title:
Improved limit on quantum-spacetime modifications of Lorentz symmetry
  from observations of gamma-ray blazars

abstract:
  In the quantum-gravity literature there has been interest in the possibility
that quantum properties of spacetime might affect the energy/momentum
dispersion relation. The most used test theory for data analysis is based on a
modification of the laws of propagation proposed in astro-ph/9712103 [Nature
393,763], and the present best limit on the quantum-gravity scale was obtained
in gr-qc/9810044 [Phys.Rev.Lett.83,2108]. I derive an improved limit using
recent experimental information on absorption by the infrared diffuse
extragalactic background of $\gamma$-rays emitted by blazars. Foreseeable more
accurate determinations of the absorption levels could achieve Planck-scale
sensitivity. As a corollary I also show that, contrary to the recent claim of
astro-ph/0208507v3, the test theory here considered does not allow decays of
photons into electron-positron pairs, and I expose the limitations of
phenomenological proposals, such as the one reported in astro-ph/0212190, in
which one attempts to infer limits on the kinematic theory here considered
through the ad hoc introduction of a dynamical framework.


title: Quantum vacua: momentum space topology of fermion zero modes

abstract:
  Quantum vacua are characterized by the topological structure of their fermion
zero modes. The vacua are distributed into universality classes protected by
topology in momentum space. The vacua whose manifold of fermion zero modes has
co-dimension 3 are of special interest because in the low-energy corner the
fermionic excitations become the Weyl relativistic chiral fermions, while the
dynamical bosonic collective modes of the fermionic vacuum interact with the
chiral fermions as the effective gravity and gauge fields. The relativistic
invariance, the chirality of fermions, the gauge and gravity fields, the
relativistic spin, etc., are the emergent low-energy properties of the quantum
vacuum with such fermion zero modes. The vacuum of the Standard Model and the
vacuum of superfluid 3He-A belong to this universality class and thus they are
described by similar effective theories. This allows us to use this quantum
liquid for the theoretical and experimental simulations of many problems
related to the quantum vacuum, such as the chiral anomaly and the cosmological
constant problems.


title: Relativity Theory and a Real Pioneer Effect

abstract:
  Keeping the relativistic laws of motion a non-conventional Pioneer effect
would prove an increase of the scale rate of atomic clocks in comparison with
planetary ones. Together with a slowly decreasing amount of about 60% due to
anisotropic radiation this would be a thinkable explanation for an apparent
anomalous acceleration of the Pioneer 10/11 probes. Such a difference between
atomic time and ephemeris time, however, (coincidentally corresponding to that
of atomic time and cosmic time as derived from any cosmological model of
general relativity, where the cosmic 'coordinate' speed of light is fixed to be
c* = c) is ruled out by solar system's observational facts. Thus a
non-conventional Pioneer effect would inevitably contradict relativity theory.


title:
A reassessment of the systematic gravitational error in the LARES
  mission

abstract:
  In this letter we reexamine the evaluation of \zone in some proposed tests of
relativistic gravitomagnetism with existing and proposed laser--ranged
LAGEOS--like satellites in the gravitational field of the Earth. A more
conservative and realistic approach is followed by using the diagonal part only
of the covariance matrix of the EGM96 Earth's gravity model up to degree l=20.
It turns out that, within this context and according to the present level of
knowledge of the terrestrial gravitational field, the best choice would be the
use of a recently proposed combination using the nodes \Omega of LAGEOS, LAGEOS
II and LARES and the perigees \omega of LAGEOS II and LARES. Indeed, it turns
out to be insensitive both to the even zonal harmonics of degree higher than
l=20 and to the correlation among them


title:
New exact cosmological solutions to Brans-Dicke gravity with a
  self-interacting scalar-field

abstract:
  We derive a new parametric class of exact cosmological solutions to
Brans-Dicke theory of gravity with a self-interacting scalar field and a
barotropic perfect fluid of ordinary matter, by assuming a linear relationship
between the Hubble expansion parameter and the time derivative of the scalar
field. As a consequence only a class of exponential potentials and their
combinations can be treated. The relevance of the solutions found for the
description of the cosmic evolution are discussed in detail. We focus our
discussion mainly on the possibility to have superquintessence behavior.


title: Brane corresponding to the Nariai bulk

abstract:
  We consider the five-dimensional bulk spacetime with negative Lambda
described by the Nariai metric (which is not conformally flat) and match it
with a vacuum brane satisfying the proper boundary conditions. It is shown that
the brane metric corresponds to a cloud of string dust of constant energy
density.


title: Test particle motion in a gravitational plane wave collision background

abstract:
  Test particle geodesic motion is analysed in detail for the background
spacetimes of the degenerate Ferrari-Ibanez colliding gravitational wave
solutions. Killing vectors have been used to reduce the equations of motion to
a first order system of differential equations which have been integrated
numerically. The associated constants of the motion have also been used to
match the geodesics as they cross over the boundary between the single plane
wave and interaction zones.


title:
A Cosmologic Model Based on the Equivalence of Expansion and Light
  Retardation Part 2: Small-Scale Aspects and Quanta

abstract:
  Interpretation of the cosmological red shift as light retardation with the
amount of (d/dt)c = -Hc yields a photon rest mass hH/c^2. A system of natural
units is introduced, in which the Planck mass is the geometric average of the
photon rest mass and the universal mass. It is shown that the equivalence of
expansion and light retardation results in a Cosmologic Uncertainty Principle
(CUP), which determines the Heisenberg Principle. Within the Retarded Light
Mode (RLM) the Dirac "coincidences" are found to be systematic, and an
explanation is provided.


title:
Testing the normality of the gravitational wave data with a low cost
  recursive estimate of the kurtosis

abstract:
  We propose a monitoring indicator of the normality of the output of a
gravitational wave detector. This indicator is based on the estimation of the
kurtosis (i.e., the 4th order statistical moment normalized by the variance
squared) of the data selected in a time sliding window. We show how a low cost
(because recursive) implementation of such estimation is possible and we
illustrate the validity of the presented approach with a few examples using
simulated random noises.


title: Neutrino Clustering in the Galaxy with a Global Monopole

abstract:
  In spherically symmetric, static spacetime, we show that only j=1/2 fermions
can satisfy both Einstein's field equation and Dirac's equation. It is also
shown that neutrinos are able to have effective masses and cluster in the
galactic halo when they are coupled to a global monopole situated at the
galactic core. Astronomical implications of the results are discussed.


title: Variable Mass Theories of Gravity

abstract:
  Several attempts to construct theories of gravity with variable mass are
considered. The theoretical impacts of allowing the rest mass to vary with
respect to time or an appropriate curve parameter are examined in the framework
of Newtonian and Einsteinian gravity theories. In further steps, scalar-tensor
theories are examined with respect to their relation to the variation of the
mass and in an ultimate step, an additional coordinate is introduced and its
possible relation to the mass is examined, yielding a five dimensional
space-time-matter theory.


title: Spacetime Foam and Vacuum Energy

abstract:
  A simple model of spacetime foam, made by spherically symmetric wormholes,
with or without a cosmological term is proposed. The black hole area
quantization and its consequences are examined in this context. We open the
possibility of probing Lorentz symmetry in this picture.


title: d-Dimensional Black Hole Entropy Spectrum from Quasi-Normal Modes

abstract:
  Starting from recent observations\cite{hod,dreyer1} about quasi-normal modes,
we use semi-classical arguments to derive the Bekenstein-Hawking entropy
spectrum for $d$-dimensional spherically symmetric black holes. We find that
the entropy spectrum is equally spaced: $S_{BH}=k \ln(m_0)n$, where $m_0$ is a
fixed integer that must be derived from the microscopic theory. As shown in
\cite{dreyer1},4-$d$ loop quantum gravity yields precisely such a spectrum with
$m_0=3$ providing the Immirzi parameter is chosen appropriately. For
$d$-dimensional black holes of radius $R_H(M)$, our analysis requires the
existence of a unique quasinormal mode frequency in the large damping limit
$\omega^{(d)}(M) = \alpha^{(d)}c/ R_H(M)$ with coefficient $\alpha^{(d)} =
{(d-3)/over 4\pi} \ln(m_0)$, where $m_0$ is an integer and $\Gamma^{(d-2)}$ is
the volume of the unit $d-2$ sphere.


title: Critical behavior of gravitating sphalerons

abstract:
  We examine the gravitational collapse of sphaleron type configurations in
Einstein--Yang--Mills--Higgs theory. Working in spherical symmetry, we
investigate the critical behavior in this model. We provide evidence that for
various initial configurations, there can be three different critical
transitions between possible endstates with different critical solutions
sitting on the threshold between these outcomes. In addition, we show that
within the dispersive and black hole regimes, there are new possible endstates,
namely a stable, regular sphaleron and a stable, hairy black hole.


title: Killing Tensors from Conformal Killing Vectors

abstract:
  Some years ago Koutras presented a method of constructing a conformal Killing
tensor from a pair of orthogonal conformal Killing vectors. When the vector
associated with the conformal Killing tensor is a gradient, a Killing tensor
(in general irreducible) can then be constructed. In this paper it is shown
that the severe restriction of orthogonality is unnecessary and thus it is
possible that many more Killing tensors can be constructed in this way. We also
extend, and in one case correct, some results on Killing tensors constructed
from a single conformal Killing vector. Weir's result that, for flat space,
there are 84 independent conformal Killing tensors, all of which are reducible,
is extended to conformally flat spacetimes. In conformally flat spacetimes it
is thus possible to construct all the conformal Killing tensors and in
particular all the Killing tensors (which in general will not be reducible)
from conformal Killing vectors.


title: Varying Fine-Structure Constant and the Cosmological Constant Problem

abstract:
  We start with a brief account of the latest analysis of the Oklo phenomenon
providing the still most stringent constraint on time-variability of the fine-
structure constant $\alpha$. Comparing this with the recent result from the
measurement of distant QSO's appears to indicate a non-uniform time-dependence,
which we argue to be related to another recent finding of the accelerating
universe. This view is implemented in terms of the scalar-tensor theory,
applied specifically to the small but nonzero cosmological constant. Our
detailed calculation shows that these two phenomena can be understood in terms
of a common origin, a particular behavior of the scalar field, dilaton. We also
sketch how this theoretical approach makes it appropriate to revisit non-
Newtonian gravity featuring small violation of Weak Equivalence Principle at
medium distances.


