
can be used in conjunction with the causal hyperbolic forms of the dynamical
Einstein equations. Specifically, the slicing function plays an essential role
(1) in a clearer form of the canonical action principle and Hamiltonian
dynamics for gravity and leads to a recasting (2) of the Bianchi identities
$\nabla_\beta G^\beta\mathstrut_\alpha \equiv 0$ as a well-posed system for the
evolution of the gravitational constraints in vacuum, and also (3) of
$\nabla_\beta T^\beta\mathstrut_\alpha \equiv 0$ as a well-posed system for
evolution of the energy and momentum components of the stress tensor in the
presence of matter, (4) in an explicit rendering of four hyperbolic
formulations of Einstein's equations with only physical characteristics, and
(5) in providing guidance to a new ``conformal thin sandwich'' form of the
initial value constraints.


title: Semi-analytical Solution of Dirac equation in Schwarzschild Geometry

abstract:
  Separation of the Dirac equation in the spacetime around a Kerr black hole
into radial and angular coordinates was done by Chandrasekhar in 1976. In the
present paper, we solve the radial equations in a Schwarzschild geometry
semi-analytically using Wentzel-Kramers-Brillouin approximation (in short WKB)
method. Among other things, we present analytical expression of the
instantaneous reflection and transmission coefficients and the radial wave
functions of the Dirac particles. Complete physical parameter space was divided
into two parts depending on the height of the potential well and energy of the
incoming waves. We show the general solution for these two regions. We also
solve the equations by a Quantum Mechanical approach, in which the potential is
approximated by a series of steps and found that these two solutions agree. We
compare solutions of different initial parameters and show how the properties
of the scattered wave depend on these parameters.


title:
The Selforganization of Vacuum, Phase Transitions and the Cosmological
  Constant

abstract:
  The problem of the physical nature and the cosmological genesis of
Lambda-term is discussed. This problem can't be solved in terms of the current
quantum field theory which operates with Higgs and non-perturbative vacuum
condensates and takes into account the changes of these condensates during
relativistic phase transitions. The problem can't be completely solved also in
terms of the conventional global quantum theory: Wheeler-DeWitt quantum
geometrodynamics does not describe the evolution of the Universe in time (RPT
in particular). We have investigated this problem in the context of energies
density of different vacuum subsystems characteristic scales of which pervaid
all energetic scale of the Universe. At first the phemenological solution of
Lambda-term problem and then the hypothesis about the possible structure of a
new global quantum theory are proposed. The main feature of this theory is the
inreversible evolution of geometry and vacuum condensates in time in the regime
of their selforganization. The transformation of the cosmological constant in
dynamical variable is inevitably.


title: Back Reaction of Gravitational Radiation on the Schwarzschild Black Hole

abstract:
  We address some of the issues that appear in the study of back reaction in
Schwarzschild backgrounds. Our main object is the effective energy-momentum
tensor (EEMT) of gravitational perturbations. It is commonly held that only
asymptotically flat or radiation gauges can be employed for these purposes. We
show that the traditional Regge-Wheeler gauge for the perturbations of the
Schwarszchild metric can also be used for computing physical quantities both at
the horizon and at infinity. In particular, we find that the physically
relevant components of the EEMT of gravitational perturbations have the same
asymptotic behaviour as the stress-energy tensor of a scalar field in the
Schwarzschild background, even though some of the metric components themselves
diverge.


title: Criticality and Averaging in Cosmology

abstract:
  We propose comparing cosmological solutions in terms of their total spatial
volumes $V(\tau)$ as functions of proper time $\tau$, assuming synchronous
gauge, and with this intention evaluate the variations of $V(\tau)$ about the
Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) solutions for dust. This can be
done successfully in a simple manner without solving perturbation equations. In
particular, we find that first variations vanish with respect to all directions
which do not possess homogeneity and isotropy preserving components; in other
words, every FLRW solution is a {\it critical point} for $V(\tau)$ in the
properly restricted subspace of the space of solutions. This property may
support a validity of the interpretation of the FLRW solutions as constituting
an averaged model. We also briefly investigate the second variations of
$V(\tau)$.


title: The untilted diffuse matter Bianchi V Universe

abstract:
  A diffuse matter filled Type V Universe is studied. The anisotropic
behaviour, the distortion caused to the CMBR and the parameter region allowed
by present cosmological bounds are examined. It is shown how the overall sky
pattern of temperature anisotropies changes under a non-infinitesimal spatial
coordinate transformation that preserves the Type V manifest homogeneity.


title: Generalised hyperbolicity in conical space-times

abstract:
  Solutions of the wave equation in a space-time containing a thin cosmic
string are examined in the context of non-linear generalised functions.
Existence and uniqueness of solutions to the wave equation in the Colombeau
algebra G is established for a conical space-time and this solution is shown to
be associated to a distributional solution. A concept of generalised
hyperbolicity, based on test fields, can be defined for such singular
space-times and it is shown that a conical space-time is G-hyperbolic.


title: ADM mass of the quantum-corrected Schwarzchild black hole

abstract:
  We study the hamiltonian and constraints of spherically symmetric dilaton
gravity model. We find the ADM mass of the solution representing the
Schwarzchild black hole in thermal equilibrium with the Hawking radiation.


title:
Gravitomagnetic Flux Quantization in superconductors and a Method for
  the Experimental Detection of Gravitomagnetism in the Terrestrial Laboratory

abstract:
  It is extraordinarely difficult to detect the extremely weak gravitomagnetic
(GM) field of even as large a body as the earth. To detect the GM field, the
gravitational analog of an ordinary magnetic field, in a modest terrestrial
laboratory should be that much more difficult. Here we show, however, that for
certain superconductor configuration and topologies, it should be possible to
detect a measurable GM field in the terrestrial laboratory, by using the
properties of superconductors imposed by quantum mechanical requirements. In
particular, we show that the GM Flux should be quantized in a superconductor
with non-vanishing genus, just like the ordinary magnetic flux. And this
magnetically induced, quantized GM Flux, for sufficiently high quantum number
and favorable geometries, should be distinguishable from the effects produced
by an ordinary magnetic field.


title: Relativistic Acoustic Geometry

abstract:
  Sound wave propagation in a relativistic perfect fluid with a non-homogeneous
isentropic flow is studied in terms of acoustic geometry. The sound wave
equation turns out to be equivalent to the equation of motion for a massless
scalar field propagating in a curved space-time geometry. The geometry is
described by the acoustic metric tensor that depends locally on the equation of
state and the four-velocity of the fluid. For a relativistic supersonic flow in
curved space-time the ergosphere and acoustic horizon may be defined in a way
analogous the non-relativistic case. A general-relativistic expression for the
acoustic analog of surface gravity has been found.


title: From spinning to non-spinning cosmic string spacetimes

abstract:
  We analyse the properties of a fluid generating a spinning cosmic string
spacetime with flat limiting cases corresponding to a constant angular momentum
in the infinite past and static configuration in the infinite future. The
spontaneous loss of angular momentum of a spinning cosmic string due to
particle emission is discussed. The rate of particle production between the
spinning and non-spinning cosmic string spacetimes is calculated.


title: Cosmic Censorship: the Role of Quantum Physics

abstract:
  The cosmic censorship hypothesis introduced by Penrose thirty years ago is
still one of the most important open questions in {\it classical} general
relativity. The main goal of this paper is to put forward the idea that cosmic
censorship is intrinsically a {\it quantum} phenomena. We construct a gedanken
experiment which seems to violate the cosmic censorship principle within the
purely {\it classical} framework of general relativity. We prove, however, that
{\it quantum} physics restores the validity of the conjecture. It is therefore
suggested that cosmic censorship might be enforced by a quantum theory of
gravity.


