title: Casimir energy, the cosmological constant and massive gravitons

abstract:
  The cosmological constant appearing in the Wheeler-De Witt equation is
considered as an eigenvalue of the associated Sturm-Liouville problem. A
variational approach with Gaussian trial wave functionals is used as a method
to study such a problem. We approximate the equation to one loop in a
Schwarzschild background and a zeta function regularization is involved to
handle with divergences. The regularization is closely related to the
subtraction procedure appearing in the computation of Casimir energy in a
curved background. A renormalization procedure is introduced to remove the
infinities together with a renormalization group equation. The case of massive
gravitons is discussed.


title:
The Galilean group and the transformation of shadows in special
  relativity

abstract:
  This paper has been withdrawn by the author, since it is now a part of
"Classical aspects of lightlike dimensional reduction"
Class.Quant.Grav.23:7085-7110, 2006, gr-qc/0610011


title: Classification of Higher Dimensional Spacetimes

abstract:
  We algebraically classify some higher dimensional spacetimes, including a
number of vacuum solutions of the Einstein field equations which can represent
higher dimensional black holes. We discuss some consequences of this work.


title: The Prevention of Singularities Inside Black Holes

abstract:
  In this paper the currently held view that the endpoint of gravitational
collapse is a singularity is refuted. A quantum mechanical calculation is done
showing that spin 0 and spin 1/2 particles inside a black hole's schwarzschild
radius aren't confined to an infinitesimal point but form bound state orbits.
As with the case of electric collapse, if an electron cannot spiral into a
nucleus, then neither does this happen in plasma consisting of many electrons
and nuclei. Showing that after undergoing gravitational collapse, like plasma,
matter will not contract to an infinitesimal point. That quantum effects
prevent singularity formation.


title:
Quasinormal modes of plane-symmetric anti-de Sitter black holes: a
  complete analysis of the gravitational perturbations

abstract:
  We study in detail the quasinormal modes of linear gravitational
perturbations of plane-symmetric anti-de Sitter black holes. The wave equations
are obtained by means of the Newman-Penrose formalism and the Chandrasekhar
transformation theory. We show that oscillatory modes decay exponentially with
time such that these black holes are stable against gravitational
perturbations. Our numerical results show that in the large (small) black hole
regime the frequencies of the ordinary quasinormal modes are proportional to
the horizon radius $r_{+}$ (wave number $k$). The frequency of the purely
damped mode is very close to the algebraically special frequency in the small
horizon limit, and goes as $ik^{2}/3r_{+}$ in the opposite limit. This result
is confirmed by an analytical method based on the power series expansion of the
frequency in terms of the horizon radius. The same procedure applied to the
Schwarzschild anti-de Sitter spacetime proves that the purely damped frequency
goes as $i(l-1)(l+2)/3r_{+}$, where $l$ is the quantum number characterizing
the angular distribution. Finally, we study the limit of high overtones and
find that the frequencies become evenly spaced in this regime. The spacing of
the frequency per unit horizon radius seems to be a universal quantity, in the
sense that it is independent of the wave number, perturbation parity and black
hole size.


title:
Correlation analysis of stochastic gravitational wave background around
  0.1-1Hz

abstract:
  We discuss prospects for direct measurement of stochastic gravitational wave
background around 0.1-1Hz with future space missions. It is assumed to use
correlation analysis technique with the optimal TDI variables for two sets of
LISA-type interferometers. The signal to noise for detection of the background
and the estimation errors for its basic parameters (amplitude, spectral index)
are evaluated for proposed missions.


title: Post-Einsteinian tests of gravitation

abstract:
  Einstein gravitation theory can be extended by preserving its geometrical
nature but changing the relation between curvature and energy-momentum tensors.
This change accounts for radiative corrections, replacing the Newton
gravitation constant by two running couplings which depend on scale and differ
in the two sectors of traceless and traced tensors. The metric and curvature
tensors in the field of the Sun, which were obtained in previous papers within
a linearized approximation, are then calculated without this restriction.
Modifications of gravitational effects on geodesics are then studied, allowing
one to explore phenomenological consequences of extensions lying in the
vicinity of general relativity. Some of these extended theories are able to
account for the Pioneer anomaly while remaining compatible with tests involving
the motion of planets. The PPN Ansatz corresponds to peculiar extensions of
general relativity which do not have the ability to meet this compatibility
challenge.


title:
Linear stability of Einstein-Gauss-Bonnet static spacetimes. Part II:
  vector and scalar perturbations

abstract:
  We study the stability under linear perturbations of a class of static
solutions of Einstein-Gauss-Bonnet gravity in $D=n+2$ dimensions with spatial
slices of the form $\Sigma_{\k}^n \times {\mathbb R}^+$, $\Sigma_{\k}^n$ an
$n-$manifold of constant curvature $\k$. Linear perturbations for this class of
space-times can be generally classified into tensor, vector and scalar types.
In a previous paper, tensor perturbations were analyzed. In this paper we study
vector and scalar perturbations. We show that vector perturbations can be
analyzed in general using an S-deformation approach and do not introduce
instabilities. On the other hand, we show by analyzing an explicit example
that, contrary to what happens in Einstein gravity, scalar perturbations may
lead to instabilities in black holes with spherical horizons when the
Gauss-Bonnet string corrections are taken into account.