title:
General Spherically Symmetric Non Singular Black Hole Solutions in
  Teleparallel Theory of Gravitation

abstract:
  We find the most general spherically symmetric non singular black hole
solution in a special class of teleparallel theory of gravitation. If $r$ is
large enough, the general solution coincides with the Schwarzschild solution.
Whereas, if $r$ is small, the general solution behaves in a manner similar to
that of de Sitter solution. Otherwise it describes a spherically symmetric
black hole singularity free everywhere. Moreover, the energy associated with
the general solution is calculated using the superpotential given by M{\o}ller
1978.


title: The Pioneer's acceleration anomaly and Hubble's constant

abstract:
  The reported anomalous acceleration acting on the Pioneers spacecrafts could
be seen as a consequence of the existence of some local curvature in light
geodesics when using the coordinate speed of light in an expanding space-time.
The effect is related with the non synchronous character of the underlying
metric and therefore, planets closed orbits can not reveal it. It is shown that
the cosmic expansion rate -the Hubble parameter H- has been indeed detected.
Additionally, a relation for an existing annual term is obtained which depends
on the cosine of the ecliptic latitude of the spacecraft, suggestingan
heuristic analogy between the effect and Foucault's experiment - light rays
playing a similar role in the expanding space than Foucault's Pendulum does
while determining Earth's rotation. This statement could be seen as a benchmark
for future experiments.


title: Implications of a Time-Varying Fine Structure Constant

abstract:
  Much work has been done after the possibility of a fine structure constant
being time-varying. It has been taken as an indication of a time-varying speed
of light. Here we prove that this is not the case. We prove that the speed of
light may or may not vary with time, independently of the fine structure
constant being constant or not. Time variations of the speed of light, if
present, have to be derived by some other means and not from the fine structure
constant. No implications based on the possible variations of the fine
structure constant can be imposed on the speed of light.


title: Quantum Spectrum for a Kerr-Newman Black Hole

abstract:
  In this paper, we consider the quantum area spectrum for a rotating and
charged (Kerr-Newman) black hole. Generalizing a recent study on Kerr black
holes (which was inspired by the static-black hole formalism of Barvinsky, Das
and Kunstatter), we show that the quantized area operator can be expressed in
terms of three quantum numbers (roughly related to the mass, charge and spin
sectors). More precisely, we find that $A=8\pi\hbar[n+{1\over 2}+{p_1\over
2}+p_2]$, where $n$, $p_1$ and $p_2$ are strictly non-negative integers. In
this way, we are able to confirm a uniformly spaced spectrum even for a fully
general Kerr-Newman black hole. Along the way, we derive certain selection
rules and use these to demonstrate that, in spite of appearances, the charge
and spin spectra are not completely independent.


title:
Five-dimensional Black Hole and Particle Solution with Non-Abelian Gauge
  Field

abstract:
  We study the 5-dimensional Einstein-Yang-Mills system with a cosmological
constant. Assuming a spherically symmetric spacetime, we find a new analytic
black hole solution, which approaches asymptotically "quasi-Minkowski", "quasi
anti-de Sitter", or "quasi de Sitter" spacetime depending on the sign of a
cosmological constant. Since there is no singularity except for the origin
which is covered by an event horizon, we regard it as a localized object. This
solution corresponds to a magnetically charged black hole.
  We also present a singularity-free particle-like solution and a non-trivial
black hole solution numerically. Those solutions correspond to the
Bartnik-McKinnon solution and a colored black hole with a cosmological constant
in the 4-dimensions. We analyze their asymptotic behaviors, spacetime
structures and thermodynamical properties. We show that there is a set of
stable solutions if a cosmological constant is negative.


title: Note on Canonical Quantization and Unitary Equivalence in Field Theory

abstract:
  The problem of defining and constructing representations of the Canonical
Commutation Relations can be systematically approached via the technique of
{\it algebraic quantization}. In particular, when the phase space of the system
is linear and finite dimensional, the `vertical polarization' provides an
unambiguous quantization. For infinite dimensional field theory systems, where
the Stone-von Neumann theorem fails to be valid, even the simplest
representation, the Schroedinger functional picture has some non-trivial
subtleties. In this letter we consider the quantization of a real free scalar
field --where the Fock quantization is well understood-- on an arbitrary
background and show that the representation coming from the most natural
application of the algebraic quantization approach is not, in general, unitary
equivalent to the corresponding Schroedinger-Fock quantization. We comment on
the possible implications of this result for field quantization.


title: Spin-1 gravitational waves

abstract:
  Gravitational fields invariant for a 2-dimensional Lie algebra of Killing
fields [ X,Y] =Y, with Y of light type, are analyzed. The conditions for them
to represent gravitational waves are verified and the definition of energy and
polarization is addressed; realistic generating sources are described.


title: A Converse Hawking-Unruh Effect and dS^2/CFT Correspondance

abstract:
  Given a local quantum field theory net A on the de Sitter spacetime dS^d,
where geodesic observers are thermalized at Gibbons-Hawking temperature, we
look for observers that feel to be in a ground state, i.e. particle evolutions
with positive generator, providing a sort of converse to the Hawking-Unruh
effect. Such positive energy evolutions always exist as noncommutative flows,
but have only a partial geometric meaning, yet they map localized observables
into localized observables.
  We characterize the local conformal nets on dS^d. Only in this case our
positive energy evolutions have a complete geometrical meaning. We show that
each net has a unique maximal expected conformal subnet, where our evolutions
are thus geometrical.
  In the two-dimensional case, we construct a holographic one-to-one
correspondence between local nets A on dS^2 and local conformal non-isotonic
families (pseudonets) B on S^1. The pseudonet B gives rise to two local
conformal nets B(+/-) on S^1, that correspond to the H(+/-)-horizon components
of A, and to the chiral components of the maximal conformal subnet of A. In
particular, A is holographically reconstructed by a single horizon component,
namely the pseudonet is a net, iff the translations on H(+/-) have positive
energy and the translations on H(-/+) are trivial. This is the case iff the
one-parameter unitary group implementing rotations on dS^2 has
positive/negative generator.


title: Geometrical description of spin-2 fields

abstract:
  We show that the torsion of a Cartan geometry can be associated to two spin-2
fields. This structure allows a new approach to deal with the proposal of
geometrization of spin-2 fields besides the traditional one dealt with in
General Relativity. We use the associated Hilbert-Einstein Lagrangian $R$ for
generating a dynamics for the fields.


title:
Transverse frames for Petrov type I spacetimes: a general algebraic
  procedure

abstract:
  We develop an algebraic procedure to rotate a general Newman-Penrose tetrad
in a Petrov type I spacetime into a frame with Weyl scalars $\Psi_{1}$ and
$\Psi_{3}$ equal to zero, assuming that initially all the Weyl scalars are non
vanishing. The new frame highlights the physical properties of the spacetime.
In particular, in a Petrov Type I spacetime, setting $\Psi_{1}$ and $\Psi_{3}$
to zero makes apparent the superposition of a Coulomb-type effect $\Psi_{2}$
with transverse degrees of freedom $\Psi_{0}$ and $\Psi_{4}$.


title:
A General PCT Theorem for the Operator Product Expansion in Curved
  Spacetime

abstract:
  We consider the operator product expansion for quantum field theories on
general analytic 4-dimensional curved spacetimes within an axiomatic framework.
We prove under certain general, model-independent assumptions that such an
expansion necessarily has to be invariant under a simultaneous reversal of
parity, time, and charge (PCT) in the following sense: The coefficients in the
expansion of a product of fields on a curved spacetime with a given choice of
time and space orientation are equal (modulo complex conjugation) to the
coefficients for the product of the corresponding charge conjugate fields on
the spacetime with the opposite time and space orientation. We propose that
this result should be viewed as a replacement of the usual PCT theorem in
Minkowski spacetime, at least in as far as the algebraic structure of the
quantum fields at short distances is concerned.


title: The harmonic oscillator, dimensional analysis and inflationary solutions

abstract:
  In this work, focused on the production of exact inflationary solutions using
dimensional analysis, it is shown how to explain inflation from a pragmatic and
basic point of view, in a step-by-step process, starting from the
one-dimensional harmonic oscillator.


title: Mass of the dilaton and the cosmological constant

abstract:
  One might raise a question if the gravitational scalar field (dilaton)
mediates a finite-range force between local objects still behaving globally as
being massless to implement the scenario of a decaying cosmological constant.
We offer a non-negative reply by a detailed analysis of the field-theoretical
quantization procedure in relation to the observationally required suppression
of the vacuum-energy.


title:
The physical graviton two-point function in de Sitter spacetime with S^3
  spatial sections

abstract:
  We compute the physical graviton two-point function in de Sitter spacetime
with three-sphere spatial sections. We demonstrate that the large-distance
growth present in the corresponding two-point function in spatially flat de
Sitter spacetime is absent. We verify that our two-point function agrees with
that in Minkowski spacetime in the zero cosmological constant limit.


title: Gauge-Invariant Perturbations of Varying-Alpha Cosmologies

abstract:
  Using a gauge-invariant formalism we derive and solve the perturbed
cosmological equations for the BSBM theory of varying fine structure
'constant'. We calculate the time evolution of inhomogeneous perturbations of
the fine structure constant, $\frac{\delta \alpha}{\alpha}$ on small and large
scales with respect to the Hubble radius. In a radiation-dominated universe
small inhomogeneities in $\alpha $ will decrease on large scales but on scales
smaller than the Hubble radius they will undergo stable oscillations. In a
dust-dominated universe small inhomogeneous perturbations in $\alpha $ will
become constant on large scales and on small scales they will increase as
$t^{2/3}$, and $\frac{\delta \alpha}{\alpha}$ will track $% \frac{\delta \rho
_{m}}{\rho_{m}}$ . If the expansion accelerates, as in the case of a $\Lambda $
or quintessence-dominated phase, inhomogeneities in $\alpha $ will decrease on
both large and small scales. The amplitude of perturbations in $\alpha $ will
be much smaller than that of matter or radiation perturbations. We also present
a numerical study of the non-linear evolution of spherical inhomogeneities in
radiation and dust universes by means of a comparison between the evolution of
flat and closed Friedmann models with time-varying $\alpha .$Various
limitations of these simple models are also discussed.