title:
Late time decay of scalar, electromagnetic, and gravitational
  perturbations outside rotating black holes

abstract:
  We study analytically, via the Newman-Penrose formalism, the late time decay
of scalar, electromagnetic, and gravitational perturbations outside a realistic
rotating (Kerr) black hole. We find a power-law decay at timelike infinity, as
well as at null infinity and along the event horizon (EH). For generic initial
data we derive the power-law indices for all radiating modes of the various
fields. We also give an exact analytic expression (accurate to leading order in
1/t) for the r-dependence of the late time tail at any r. Some of our main
conclusions are: (i) For generic initial data, the late time behavior of the
fields is dominated by the mode l=|s| (with s being the spin parameter), which
dies off at fixed $r$ as $t^{-2|s|-3}$ --- as in the Schwarzschild background.
(ii) However, other modes admit decay rates slower than in the Schwarzschild
case. (iii) For s>0 fields, non-axially symmetric modes dominate the late time
behavior along the EH. These modes oscillate along the null generators of the
EH.


title: A Hamiltonian Approach to the Mass of Isolated Black Holes

abstract:
  Boundary conditions defining a non-rotating isolated horizon are given in
Einstein-Maxwell theory. A spacetime representing a black hole which itself is
in equilibrium but whose exterior contains radiation admits such a horizon.
Inspired by Hamiltonian mechanics, a (quasi-)local definition of isolated
horizon mass is formulated. Although its definition does not refer to infinity,
this mass takes the standard value in a Reissner-Nordstrom solution.
Furthermore, under certain technical assumptions, the mass of an isolated
horizon is shown to equal the future limit of the Bondi energy.


title: String excitation inside generic black holes

abstract:
  We calculate how much a first-quantized string is excited after crossing the
inner horizon of charged Vaidya solutions, as a simple model of generic black
holes. To quantize a string suitably, we first show that the metric is
approximated by a {\it plane-wave} metric near the inner horizon when the
surface gravity of the horizon $\kappa_I$ is small enough. Next, it is
analytically shown that the string crossing the inner horizon is excited
infinitely in an asymptotically flat spacetime, while it is finite in an
asymptotically de Sitter spacetime and the string can pass across the inner
horizon when $\kappa_I<2\kappa:= 2 {min}\{\kappa_B,\kappa_C \}$, where
$\kappa_B$~($\kappa_C$) is the surface gravity of the black hole~(cosmological)
event horizon. This implies that the strong cosmic censorship holds in an
asymptotically flat spacetime, while it is violated in an asymptotically de
Sitter spacetime from the point of view of string theory.


title:
Nonexpanding impulsive gravitational waves with an arbitrary
  cosmological constant

abstract:
  Exact solutions for nonexpanding impulsive waves in a background with nonzero
cosmological constant are constructed using a `cut and paste' method. These
solutions are presented using a unified approach which covers the cases of de
Sitter, anti-de Sitter and Minkowski backgrounds. The metrics are presented in
continuous and distributional forms, both of which are conformal to the
corresponding metrics for impulsive pp-waves, and for which the limit as
$\Lambda\to 0$ can be made explicitly.


title: Revisiting the Einstein field of a mass point

abstract:
  The Einstein gravitational field of a material point at rest is derived anew
- by a suitable limit process - from the field of a sphere of a homogeneous and
incompressible fluid. This result supports clearly the thesis according to
which the physically interesting singularities must correspond to the presence
of matter in loco.


title:
Nonlinear hydrodynamical evolution of rotating relativistic stars:
  Numerical methods and code tests

abstract:
  We present numerical hydrodynamical evolutions of rapidly rotating
relativistic stars, using an axisymmetric, nonlinear relativistic hydrodynamics
code. We use four different high-resolution shock-capturing (HRSC)
finite-difference schemes (based on approximate Riemann solvers) and compare
their accuracy in preserving uniformly rotating stationary initial
configurations in long-term evolutions. Among these four schemes, we find that
the third-order PPM scheme is superior in maintaining the initial rotation law
in long-term evolutions, especially near the surface of the star. It is further
shown that HRSC schemes are suitable for the evolution of perturbed neutron
stars and for the accurate identification (via Fourier transforms) of normal
modes of oscillation. This is demonstrated for radial and quadrupolar
pulsations in the nonrotating limit, where we find good agreement with
frequencies obtained with a linear perturbation code. The code can be used for
studying small-amplitude or nonlinear pulsations of differentially rotating
neutron stars, while our present results serve as testbed computations for
three-dimensional general-relativistic evolution codes.


title: Time emergence by self-measurement in a quantum anisotropic universe

abstract:
  We begin this work calculating Halliwell's propagator in the case of a
Mixmaster universe with small anisotropy. Afterwards in the context of the
Decoherence Model we introduce in our system terms that comprise the
self-measurement of the universe of this model by higher multipoles of matter.
Analyzing self-measurement with the Restricted Path Integral Formalism we
obtain Halliwell's modified propagator and find that a gauge invariant physical
time emerges as consequence of this process. The conditions leading to
Wheeler-DeWitt dynamics are also obtained. The comparison of our results with
those of the isotropic case will enable us to conclude that the number of
conditions to be satisfied in order to have Halliwell's regime is in the
anisotropic situation bigger than in an isotropic universe. We obtain also in
terms of the parameters of the measurement process an expression for the
threshold in time beyond which the scale factors of this model are meaningless.


title:
Symmetry without Symmetry: Numerical Simulation of Axisymmetric Systems
  using Cartesian Grids

abstract:
  We present a new technique for the numerical simulation of axisymmetric
systems. This technique avoids the coordinate singularities which often arise
when cylindrical or polar-spherical coordinate finite difference grids are
used, particularly in simulating tensor partial differential equations like
those of 3+1 numerical relativity. For a system axisymmetric about the z axis,
the basic idea is to use a 3-dimensional Cartesian (x,y,z) coordinate grid
which covers (say) the y=0 plane, but is only one
finite-difference-molecule--width thick in the y direction. The field variables
in the central y=0 grid plane can be updated using normal (x,y,z)--coordinate
finite differencing, while those in the y \neq 0 grid planes can be computed
from those in the central plane by using the axisymmetry assumption and
interpolation. We demonstrate the effectiveness of the approach on a set of
fully nonlinear test computations in 3+1 numerical general relativity,
involving both black holes and collapsing gravitational waves.


title:
Vacuum effects of ultra-low mass particle account for Recent
  Acceleration of Universe

abstract:
  In recent work, we showed that non-perturbative vacuum effects of a very low
mass particle could induce, at a redshift of order 1, a transition from a
matter-dominated to an accelerating universe. In that work, we used the
simplification of a sudden transition out of the matter-dominated stage and
were able to fit the Type Ia supernovae (SNe-Ia) data points with a
spatially-open universe. In the present work, we find a more accurate, smooth
{\it spatially-flat} analytic solution to the quantum-corrected Einstein
equations. This solution gives a good fit to the SNe-Ia data with a particle
mass parameter $m_h$ in the range $6.40 \times 10^{-33}$ eV to $7.25 \times
10^{-33}$ eV. It follows that the ratio of total matter density (including dark
matter) to critical density, $\O_0$, is in the range 0.58 to 0.15, and the age
$t_0$ of the universe is in the range $8.10 h^{-1}$ Gyr to $12.2 h^{-1}$ Gyr,
where $h$ is the present value of the Hubble constant, measured as a fraction
of the value 100 km/(s Mpc). This spatially-flat model agrees with estimates of
the position of the first acoustic peak in the small angular scale fluctuations
of the cosmic background radiation, and with light-element abundances of
standard big-bang nucleosynthesis. Our model has only a single free parameter,
$m_h$, and does not require that we live at a special time in the evolution of
the universe.


title: A note on the entropy of charged multi - black - holes

abstract:
  Majumdar--Papapetrou multi--black-hole solutions of the Einstein--Maxwell
equations are considered in four and higher dimensions. The Euclidean action
with boundary conditions appropriate to the canonical ensemble is shown to lead
to zero entropy.