title:
Effects of Lovelock terms on the final fate of gravitational collapse:
  analysis in dimensionally continued gravity

abstract:
  We find an exact solution in dimensionally continued gravity in arbitrary
dimensions which describes the gravitational collapse of a null dust fluid.
Considering the situation that a null dust fluid injects into the initially
anti-de Sitter spacetime, we show that a naked singularity can be formed. In
even dimensions, a massless ingoing null naked singularity emerges. In odd
dimensions, meanwhile, a massive timelike naked singularity forms. These naked
singularities can be globally naked if the ingoing null dust fluid is switched
off at a finite time; the resulting spacetime is static and asymptotically
anti-de Sitter spacetime. The curvature strength of the massive timelike naked
singularity in odd dimensions is independent of the spacetime dimensions or the
power of the mass function. This is a characteristic feature in Lovelock
gravity.


title: Solutions for Klein-Gordon equation in Randall-Sundrum-Kerr scenario

abstract:
  We study the scalar perturbations of rotating black holes in framework of
extra dimensions type Randall-Sundrum(RS).


title: The Confrontation between General Relativity and Experiment

abstract:
  The status of experimental tests of general relativity and of theoretical
frameworks for analysing them is reviewed. Einstein's equivalence principle
(EEP) is well supported by experiments such as the Eotvos experiment, tests of
special relativity, and the gravitational redshift experiment. Future tests of
EEP and of the inverse square law are searching for new interactions arising
from unification or quantum gravity. Tests of general relativity at the
post-Newtonian level have reached high precision, including the light
deflection, the Shapiro time delay, the perihelion advance of Mercury, and the
Nordtvedt effect in lunar motion. Gravitational-wave damping has been detected
in an amount that agrees with general relativity to better than half a percent
using the Hulse-Taylor binary pulsar, and other binary pulsar systems have
yielded other tests, especially of strong-field effects. When direct
observation of gravitational radiation from astrophysical sources begins, new
tests of general relativity will be possible.


title: New anisotropic models from isotropic solutions

abstract:
  We establish an algorithm that produces a new solution to the Einstein field
equations, with an anisotropic matter distribution, from a given seed isotropic
solution. The new solution is expressed in terms of integrals of known
functions, and the integration can be completed in principle. The applicability
of this technique is demonstrated by generating anisotropic isothermal spheres
and anisotropic constant density Schwarzschild spheres. Both of these solutions
are expressed in closed form in terms of elementary functions, and this
facilitates physical analysis.


title:
Second Order Post Newtonian Equations of Light Propagation in Multiple
  Systems

abstract:
  The first order post Newtonian scheme in multiple systems presented by
Damour-Soffel-Xu is extended to the second order one for light propagation
without changing the advantage of the scheme on the linear partial differential
equations of potential and vector potential. The spatial components of the
metric tensor are extended to the second order level both in the global
coordinates ($q_{ij}/c^4$ term) and in a local coordinates ($Q_{ab}/c^4$ term).
The equations of $q_{ij}$ (or $Q_{ab}$) are deduced from Einstein field
equations. The linear relationship between $q_{ij}$ and $Q_{ab}$ are presented
also. The 2PN equations of light ray based on the extended scheme are deduced
by means of the iterative method. We also use parametrized second post
Newtonian metric tensor to substitute into the null geodetic equations to
obtain the parametrized second order equations of light ray which might be
useful in the observation and measurement in the future space missions.


title: Maxwell-type behaviour from a geometrical structure

abstract:
  We study which geometric structure can be constructed from the vierbein
(frame/coframe) variables and which field models can be related to this
geometry. The coframe field models, alternative to GR, are known as viable
models for gravity, since they have the Schwarzschild solution. Since the local
Lorentz invariance is violated, a physical interpretation of additional six
degrees of freedom is required. The geometry of such models is usually given by
two different connections -- the Levi-Civita symmetric and metric-compatible
connection and the Weitzenbock flat connection. We construct a general family
of linear connections of the same type, which includes two connections above as
special limiting cases. We show that for dynamical propagation of six
additional degrees of freedom it is necessary for the gauge field of
infinitesimal transformations (antisymmetric tensor) to satisfy the system of
two first order differential equations. This system is similar to the vacuum
Maxwell system and even coincides with it on a flat manifold. The corresponding
``Maxwell-compatible connections'' are derived. Alternatively, we derive the
same Maxwell-type system as a symmetry conditions of the viable models
Lagrangian. Consequently we derive a nontrivial decomposition of the coframe
field to the pure metric field plus a dynamical field of infinitesimal Lorentz
rotations. Exact spherical symmetric solution for our dynamical field is
derived. It is bounded near the Schwarzschild radius. Further off, the solution
is close to the Coulomb field.


title: Metric of a tidally perturbed spinning black hole

abstract:
  We explicitly construct the metric of a Kerr black hole that is tidally
perturbed by the external universe in the slow-motion approximation. This
approximation assumes that the external universe changes slowly relative to the
rotation rate of the hole, thus allowing the parameterization of the
Newman-Penrose scalar $\psi_0$ by time-dependent electric and magnetic tidal
tensors. This approximation, however, does not constrain how big the spin of
the background hole can be and, in principle, the perturbed metric can model
rapidly spinning holes. We first generate a potential by acting with a
differential operator on $\psi_0$. From this potential we arrive at the metric
perturbation by use of the Chrzanowski procedure in the ingoing radiation
gauge. We provide explicit analytic formulae for this metric perturbation in
spherical Kerr-Schild coordinates, where the perturbation is finite at the
horizon. This perturbation is parametrized by the mass and Kerr spin parameter
of the background hole together with the electric and magnetic tidal tensors
that describe the time evolution of the perturbation produced by the external
universe. In order to take the metric accurate far away from the hole, these
tidal tensors should be determined by asymptotically matching this metric to
another one valid far from the hole. The tidally perturbed metric constructed
here could be useful in initial data constructions to describe the metric near
the horizons of a binary system of spinning holes. This perturbed metric could
also be used to construct waveforms and study the absorption of mass and
angular momentum by a Kerr black hole when external processes generate
gravitational radiation.