title: Discrete quantum gravity: applications to cosmology

abstract:
  We consider the application of the consistent lattice quantum gravity
approach we introduced recently to the situation of a Friedmann cosmology and
also to Bianchi cosmological models. This allows us to work out in detail the
computations involved in the determination of the Lagrange multipliers that
impose consistency, and the implications of this determination. It also allows
us to study the removal of the Big Bang singularity. Different discretizations
can be achieved depending on the version of the classical theory chosen as a
starting point and their relationships studied. We analyze in some detail how
the continuum limit arises in various models. In particular we notice how
remnants of the symmetries of the continuum theory are embodied in constants of
the motion of the consistent discrete theory. The unconstrained nature of the
discrete theory allows the consistent introduction of a relational time in
quantum cosmology, free from the usual conceptual problems.


title: The Equivalence Principle Revisited

abstract:
  A precise formulation of the strong Equivalence Principle is essential to the
understanding of the relationship between gravitation and quantum mechanics.
The relevant aspects are reviewed in a context including General Relativity,
but allowing for the presence of torsion. For the sake of brevity, a concise
statement is proposed for the Principle: "An ideal observer immersed in a
gravitational field can choose a reference frame in which gravitation goes
unnoticed". This statement is given a clear mathematical meaning through an
accurate discussion of its terms. It holds for ideal observers (time-like
smooth non-intersecting curves), but not for real, spatially extended
observers. Analogous results hold for gauge fields. The difference between
gravitation and the other fundamental interactions comes from their distinct
roles in the equation of force.


title: The scalar perturbation of the higher-dimensional rotating black holes

abstract:
  The massless scalar field in the higher-dimensional Kerr black hole (Myers-
Perry solution with a single rotation axis) has been investigated. It has been
shown that the field equation is separable in arbitrary dimensions. The
quasi-normal modes of the scalar field have been searched in five dimensions
using the continued fraction method. The numerical result shows the evidence
for the stability of the scalar perturbation of the five-dimensional Kerr black
holes. The time scale of the resonant oscillation in the rapidly rotating black
hole, in which case the horizon radius becomes small, is characterized by
(black hole mass)^{1/2}(Planck mass)^{-3/2} rather than the light-crossing time
of the horizon.


title: FLRW Universes from "Wave-Like" Cosmologies in 5D

abstract:
  We consider the evolution of a 4D-universe embedded in a five-dimensional
(bulk) world with a large extra dimension and a cosmological constant. The
cosmology in 5D possesses "wave-like" character in the sense that the metric
coefficients in the bulk are functions of the extra coordinate and time in a
way similar to a pulse or traveling wave propagating along the fifth dimension.
This assumption is motivated by some recent work presenting the big-bang as a
higher dimensional shock wave. We show that this assumption, together with an
equation of state for the effective matter quantities in 4D, allows Einstein's
equations to be fully integrated. We then recover the familiar FLRW universes,
on the four-dimensional hypersurfaces orthogonal to the extra dimension.
Regarding the extra dimension we find that it is {\em growing} in size if the
universe is speeding up its expansion. We also get an estimate for the relative
change of the extra dimension over time. This estimate could have important
observational implications, notably for the time variation of rest mass,
electric charge and the gravitational "constant". Our results extend previous
ones in the literature.


title: Geometry of Manifolds and Dark Matter

abstract:
  It is shown that the theory of dark matter can be derived from the first
principles. Particles representing a new form of matter gravitate but do not
interact electromagnetically, strongly and weakly with the known elementary
particles. Physics of these particles is defined by the Planck scales.


title:
Flows and particles with centrifugal (centripetal) and Coriolis'
  velocities and accelerations. Hubble's law in spaces with affine connections
  and metrics

abstract:
  The notions of centrifugal (centripetal) and Coriols' velocities and
accelerations are introduced and considered in spaces with affine connections
and metrics as velocities and accelerations of flows of mass elements
(particles) moving in space-time. It is shown that these types of velocities
and accelerations are generated by the relative motions between the mass
elements. They are closely related to the kinematic characteristics of the
relative velocity and the relative acceleration. The null (isotropic) vector
fields are considered and their relations with the centrifugal (centripetal)
velocity are established. The centrifugal (centripetal) velocity is found to be
in connection with the Hubble law and the generalized Doppler effect in spaces
with affine connections and metrics. The centrifugal (centripetal) acceleration
could be interpreted as gravitational acceleration as it has been done in the
Einstein theory of gravitation. This fact could be used as a basis for working
out of new gravitational theories in spaces with affine connections and
metrics.


title: Initial data for black hole collisions

abstract:
  I describe the construction of initial data for the Einstein vacuum equations
that can represent a collision of two black holes. I stress in the main
physical ideas.


title: On the Penrose Inequality

abstract:
  We summarize results on the Penrose inequality bounding the ADM-mass or the
Bondi mass in terms of the area of an outermost apparent horizon for
asymptotically flat initial data of Einstein's equations. We first recall the
proof, due to Geroch and to Jang and Wald, of monotonicity of the
Geroch-Hawking mass under a smooth inverse mean curvature flow for data with
non-negative Ricci scalar, which leads to a Penrose inequality if the apparent
horizon is a minimal surface.We then sketch a proof of the Penrose inequality
of Malec, Mars and Simon which holds for general horizons and for data
satisfying the dominant energy condition, but imposes (in addition to smooth
inverse mean curvature flow) suitable restrictions on the data on a spacelike
surface. These conditions can, however, at least locally be fulfilled by a
suitable choice of the initial surface in a given spacetime. Remarkably, they
are also (formally) identical to ones employed earlier by Hayward in order to
define a 2+1 foliation on null surfaces, with respect to which the Hawking mass
is again monotonic.


title: Clifford Geometrodynamics

abstract:
  Classical anti-commuting spinor fields and their dynamics are derived from
the geometry of the Clifford bundle over spacetime via the BRST formulation. In
conjunction with Kaluza-Klein theory, this results in a geometric description
of all the fields and dynamics of the standard model coupled to gravity and
provides the starting point for a new approach to quantum gravity.


title: (1+1)-dimensional formalism and quasi-local conservation equations

abstract:
  A set of exact quasi-local conservation equations is obtained in the
(1+1)-dimensional description of the Einstein's equations of (3+1)-dimensional
spacetimes. These equations are interpreted as quasi-local energy, linear
momentum, and angular momentum conservation equations. In the asymptotic region
of asymptotically flat spacetimes, it is shown that these quasi-local
conservation equations reduce to the conservation equations of Bondi energy,
linear momentum, and angular momentum, respectively. When restricted to the
quasi-local horizon of a generic spacetime, which is defined without referring
to the infinity, the quasi-local conservation equations coincide with the
conservation equations on the stretched horizon studied by Price and Thorne.
All of these quasi-local quantities are expressed as invariant two-surface
integrals, and geometrical interpretations in terms of the area of a given
two-surface and a pair of null vector fields orthogonal to that surface are
given.


title:
Gravitational Acceleration of Spinning Bodies From Lunar Laser Ranging
  Measurements

abstract:
  The Sun's relativistic gravitational gradient accelerations of Earth and
Moon, dependent on the motions of the latter bodies, act upon the system's
internal angular momentum. This spin-orbit force (which plays a part in
determining the gravity wave signal templates for astrophysical sources)
slightly accelerates the Earth-Moon system as a whole, but it more robustly
perturbs that system's internal dynamics with a 5 cm, synodically oscillating
range contribution which is presently measured to 4 mm precision by more than
three decades of lunar laser ranging.


title: Space-Time Variation of Physical Constants and the Equivalence Principle

abstract:
  Location dependence of physical parameters such as the electromagnetic fine
structure constant and Newton's G produce body accelerations which violate
universality of free fall rates testable with laboratory and space experiments.
Theoretically related cosmological time variation of these same parameters are
also constrained by experiments such as lunar laser ranging, and these time
variations produce accelerations of bodies relative to a preferred cosmological
frame.


title:
Does Cosmic No-Hair Conjecture in Brane Scenarios follow from General
  Relativity?

abstract:
  In this paper we examine the Cosmic No-Hair Conjecture (CNHC) in brane world
scenarios. For the validity of this conjecture, in addition to the strong and
weak energy conditions for the matter field, a similar type of assumption is to
be made on the quadratic correction term and there is a restriction on the
non-local term. It is shown by examples with realistic fluid models that strong
and weak energy conditions are sufficient for CNHC in brane world.


title: Viscous cosmological models and accelerated Universes

abstract:
  It is shown that a present acceleration with a past deceleration is a
possible solution of the Friedmann equation by considering the Universe as a
mixture of a scalar with a matter field and by including a non-equilibrium
pressure term in the energy-momentum tensor. The dark energy density decays
more slowly with respect to the time than the matter energy density does. The
inclusion of the non-equilibrium pressure leads to a less pronounced decay of
the matter field with a shorter period of past deceleration.


title: Renormalization of Discrete Models without Background

abstract:
  Conventional renormalization methods in statistical physics and lattice
quantum field theory assume a flat metric background. We outline here a
generalization of such methods to models on discretized spaces without metric
background. Cellular decompositions play the role of discretizations. The group
of scale transformations is replaced by the groupoid of changes of cellular
decompositions. We introduce cellular moves which generate this groupoid and
allow to define a renormalization groupoid flow.
  We proceed to test our approach on several models. Quantum BF theory is the
simplest example as it is almost topological and the renormalization almost
trivial. More interesting is generalized lattice gauge theory for which a
qualitative picture of the renormalization groupoid flow can be given. This is
confirmed by the exact renormalization in dimension two.
  A main motivation for our approach are discrete models of quantum gravity. We
investigate both the Reisenberger and the Barrett-Crane spin foam model in view
of their amenability to a renormalization treatment. In the second case a lack
of tunable local parameters prompts us to introduce a new model. For the
Reisenberger and the new model we discuss qualitative aspects of the
renormalization groupoid flow. In both cases quantum BF theory is the UV fixed
point.


title: Complex Kerr Geometry and Nonstationary Kerr Solutions

abstract:
  In the frame of the Kerr-Schild approach, we consider the complex structure
of Kerr geometry which is determined by a complex world line of a complex
source. The real Kerr geometry is represented as a real slice of this complex
structure. The Kerr geometry is generalized to the nonstationary case when the
current geometry is determined by a retarded time and is defined by a
retarded-time construction via a given complex world line of source. A general
exact solution corresponding to arbitrary motion of a spinning source is
obtained. The acceleration of the source is accompanied by a lightlike
radiation along the principal null congruence. It generalizes to the rotating
case the known Kinnersley class of "photon rocket" solutions.