title:
The true and eccentric anomaly parametrizations of the perturbed Kepler
  motion

abstract:
  The true and eccentric anomaly parametrizations of the Kepler motion are
generalized to quasiperiodic orbits, by considering perturbations of the radial
part of the kinetic energy in a form of a series of negative powers of the
orbital radius. A toolchest of methods for averaging observables as functions
of the energy $E$ and angular momentum $L$ is developed. A broad range of
systems governed by the generic Brumberg force and recent applications in the
theory of gravitational radiation involve integrals of these functions over a
period of motion. These integrals are evaluated by using the residue theorem.
In the course of this work two important questions emerge: (1) When does the
true and eccentric anomaly parameter exist? (2) Under what circumstances and
why are the poles in the origin? The purpose of this paper is to find the
answer to these queries.


title: Symmetry-seeking spacetime coordinates

abstract:
  In numerically constructing a spacetime that has an approximate timelike
Killing vector, it is useful to choose spacetime coordinates adapted to the
symmetry, so that the metric and matter variables vary only slowly with time in
these coordinates. In particular, this is a crucial issue in numerically
calculating a binary black hole inspiral. An approximate homothetic vector
plays a role in critical gravitational collapse. We summarize old and new
suggestions for finding such coordinates from a general point of view. We then
test some of these in various toy models with spherical symmetry, including
critical fluid collapse and critical scalar field collapse.


title: Some brane theoretic no-hair results (and their field theory duals)

abstract:
  This contribution to the proceedings of the 1999 Canadian Conference on
General Relativity and Relativistic Astrophysics is a brief exposition of
earlier work, with Sumati Surya (hep-th/9805121) Amanda Peet (hep-th/9903213),
addressing certain results in higher dimensional supergravity that are related
to black hole no-hair theorems. Its purpose is to describe, in language
appropriate for an audience of relativists, how these results can be related to
the Maldacena conjecture (aka, the AdS/CFT correspondence). The end product may
be taken as a new kind of quantitative evidence in support of the Maldacena
conjecture.


title: Causality in Spin Foam Models

abstract:
  We compute Teitelboim's causal propagator in the context of canonical loop
quantum gravity. For the Lorentzian signature, we find that the resultant power
series can be expressed as a sum over branched, colored two-surfaces with an
intrinsic causal structure. This leads us to define a general structure which
we call a ``causal spin foam''. We also demonstrate that the causal evolution
models for spin networks fall in the general class of causal spin foams.


title: Towards a physical interpretation for the Stephani Universes

abstract:
  A physicaly reasonable interpretation is provided for the perfect fluid,
sphericaly symmetric, conformally flat ``Stephani Universes''. The free
parameters of this class of exact solutions are determined so that the ideal
gas relation $p=n k T$ is identicaly fulfiled, while the full equation of state
of a classical monatomic ideal gas and a matter-radiation mixture holds up to a
good approximation in a near dust, matter dominated regime. Only the models
having spacelike slices with positive curvature admit a regular evolution
domain that avoids an unphysical singularity. In the matter dominated regime
these models are dynamicaly and observationaly indistinguishable from
``standard'' FLRW cosmology with a dust source.


title:
Gravitational Thermodynamics of Space-time Foam in One-loop
  Approximation

abstract:
  We show from one-loop quantum gravity and statistical thermodynamics that the
thermodynamics of quantum foam in flat space-time and Schwarzschild space-time
is exactly the same as that of Hawking-Unruh radiation in thermal equilibrium.
This means we show unambiguously that Hawking-Unruh thermal radiation should
contain thermal gravitons or the contribution of quantum space-time foam. As a
by-product, we give also the quantum gravity correction in one-loop
approximation to the classical black hole thermodynamics.


title: A two-scalar model for a small but nonzero cosmological constant

abstract:
  We revisit a model of the two-scalar system proposed previously for
understanding a small but nonzero cosmological constant. The model provides
solutions of the scalar-fields energy $\rho_s$ which behaves truly constant for
a limited time interval rather than in the way of tracker- or scaling-type
variations. This causes a mini-inflation, as indicated by recent observations.
As another novel feature, $\rho_s$ and the ordinary matter density $\rho_m$
fall off always side by side, but interlacing, also like (time)$^{-2}$ as an
overall behavior in conformity with the scenario of a decaying cosmological
constant. A mini-inflation occurs whenever $\rho_s$ overtakes $\rho_m$, which
may happen more than once, shedding a new light on the coincidence problem. We
present a new example of the solution, and offer an intuitive interpretation of
the mechanism of the nonlinear dynamics. We also discuss a chaos-like nature of
the solution.


title: Pseudo-Riemannian Metrics in Models Based on Noncommutative Geometry

abstract:
  Several examples and models based on noncommutative differential calculi on
commutative algebras indicate that a metric should be regarded as an element of
the left-linear tensor product of the space of 1-forms with itself. We show how
the metric compatibility condition with a linear connection generalizes to this
framework.


title: Perturbative superluminal censorship and the null energy condition

abstract:
  We argue that ``effective'' superluminal travel, potentially caused by the
tipping over of light cones in Einstein gravity, is always associated with
violations of the null energy condition (NEC). This is most easily seen by
working perturbatively around Minkowski spacetime, where we use linearized
Einstein gravity to show that the NEC forces the light cones to contract
(narrow). Given the NEC, the Shapiro time delay in any weak gravitational field
is always a delay relative to the Minkowski background, and never an advance.
Furthermore, any object travelling within the lightcones of the weak
gravitational field is similarly delayed with respect to the minimum traversal
time possible in the background Minkowski geometry.


title: Geometric Background for Thermal Field Theories

abstract:
  We study a new spacetime which is shown to be the general geometrical
background for Thermal Field Theories at equilibrium. The different formalisms
of Thermal Field Theory are unified in a simple way in this spacetime. The set
of time-paths used in the Path Ordered Method is interpreted in geometrical
terms.


title: (2+1)-dimensional Einstein-Kepler problem in the centre-of-mass frame

abstract:
  We formulate and analyze the Hamiltonian dynamics of a pair of massive
spinless point particles in (2+1)-dimensional Einstein gravity by anchoring the
system to a conical infinity, isometric to the infinity generated by a single
massive but possibly spinning particle. The reduced phase space \Gamma_{red}
has dimension four and topology R^3 x S^1. \Gamma_{red} is analogous to the
phase space of a Newtonian two-body system in the centre-of-mass frame, and we
find on \Gamma_{red} a canonical chart that makes this analogue explicit and
reduces to the Newtonian chart in the appropriate limit. Prospects for
quantization are commented on.


title:
Self-similar cosmological solutions with a non-minimally coupled scalar
  field

abstract:
  We present self-similar cosmological solutions for a barotropic fluid plus
scalar field with Brans-Dicke-type coupling to the spacetime curvature and an
arbitrary power-law potential energy. We identify all the fixed points in the
autonomous phase-plane, including a scaling solution where the fluid density
scales with the scalar field's kinetic and potential energy. This is related by
a conformal transformation to a scaling solution for a scalar field with
exponential potential minimally coupled to the spacetime curvature, but
non-minimally coupled to the barotropic fluid. Radiation is automatically
decoupled from the scalar field, but energy transfer between the field and
non-relativistic dark matter can lead to a change to an accelerated expansion
at late times in the Einstein frame. The scalar field density can mimic a
cosmological constant even for steep potentials in the strong coupling limit.


title:
Fully general relativistic simulation of coalescing binary neutron
  stars: Preparatory tests

abstract:
  We present our first successful numerical results of 3D general relativistic
simulations in which the Einstein equation as well as the hydrodynamic
equations are fully solved. This paper is especially devoted to simulations of
test problems such as spherical dust collapse, stability test of perturbed
spherical stars, and preservation of (approximate) equilibrium states of
rapidly rotating neutron star and/or corotating binary neutron stars. These
test simulations confirm that simulations of coalescing binary neutron stars
are feasible in a numerical relativity code. It is illustrated that using our
numerical code, simulations of these problems, in particular those of
corotating binary neutron stars, can be performed stably and fairly accurately
for a couple of dynamical timescales. These numerical results indicate that our
formulation for solving the Einstein field equation and hydrodynamic equations
are robust and make it possible to perform a realistic simulation of coalescing
binary neutron stars for a long time from the innermost circular orbit up to
formation of a black hole or neutron star.