title:
Gravimagnetism, Causality, and Aberration of Gravity in the
  Gravitational Light-Ray Deflection Experiments

abstract:
  Experimental verification of the existence of gravimagnetic fields generated
by currents of matter is important for a complete understanding and formulation
of gravitational physics. Although the rotational `intrinsic' gravimagnetic
field has been extensively studied and is now being measured by the Gravity
Probe B, the `extrinsic' gravimagnetic field generated by the translational
current of matter is less well studied. The present paper uses the
post-Newtonian parametrized Einstein and light geodesics equations to show that
the `extrinsic' gravimagnetic field generated by the translational current of
matter can be measured by observing the relativistic time delay and/or light
deflection caused by the moving mass. We prove that the `extrinsic'
gravimagnetic field is generated by the relativistic effect of the aberration
of the gravity force caused by the Lorentz transformation of the metric tensor
and the Levi-Civita connection. We show that the Lorentz transformation of the
gravity field variables is equivalent to the technique of the retarded
Lienard-Wiechert gravitational potentials predicting that a light particle is
deflected by gravitational field of a moving body from its retarded position so
that both general-relativistic phenomena -- the aberration and the retardation
of gravity -- are tightly connected and observing the aberration of gravity
proves that gravity has a causal nature. We explain in this framework the 2002
deflection experiment of a quasar by Jupiter where the aberration of gravity
from its orbital motion was measured with accuracy 20%. We describe a theory of
VLBI experiment to measure the gravitational deflection of radio waves from a
quasar by the Sun, as viewed by a moving observer from the geocentric frame, to
improve the measurement accuracy of the aberration of gravity to a few percent.


title: Long-wavelength metric backreactions in slow-roll inflation

abstract:
  We examine the importance of second order corrections to linearized
cosmological perturbation theory in an inflationary background, taken to be a
spatially flat FRW spacetime. The full second order problem is solved in the
sense that we evaluate the effect of the superhorizon second order corrections
on the inhomogeneous and homogeneous modes of the linearized flucuations. These
second order corrections enter in the form of a {\it cumulative} contribution
from {\it all} of their Fourier modes. In order to quantify their physical
significance we study their effective equation of state by looking at the
perturbed energy density and isotropic pressure to second order. We define the
energy density (isotropic pressure) in terms of the (averaged) eigenvalues
associated with timelike (spacelike) eigenvectors of a total stress energy for
the metric and matter fluctuations. Our work suggests that that for many
parameters of slow-roll inflation, the second order contributions to these
energy density and pressures may dominate over the first order effects for the
case of super-Hubble evolution. These results hold in our choice of first and
second order coordinate conditions however we also argue that other
`reasonable` coordinate conditions do not alter the relative importance of the
second order terms. We find that these second order contributions approximately
take the form of a cosmological constant in this coordinate gauge, as found by
others using effective methods.


title:
Problems with wormholes which involve arbitrarily small amounts of
  exotic matter

abstract:
  A quantum inequality bound on the expectation value of the null-contracted
stress tensor in an arbitrary Hadamard state is used to obtain constraints on
the geometries of traversable wormholes. Particular attention is given to the
wormhole models of Visser, Kar, and Dadhich (VKD) and to those of Kuhfittig.
These are models which use arbitrarily small amounts of exotic matter for
wormhole maintenance. It is shown that macroscopic VKD models are either ruled
out or severely constrained, while a recent model of Kuhfittig is shown to be,
in fact, non-traversable.


title:
Towards a general solution of the Hamiltonian constraints of General
  Relativity

abstract:
  The present work has a double aim. On the one hand we call attention on the
relationship existing between the Ashtekar formalism and other
gauge-theoretical approaches to gravity, in particular the Poincar\'e Gauge
Theory. On the other hand we study two kinds of solutions for the constraints
of General Relativity, consisting of two mutually independent parts, namely a
general three-metric-dependent contribution to the extrinsic curvature $K_{ab}$
in terms of the Cotton-York tensor, and besides it further metric independent
contributions, which we analyze in particular in the presence of isotropic
three-metrics.


title: The Pioneer Anomaly and Its Implications

abstract:
  The Pioneer 10/11 spacecraft yielded the most precise navigation in deep
space to date. However, their radio-metric tracking data has consistently
indicated the presence of a small, anomalous, Doppler frequency drift. The
drift is a blue-shift, uniformly changing with a rate of ~6 x 10^{-9} Hz/s and
can be interpreted as a constant sunward acceleration of each particular
spacecraft of a_P =(8.74 +/- 1.33) x 10^{-10} m/s^2. The nature of this anomaly
remains unexplained. Here we summarize our current knowledge of the discovered
effect and review some of the mechanisms proposed for its explanation.
Currently we are preparing for the analysis of the entire set of the available
Pioneer 10/11 Doppler data which may shed a new light on the origin of the
anomaly. We present a preliminary assessment of such an intriguing possibility.


title:
Conserved gravitational charges, locality and the holographic Weyl
  anomaly - a fresh viewpoint

abstract:
  Since the proposal of the AdS/CFT correspondence, made by Maldacena and
Witten, there has been some controversy about the definition of conserved
Noether charges associated to asymptotic isometries in asymptotically AdS
spacetimes, namely, whether they form an anomalous (i.e., a nontrivial central
extension) representation of the Lie algebra of the conformal group in odd bulk
dimensions or not. In the present work, we shall review the derivation of these
charges by using covariant phase space techniques, emphasizing the principle of
locality underlying it. We shall also comment on how these issues manifest
themselves in the quantum setting.