title:
On the causal Barrett--Crane model: measure, coupling constant, Wick
  rotation, symmetries and observables

abstract:
  We discuss various features and details of two versions of the Barrett-Crane
spin foam model of quantum gravity, first of the Spin(4)-symmetric Riemannian
model and second of the SL(2,C)-symmetric Lorentzian version in which all
tetrahedra are space-like. Recently, Livine and Oriti proposed to introduce a
causal structure into the Lorentzian Barrett--Crane model from which one can
construct a path integral that corresponds to the causal (Feynman) propagator.
We show how to obtain convergent integrals for the 10j-symbols and how a
dimensionless constant can be introduced into the model. We propose a `Wick
rotation' which turns the rapidly oscillating complex amplitudes of the Feynman
path integral into positive real and bounded weights. This construction does
not yet have the status of a theorem, but it can be used as an alternative
definition of the propagator and makes the causal model accessible by standard
numerical simulation algorithms. In addition, we identify the local symmetries
of the models and show how their four-simplex amplitudes can be re-expressed in
terms of the ordinary relativistic 10j-symbols. Finally, motivated by possible
numerical simulations, we express the matrix elements that are defined by the
model, in terms of the continuous connection variables and determine the most
general observable in the connection picture. Everything is done on a fixed
two-complex.


title:
"No-Scalar-Hair" Theorems for Nonminimally Coupled Fields with Quartic
  Self-Interaction

abstract:
  Self-gravitating scalar fields with nonminimal coupling to gravity and having
a quartic self-interaction are considered in the domain of outer communications
of a static black hole. It is shown that there is no value of the nonminimal
coupling parameter $\zeta$ for which nontrivial static black hole solutions
exist. This result establishes the correctness of Bekenstein ``no-scalar-hair''
conjecture for quartic self-interactions.


title: Electrovacuum Static Counter-Rotating Relativistic Dust Disks

abstract:
  A detailed study of the Counter-Rotating Model (CRM) for generic
electrostatic (magnetostatic) axially symmetric thin disks without radial
pressure is presented. We find a general constraint over the counter-rotating
tangential velocities needed to cast the surface energy-momentum tensor of the
disk as the superposition of two counter-rotating charged dust fluids. We then
show that this constraint is satisfied if we take the two counter-rotating
streams as circulating along electrogeodesics with equal and opposite
tangential velocities. We also find explicit expressions for the energy
densities, electrostatic (magnetostatic) charge densities and velocities of the
counter-rotating fluids. Three specific examples are considered where we obtain
some CRM well behaved based in simple solutions to the Einstein-Maxwell
equations. The considered solutions are Reissner-Nordstrom in the electrostatic
case, its magnetostatic counterpart and two solutions obtained from Taub-NUT
and Kerr solutions.


title: Rotating Relativistic Thin Disks as Sources of the Taub-NUT Solution

abstract:
  Rotating disks with nonzero radial pressure and finite radius are studied.
The models are based in the Taub-NUT metric and constructed using the
well-known ``displace, cut and reflect'' method. We find that the disks are
made of perfect fluids with constant energy density and pressure. The energy
density is negative, but the effective Newotnian density is possitive as the
strong energy condition requires. We also find that the disks are not stable
under radial perturbations and that there are regions of the disks where the
particles move with superluminal velocities.


title:
The special relativistic equivalence principle: gravity theory's
  foundation

abstract:
  On incorporating special relativity theory into an extended equivalence
principle, post-Newtonian gravitational phenomena beyond that originally
predicted by Einstein are predicted (required), such as geodetic and
gravitomagnetic precessions of local inertial frames, and precession of
Mercury's orbital perihelion. Why were not these phenomena predicted in the
years 1907-1911? The unique 1/c^2 order dynamical equations for clock rates and
motion of both bodies and light in local gravity are derived which guarantee
fulfillment of the special relativistic equivalence principle.


title:
The Riemann-Lanczos Problem as an Exterior Differential System with
  Examples in 4 and 5 Dimensions

abstract:
  The key problem of the theory of exterior differential systems (EDS) is to
decide whether or not a system is in involution. The special case of EDSs
generated by one-forms (Pfaffian systems) can be adequately illustrated by a
2-dimensional example. In 4 dimensions two such problems arise in a natural
way, namely, the Riemann-Lanczos and the Weyl-Lanczos problems. It is known
from the work of Bampi and Caviglia that the Weyl-Lanczos problem is always in
involution in both 4 and 5 dimensions but that the Riemann-Lanczos problem
fails to be in involution even for 4 dimensions. However, singular solutions of
it can be found. We give examples of singular solutions for the Goedel, Kasner
and Debever-Hubaut spacetimes. It is even possible that the singular solution
can inherit the spacetime symmetries as in the Debever-Hubaut case. We comment
on the Riemann-Lanczos problem in 5 dimensions which is neither in involution
nor does it admit a 5-dimensional involution of Vessiot vector fields in the
generic case.


title:
Janet-Riquier Theory and the Riemann-Lanczos Problems in 2 and 3
  Dimensions

abstract:
  The Riemann-Lanczos problem for 4-dimensional manifolds was discussed by
Bampi and Caviglia. Using exterior differential systems they showed that it was
not an involutory differential system until a suitable prolongation was made.
Here, we introduce the alternative Janet-Riquier theory and use it to consider
the Riemann-Lanczos problem in 2 and 3 dimensions. We find that in 2
dimensions, the Riemann-Lanczos problem is a differential system in involution.
It depends on one arbitrary function of 2 independent variables when no
differential gauge condition is imposed but on 2 arbitrary functions of one
independent variable when the differential gauge condition is imposed. For each
of the two possible signatures we give the general solution in both instances
to show that the occurrence of characteristic coordinates need not affect the
result. In 3 dimensions, the Riemann-Lanczos problem is not in involution as a
identity occurs. This does not prevent the existence of singular solutions. A
prolongation of this problem, where an integrability condition is added, leads
to an involutory prolonged system and thereby generates non-singular solutions
of the prolonged Riemann-Lanczos problem. We give a singular solution for the
unprolonged Riemann-Lanczos problem for the 3-dimensional reduced Goedel
spacetime.


title:
The Weyl-Lanczos Equations and the Lanczos Wave Equation in 4 Dimensions
  as Systems in Involution

abstract:
  Using the work by Bampi and Caviglia, we write the Weyl-Lanczos equations as
an exterior differential system. Using Janet-Riquier theory, we compute the
Cartan characters for all spacetimes with a diagonal metric and for the plane
wave spacetime since all spacetimes have a plane wave limit. We write the
Lanczos wave equation as an exterior differential system and, with assistance
from Janet-Riquier theory, we find that it forms a system in involution. This
result can be derived from the scalar wave equation itself. We compute its
Cartan characters and compare them with those of the Weyl-Lanczos equations.


title: Asymptotically non-flat rotating dilaton black holes

abstract:
  Dilaton black hole solutions which are neither asymptotically flat nor
(anti)-de Sitter but reduce to asymptotically flat solutions in some special
limits have been known for a Liouville type dilatonic potential. It is shown
how, by solving a pair of coupled differential equations, infinitesimally small
angular momentum can be added to these static solutions to produce rotating
black hole solutions.


title: Brane-world models emerging from collisions of plane waves in 5D

abstract:
  We consider brane-world models embedded in a five-dimensional bulk spacetime
with a large extra dimension and a cosmological constant. The cosmology in $5D$
possesses "wave-like" character in the sense that the metric coefficients in
the bulk are assumed to have the form of plane waves propagating in the fifth
dimension. We model the brane as the "plane" of collision of waves propagating
in opposite directions along the extra dimension. This plane is a jump
discontinuity which presents the usual ${\bf Z}_2$ symmetry of brane models.
The model reproduces the {\em generalized} Friedmann equation for the evolution
on the brane, regardless of the specific details in $5D$. Model solutions with
spacelike extra coordinate show the usual {\em big-bang} behavior, while those
with timelike extra dimension present a {\em big bounce}. This bounce is an
genuine effect of a timelike extra dimension. We argue that, based on our
current knowledge, models having a large timelike extra dimension cannot be
dismissed as mathematical curiosities in non-physical solutions. The size of
the extra dimension is small today, but it is {\em increasing} if the universe
is expanding with acceleration. Also, the expansion rate of the fifth dimension
can be expressed in a simple way through the four-dimensional "deceleration"
and Hubble parameters as $- q H$. These predictions could have important
observational implications, notably for the time variation of rest mass,
electric charge and the gravitational "constant". They hold for the three $(k =
0, + 1, - 1)$ models with arbitrary cosmological constant, and are independent
of the signature of the extra dimension.


title: On Schwarzschild's Topology in Brane-Worlds

abstract:
  The topological structure of Schwarzschild's space-time and its maximal
analytic extension are investigated in context of brane-worlds. Using the
embedding coordinates, these geometries are seen as different states of the
evolution of a single brane-world. Comparing the topologies and the embeddings
it is shown that this evolution must be followed by a signature change in the
bulk.


title:
Entropy of Scalar Field in 3+1 Dimensional Reissner-Nordstrom de Sitter
  Black Hole Background

abstract:
  We consider the thermodynamics of minimally coupled massive scalar field in
3+1 dimensional constant curvature black hole background. The brick wall model
of 't Hooft is used. When Schwarzschild like coordinates are used it is found
that two radial brick wall cut-off parameters are required to regularize the
solution. Free energy of the scalar field is obtained through counting of
states using the WKB approximation. It is found that the free energy and the
entropy are divergent in both the cut-off parameters.


title:
Naked singularity formation for higher dimensional inhomogeneous dust
  collapse

abstract:
  We investigate the occurrence and nature of a naked singularity in the
gravitational collapse of an inhomogeneous dust cloud described by higher
dimensional Tolman-Bondi space-time. The naked singularities are found to be
gravitationally strong.


title:
The study of gravitational collapse model in higher dimensional
  space-time

abstract:
  We investigate the end state of the gravitational collapse of an
inhomogeneous dust cloud in higher dimensional space-time. The naked
singularities are shown to be developing as the final outcome of non-marginally
bound collapse. The naked singularities are found to be gravitationally strong
in the sense of Tipler .


title: Generalizations of pp-wave spacetimes in higher dimensions

abstract:
  We shall investigate $D$-dimensional Lorentzian spacetimes in which all of
the scalar invariants constructed from the Riemann tensor and its covariant
derivatives are zero. These spacetimes are higher-dimensional generalizations
of $D$-dimensional pp-wave spacetimes, which have been of interest recently in
the context of string theory in curved backgrounds in higher dimensions.