title: Ermakov approach for minisuperspace oscillators

abstract:
  The WDW equation of arbitrary Hartle-Hawking factor ordering for several
minisuperspace universe models, such as the pure gravity FRW and Taub ones, is
mapped onto the dynamics of corresponding classical oscillators. The latter
ones are studied by the classical Ermakov invariant method, which is a natural
aproach in this context. For the more realistic case of a minimally coupled
massive scalar field, one can study, within the same type of approach, the
corresponding squeezing features as a possible means of describing cosmological
evolution. Finally, we comment on the analogy with the accelerator physics


title: Traversable wormholes from massless conformally coupled scalar fields

abstract:
  The massless conformally coupled scalar field is characterized by the
so-called "new improved stress-energy tensor", which is capable of classically
violating the null energy condition. When coupled to Einstein gravity we find a
three-parameter class of exact solutions. These exact solutions include the
Schwarzschild geometry, assorted naked singularities, and a large class of
traversable wormholes.


title:
Gauge freedom for Gravitational Wave problems in tensor-scalar theories
  of gravity

abstract:
  A specific choice of gauge is shown to imply a decoupling between the tensor
and scalar components of Gravitational Radiation in the context of Brans-Dicke
type theories of gravitation. The comparison of the predictions of these
theories with those of General Relativity is thereby made straightforward.


title: On the nature of black hole entropy

abstract:
  I argue that black hole entropy counts only those states of a black hole that
can influence the outside, and attempt (with only partial success) to defend
this claim against various objections, all but one coming from string theory.
Implications for the nature of the Bekenstein bound are discussed, and in
particular the case for a holographic principle is challenged. Finally, a
generalization of black hole thermodynamics to "partial event horizons" in
general spacetimes without black holes is proposed.


title:
A Modified Variational Principle in Relativistic Hydrodynamics.
  I.Commutativity and Noncommutativity of the Variation Operator with the
  Partial Derivative

abstract:
  A model is proposed, according to which the metric tensor field in the
standard gravitational Lagrangian is decomposed into a projection (generally -
with a non-zero covariant derivative) tensor field, orthogonal to an arbitrary
4-vector field and a tensor part along the same vector field. A theorem has
been used, according to which the variation and the partial derivative, when
applied to a tensor field, commute with each other if and only if the tensor
field and its variation have zero covariant derivatives, provided also the
connection variation is zero. Since the projection field obviously does not
fulfill the above requirements of the ''commutation'' theorem, the exact
expression for the (non-zero) commutator of the variation and the partial
derivative, applied to the projection tensor field, can be found from a set of
the three defining equations. The above method will be used to construct a
modified variational approach in relativistic hydrodynamics, based on variation
of the vector field and the projection field, the last one thus accounting for
the influence of the reference system of matter (characterized by the 4-vector)
on the gravitational field.


title:
A Simple Formula for Generating Chern Characters by Repeated Exterior
  Differentiation

abstract:
  A simple formula is given for generating Chern characters by repeated
exterior differentiation for n-dimensional differentiable manifolds having a
general linear connection.


title:
A Sequence of Generalizations of Cartan's Conservation of Torsion
  Theorem

abstract:
  A sequence of generalizations of Cartan's conservation of torsion theorem is
given for n-dimensional differentiable manifolds having a general linear
connection.


title:
A Simple Derivation of the Einstein-Maxwell Field Equations from the 2nd
  Ordinary Exterior Differential of a Precursor to the Soldering Form

abstract:
  A simple derivation is given of the Einstein-Maxwell field equations from the
2nd ordinary exterior differential of a precursor to the soldering form for
n-dimensional differentiable manifolds having a general linear connection and
in 5-dimensional general relativity in particular.


title: The Mass Quantum and Black Hole Entropy

abstract:
  We give a method in which a quantum of mass equal to twice the Planck mass
arises naturally. Then using Bose-Einstein statistics we derive an expression
for the black hole entropy which physically tends to the Bekenstein-Hawking
formula.


title:
One-loop $\lambda \phi^4$ theory in Robertson-Walker spacetimes:
  adiabatic regularization and analytic approximation

abstract:
  The renormalization of a scalar field theory with a quartic self-coupling (a
$\lambda \phi^4$ theory) via adiabatic regularization in a general
Robertson-Walker spacetime is discussed. The adiabatic counterterms are
presented in a way that is most conducive to numerical computations. A
variation of the adiabatic regularization method is presented which leads to
analytic approximations for the energy-momentum tensor of the field and the
quantum contribution to the effective mass of the mean field. Conservation of
the energy-momentum tensor for the field is discussed and it is shown that the
part of the energy-momentum tensor which depends only on the mean field is not
conserved but the full renormalized energy-momentum tensor is conserved as
expected and required by the semiclassical Einstein's equation. It is also
shown that if the analytic approximations are used then the resulting
approximate energy-momentum tensor is conserved. This allows a self-consistent
backreaction calculation to be performed using the analytic approximations. The
usefulness of the approximations is discussed.


title: Some Remarks on Gravitational Global Monopoles

abstract:
  Using mainly analytical arguments, we derive the exact relation
$\eta_{max}=\sqrt{3/8\pi}$ for the maximal vacuum value of the Higgs field for
static gravitational global monopoles. For this value, the global monopole
bifurcates with the de Sitter solution obtained for vanishing Higgs field. In
addition, we analyze the stability properties of the solutions.


title: Chaotic Scattering and Capture of Strings by Black Hole

abstract:
  We consider scattering and capture of circular cosmic strings by a
Schwarzschild black hole. Although being a priori a very simple axially
symmetric two-body problem, it shows all the features of chaotic scattering. In
particular, it contains a fractal set of unstable periodic solutions; a
so-called strange repellor. We study the different types of trajectories and
obtain the fractal dimension of the basin-boundary separating the space of
initial conditions according to the different asymptotic outcomes. We also
consider the fractal dimension as a function of energy, and discuss the
transition from order to chaos.


title: Quasi-Normal Modes of General Relativistic Superfluid Neutron Stars

abstract:
  We develop a general formalism to treat, in general relativity, the linear
oscillations of a two-fluid star about static (non-rotating) configurations.
Such a formalism is intended for neutron stars, whose matter content can be
described, as a first approximation, by a two-fluid model: one fluid is the
neutron superfluid, which is believed to exist in the core and inner crust of
mature neutron stars; the other fluid is a conglomerate of all other
constituents (crust nuclei, protons, electrons, etc...). We obtain a system of
equations which govern the perturbations both of the metric and of the matter
variables, whatever the equation of state for the two fluids. As a first
application, we consider the simplified case of two non-interacting fluids,
each with a polytropic equation of state. We compute numerically the
quasi-normal modes (i.e. oscillations with purely outgoing gravitational
radiation) of the corresponding system. When the adiabatic indices of the two
fluids are different, we observe a splitting for each frequency of the
analogous single fluid spectrum. The analysis also substantiates the claim that
w-modes are largely due to spacetime oscillations.


title: Radiative falloff in black-hole spacetimes

abstract:
  This two-part contribution to the Proceedings of the Eighth Canadian
Conference on General Relativity and Relativistic Astrophysics is devoted to
the evolution of a massless scalar field in two black-hole spacetimes which are
not asymptotically flat.
  In Part I (authored by Eric Poisson) we consider the evolution of a scalar
field propagating in Schwarzschild-de Sitter spacetime. The spacetime possesses
a cosmological horizon in addition to the usual event horizon. The presence of
this new horizon affects the late-time evolution of the scalar field.
  In part II (authored by William G. Laarakkers) we consider the evolution of a
scalar field propagating in Schwarzschild-Einstein-de Sitter spacetime. The
spacetime has two distinct regions: an inner black-hole region and an outer
cosmological region. Early on in the evolution, the field behaves as if it were
in pure Schwarzschild spacetime. Later, the field learns of the existence of
the cosmological region and alters its behaviour.