title: Production and decay of evolving horizons

abstract:
  We consider a simple physical model for an evolving horizon that is strongly
interacting with its environment, exchanging arbitrarily large quantities of
matter with its environment in the form of both infalling material and outgoing
Hawking radiation. We permit fluxes of both lightlike and timelike particles to
cross the horizon, and ask how the horizon grows and shrinks in response to
such flows. We place a premium on providing a clear and straightforward
exposition with simple formulae.
  To be able to handle such a highly dynamical situation in a simple manner we
make one significant physical restriction, that of spherical symmetry, and two
technical mathematical restrictions: (1) We choose to slice the spacetime in
such a way that the space-time foliations (and hence the horizons) are always
spherically symmetric. (2) Furthermore we adopt Painleve-Gullstrand coordinates
(which are well suited to the problem because they are nonsingular at the
horizon) in order to simplify the relevant calculations.
  We find particularly simple forms for surface gravity, and for the first and
second law of black hole thermodynamics, in this general evolving horizon
situation. Furthermore we relate our results to Hawking's apparent horizon,
Ashtekar et al's isolated and dynamical horizons, and Hayward's trapping
horizons. The evolving black hole model discussed here will be of interest,
both from an astrophysical viewpoint in terms of discussing growing black
holes, and from a purely theoretical viewpoint in discussing black hole
evaporation via Hawking radiation.


title:
General Relativistic Theory of Light Propagation in the Field of
  Radiative Gravitational Multipoles

abstract:
  The extremely high precision of current astronomical observations demands a
much better theoretical treatment of relativistic effects in the propagation of
electromagnetic signals through variable gravitational fields of isolated
astronomical systems emitting gravitational waves. This paper presents a
consistent approach giving a complete and exhaustive solution of this problem
in the first post-Minkowskian approximation of general relativity.


title:
Metrically Stationary, Axially Symmetric, Isolated Systems in
  Quasi-Metric Gravity

abstract:
  The gravitational field exterior respectively interior to an axially
symmetric, metrically stationary, isolated spinning source made of perfect
fluid is examined within the quasi-metric framework. (A metrically stationary
system is defined as a system which is stationary except for the direct effects
of the global cosmic expansion on the space-time geometry.) Field equations are
set up and an attempt is made to find an approximate series solution for the
exterior part. However, the result is that no stationary solution corresponding
to a spinning source can exist when considering terms beyond a certain order in
small quantities. That is, except for metrically static systems, axially
symmetric systems must necessarily be non-stationary in quasi-metric gravity.
However, sufficiently weak, axially symmetric gravitational fields associated
with slowly rotating sources, may still be considered as stationary as an
excellent approximation.
  Thus a truncated, approximately stationary solution is found for the exterior
field. To lowest order in small quantities, the gravito-magnetic part of the
found metric family corresponds with the Kerr metric in the metric
approximation. On the other hand, the gravito-electric part of the found metric
family also includes a tidal term characterized by the free quadrupole-moment
parameter $J_2$ describing the effect of source deformation due to the
rotation. This term has no counterpart in the Kerr metric. Finally, the
geodetic effect for a gyroscope in orbit is calculated. There is a correction
term, unfortunately barely too small to be detectable by Gravity Probe B, to
the standard expression.


title: Dual Nature of the Ricci Scalar and its Certain Consequences

abstract:
  Ricci scalar is the key ingredient of non-Newtonian theory of gravity, where
space-time geometry has a crucial role. Normally, it is supposed to be a
geometrical field, but interestingly it also behaves like a physical field.
Thus it plays dual role in the arena of gravitation. This article is an
overview of the work related to dual roles of the Ricci scalar. A scalar is a
mathematical concept representing a spinless particle.Here, particle concept,
manifesting the physical aspect of the Ricci scalar, is termed as riccion.It is
a scalar particle with (mass)$^2$ inversely proportional to the gravitational
constant. Many intereseting consequences of dual role of the Ricci scalar are
discussed here. It causes inflationary scenario in the early universe without
taking another scalar like ``inflaton''. It is found that a riccion behaves
like an instanton also. This feature inspires``primordial inflation''.It is
interesting to see that a riccion, obtained from higher-dimensional space-time,
decouples into fermion and anti-fermion pair, if parity is violated. One-loop
renormalization of riccion indicates fractal geometry at high
energy.Homogeneous and inhomogeneous models of the early universe are derived
using dual role of the Ricci scalar. Production of spinless and spin-1/2
particles, due to riccion coupling, is discussed here. Contribution of riccion
to the cosmic dark energy is obtained here through one-loop renormalization and
it is shown that dark energy decays to dark matter during expansion of the
universe. It inspires a new cosmological scenario consistent with observational
evidences.


title:
On the Gravitational Collapse of a Gas Cloud in Presence of Bulk
  Viscosity

abstract:
  We analyze the effects induced by the bulk viscosity on the dynamics
associated to the extreme gravitational collapse. Aim of the work is to
investigate whether the presence of viscous corrections to the evolution of a
collapsing gas cloud influence the fragmentation process. To this end we study
the dynamics of a uniform and spherically symmetric cloud with corrections due
to the negative pressure contribution associated to the bulk viscosity
phenomenology. Within the framework of a Newtonian approach (whose range of
validity is outlined), we extend to the viscous case either the Lagrangian,
either the Eulerian motion of the system and we treat the asymptotic evolution
in correspondence to a viscosity coefficient of the form $\zeta=\zeta_0
\rho^{nu}$ ($\rho$ being the cloud density and $\zeta_0=const.$). We show how,
in the adiabatic-like behavior of the gas (i.e. when the politropic index takes
values $4/3<\gamma\leq5/3$), density contrasts acquire, asymptotically, a
vanishing behavior which prevents the formation of sub-structures. We can
conclude that in the adiabatic-like collapse the top down mechanism of
structures formation is suppressed as soon as enough strong viscous effects are
taken into account. Such a feature is not present in the isothermal-like (i.e.
$1\leq\gamma<4/3$) collapse because the sub-structures formation is yet present
and outlines the same behavior as in the non-viscous case. We emphasize that in
the adiabatic-like collapse the bulk viscosity is also responsible for the
appearance of a threshold scale beyond which perturbations begin to increase.