title: Dynamics of Causal Sets

abstract:
  The Causal Set approach to quantum gravity asserts that spacetime, at its
smallest length scale, has a discrete structure. This discrete structure takes
the form of a locally finite order relation, where the order, corresponding
with the macroscopic notion of spacetime causality, is taken to be a
fundamental aspect of nature.
  After an introduction to the Causal Set approach, this thesis considers a
simple toy dynamics for causal sets. Numerical simulations of the model provide
evidence for the existence of a continuum limit. While studying this toy
dynamics, a picture arises of how the dynamics can be generalized in such a way
that the theory could hope to produce more physically realistic causal sets. By
thinking in terms of a stochastic growth process, and positing some fundamental
principles, we are led almost uniquely to a family of dynamical laws
(stochastic processes) parameterized by a countable sequence of coupling
constants. This result is quite promising in that we now know how to speak of
dynamics for a theory with discrete time. In addition, these dynamics can be
expressed in terms of state models of Ising spins living on the relations of
the causal set, which indicates how non-gravitational matter may arise from the
theory without having to be built in at the fundamental level.
  These results are encouraging in that there exists a natural way to transform
this classical theory, which is expressed in terms of a probability measure, to
a quantum theory, expressed in terms of a quantum measure. A sketch as to how
one might proceed in doing this is provided. Thus there is good reason to
expect that Causal Sets are close to providing a background independent theory
of quantum gravity.


title:
Scalar fields in multidimensional gravity. No-hair and other no-go
  theorems

abstract:
  Global properties of static, spherically symmetric configurations of scalar
fields of sigma-model type with arbitrary potentials are studied in $D$
dimensions, including space-times containing multiple internal factor spaces.
The latter are assumed to be Einstein spaces, not necessarily Ricci-flat, and
the potential $V$ includes contributions from their curvatures. The following
results generalize those known in four dimensions: (A) a no-hair theorem: in
case $V\geq 0$, an asymptotically flat black hole cannot have varying scalar
fields or moduli fields outside the event horizon; (B) nonexistence of
particlelike solutions in models with $V\geq 0$; (C) nonexistence of wormholes
under very general conditions; (D) a restriction on possible global causal
structures (represented by Carter-Penrose diagrams). The list of structures in
all models under consideration is the same as is known for vacuum with a
cosmological constant in general relativity: Minkowski (or AdS), Schwarzschild,
de Sitter and Schwarzschild--de Sitter, and horizons which bound a static
region are always simple. The results are applicable to a wide range of
Kaluza-Klein, supergravity and stringy models with multiple dilaton and moduli
fields.


title:
Thermodynamics with long-range interactions: from Ising models to
  black-holes

abstract:
  New methods are presented which enables one to analyze the thermodynamics of
systems with long-range interactions. Generically, such systems have entropies
which are non-extensive, (do not scale with the size of the system). We show
how to calculate the degree of non-extensivity for such a system. We find that
a system interacting with a heat reservoir is in a probability distribution of
canonical ensembles. The system still possesses a parameter akin to a global
temperature, which is constant throughout the substance. There is also a useful
quantity which acts like a {\it local temperatures} and it varies throughout
the substance. These quantities are closely related to counterparts found in
general relativity. A lattice model with long-range spin-spin coupling is
studied. This is compared with systems such as those encountered in general
relativity, and gravitating systems with Newtonian-type interactions. A
long-range lattice model is presented which can be seen as a black-hole analog.
One finds that the analog's temperature and entropy have many properties which
are found in black-holes. Finally, the entropy scaling behavior of a
gravitating perfect fluid of constant density is calculated. For weak
interactions, the entropy scales like the volume of the system. As the
interactions become stronger, the entropy becomes higher near the surface of
the system, and becomes more area-scaling.


title:
Non-marginally bound inhomogeneous dust collapse in higher dimensional
  space-time

abstract:
  We investigate the occurrence and nature of a naked singularity in the
gravitational collapse of an inhomogeneous dust cloud described by a
self-similar higher dimensional Tolman-Bondi space-time. Bound, marginally
bound and unbound space-times are analyzed. The degree of inhomogeneity of the
collapsing matter necessary to form a naked singularity is given.


title:
Dynamical System Approach to Cosmological Models with a Varying Speed of
  Light

abstract:
  Methods of dynamical systems have been used to study homogeneous and
isotropic cosmological models with a varying speed of light (VSL). We propose
two methods of reduction of dynamics to the form of planar Hamiltonian
dynamical systems for models with a time dependent equation of state. The
solutions are analyzed on two-dimensional phase space in the variables $(x,
\dot{x})$ where $x$ is a function of a scale factor $a$. Then we show how the
horizon problem may be solved on some evolutional paths. It is shown that the
models with negative curvature overcome the horizon and flatness problems. The
presented method of reduction can be adopted to the analysis of dynamics of the
universe with the general form of the equation of state $p=\gamma(a)\epsilon$.
This is demonstrated using as an example the dynamics of VSL models filled with
a non-interacting fluid. We demonstrate a new type of evolution near the
initial singularity caused by a varying speed of light. The singularity-free
oscillating universes are also admitted for positive cosmological constant. We
consider a quantum VSL FRW closed model with radiation and show that the
highest tunnelling rate occurs for a constant velocity of light if $c(a)
\propto a^n$ and $-1 < n \le 0$. It is also proved that the considered class of
models is structurally unstable for the case of $n < 0$.


title:
Covariant Calculation of General Relativistic Effects in an Orbiting
  Gyroscope Experiment

abstract:
  We carry out a covariant calculation of the measurable relativistic effects
in an orbiting gyroscope experiment. The experiment, currently known as Gravity
Probe B, compares the spin directions of an array of spinning gyroscopes with
the optical axis of a telescope, all housed in a spacecraft that rolls about
the optical axis. The spacecraft is steered so that the telescope always points
toward a known guide star. We calculate the variation in the spin directions
relative to readout loops rigidly fixed in the spacecraft, and express the
variations in terms of quantities that can be measured, to sufficient accuracy,
using an Earth-centered coordinate system. The measurable effects include the
aberration of starlight, the geodetic precession caused by space curvature, the
frame-dragging effect caused by the rotation of the Earth and the deflection of
light by the Sun.


title:
Averaging out Inhomogeneous Newtonian Cosmologies: I. Fluid Mechanics
  and the Navier-Stokes Equation

abstract:
  The basic concepts and equations of classical fluid mechanics are presented
in the form necessary for the formulation of Newtonian cosmology and for
derivation and analysis of a system of the averaged Navier-Stokes-Poisson
equations. A special attention is paid to the analytic formulation of the
definitions and equations of moving fluids and to their physical content.


title:
Averaging out Inhomogeneous Newtonian Cosmologies: II. Newtonian
  Cosmology and the Navier-Stokes-Poisson Equations

abstract:
  The basic concepts and equations of Newtonian Cosmology are presented in the
form necessary for the derivation and analysis of the averaged
Navier-Stokes-Poisson equations. A particular attention is paid to the physical
and cosmological hypotheses about the structure of Newtonian universes. The
system of the Navier-Stokes-Poisson equations governing the cosmological
dynamics of Newtonian universes is presented and discussed. A reformulation of
the Navier-Stokes-Poisson equations in terms of the fluid kinematic quantities
is given and the structure of this system of equations is analyzed.


title:
Averaging out Inhomogeneous Newtonian Cosmologies: III. The Averaged
  Navier-Stokes-Poisson Equations

abstract:
  The basic concepts and hypotheses of Newtonian Cosmology necessary for a
consistent treatment of the averaged cosmological dynamics are formulated and
discussed in details. The space-time, space, time and ensemble averages for the
cosmological fluid fields are defined and analyzed with a special attention
paid to their analytic properties. It is shown that all averaging procedures
require an arrangement for a standard measurement device with the same
measurement time interval and the same space region determined by the
measurement device resolution to be prescribed to each position and each moment
of time throughout a cosmological fluid configuration. The formulae for
averaging out the partial derivatives of the averaged cosmological fluid fields
and the main formula for averaging out the material derivatives have been
proved. The full system of the averaged Navier-Stokes-Poisson equations in
terms of the fluid kinematic quantities is derived.


title:
Explicit Kundt type II and N solutions as gravitational waves in various
  type D and O universes

abstract:
  A particular yet large class of non-diverging solutions which admits a
cosmological constant, electromagnetic field, pure radiation and/or general
non-null matter component is explicitly presented. These spacetimes represent
exact gravitational waves of arbitrary profiles which propagate in background
universes such as Minkowski, conformally flat (anti-)de Sitter, Edgar-Ludwig,
Bertotti-Robinson, and type D (anti-)Nariai or Plebanski-Hacyan spaces, and
their generalizations. All possibilities are discussed and are interpreted
using a unifying simple metric form. Sandwich and impulsive waves propagating
in the above background spaces with different geometries and matter content can
easily be constructed. New solutions are identified, e.g. type D pure radiation
or explicit type II electrovacuum waves in (anti-)Nariai universe. It is also
shown that, in general, there are no conformally flat Einstein-Maxwell fields
with a non-vanishing cosmological constant.


title:
Diamonds's Temperature: Unruh effect for bounded trajectories and
  thermal time hypothesis

abstract:
  We study the Unruh effect for an observer with a finite lifetime, using the
thermal time hypothesis. The thermal time hypothesis maintains that: (i) time
is the physical quantity determined by the flow defined by a state over an
observable algebra, and (ii) when this flow is proportional to a geometric flow
in spacetime, temperature is the ratio between flow parameter and proper time.
An eternal accelerated Unruh observer has access to the local algebra
associated to a Rindler wedge. The flow defined by the Minkowski vacuum of a
field theory over this algebra is proportional to a flow in spacetime and the
associated temperature is the Unruh temperature. An observer with a finite
lifetime has access to the local observable algebra associated to a finite
spacetime region called a "diamond". The flow defined by the Minkowski vacuum
of a (four dimensional, conformally invariant) quantum field theory over this
algebra is also proportional to a flow in spacetime. The associated temperature
generalizes the Unruh temperature to finite lifetime observers.
  Furthermore, this temperature does not vanish even in the limit in which the
acceleration is zero. The temperature associated to an inertial observer with
lifetime T, which we denote as "diamond's temperature", is 2hbar/(pi k_b
T).This temperature is related to the fact that a finite lifetime observer does
not have access to all the degrees of freedom of the quantum field theory.