title:
Exact Relativistic Gravitational Field of a Stationary Counterrotating
  Dust Disk

abstract:
  Disks of collisionless particles are important models for certain galaxies
and accretion disks in astrophysics. We present here a solution to the
stationary axisymmetric Einstein equations which represents an infinitesimally
thin dust disk consisting of two streams of particles circulating with constant
angular velocity in opposite directions. These streams have the same density
distribution but their relative density may vary continuously. In the limit of
only one component of dust, we get the solution for the rigidly rotating dust
disk previously given by Neugebauer and Meinel, in the limit of identical
densities, the static disk of Morgan and Morgan is obtained. We discuss the
Newtonian and the ultrarelativistic limit, the occurrence of ergospheres, and
the regularity of the solution.


title: Detection of Gravitational Waves from Eccentric Compact Binaries

abstract:
  Coalescing compact binaries have been pointed out as the most promising
source of gravitational waves for kilometer-size interferometers such as LIGO.
Gravitational wave signals are extracted from the noise in the detectors by
matched filtering. This technique performs really well if an a priori
theoretical knowledge of the signal is available. The information known about
the possible sources is used to construct a model of the expected waveforms
(templates). A common assumption made when constructing templates for
coalescing compact binaries is that the companions move in a quasi-circular
orbit. Some scenarios, however, predict the existence of eccentric binaries. We
investigate the loss in signal-to-noise ratio induced by non-optimal filtering
of eccentric signals.


title: Choptuik scaling in six dimensions

abstract:
  We perform numerical simulations of the critical gravitational collapse of a
spherically symmetric scalar field in 6 dimensions. The critical solution has
discrete self-similarity. We find the critical exponent \gamma and the
self-similarity period \Delta.


title: String/M-branes for Relativists

abstract:
  These notes present an introduction to branes in ten and eleven dimensional
supergravity and string/M-theory which is geared to an audience of traditional
relativists, especially graduate students and others with little background in
supergravity. They are designed as a tutorial and not as a thorough review of
the subject; as a result, many topics of current interest are not addressed.
However, a guide to further reading is included. The presentation begins with
eleven dimensional supergravity, stressing its relation to 3+1 Einstein-Maxwell
theory. The notion of Kaluza-Klein compactification is then introduced, and is
used to relate the eleven dimensional discussion to supergravity in 9+1
dimensions and to string theory. The focus is on type IIA supergravity, but the
type IIB theory is also addressed, as is the T-duality symmetry that relates
them. Branes in both 10+1 and 9+1 dimensions are included. Finally, although
the details are not discussed, a few comments are provided on the relation
between supergravity and string perturbation theory and on black hole entropy.
The goal is to provide traditional relativists with a kernel of knowledge from
which to grow their understanding of branes and strings.


title: Continuous Self-Similarity Breaking in Critical Collapse

abstract:
  This paper studies near-critical evolution of the spherically symmetric
scalar field configurations close to the continuously self-similar solution.
Using analytic perturbative methods, it is shown that a generic growing
perturbation departs from the critical Roberts solution in a universal way. We
argue that in the course of its evolution, initial continuous self-similarity
of the background is broken into discrete self-similarity with echoing period
$\Delta = \sqrt{2}\pi = 4.44$, reproducing the symmetries of the critical
Choptuik solution.


title: Entropy Bounds, Holographic Principle and Uncertainty Relation

abstract:
  A simple derivation of the bound on entropy is given and the holographic
principle is discussed. We estimate the number of quantum states inside space
region on the base of uncertainty relation. The result is compared with the
Bekenstein formula for entropy bound, which was initially derived from the
generalized second law of thermodynamics for black holes. The holographic
principle states that the entropy inside a region is bounded by the area of the
boundary of that region. This principle can be called the kinematical
holographic principle. We argue that it can be derived from the dynamical
holographic principle which states that the dynamics of a system in a region
should be described by a system which lives on the boundary of the region. This
last principle can be valid in general relativity because the ADM hamiltonian
reduces to the surface term.


title:
The origin of the spacetime metric: Bell's `Lorentzian pedagogy' and its
  significance in general relativity

abstract:
  The purpose of this paper is to evaluate the `Lorentzian pedagogy' defended
by J.S. Bell in his essay ``How to teach special relativity'', and to explore
its consistency with Einstein's thinking from 1905 to 1952. Some remarks are
also made in this context on Weyl's philosophy of relativity and his 1918 gauge
theory. Finally, it is argued that the Lorentzian pedagogy - which stresses the
important connection between kinematics and dynamics - clarifies the role of
rods and clocks in general relativity.


title: New vacuum solutions of conformal Weyl gravity

abstract:
  The Bach equation, i.e., the vacuum field equation following from the
Lagrangian L=C_{ijkl}C^{ijkl}, will be completely solved for the case that the
metric is conformally related to the cartesian product of two 2-spaces; this
covers the spherically and the plane symmetric space-times as special subcases.
Contrary to other approaches, we make a covariant 2+2-decomposition of the
field equation, and so we are able to apply results from 2-dimensional gravity.
Finally, some cosmological solutions will be presented and discussed.


title: Non-Riemannian cosmic walls from gravitational collapse

abstract:
  Two classes of metrics obtained from non-Riemannian gravitational collapse
are presented.The first is the Taub planar symmetric exact solutions of
Einstein-Cartan field equations of gravity describing torsion walls which are
obtained from gravitational collapse of time dependent perturbation of
Riemannian Taub symmetric solutions of General Relativity.The second is a
modification of the Vilenkin Riemannian planar wall which is obtained from a
non-Riemannian planar distribution of spinning matter.


title: Covariant gauge fixing and Kuchar decomposition

abstract:
  The symplectic geometry of a broad class of generally covariant models is
studied. The class is restricted so that the gauge group of the models
coincides with the Bergmann-Komar group and the analysis can focus on the
general covariance. A geometrical definition of gauge fixing at the constraint
manifold is given; it is equivalent to a definition of a background (spacetime)
manifold for each topological sector of a model. Every gauge fixing defines a
decomposition of the constraint manifold into the physical phase space and the
space of embeddings of the Cauchy manifold into the background manifold (Kuchar
decomposition). Extensions of every gauge fixing and the associated Kuchar
decomposition to a neighbourhood of the constraint manifold are shown to exist.


title: A solution to the problem posed by Byland and Scialom

abstract:
  Recently, Byland and Scialom studied the evolution of the Bianchi I, the
Bianchi III and the Kantowski-Sachs universe on the basis of dynamical systems
methods (Phys. Rev. D57, 6065 (1998), gr-qc/9802043). In particular, they have
pointed out a problem to determine the stability properties of one of the
degenerate critical points of the corresponding dynamical system. Here we give
a solution, showing that this point is unstable both to the past and to the
future. We also discuss the asymptotic behavior of the trajectories in the
vicinity of another critical point.


title: The initial fate of an anisotropic JBD universe

abstract:
  The dynamical effects on the scale factors due to the scalar $\phi$-field at
the early stages of a supposedly anisotropic Universe expansion in the
scalar-tensor cosmology of Jordan-Brans and Dicke is studied. This universe
shows an {\sl isotropic} evolution and, depending on the value of the theorie's
coupling parameter $\omega$, it can begin from a singularity if $\omega>0$ and
after expanding shrink to another one; or, if $\omega <0$ and $-3/2< \omega\leq
-4/3$, it can evolve from a flat spatially-infinite state to a non extended
singularity; or, if $ -4/3 < \omega < 0$, evolve from an extended singularity
to a non singular state and, at last, proceed towards a singularity.


title:
Horizon Dynamics of Evaporating Black Holes in a Higher Dimensional
  Inflationary Universe

abstract:
  Spherically symmetric Black Holes of the Vaidya type are examined in an
asymptotically de Sitter, higher dimensional spacetime. The various horizons
are located. The structure and dynamics of such horizons are studied.