title: A Solution to the Cosmological Constant Problem

abstract:
  According to general relativity, the present analysis shows on geometrical
grounds that the cosmological constant problem is an artifact due to the
unfounded link of this fundamental constant to vacuum energy density of quantum
fluctuations.


title: Gauge theories of gravity: the nonlinear framework

abstract:
  Nonlinear realizations of spacetime groups are presented as a versatile
mathematical tool providing a common foundation for quite different
formulations of gauge theories of gravity. We apply nonlinear realizations in
particular to both the Poincar\'e and the affine group in order to develop
Poincar\'e gauge theory (PGT) and metric-affine gravity (MAG) respectively.
Regarding PGT, two alternative nonlinear treatments of the Poincar\'e group are
developed, one of them being suitable to deal with the Lagrangian and the other
one with the Hamiltonian version of the same gauge theory. We argue that our
Hamiltonian approach to PGT is closely related to Ashtekar's approach to
gravity. On the other hand, a brief survey on MAG clarifies the role played by
the metric--affine metric tensor as a Goldsone field. All gravitational
quantities in fact --the metric as much as the coframes and connections-- are
shown to acquire a simple gauge--theoretical interpretation in the nonlinear
framework.


title: Einstein And The Evolving Universe

abstract:
  A panoramic view, preceded by a short background of Newtonian mechanics and
Maxwellian electrodynamics, is offered on the extent of how Einstein's
space-time geometry, believed to be central to an understanding of the
structure of the universe, is overshadowed by several hitherto unheard of
features like dark matter and dark energy, that seem to be necessary, but by no
means sufficient, for a more complete picture.


title: A new track for unifying general relativity with quantum field theories

abstract:
  In the perspective of unifying quantum field theories with general
relativity,the equations of the internal dynamics of the vacuum and mass
structures of a set of interacting particles are proved to be in one-to-one
correspondence with the equations of general relativity. This leads us to
envisage a high value for the cosmological constant,as expected theoretically.


title: Gravitational energy

abstract:
  Observers at rest in a stationary spacetime flat at infinity can measure
small amounts of rest-mass+internal energies+kinetic energies+pressure energy
in a small volume of fluid attached to a local inertial frame. The sum of these
small amounts is the total "matter energy" for those observers. The total
mass-energy minus the matter energy is the binding gravitational energy.
  Misner, Thorne and Wheeler evaluated the gravitational energy of a
spherically symmetric static spacetime. Here we show how to calculate
gravitational energy in any static and stationary spacetime for isolated
sources with a set of observers at rest.
  The result of MTW is recovered and we find that electromagnetic and
gravitational 3-covariant energy densities in conformastatic spacetimes are of
opposite signs. Various examples suggest that gravitational energy is negative
in spacetimes with special symmetries or when the energy-momentum tensor
satisfies usual energy conditions.


title:
Alternative Methods of Describing Structure Formation in the
  Lemaitre-Tolman Model

abstract:
  We describe several new ways of specifying the behaviour of Lemaitre-Tolman
(LT) models, in each case presenting the method for obtaining the LT arbitrary
functions from the given data, and the conditions for existence of such
solutions. In addition to our previously considered `boundary conditions', the
new ones include: a simultaneous big bang, a homogeneous density or velocity
distribution in the asymptotic future, a simultaneous big crunch, a
simultaneous time of maximal expansion, a chosen density or velocity
distribution in the asymptotic future, only growing or only decaying
fluctuations. Since these conditions are combined in pairs to specify a
particular model, this considerably increases the possible ways of designing LT
models with desired properties.


title:
Charged particles with spin in a gravitational wave and a uniform
  magnetic field

abstract:
  We study the motion of a pseudo-classical charged particle with spin in the
space-time of a gravitational pp wave in the presence of a uniform magnetic
field.


title:
Curvature tensors on distorted Killing horizons and their algebraic
  classification

abstract:
  We consider generic static spacetimes with Killing horizons and study
properties of curvature tensors in the horizon limit. It is determined that the
Weyl, Ricci, Riemann and Einstein tensors are algebraically special and
mutually aligned on the horizon. It is also pointed out that results obtained
in the tetrad adjusted to a static observer in general differ from those
obtained in a free-falling frame. This is connected to the fact that a static
observer becomes null on the horizon.
  It is also shown that finiteness of the Kretschmann scalar on the horizon is
compatible with the divergence of the Weyl component $\Psi_{3}$ or $\Psi_{4}$
in the freely falling frame. Furthermore finiteness of $\Psi_{4}$ is compatible
with divergence of curvature invariants constructed from second derivatives of
the Riemann tensor.
  We call the objects with finite Krestschmann scalar but infinite $\Psi_{4}$
``truly naked black holes''. In the (ultra)extremal versions of these objects
the structure of the Einstein tensor on the horizon changes due to extra terms
as compared to the usual horizons, the null energy condition being violated at
some portions of the horizon surface. The demand to rule out such divergencies
leads to the constancy of the factor that governs the leading term in the
asymptotics of the lapse function and in this sense represents a formal analog
of the zeroth law of mechanics of non-extremal black holes. In doing so, all
extra terms in the Einstein tensor automatically vanish.