title: Viscous Bianchi type I universes in brane cosmology

abstract:
  We consider the dynamics of a viscous cosmological fluid in the generalized
Randall-Sundrum model for an anisotropic, Bianchi type I brane. To describe the
dissipative effects we use the Israel-Hiscock-Stewart full causal thermodynamic
theory. By assuming that the matter on the brane obeys a linear barotropic
equation of state, and the bulk viscous pressure has a power law dependence on
the energy density, the general solution of the field equations can be obtained
in an exact parametric form. The obtained solutions describe generally a
non-inflationary brane world. In the large time limit the brane Universe
isotropizes, ending in an isotropic and homogeneous state. The evolution of the
temperature and of the comoving entropy of the Universe is also considered, and
it is shown that due to the viscous dissipative processes a large amount of
entropy is created in the early stages of evolution of the brane world.


title: Quantum Mechanics in Curved Configurational Space

abstract:
  Different approaches are compared to formulation of quantum mechanics of a
particle on the curved spaces. At first, the canonical, quasi-classical and
path integration formalisms are considered for quantization of geodesic motion
on the Rimannian configurational spaces. A unique rule of ordering of operators
in the canonical formalism and a unique definition of the path integral are
established and, thus, a part of ambiguities in the quantum counterpart of
geodesic motion is removed. A geometric interpretation is proposed for
non-invariance of the quantum mechanics on coordinate transformations. An
approach alternative to the quantization of geodesic motion is surveyed, which
starts with the quantum theory of a neutral scalar field. Consequences of this
alternative approach and the three formalisms of quantization are compared. In
particular, the field theoretical approach generates a deformation of the
canonical commutation relations between coordinates and momenta of a prticle. A
possible cosmological consequence of the deformation is presented in short. Key
words: quantum mechanics, Riemannian space, geodesic motion, deformation.


title: Spectra of Length and Area in 2+1 Lorentzian Loop Quantum Gravity

abstract:
  We study the spectrum of the length and area operators in Lorentzian loop
quantum gravity, in 2+1 spacetime dimensions. We find that the spectrum of
spacelike intervals is continuous, whereas the spectrum of timelike intervals
is discrete. This result contradicts the expectation that spacelike intervals
are always discrete. On the other hand, it is consistent with the results of
the spin foam quantization of the same theory.


title: Teleparallel origin of the Fierz picture for spin-2 particle

abstract:
  A new approach to the description of spin-2 particle in flat and curved
spacetime is developed on the basis of the teleparallel gravity theory. We show
that such an approach is in fact a true and natural framework for the Fierz
representation proposed recently by Novello and Neves. More specifically, we
demonstrate how the teleparallel theory fixes uniquely the structure of the
Fierz tensor, discover the transparent origin of the gauge symmetry of the spin
2 model, and derive the linearized Einstein operator from the fundamental
identity of the teleparallel gravity. In order to cope with the consistency
problem on the curved spacetime, similarly to the usual Riemannian approach,
one needs to include the non-minimal (torsion dependent) coupling terms.


title: Non-Existence of Black Holes in Certain $\Lambda<0$ Spacetimes

abstract:
  Assuming certain asymptotic conditions, we prove a general theorem on the
non-existence of static regular (i.e., nondegenerate) black holes in spacetimes
with a negative cosmological constant, given that the fundamental group of
space is infinite. We use this to rule out the existence of regular negative
mass AdS black holes with Ricci flat scri. For any mass, we also rule out a
class of conformally compactifiable static black holes whose conformal infinity
has positive scalar curvature and infinite fundamental group, subject to our
asymptotic conditions. In a limited, but important, special case our result
adds new support to the AdS/CFT inspired positive mass conjecture of Horowitz
and Myers.


title: Metric-affine approach to teleparallel gravity

abstract:
  The teleparallel gravity theory, treated physically as a gauge theory of
translations, naturally represents a particular case of the most general
gauge-theoretic model based on the general affine group of spacetime. On the
other hand, geometrically, the Weitzenboeck spacetime of distant parallelism is
a particular case of the general metric-affine spacetime manifold. These
physical and geometrical facts offer a new approach to the teleparallelism. We
present a systematic treatment of the teleparallel gravity within the framework
of the metric-affine theory. The symmetries, conservation laws and the field
equations are consistently derived, and the physical consequences are discussed
in detail. We demonstrate that the so-called teleparallel GR-equivalent model
has a number of attractive features which distinguishes it among the general
teleparallel theories, although it has a consistency problem when dealing with
spinning matter sources.


title: Quantum locking of mirrors in interferometers

abstract:
  We show that quantum noise in very sensitive interferometric measurements
such as gravitational-waves detectors can be drastically modified by quantum
feedback. We present a new scheme based on active control to lock the motion of
a mirror to a reference mirror at the quantum level. This simple technique
allows to reduce quantum effects of radiation pressure and to greatly enhance
the sensitivity of the detection.


title: New mathematical framework for spherical gravitational collapse

abstract:
  A theorem, giving necessary and sufficient condition for naked singularity
formation in spherically symmetric non static spacetimes under hypotheses of
physical acceptability, is formulated and proved. The theorem relates existence
of singular null geodesics to existence of regular curves which are
super-solutions of the radial null geodesic equation, and allows us to treat
all the known examples of naked singularities from a unified viewpoint. New
examples are also found using this approach, and perspectives are discussed.


title:
A Relativistic Mean Field Model for Entrainment in General Relativistic
  Superfluid Neutron Stars

abstract:
  General relativistic superfluid neutron stars have a significantly more
intricate dynamics than their ordinary fluid counterparts. Superfluidity allows
different superfluid (and superconducting) species of particles to have
independent fluid flows, a consequence of which is that the fluid equations of
motion contain as many fluid element velocities as superfluid species. Whenever
the particles of one superfluid interact with those of another, the momentum of
each superfluid will be a linear combination of both superfluid velocities.
This leads to the so-called entrainment effect whereby the motion of one
superfluid will induce a momentum in the other superfluid. We have constructed
a fully relativistic model for entrainment between superfluid neutrons and
superconducting protons using a relativistic $\sigma - \omega$ mean field model
for the nucleons and their interactions. In this context there are two notions
of ``relativistic'': relativistic motion of the individual nucleons with
respect to a local region of the star (i.e. a fluid element containing, say, an
Avogadro's number of particles), and the motion of fluid elements with respect
to the rest of the star. While it is the case that the fluid elements will
typically maintain average speeds at a fraction of that of light, the
supranuclear densities in the core of a neutron star can make the nucleons
themselves have quite high average speeds within each fluid element. The
formalism is applied to the problem of slowly-rotating superfluid neutron star
configurations, a distinguishing characteristic being that the neutrons can
rotate at a rate different from that of the protons.


title:
Interpolating between the Bose-Einstein and the Fermi-Dirac
  distributions in odd dimensions

abstract:
  We consider the response of a uniformly accelerated monopole detector that is
coupled to a superposition of an odd and an even power of a quantized, massless
scalar field in flat spacetime in arbitrary dimensions. We show that, when the
field is assumed to be in the Minkowski vacuum, the response of the detector is
characterized by a Bose-Einstein factor in even spacetime dimensions, whereas a
Bose-Einstein as well as a Fermi-Dirac factor appear in the detector response
when the dimension of spacetime is odd. Moreover, we find that, it is possible
to interpolate between the Bose-Einstein and the Fermi-Dirac distributions in
odd spacetime dimensions by suitably adjusting the relative strengths of the
detector's coupling to the odd and the even powers of the scalar field. We
point out that the response of the detector is always thermal and we, finally,
close by stressing the apparent nature of the appearance of the Fermi-Dirac
factor in the detector response.


title: A Rainich-like approach to the Killing-Yano tensors

abstract:
  The Rainich problem for the Killing-Yano tensors posed by Collinson
\cite{col} is solved. In intermediate steps, we first obtain the necessary and
sufficient conditions for a 2+2 almost-product structure to determine the
principal 2--planes of a skew-symmetric Killing-Yano tensor and then we give
the additional conditions on a symmetric Killing tensor for it to be the square
of a Killing-Yano tensor.We also analyze a similar problem for the conformal
Killing-Yano and the conformal Killing tensors. Our results show that, in both
cases, the principal 2--planes define a maxwellian structure. The associated
Maxwell fields are obtained and we outline how this approach is of interest in
studying the spacetimes that admit these kind of first integrals of the
geodesic equation.


title: On the classification of type D spacetimes

abstract:
  We give a classification of the type D spacetimes based on the invariant
differential properties of the Weyl principal structure. Our classification is
established using tensorial invariants of the Weyl tensor and, consequently,
besides its intrinsic nature, it is valid for the whole set of the type D
metrics and it applies on both, vacuum and non-vacuum solutions. We consider
the Cotton-zero type D metrics and we study the classes that are compatible
with this condition. The subfamily of spacetimes with constant argument of the
Weyl eigenvalue is analyzed in more detail by offering a canonical expression
for the metric tensor and by giving a generalization of some results about the
non-existence of purely magnetic solutions. The usefulness of these results is
illustrated in characterizing and classifying a family of Einstein-Maxwell
solutions. Our approach permits us to give intrinsic and explicit conditions
that label every metric, obtaining in this way an operational algorithm to
detect them. In particular a characterization of the Reissner-Nordstr\"{o}m
metric is accomplished.


title: Extensive Entropy Bounds

abstract:
  It is shown that, for systems in which the entropy is an extensive function
of the energy and volume, the Bekenstein and the holographic entropy bounds
predict new results. More explicitly, the Bekenstein entropy bound leads to the
entropy of thermal radiation (the Unruh-Wald bound) and the spherical entropy
bound implies the "causal entropy bound". Surprisingly, the first bound shows a
close relationship between black hole physics and the Stephan-Boltzmann law
(for the energy and entropy flux densities of the radiation emitted by a hot
blackbody). Furthermore, we find that the number of different species of
massless fields is bounded by $\sim 10^{4}$.

categories: gr-qc cond-mat.stat-mech hep-th quant-ph


title: Primordial Magnetic Fields and Stochastic GW Backgrounds

abstract:
  Operating resonant mass detectors set interesting bounds on diffused
backgrounds of gravitational radiation and in the next five years the wide-band
interferometers will also look for stochastic sources. In this lecture the
interplay among relic GW backgrounds and large scale magnetic fields will be
discussed. Magnetic fields may significantly affect the thermal history of the
Universe in particular at the epoch electroweak symmetry breaking and shortly
after. A review of some old an new results on the spectral properties of
stochastic GW backgrounds will be presented. The possible r\^ole of primordial
magnetic fields as a source of gravitational radiation will be outlined. It
will be shown that the usual bound on stochastic GW backgrounds coming from the
standard big bang nucleosynthesis (BBN) scenario can be significantly relaxed.