title: Backgrounds of squeezed relic photons and their spatial correlations

abstract:
  We discuss the production of multi-photons squeezed states induced by the
time variation of the (Abelian) gauge coupling constant in a string
cosmological context. Within a fully quantum mechanical approach we solve the
time evolution of the mean number of produced photons in terms of the squeezing
parameters and in terms of the gauge coupling. We compute the first (amplitude
interference) and second order (intensity interference) correlation functions
of the magnetic part of the photon background. The photons produced thanks to
the variation of the dilaton coupling are strongly bunched for the realistic
case where the growth of the dilaton coupling is required to explain the
presence of large scale magnetic fields and, possibly of a Faraday rotation of
the Cosmic Microwave Background.


title: Phase transition in quantum gravity

abstract:
  A fundamental problem with attempting to quantize general relativity is its
perturbative non-renormalizability. However, this fact does not rule out the
possibility that non-perturbative effects can be computed, at least in some
approximation. We outline a quantum field theory calculation, based on general
relativity as the classical theory, which implies a phase transition in quantum
gravity. The order parameters are composite fields derived from spacetime
metric functions. These are massless below a critical energy scale and become
massive above it. There is a corresponding breaking of classical symmetry.


title: The Zero-Point Field and Inertia

abstract:
  A brief overview is presented of the basis of the electromagnetic zero-point
field in quantum physics and its representation in stochastic electrodynamics.
Two approaches have led to the proposal that the inertia of matter may be
explained as an electromagnetic reaction force. The first is based on the
modeling of quarks and electrons as Planck oscillators and the method of
Einstein and Hopf to treat the interaction of the zero-point field with such
oscillators. The second approach is based on analysis of the Poynting vector of
the zero-point field in accelerated reference frames. It is possible to derive
both Newton's equation of motion, F=ma, and its relativistic co-variant form
from Maxwell's equations as applied to the zero-point field of the quantum
vacuum. This appears to account, at least in part, for the inertia of matter.


title: Variable Light-Cone Theory of Gravity

abstract:
  We show how to reformulate Variable Speed of Light Theories (VSLT) in a
covariant fashion as Variable Light-Cone Theories (VLCT) by introducing two
vierbein bundles each associated with a distinct metric. The basic
gravitational action relates to one bundle while matter propagates relative to
the other in a conventional way. The variability of the speed of light is
represented by the variability of the matter light-cone relative to the
gravitational light-cone. The two bundles are related locally by an element M,
of SL(4,R). The dynamics of the field M is that of a SL(4,R)-sigma model gauged
with respect to local (orthochronous) Lorentz transformations on each of the
bundles. Only the ``massless'' version of the model with a single new coupling,
F, that has the same dimensions as Newton's constant $G_N$, is considered in
this paper. When F vanishes the theory reduces to standard General Relativity.
  We verify that the modified Bianchi identities of the model are consistent
with the standard conservation law for the matter energy-momentum tensor in its
own background metric.
  The implications of the model for some simple applications are examined, the
Newtonian limit, the flat FRW universe and the spherically symmetric static
solution.


title:
A new numerical method for constructing quasi-equilibrium sequences of
  irrotational binary neutron stars in general relativity

abstract:
  We propose a new numerical method to compute quasi-equilibrium sequences of
general relativistic irrotational binary neutron star systems. It is a good
approximation to assume that (1) the binary star system is irrotational, i.e.
the vorticity of the flow field inside component stars vanishes everywhere
(irrotational flow), and (2) the binary star system is in quasi-equilibrium,
for an inspiraling binary neutron star system just before the coalescence as a
result of gravitational wave emission. We can introduce the velocity potential
for such an irrotational flow field, which satisfies an elliptic partial
differential equation (PDE) with a Neumann type boundary condition at the
stellar surface. For a treatment of general relativistic gravity, we use the
Wilson--Mathews formulation, which assumes conformal flatness for spatial
components of metric. In this formulation, the basic equations are expressed by
a system of elliptic PDEs. We have developed a method to solve these PDEs with
appropriate boundary conditions. The method is based on the established
prescription for computing equilibrium states of rapidly rotating axisymmetric
neutron stars or Newtonian binary systems. We have checked the reliability of
our new code by comparing our results with those of other computations
available. We have also performed several convergence tests. By using this
code, we have obtained quasi-equilibrium sequences of irrotational binary star
systems with strong gravity as models for final states of real evolution of
binary neutron star systems just before coalescence. Analysis of our
quasi-equilibrium sequences of binary star systems shows that the systems may
not suffer from dynamical instability of the orbital motion and that the
maximum density does not increase as the binary separation decreases.


title: Telaparallel Textures

abstract:
  An example of a teleparallel texture is given by an appropriate choice of
torsion components in the tetrad frame.In the light cone limit the metric is
not globally Euclidean and the spherical angles depend on torsion similarly to
what happens in cosmic string space-times.In this limit torsion produces a
force which decays with $r^{-3}$.


title: Frames of reference in spaces with affine connections and metrics

abstract:
  A generalized definition of a frame of reference in spaces with affine
connections and metrics is proposed based on the set of the following
differential-geometric objects:
  (a) a non-null (non-isotropic) vector field,
  (b) the orthogonal to the vector field sub space,
  (c) an affine connection and the related to it covariant differential
operator determining a transport along the given non-null vector filed.
  On the grounds of this definition other definitions related to the notions of
accelerated, inertial, proper accelerated and proper inertial frames of
reference are introduced and applied to some mathematical models for the
space-time. The auto-parallel equation is obtained as an Euler-Lagrange's
equation. Einstein's theory of gravitation appears as a theory for
determination of a special frame of reference (with the gravitational force as
inertial force) by means of the metrics and the characteristics of a material
distribution.
  PACS numbers: 0490, 0450, 1210G, 0240V


title: A dynamical systems approach to geodesics in Bianchi cosmologies

abstract:
  To understand the observational properties of cosmological models, in
particular, the temperature of the cosmic microwave background radiation, it is
necessary to study their null geodesics. Dynamical systems theory, in
conjunction with the orthonormal frame approach, has proved to be an invaluable
tool for analyzing spatially homogeneous cosmologies. It is thus natural to use
such techniques to study the geodesics of these models. We therefore augment
the Einstein field equations with the geodesic equations, all written in
dimensionless form, obtaining an extended system of first-order ordinary
differential equations that simultaneously describes the evolution of the
gravitational field and the behavior of the associated geodesics. It is shown
that the extended system is a powerful tool for investigating the effect of
spacetime anisotropies on the temperature of the cosmic microwave background
radiation, and that it can also be used for studying geodesic chaos.


title:
Primordial fluctuations in the warm inflation scenario with a more
  realistic coarse - grained field

abstract:
  I study a semiclassical approach to warm inflation scenario introduced in
previous works. In this work, I define the fluctuations for the matter field by
means of a new coarse - grained field with a suppression factor G. This field
describes the matter field fluctuations on the now observable scale of the
universe. The power spectrum for the fluctuations of the matter field is
analyzed in both, de Sitter and power - law expansions for the universe. The
constraint for the spectral index gives a constraint for the mass of the matter
field in the de Sitter expansion and a constraint for the friction parameter in
the power - law expansion for the universe.


title: Towards Hypergravity

abstract:
  The aim of this paper is to discuss a kinematical algebraic structure of a
theory of gravity, that would be unitary, renormalizable and coupled in the
same manner to both spinorial and tensorial matter fields. An analysis of the
common features as well as differences of the Yang-Mills theories and gauge
theories of gravity is carried out. In particular, we consider the following
issues: (i) Representations of the relevant global symmetry on states and on
fields, (ii) Relations between the relevant global and local symmetries, (iii)
Representations of the local symmetries on states and fields, (iv) Dimensional
analysis of the gauge algebra generators and the number of counter terms, and
(v) Coupling to the spinorial matter fields. We conclude, that various
difficulties on the gravity side can be overcome by considering the below
outlined Hypergravity gauge theory, that to some extend parallels the
string/membrane theories. This theory is based on an infinite Lie algebraic
structure of generators that transforms as "states" of the infinite-dimensional
irreducible representation of the $\bar{SL}(4,R)$ subgroup of the Group of
General Coordinate Transformations of R^4. The metric-affine and Poincar\'e
gauge theories of gravity are obtained through a spontaneous symmetry breaking
mechanism, with the metric field as nonlinear symmetry realizer.