title: A radiometer for stochastic gravitational waves

abstract:
  The LIGO Scientific Collaboration recently reported a new upper limit on an
isotropic stochastic background of gravitational waves obtained based on the
data from the 3rd LIGO science Run (S3). Now I present a new method for
obtaining directional upper limits that the LIGO Scientific Collaboration
intends to use for future LIGO science runs and that essentially implements a
gravitational wave radiometer.


title:
Beyond partial differential equations: A course on linear and
  quasi-linear abstract hyperbolic evolution equations

abstract:
  This course introduces the use of semigroup methods in the solution of linear
and nonlinear (quasi-linear) hyperbolic partial differential equations, with
particular application to wave equations and Hermitian hyperbolic systems.
Throughout the course applications to problems from current relativistic
(hyperbolic) physics are provided, which display the potential of semigroup
methods in the solution of current research problems in physics.


title: Intrinsic momentum in Poincare gauge theory

abstract:
  While it is generally accepted, in the framework of Poincare gauge theory,
that the Lorentz connection couples minimally to spinor fields, there is no
general agreement on the coupling of the translational gauge field to fermions.
We will show that the assumption that spinors carry a full Poincare
representation leads to inconsistencies, whose origins will be traced back by
considering the Poincare group both as the contraction of the de Sitter group,
and as a subgroup of the conformal group. As a result, the translational fields
do not minimally couple to fermions, and consequently, fermions do not possess
an intrinsic momentum.


title:
Potential symmetry and invariant solutions of Fokker-Planck equation in
  cylindrical coordinates related to magnetic field diffusion in
  magnetohydrodynamics including the Hall current

abstract:
  Lie groups involving potential symmetries are applied in connection with the
system of magnetohydrodynamic equations for incompressible matter with Ohm's
law for finite resistivity and Hall current in cylindrical geometry. Some
simplifications allow to obtain a Fokker-Planck type equation. Invariant
solutions are obtained involving the effects of time-dependent flow and the
Hall-current. Some interesting side results of this approach are new exact
solutions that do not seem to have been reported in the literature.


title: Topology, Mass and Casimir energy

abstract:
  The vacuum expectation value of the stress energy tensor for a massive scalar
field with arbitrary coupling in flat spaces with non-trivial topology is
discussed. We calculate the Casimir energy in these spaces employing the
recently proposed {\it optical approach} based on closed classical paths. The
evaluation of the Casimir energy consists in an expansion in terms of the
lengths of these paths. We will show how different paths with corresponding
weight factors contribute in the calculation. The optical approach is also used
to find the mass and temperature dependence of the Casimir energy in a cavity
and it is shown that the massive fields cannot be neglected in high and low
temperature regimes. The same approach is applied to twisted as well as spinor
fields and the results are compared with those in the literature.


title: Accelerated black holes in an anti-de Sitter universe

abstract:
  The C-metric is one of few known exact solutions of Einstein's field
equations which describes the gravitational field of moving sources. For a
vanishing or positive cosmological constant, the C-metric represents two
accelerated black holes in asymptotically flat or de Sitter spacetime. For a
negative cosmological constant the structure of the spacetime is more
complicated. Depending on the value of the acceleration, it can represent one
black hole or a sequence of pairs of accelerated black holes in the spacetime
with an anti-de Sitter-like infinity. The global structure of this spacetime is
analyzed and compared with an empty anti-de Sitter universe. It is illustrated
by 3D conformal-like diagrams.


title:
Aspects of the long time evolution in General Relativity and
  Geometrizations of Three-Manifolds

abstract:
  This paper has been withdrawn. (Reason) Its contents have been entirely
superseded by the contents of the articles arXiv:0809.3444 and arXiv:0705.3070.
There is no profitable reason to keep it alive. No material on it is however
wrong.


title: Improved WKB analysis of Slow-Roll Inflation

abstract:
  We extend the WKB method for the computation of cosmological perturbations
during inflation beyond leading order and provide the power spectra of scalar
and tensor perturbations to second order in the slow-roll parameters. Our
method does not require that the slow-roll parameters be constant. Although
leading and next-to-leading results in the slow-roll parameters depend on the
approximation technique used in the computation, we find that the inflationary
theoretical predictions obtained may reach the accuracy required by planned
observations. In two technical appendices, we compare our techniques and
results with previous findings.


title:
Quantum effects, soft singularities and the fate of the universe in a
  braneworld cosmology

abstract:
  We examine a class of braneworld models in which the expanding universe
encounters a "quiescent" future singularity. At a quiescent singularity, the
energy density and pressure of the cosmic fluid as well as the Hubble parameter
remain finite while all derivatives of the Hubble parameter diverge (i.e.,
${\dot H}$, ${\ddot H}$, etc. $\to \infty$). Since the Kretschmann invariant
diverges ($R_{iklm}R^{iklm} \to \infty$) at the singularity, one expects
quantum effects to play an important role as the quiescent singularity is
approached. We explore the effects of vacuum polarization due to massless
conformally coupled fields near the singularity and show that these can either
cause the universe to recollapse or, else, lead to a softer singularity at
which $H$, ${\dot H}$, and ${\ddot H}$ remain finite while ${\dddot H}$ and
higher derivatives of the Hubble parameter diverge. An important aspect of the
quiescent singularity is that it is encountered in regions of low density,
which has obvious implications for a universe consisting of a cosmic web of
high and low density regions -- superclusters and voids. In addition to vacuum
polarization, the effects of quantum particle production of non-conformal
fields are also likely to be important. A preliminary examination shows that
intense particle production can lead to an accelerating universe whose Hubble
parameter shows oscillations about a constant value.