title: Gravitational collapse of an infinite dust cylinder

abstract:
  We examine the gravitational collapse of an infinite cylindrical distribution
of time like dust. In order to simplify the calculation we make an assumption
that the axial and azimuthal metric functions are equal. It is shown that the
resulting solution describes homogeneous collapse. We show that the interior
metric can be matched to a time dependent exterior. We also discuss the nature
of the singularity in the matter region and show that it is covered.


title: Nonlinear Relativistic Invariance For Quadrahyperbolic Numbers

abstract:
  One may ask whether an extended group of invariance can naturally be
attributed to the space of associative commutative Quadrahyperbolic Numbers? To
search for a rigorous and positive answer to the question, we shall focus on
the method of derivation of the respective invariance. The outcome that there
exist 3--parametric nonlinear transformations which leave invariant the scalar
product chosen appropriately for The Quadrahyperbolic Numbers, is the main
result of the present publication.


title: Global Monopole in General Relativity

abstract:
  We consider the gravitational properties of a global monopole on the basis of
the simplest Higgs scalar triplet model in general relativity. We begin with
establishing some common features of hedgehog-type solutions with a regular
center, independent of the choice of the symmetry-breaking potential. There are
six types of qualitative behavior of the solutions; we show, in particular,
that the metric can contain at most one simple horizon. For the standard
Mexican hat potential, the previously known properties of the solutions are
confirmed and some new results are obtained. Thus, we show analytically that
solutions with monotonically growing Higgs field and finite energy in the
static region exist only in the interval $1<\gamma <3$, $\gamma $ being the
squared energy of spontaneous symmetry breaking in Planck units. The
cosmological properties of these globally regular solutions apparently favor
the idea that the standard Big Bang might be replaced with a nonsingular static
core and a horizon appearing as a result of some symmetry-breaking phase
transition on the Planck energy scale. In addition to the monotonic solutions,
we present and analyze a sequence of families of new solutions with oscillating
Higgs field. These families are parametrized by $n$, the number of knots of the
Higgs field, and exist for $\gamma < \gamma_n = 6/[(2n+1) (n+2)]$; all such
solutions possess a horizon and a singularity beyond it.


title: Chaos around charged black hole with dipoles

abstract:
  We investigated dynamics of the test particle in the gravitational field of
the charged black hole with dipoles in this paper. At first we have studied the
gravitational potential, by the numerical simulations, we found, for
appropriate parameters, that there are two different cases in the potential
curve, one is a well case with a stable critical point, and the other is three
wells case with three stable critical points and two unstable critical points.
As consequence, the chaotic motion will rise. We have performed the evolution
of the orbits of the test particle in phase space, we found that the orbits of
the test particle randomly oscillate without any periods, even sensitively
depend on the initial conditions and parameters. By performing Poincar\'{e}
sections for different values of the parameters and initial condition, we have
found regular motion and chaotic motion. By comparing these Poincar\'{e}
sections, we further conformed that the chaotic motion of the test particle
mainly origins from the dipoles of the black hole.


title: Complex angular momentum in black hole physics and quasinormal modes

abstract:
  By using the complex angular momentum approach, we prove that the quasinormal
mode complex frequencies of the Schwarzschild black hole are Breit-Wigner type
resonances generated by a family of surface waves propagating close to the
unstable circular photon (graviton) orbit at $r=3M$. Furthermore, because each
surface wave is associated with a given Regge pole of the $S$-matrix, we can
construct the spectrum of the quasinormal-mode complex frequencies from Regge
trajectories. The notion of surface wave orbiting around black holes thus
appears as a fundamental concept which could be profitably introduced in
various areas of black hole physics in connection with the complex angular
momentum approach.


title: Bianchi IX Brane-world Cosmologies

abstract:
  We shall investigate the asymptotic properties of the Bianchi type IX
cosmological model in the Brane-world scenario. The matter content is assumed
to be a combination of a perfect fluid and a minimimally coupled scalar field
that is restricted to the Brane. A detailed qualitative analysis of the Bianchi
type IX braneworld containing a scalar field having an exponential potential is
undertaken. It is found that the Brane-Robertson Walker solution is a local
source for the expanding Bianchi IX models, and if $k^2<2$ the expanding
Bianchi IX models asymptote to the power-law inflationary solution. The only
other local sink is the contracting Brane-Robertson Walker solution. An
analysis of the Bianchi IX models with a scalar field with a general potential
is discussed, and it is shown that in the case of expanding models, for
physical scalar field potentials close to the initial singularity, the scalar
field is effectively massless, and the solution is approximated by the
Brane-Robertson Walker model.


title: Bianchi II Brane-world Cosmologies (${\cal U}\geq 0$)

abstract:
  The asymptotic properties of the Bianchi type II cosmological model in the
Brane-world scenario are investigated. The matter content is assumed to be a
combination of a perfect fluid and a minimimally coupled scalar field that is
restricted to the Brane. The isotropic braneworld solution is determined to
represent the initial singularity in all brane-world cosmologies. Additionally,
it is shown that it is the kinetic energy of the scalar field which dominates
the initial dynamics in these brane-world cosmologies. It is important to note
that, the dynamics of these brane-world cosmologies is not necessarily
asymptotic to general relativistic cosmologies to the future in the case of a
zero four-dimensional cosmological constant.


title:
An analytical computation of asymptotic Schwarzschild quasinormal
  frequencies

abstract:
  Recently it has been proposed that a strange logarithmic expression for the
so-called Barbero-Immirzi parameter, which is one of the ingredients that are
necessary for Loop Quantum Gravity (LQG) to predict the correct black hole
entropy, is not another sign of the inconsistency of this approach to
quantization of General Relativity, but is rather a meaningful number that can
be independently justified in classical GR. The alternative justification
involves the knowledge of the real part of the frequencies of black hole
quasinormal states whose imaginary part blows up. In this paper we present an
analytical derivation of the states with frequencies approaching a large
imaginary number plus ln 3 / 8 pi M; this constant has been only known
numerically so far. We discuss the structure of the quasinormal states for
perturbations of various spin. Possible implications of these states for
thermal physics of black holes and quantum gravity are mentioned and
interpreted in a new way. A general conjecture about the asymptotic states is
stated. Although our main result lends some credibility to LQG, we also review
some of its claims in a critical fashion and speculate about its possible
future relevance for Quantum Gravity.


title: Spherical Dust Collapse in Higher Dimensions

abstract:
  We consider here the question if it is possible to recover cosmic censorship
when a transition is made to higher dimensional spacetimes, by studying the
spherically symmetric dust collapse in an arbitrary higher spacetime dimension.
It is pointed out that if only black holes are to result as end state of a
continual gravitational collapse, several conditions must be imposed on the
collapsing configuration, some of which may appear to be restrictive, and we
need to study carefully if these can be suitably motivated physically in a
realistic collapse scenario. It would appear that in a generic higher
dimensional dust collapse, both black holes and naked singularities would
develop as end states as indicated by the results here. The mathematical
approach developed here generalizes and unifies the earlier available results
on higher dimensional dust collapse as we point out. Further, the dependence of
black hole or naked singularity end states as collapse outcomes, on the nature
of the initial data from which the collapse develops, is brought out explicitly
and in a transparent manner as we show here. Our method also allows us to
consider here in some detail the genericity and stability aspects related to
the occurrence of naked singularities in gravitational collapse.


title:
5-Dimensional Covariance and Generation of Solutions of Einstein
  Equations

abstract:
  A generation procedure, based on the 5-dimensional covariance of the
Kaluza-Klein theory, is developed. The procedure allows one to obtain exact
solutions of the 4-dimensional Einstein equations with electromagnetic and
scalar fields from vacuum 5-dimensional solutions using special 5-dimensional
coordinate transformations. Relations between the physical properties of the
resulting solutions and invariant geometrical properties of the generating
Killing vectors are found out.


title:
On the Difference of Energy between the Einstein and M{\o}ller
  Prescription

abstract:
  In some black hole solutions, these do not exist the same energy-momentum
complexes associated with using definition of Einstein and M{\o}ller in given
coordinates. Here, we consider the difference of energy between the Einstein
and M{\o}ller prescription, and compare it with the energy density of those
black hole solutions. We found out a special relation between the difference of
energy between the Einstein and M{\o}ller prescription and the energy density
for considered black hole solutions.


title: What can we learn studying quantum black holes?

abstract:
  In this paper we try to answer the main question: what is a quantum black
hole?


title: Actions for Vacuum Einstein's Equation with a Killing Symmetry

abstract:
  In a space-time $M$ with a Killing vector field $\xi^a$ which is either
everywhere timelike or everywhere spacelike, the collection of all trajectories
of $\xi^a$ gives a 3-dimension space $S$. Besides the symmetry-reduced action
from that of Einstein-Hilbert, an alternative action of the fields on $S$ is
also proposed, which gives the same fields equations as those reduced from the
vacuum Einstein equation on $M$.


title: Path Group in gauge theory and gravity

abstract:
  Applications of the Path Group (consisting of classes of continuous curves in
Minkowski space-time) to gauge theory and gravity are reviewed. Covariant
derivatives are interpreted as generators of an induced representation of Path
Group. Non-Abelian generalization of Stokes theorem is naturally formulated and
proved in terms of paths. Quantum analogue of Equivalence Principle is
formulated in terms of Path Group and Feynman path integrals.


title: Gravitational self-force on a particle orbiting a Kerr black hole

abstract:
  We present a practical method for calculating the gravitational self-force,
as well as the electromagnetic and scalar self forces, for a particle in a
generic orbit around a Kerr black hole. In particular, we provide the values of
all the regularization parameters needed for implementing the (previously
introduced) {\it mode-sum regularization} method. We also address the
gauge-regularization problem, as well as a few other issues involved in the
calculation of gravitational radiation-reaction in Kerr spacetime.