title: Dirac-like Affine Fields in 3D

abstract:
  A generalization of the Dirac field equation in three-dimensional Minkowski
space-time to the case of the $\bar{SL}(3,R)$ $\subset$ $\bar{SA}(3,R)$
symmetry is considered. Constraints that ensure a correct physical
interpretation of the corresponding particle states are presented. Dirac-like
equations based on both multiplicity-free and generic infinite-component
$\bar{SL}(3,R)$ representations are outlined.


title: Test Evolution of Non-Axisymmetric Gravitational Waves

abstract:
  We give a preliminary report on one of the tests we have performed of a full
non-axisymmetric general relativistic code. The test considered here concerns
the numerical evolution of vacuum non-axisymmetric gravitational waves and
their comparison at low amplitudes with theoretical waveforms obtained from
linearised theory.


title:
The Asymptotic Behaviour of Cosmological Models Containing Matter and
  Scalar Fields

abstract:
  The asymptotic behaviour of two classes of scalar field cosmological models
are studied using the theory of dynamical systems: general relativistic Bianchi
models containing matter and a scalar field with an exponential potential and a
class of spatially homogeneous string cosmological models. The purpose of this
thesis is to examine some of the outstanding problems which currently exist in
cosmology, particularly regarding isotropization and inflation. It is shown
that the matter scaling solutions are unstable to curvature perturbations. It
is then shown that the Bianchi class B exponential potential models can
alleviate the isotropy problem; an open set of models within this class do
isotropize to the future. It is also shown that the presence of an interaction
term in the subclass of isotropic models can lead to inflationary models with
late-time oscillatory behaviour in which the matter is not driven to zero.
Next, within the class of the string cosmologies studied, it is shown that
there is a subclass which do not inflate at late times in the post-big bang
regime. Furthermore, all string models studied typically do not have a
late--time flatness problem. Indeed, it is shown that curvature typically plays
an important r\^{o}le only at intermediate times in most models. It is also
shown that the presence of a positive cosmological constant in the models
studied can lead to interesting physical behaviour, such as multi-bouncing
universes. A mathematical equivalence between general relativistic scalar field
theories and scalar-tensor theories and string theories has been extensively
exploited and thus the results obtained from the string analysis compliment the
results obtained from the Bianchi class B exponential potential analysis.


title:
Proof of the symmetry of the off-diagonal Hadamard/Seeley-deWitt's
  coefficients in $C^{\infty}$ Lorentzian manifolds by a local Wick rotation

abstract:
  Completing the results obtained in a previous paper, we prove the symmetry of
Hadamard/Seeley-deWitt off-diagonal coefficients in smooth $D$-dimensional
Lorentzian manifolds. To this end, it is shown that, in any Lorentzian
manifold, a sort of ``local Wick rotation'' of the metric can be performed
provided the metric is a locally analytic function of the coordinates and the
coordinates are ``physical''. No time-like Killing field is necessary. Such a
local Wick rotation analytically continues the Lorentzian metric in a
neighborhood of any point, or, more generally, in a neighborhood of a
space-like (Cauchy) hypersurface, into a Riemannian metric. The continuation
locally preserves geodesically convex neighborhoods. In order to make rigorous
the procedure, the concept of a complex pseudo-Riemannian (not Hermitian or
K\"ahlerian) manifold is introduced and some features are analyzed. Using these
tools, the symmetry of Hadamard/Seeley-deWitt off-diagonal coefficients is
proven in Lorentzian analytical manifolds by analytical continuation of the
(symmetric) Riemannian heat-kernel coefficients. This continuation is performed
in geodesically convex neighborhoods in common with both the metrics. Then, the
symmetry is generalized to $C^\infty$ non analytic Lorentzian manifolds by
approximating Lorentzian $C^{\infty}$ metrics by analytic metrics in common
geodesically convex neighborhoods. The symmetry requirement plays a central
r\^{o}le in the point-splitting renormalization procedure of the one-loop
stress-energy tensor in curved spacetimes for Hadamard quantum states.


title: Vacuum-driven Metamorphosis

abstract:
  We show that nonperturbative vacuum effects can produce a vacuum-driven
transition from a matter-dominated universe to one in which the effective
equation of state is that of radiation plus cosmological constant. The actual
material content of the universe after the transition remains that of
non-relativistic matter. This metamorphosis of the equation of state can be
traced to nonperturbative vacuum effects that cause the scalar curvature to
remain nearly constant at a well-defined value after the transition, and is
responsible for the observed acceleration of the recent expansion of the
universe.


title: Double cosmic walls in Teleparallel Gravity

abstract:
  An example is given of a plane topological torsion defect representing a
cosmic wall double wall in teleparallel gravity.The parallel planar walls
undergone a repulsive gravitational force due to Cartan torsion.This is the
first example of a non-Riemannian double cosmic wall.It is shown that the walls
oscillate with a speed that depends on torsion and on the surface density of
the wall.Cartan torsion acts also as a damping force reducing the speed of
oscillation when it is stronger.


title: A constant equation of state for quintessence ?

abstract:
  Quintessence is often invoked to explain the universe acceleration suggested
by the type Ia supernovae observations. The aim of this letter is to study the
validity of using a constant equation of state for quintessence models. We
shall show that this hypothesis strongly constraint the form of the scalar
potential.


title:
A class of plane symmetric perfect-fluid cosmologies with a Kasner-like
  singularity

abstract:
  We prove the existence of a class of plane symmetric perfect-fluid
cosmologies with a (-1/3, 2/3, 2/3) Kasner-like singularity. These solutions of
the Einstein equations depend on two smooth functions of one space coordinate.
They are constructed by solving a symmetric hyperbolic system of Fuchsian
equations.


title: Quantum inequalities and `quantum interest' as eigenvalue problems

abstract:
  Quantum inequalities (QI's) provide lower bounds on the averaged energy
density of a quantum field. We show how the QI's for massless scalar fields in
even dimensional Minkowski space may be reformulated in terms of the positivity
of a certain self-adjoint operator - a generalised Schroedinger operator with
the energy density as the potential - and hence as an eigenvalue problem. We
use this idea to verify that the energy density produced by a moving mirror in
two dimensions is compatible with the QI's for a large class of mirror
trajectories. In addition, we apply this viewpoint to the `quantum interest
conjecture' of Ford and Roman, which asserts that the positive part of an
energy density always overcompensates for any negative components. For various
simple models in two and four dimensions we obtain the best possible bounds on
the `quantum interest rate' and on the maximum delay between a negative pulse
and a compensating positive pulse. Perhaps surprisingly, we find that - in four
dimensions - it is impossible for a positive delta-function pulse of any
magnitude to compensate for a negative delta-function pulse, no matter how
close together they occur.


title: Flux Tubes in Weyl Gravity

abstract:
  The spherically symmetric solutions in Weyl gravity interacting with U(1) or
SU(2) gauge fields are examined. It is shown that these solutions are
conformally equivalent to an infinite flux tube with constant (color) electric
and magnetic fields. This allows us to say that Weyl gravity has in some sense
a classical confinement mechanism. We discuss a possible connection with flux
tubes in quantum chromodynamics.


title: Brans-Dicke-type theories and avoidance of the cosmological singularity

abstract:
  We tudy flat Friedmann-Robertson-Walker cosmology in Brans-Dicke-type
theories of gravitation with minimal coupling between the scalar field and the
matter fields in the Einstein frame (general relativity with an extra scalar
field) for arbitrary values of the Brans-Dicke parameter $\omega>-{3/2}$. It is
shown that the cosmological singularity occuring in the Einstein frame
formulation of this theory is removed in the Jordan frame in the range
$-{3/2}<\omega<\leq-{4/3}$. This result is interpreted in the ligth of a
viewpoint (first presented in reference gr-qc/9905071) asserting that both
Jordan frame and Einstein frame formulations of general relativity are
physically equivalent. The implications of the obtained result for string
theory are outlined.