title:
On the perspectives of testing the Dvali-Gabadadze-Porrati gravity model
  with the outer planets of the Solar System

abstract:
  The multidimensional braneworld gravity model by Dvali, Gabadadze and Porrati
was primarily put forth to explain the observed acceleration of the expansion
of the Universe without resorting to dark energy. One of the most intriguing
features of such a model is that it also predicts small effects on the orbital
motion of test particles which could be tested in such a way that local
measurements at Solar System scales would allow to get information on the
global properties of the Universe. Lue and Starkman derived a secular
extra-perihelion \omega precession of 5\times 10^-4 arcseconds per century,
while Iorio showed that the mean longitude \lambda is affected by a secular
precession of about 10^-3 arcseconds per century. Such effects depend only on
the eccentricities e of the orbits via second-order terms: they are, instead,
independent of their semimajor axes a. Up to now, the observational efforts
focused on the dynamics of the inner planets of the Solar System whose orbits
are the best known via radar ranging. Since the competing Newtonian and
Einsteinian effects like the precessions due to the solar quadrupole mass
moment J2, the gravitoelectric and gravitomagnetic part of the equations of
motion reduce with increasing distances, it would be possible to argue that an
analysis of the orbital dynamics of the outer planets of the Solar System, with
particular emphasis on Saturn because of the ongoing Cassini mission with its
precision ranging instrumentation, could be helpful in evidencing the predicted
new features of motion. In this note we investigate this possibility in view of
the latest results in the planetary ephemeris field. Unfortunately, the current
level of accuracy rules out this appealing possibility and it appears unlikely
that Cassini and GAIA will ameliorate the situation.


title:
Relativistic Structure, Stability and Gravitational Collapse of Charged
  Neutron Stars

abstract:
  Charged stars have the potential of becoming charged black holes or even
naked singularities. It is presented a set of numerical solutions of the
Tolman-Oppenheimer-Volkov equations that represents spherical charged compact
stars in hydrostatic equilibrium. The stellar models obtained are evolved
forward in time integrating the Einstein-Maxwell field equations. It is assumed
an equation of state of a neutron gas at zero temperature. The charge
distribution is taken as been proportional to the rest mass density
distribution. The set of solutions present an unstable branch, even with charge
to mass ratios arbitrarily close to the extremum case. It is performed a direct
check of the stability of the solutions under strong perturbations, and for
different values of the charge to mass ratio. The stars that are in the stable
branch oscillates and do not collapse, while models in the unstable branch
collapse directly to form black holes. Stars with a charge greater or equal
than the extreme value explode. When a charged star is suddenly discharged, it
don't necessarily collapse to form a black hole. A non-linear effect that gives
rise to the formation of an external shell of matter (see Ghezzi and Letelier
2005), is negligible in the present simulations. The results are in agreement
with the third law of black hole thermodynamics and with the cosmic censorship
conjecture.


title: Self-stabilization of extra dimensions

abstract:
  We show that the problem of stabilization of extra dimensions in Kaluza-Klein
type cosmology may be solved in a theory of gravity involving high-order
curvature invariants. The method suggested (employing a slow-change
approximation) can work with rather a general form of the gravitational action.
As examples, we consider pure gravity with Lagrangians quadratic and cubic in
the scalar curvature and some more complex ones in a simple Kaluza-Klein
framework. After a transition to the 4D Einstein conformal frame, this results
in effective scalar field theories with certain effective potentials, which in
many cases possess positive minima providing stable small-size extra
dimensions. Estimates made in the original (Jordan) conformal frame show that
the problem of a small value of the cosmological constant in the present
Universe is softened in this framework but is not solved completely.}


title: Monopole-Monopole solutions of Einstein-Yang-Mills-Higgs Theory

abstract:
  New static regular axially symmetric solutions of SU(2) Yang-Mills-Higgs
theory are constructed. They are asymptotically flat and represent gravitating
monopole-monopole pairs. The solutions form two branches linked to the second
Bartnik-McKinnon solution on upper mass branch and to the unstable
monopole-monopole configuration in flat space on the lower branch,
respectively.


title: Unitary evolution in Gowdy cosmology

abstract:
  Recent results on the non-unitary character of quantum time evolution in the
family of Gowdy T**3 spacetimes bring the question of whether one should
renounce in cosmology to the most sacred principle of unitary evolution. In
this work we show that the answer is in the negative. We put forward a full
nonperturbative canonical quantization of the polarized Gowdy T**3 model that
implements the dynamics while preserving unitarity. We discuss possible
implications of this result.


title:
Decaying cosmological parameter in the early universe from NKK theory of
  gravity

abstract:
  Using a formalism recently introduced we study the decaying of the
cosmological parameter during the early evolution of an universe, whose
evolution is governed by a vacuum equation of state. We use a stochastic
approach in a nonperturbative treatment of the inflaton field from a Noncompact
Kaluza-Klein (NKK) theory, to study the evolution of energy density
fluctuations in the early universe.