title: Scaling solutions on a brane

abstract:
  We investigate the dynamics of a flat isotropic brane Universe with
two-component matter source: perfect fluid with the equation of state
$p=(\gamma-1) \rho$ and a scalar field with a power-law potential $V \sim
\phi^{\alpha}$. The index $\alpha$ can be either positive or negative. We
describe solutions for which the scalar field energy density scales as a
power-law of the scale factor (so called scaling solutions). In the nonstandard
brane regime when the brane is driven by energy density square term these
solutions are rather different from their analogs in the standard cosmology. A
particular attention is paid to the inverse square potential. Its dynamical
properties in the nonstandard brane regime are in some sense analogous to those
of the exponential potential in the standard cosmology. Stability analysis of
the scaling solutions are provided. We also describe solutions existing in
regions of the parameter space where the scaling solutions are unstable or do
not exist.


title: Instabilities of Relativistic Stars

abstract:
  Recent developments on the rotational instabilities of relativistic stars are
reviewed. The article provides an account of the theory of stellar
instabilities with emphasis on the rotational ones. Special attention is being
paid to the study of these instabilities in the general relativistic regime.
Issues such as the existence relativistic r-modes, the existence of a
continuous spectrum and the CFS instability of the w-modes are discussed in the
second half of the article.


title:
Construction and enlargement of dilatonic wormholes by impulsive
  radiation

abstract:
  The dynamical behavior of traversable wormholes and black holes under
impulsive radiation is studied in an exactly soluble dilaton gravity model.
Simple solutions are presented where a traversable wormhole is constructed from
a black hole, or the throat of a wormhole is stably enlarged or reduced. These
solutions illustrate the basic operating principles needed to construct similar
analytic solutions in full Einstein gravity.


title:
General solutions for flat Friedmann universe filled by perfect fluid
  and scalar field with exponential potential

abstract:
  We study integrability by quadrature of a spatially flat Friedmann model
containing both a minimally coupled scalar field $\phi$ with an exponential
potential $V(\phi)\sim\exp[-\sqrt{6}\sigma\kappa\phi]$, $\kappa=\sqrt{8\pi
G_N}$, of arbitrary sign and a perfect fluid with barotropic equation of state
$p=(1-h)\rho$. From the mathematical view point the model is pseudo-Euclidean
Toda-like system with 2 degrees of freedom. We apply the methods developed in
our previous papers, based on the Minkowsky-like geometry for 2 characteristic
vectors depending on the parameters $\sigma$ and $h$. In general case the
problem is reduced to integrability of a second order ordinary differential
equation known as the generalized Emden-Fowler equation, which was investigated
by discrete-group methods. We present 4 classes of general solutions for the
parameters obeying the following relations: {\bf A}. $\sigma$ is arbitrary,
$h=0$; {\bf B}. $\sigma=1-h/2$, $0<h<2$; {\bf C1}. $\sigma=1-h/4$, $0<h\leq 2$;
{\bf C2}. $\sigma=|1-h|$, $0<h\leq 2$, $h\neq 1,4/3$. We discuss the properties
of the exact solutions near the initial singularity and at the final stage of
evolution.


title:
Tilted Bianchi Type I Cosmological Models Filled with Disordered
  Radiation in General Relativity Revisited

abstract:
  Tilted Bianchi type I cosmological models filled with disordered radiation in
presence of a bulk viscous fluid and heat flow are investigated. The
coefficient of bulk viscosity is assumed to be a power function of mass
density. Some physical and geometric properties of the models are also
discussed.


title:
Bianchi Type I Anisotropic Magnetized Cosmological Models with Varying
  $\Lambda$

abstract:
  Bianchi type I magnetized cosmological models in the presence of a bulk
viscous fluid are investigated. The source of the magnetic field is due to an
electric current produced along x-axis. The distribution consists of an
electrically neutral viscous fluid with an infinite electrical conductivity.
The coefficient of bulk viscosity is assumed to be a power function of mass
density. The cosmological constant $\Lambda$ is found to be positive and is a
decreasing function of time which is supported by results from recent
supernovae observations. The behaviour of the models in presence and absence of
magnetic field are also discussed.


title: Area expectation values in quantum area Regge calculus

abstract:
  The Regge calculus generalised to independent area tensor variables is
considered. The continuous time limit is found and formal Feynman path integral
measure corresponding to the canonical quantisation is written out. The quantum
measure in the completely discrete theory is found which possesses the property
to lead to the Feynman path integral in the continuous time limit whatever
coordinate is chosen as time. This measure can be well defined by passing to
the integration over imaginary field variables (area tensors). Averaging with
the help of this measure gives finite expectation values for areas.


title:
The Principles of Self Creation Cosmology and its Comparison with
  General Relativity

abstract:
  There are, at present, several gravitational and cosmological anomalies; the
dark energy problem, the lambda problem, accelerating cosmological expansion,
the anomalous Pioneer spacecraft acceleration, a spin-up of the Earth and an
apparent variation of G observed from analysis of the evolution of planetary
longitudes. These conundrums may be resolved in the theory of Self Creation
Cosmology, in which the Principle of Mutual Interaction subsumes both Mach's
Principle and the Local Conservation of Energy. The theory is conformally
equivalent to General Relativity in vacuo with the consequence that predictions
of the theory are identical with General Relativity in the standard solar
system experiments. Other observable local and cosmological consequences offer
an explanation for the anomalies above. The SCC universe expands linearly in
its Einstein Frame and it is static in its Jordan Frame; hence, as there are no
density, smoothness or horizon problems, there is no requirement for Inflation.
The theory determines the total density parameter to be one third, and the cold
dark matter density parameter to be two ninths, yet in the Jordan frame the
universe is similar to Einstein's original static cylindrical model and
spatially flat. Therefore there is no need for a 'Dark Energy' hypothesis. As
the field equations determine the false vacuum energy density to be a specific,
and feasibly small, value there is no 'Lambda Problem'. Finally certain
observations in SCC would detect cosmic acceleration.


title: Possible wormholes in a brane world

abstract:
  The condition R=0, where R is the four-dimensional scalar curvature, is used
for obtaining a large class (with an arbitrary function of r) of static,
spherically symmetric Lorentzian wormhole metrics. The wormholes are globally
regular and traversable, can have throats of arbitrary size and can be both
symmetric and asymmetric. These metrics may be treated as possible wormhole
solutions in a brane world since they satisfy the vacuum Einstein equations on
the brane where effective stress-energy is induced by interaction with the bulk
gravitational field. Some particular examples are discussed.


title:
Multi-graviton theory, a latticized dimension, and the cosmological
  constant

abstract:
  Beginning with the Pauli-Fierz theory, we construct a model for
multi-graviton theory. Couplings between gravitons belonging to
nearest-neighbor ``theory spaces'' lead to a discrete mass spectrum. Our model
coincides with the Kaluza-Klein theory whose fifth dimension is latticized.
  We evaluate one-loop vacuum energy in models with a circular latticized extra
dimension as well as with compact continuous dimensions. We find that the
vacuum energy can take a positive value, if the dimension of the continuous
space time is $6, 10,...$. Moreover, since the amount of the vacuum energy can
be an arbitrary small value according to the choice of parameters in the model,
our models is useful to explain the small positive dark energy in the present
universe.


title: Braneworld reheating in the bulk inflaton model

abstract:
  In the context of the braneworld inflation driven by a bulk scalar field, we
study the energy dissipation from the bulk scalar field into the matter on the
brane in order to understand the reheating after inflation. Deriving the
late-time behavior of the bulk field with dissipation by using the Green's
function method, we give a rigorous justification of the statement that the
standard reheating process is reproduced in this bulk inflaton model as long as
the Hubble parameter on the brane and the mass of the bulk scalar field are
much smaller than the 5-dimensional inverse curvature scale. Our result
supports the idea that the brane inflation model caused by a bulk scalar field
is expected to be a viable alternative scenario of the early universe.


title: Conservation of Energy in Black Holes and in Cosmology

abstract:
  We first review the various definition of the total energy in the
gravitational system. The naive definition has some defects, and we review how
to modify the definition of the total energy. Then we explicitly demonstrate
how to calculate the total energy of the system. Our example is the total
energy of a black hole in the expanding closed de Sitter universe in (2+1)
dimension. In general, we find that the contribution to the total energy comes
only from the singularity. Then we can calculate the total energy by evaluating
the contribution around the singularity.


title: Spinor field with induced nonlinearity in a Bianchi type-I Universe

abstract:
  Self-consistent solutions to the spinor, scalar and BI gravitational field
equations are obtained. The problems of initial singularity and asymptotically
isotropization process of the initially anisotropic space-time are studied. It
is also shown that the introduction of the Cosmological constant
($\Lambda$-term) in the Lagrangian generates oscillations of the BI model,
which is not the case in absence of $\Lambda$ term.


title:
The expectation value of the metric operator with respect to Gaussian
  weave state in loop quantum gravity

abstract:
  Loop Quantum Gravity is the major candidate of quantum gravity. It is
interesting to consider its continuum limit, which corresponds to the classical
limit. We consider the Gaussian weave state, which describes a semi-classical
picture. We calculate the expectation value of metric operator with respect to
this state.


title: An Eternal Time Machine in 2+1 Dimensional anti-de Sitter Space

abstract:
  2+1 dimensional anti-de Sitter space has been the subject of much recent
investigation. Studies of the behaviour of point particles in this space have
given us a greater understanding of the BTZ black hole solutions produced by
topological identification of adS isometries. In this paper, we present a new
configuration of two orbiting massive point particles that leads to an
``eternal'' time machine, where closed timelike curves fill the entire space.
In contrast to previous solutions, this configuration has no event or
chronology horizons. Another interesting feature is that there is no lower
bound on the relative velocities of the point masses used to construct the time
machine; as long as the particles exceed a certain mass threshold, an eternal
time machine will be produced.


title:
Energy density in general relativity: a possible role for cosmological
  constant

abstract:
  We consider a static spherically symmetric charged anisotropic fluid source
of finite physical radius (\sim 10^{-16} cm) by introducing a scalar variable
\Lambda dependent on the radial coordinate r under general relativity. From the
solution sets a possible role of the cosmological constant is investigated
which indicates the dependency of energy density of electron on the variable
\Lambda.


title:
Classical Electron Model with Negative Energy Density in Einstein-Cartan
  Theory of Gravitation

abstract:
  Experimental result regarding the maximum limit of the radius of the electron
\sim 10^{-16} cm and a few of the theoretical works suggest that the
gravitational mass which is a priori a positive quantity in Newtonian mechanics
may become negative in general theory of relativity. It is argued that such a
negative gravitational mass and hence negative energy density also can be
obtained with a better physical interpretation in the framework of
Einstein-Cartan theory.