title: 4D Wormhole with Signature Change in the Presence of Extra Dimensions

abstract:
  A regular vacuum solution in 5D gravity on the principal bundle with the U(1)
structural group is proposed as a 4D wormhole. This solution has two null
hypersurfaces where an interchange of the sign of some 5D metric components
happens. For a 4D observer living on the base of this principal bundle this is
a wormhole with two asymptotically flat Lorentzian (Euclidean) spacetimes
connected by a Euclidean (Lorentzian) throat. The 4D Lorentzian observer sees
these two null hypersurfaces as electric charges.


title: Painleve III Equation and Bianchi VII_0 Model

abstract:
  We examine the reduced phase space of the Bianchi VII_0 cosmological model,
including the moduli sector. We show that the dynamics of the relevant sector
of local degrees of freedom is given by a Painleve III equation. We then obtain
a zero-curvature representation of this Painleve III equation by applying the
Belinskii-Zakharov method to the Bianchi VII_0 model.


title: Space of spaces as a metric space

abstract:
  In spacetime physics, we frequently need to consider a set of all spaces
(`universes') as a whole. In particular, the concept of `closeness' between
spaces is essential. However, there has been no established mathematical theory
so far which deals with a space of spaces in a suitable manner for spacetime
physics.
  Based on the scheme of the spectral representation of geometry, we construct
a space of all compact Riemannian manifolds equipped with the spectral measure
of closeness. We show that this space of all spaces can be regarded as a metric
space. We also show other desirable properties of this space, such as the
partition of unity, locally-compactness and the second countability. These
facts show that this space of all spaces can be a basic arena for spacetime
physics.


title:
Towards an understanding of the stability properties of the 3+1
  evolution equations in general relativity

abstract:
  We study the stability properties of the standard ADM formulation of the 3+1
evolution equations of general relativity through linear perturbations of flat
spacetime. We focus attention on modes with zero speed of propagation and
conjecture that they are responsible for instabilities encountered in numerical
evolutions of the ADM formulation. These zero speed modes are of two kinds:
pure gauge modes and constraint violating modes. We show how the decoupling of
the gauge by a conformal rescaling can eliminate the problem with the gauge
modes. The zero speed constraint violating modes can be dealt with by using the
momentum constraints to give them a finite speed of propagation. This analysis
sheds some light on the question of why some recent reformulations of the 3+1
evolution equations have better stability properties than the standard ADM
formulation.


title:
An alternative derivation of the Lense-Thirring drag on the orbit of a
  test body

abstract:
  A new strategy in deriving the Lense-Thirring effect, in the weak field and
slow motion approximation of general relativity, on the orbital elements of a
test body in the field of different central rotating sources exhibiting axial
symmetry is presented. The approach adopted in the present work, in the case of
a perfectly spherical source, leads for all the Keplerian orbital elements of
the freely falling particle to the well known Lense-Thirring equations. The
case of a central nonspherical body is also worked out.

categories: gr-qc astro-ph physics.geo-ph physics.space-ph


title: Earth tides and Lense-Thirring effect

abstract:
  The general relativistic Lense-Thirring effect can be measured by inspecting
a suitable combination of the orbital residuals of the nodes of LAGEOS and
LAGEOS II and the perigee of LAGEOS II. The solid and ocean Earth tides affect
the recovery of the parameter by means of which the gravitomagnetic force is
accounted for in the combined residuals. Thus an extensive analysis of the
perturbations induced on these orbital elements by the solid and ocean Earth
tides is carried out. It involves the l=2 terms for the solid tides and the
l=2,3,4 terms for the ocean tides. The perigee of LAGEOS II turns out to be
very sensitive to the l=3 part of the ocean tidal spectrum, contrary to the
nodes of LAGEOS and LAGEOS II. The uncertainty in the solid tidal
perturbations, mainly due to the Love number k2, ranges from 0.4% to 1.5%,
while the ocean tides are uncertain at 5%-15% level. The obtained results are
used in order to check in a preliminary way which tidal constituents the
Lense-Thirring shift is sensitive to. In particular it is tested if the
semisecular 18.6-year zonal tide really does not affect the combined residuals.
It turns out that, if modeled at the level of accuracy worked out in the paper,
the l=2,4 m=0 and also, to a lesser extent, the l=3 m=0 tidal perturbations
cancel out.


title: Iterative Approach to Gravitational Lensing Theory

abstract:
  We develop an iterative approach to gravitational lensing theory based on
approximate solutions of the null geodesic equations. The approach can be
employed in any space-time which is ``close'' to a space-time in which the null
geodesic equations can be completely integrated, such as Minkowski space-time,
Robertson-Walker cosmologies, or Schwarzschild-Kerr geometries. To illustrate
the method, we construct the iterative gravitational lens equations and time of
arrival equation for a single Schwarzschild lens. This example motivates a
discussion of the relationship between the iterative approach, the standard
thin lens formulation, and an exact formulation of gravitational lensing.


title: Gravitational-wave driven instability of rotating relativistic stars

abstract:
  A brief review of the stability of rotating relativistic stars is followed by
a more detailed discussion of recent work on an instability of r-modes, modes
of rotating stars that have axial parity in the slow-rotation limit. These
modes may dominate the spin-down of neutron stars that are rapidly rotating at
birth, and the gravitational waves they emit may be detectable.


title: Gravitational Wave Experiments and Early Universe Cosmology

abstract:
  Gravitational-wave experiments with interferometers and with resonant masses
can search for stochastic backgrounds of gravitational waves of cosmological
origin. We review both experimental and theoretical aspects of the search for
these backgrounds. We give a pedagogical derivation of the various relations
that characterize the response of a detector to a stochastic background. We
discuss the sensitivities of the large interferometers under constructions
(LIGO, VIRGO, GEO600, TAMA300, AIGO) or planned (Avdanced LIGO, LISA) and of
the presently operating resonant bars, and we give the sensitivities for
various two-detectors correlations. We examine the existing limits on the
energy density in gravitational waves from nucleosynthesis, COBE and pulsars,
and their effects on theoretical predictions. We discuss general theoretical
principles for order-of-magnitude estimates of cosmological production
mechanisms, and then we turn to specific theoretical predictions from
inflation, string cosmology, phase transitions, cosmic strings and other
mechanisms. We finally compare with the stochastic backgrounds of astrophysical
origin.


title:
Canonical Quantization of a Closed Euclidean Universe with a
  Cosmological Constant

abstract:
  We study canonical quantization of a closed Euclidean universe with a
cosmological constant and a massless scalar field. The closed Euclidean
universe with an ordinary matter state can be matched at a finite radius only
with the closed Lorentzian universe with the Wick-rotated exotic state. The
exotic state provides the Lorentzian universe with a potential barrier
extending from the cosmological singularity to the classical turning point and
corresponding to the Euclidean geometry through the Wick-rotation, and avoid
the singularity problem at the matching boundary. We find analytically the
approximate wave functions for quantum creation of the Universe from the {\it
nothingness}. We prescribe the Hartle-Hawking's no-boundary wave function,
Linde's wave function and Vilenkin's tunneling wave function. In particular, we
find the wave function for the Euclidean geometry, whose semiclassical solution
is regular at the matching boundary with the Lorentzian geometry but singular
at the cosmological singularity.


title: A Twisting Electrovac Solution of Type II with the Cosmological Constant

abstract:
  An exact solution of the current-free Einstein-Maxwell equations with the
cosmological constant is presented. It is of Petrov type II, and its double
principal null vector is geodesic, shear-free, expanding, and twisting. The
solution contains five constants. Its electromagnetic field is non-null and
aligned. The solution admits only one Killing vector and includes, as special
cases, several known solutions.


title: Teleparallel Equivalent of the Kaluza-Klein Theory

abstract:
  Relying upon the equivalence between a gauge theory for the translation group
and general relativity, a teleparallel version of the original Kaluza-Klein
theory is developed. In this model, only the internal space (fiber) turns out
to be five dimensional, spacetime being kept always four dimensional. A
five-dimensional translational gauge theory is obtained which unifies, in the
sense of Kaluza-Klein theories, gravitational and electromagnetic interactions.