title: AMR, stability and higher accuracy

abstract:
  Efforts to achieve better accuracy in numerical relativity have so far
focused either on implementing second order accurate adaptive mesh refinement
or on defining higher order accurate differences and update schemes. Here, we
argue for the combination, that is a higher order accurate adaptive scheme.
This combines the power that adaptive gridding techniques provide to resolve
fine scales (in addition to a more efficient use of resources) together with
the higher accuracy furnished by higher order schemes when the solution is
adequately resolved. To define a convenient higher order adaptive mesh
refinement scheme, we discuss a few different modifications of the standard,
second order accurate approach of Berger and Oliger. Applying each of these
methods to a simple model problem, we find these options have unstable modes.
However, a novel approach to dealing with the grid boundaries introduced by the
adaptivity appears stable and quite promising for the use of high order
operators within an adaptive framework.


title: Noncommutative geometry inspired Schwarzschild black hole

abstract:
  We investigate the behavior of a noncommutative radiating Schwarzschild black
hole. It is shown that coordinate noncommutativity cures usual problems
encountered in the description of the terminal phase of black hole evaporation.
More in detail, we find that: the evaporation end-point is a zero temperature
extremal black hole even in the case of electrically neutral, non-rotating,
objects; there exists a finite maximum temperature that the black hole can
reach before cooling down to absolute zero; there is no curvature singularity
at the origin, rather we obtain a regular DeSitter core at short distance.


title: Relativistic Anelasticity

abstract:
  A formulation of Continuum Mechanics within the context of General Relativity
is presented that allows for the incorporation of certain types of anelastic
material behaviour, such as viscoelasticity and plasticity. The approach is
based on the concept of a four-dimensional body-time complex structured as a
principal bundle. The anelastic response is regarded as the result of a
continuous distribution of inhomogeneities, whose evolution is dictated by a
suggested relativistic version of the Eshelby tensor. The role played by
various groups is emphasized throughout the presentation and illustrated by
means of the example of an anelastic fluid.


title:
The averaged tensors of the relative energy-momentum and angular
  momentum in general relativity and some their applications

abstract:
  There exist at least a few different kind of averaging of the differences of
the energy-momentum and angular momentum in normal coordinates {\bf NC(P)}
which give tensorial quantities. The obtained averaged quantities are
equivalent mathematically because they differ only by constant scalar
dimensional factors. One of these averaging was used in our papers [1-8] giving
the {\it canonical superenergy and angular supermomentum tensors}.
  In this paper we present another averaging of the differences of the
energy-momentum and angular momentum which gives tensorial quantities with
proper dimensions of the energy-momentum and angular momentum densities. But
these averaged relative energy-momentum and angular momentum tensors, closely
related to the canonical superenergy and angular supermomentum tensors, {\it
depend on some fundamental length $L>0$}.
  The averaged relative energy-momentum and angular momentum tensors of the
gravitational field obtained in the paper can be applied, like the canonical
superenergy and angular supermomentum tensors, to {\it coordinate independent}
analysis (local and in special cases also global) of this field.
  We have applied the averaged relative energy-momentum tensors to analyze
vacuum gravitational energy and momentum and to analyze energy and momentum of
the Friedman (and also more general) universes. The obtained results are very
interesting, e.g., the averaged relative energy density is {\it positive
definite} for the all Friedman universes.


title: Moving mirrors and black hole evaporation in non-commutative space-times

abstract:
  We study the evaporation of black holes in non-commutative space-times. We do
this by calculating the correction to the detector's response function for a
moving mirror in terms of the noncommutativity parameter $\Theta$ and then
extracting the number density as modified by this parameter. We find that
allowing space and time to be non-commutative increases the decay rate of a
black hole.


title: Tachyon Monopole

abstract:
  The property and gravitational field of global monopole of tachyon are
investigated in a four dimensional static space-time. We give an exact solution
of the tachyon field in the flat space-time background. Using the linearized
approximation of gravity, we get the approximate solution of the metric. We
also solve analytically the coupled Einstein and tachyon field equations which
is beyond the linearized approximation to determine the gravitational
properties of the monopole solution. We find that the metric of tachyon
monopole represents an asymptotically AdS space-time with a small effective
mass at the origin. We show that this relatively tiny mass is actually
negative, as it is in the case of ordinary scalar field.


title:
Exact solutions of Brans-Dicke cosmology and the cosmic coincidence
  problem

abstract:
  We present some cosmological solutions of Brans-Dicke theory, characterized
by a decaying vacuum energy density and by a constant relative matter density.
With these features, they shed light on the cosmological constant problems,
leading to a presently small vacuum term, and to a constant ratio between the
vacuum and matter energy densities. By fixing the only free parameter of our
solutions, we obtain cosmological parameters in accordance with observations of
the relative matter density, the universe age and redshift-distance relations.


title: Universal homogeneous causal sets

abstract:
  Causal sets are particular partially ordered sets which have been proposed as
a basic model for discrete space-time in quantum gravity. We show that the
class C of all countable past-finite causal sets contains a unique causal set
(U,<) which is universal (i.e., any member of C can be embedded into (U,<)) and
homogeneous (i.e., (U,<) has maximal degree of symmetry). Moreover, (U,<) can
be constructed both probabilistically and explicitly. In contrast, the larger
class of all countable causal sets does not contain a universal object.


title: Extension of geodesic algebras to continuous genus

abstract:
  Using the Penner--Fock parameterization for Teichmuller spaces of Riemann
surfaces with holes, we construct the string-like free-field representation of
the Poisson and quantum algebras of geodesic functions in the continuous-genus
limit. The mapping class group acts naturally in the obtained representation.


title: Lamb Shift of Unruh Detector Levels

abstract:
  We argue that the energy levels of an Unruh detector experience an effect
similar to the Lamb shift in Quantum Electrodynamics. As a consequence, the
spectrum of energy levels in a curved background is different from that in flat
space. As examples, we consider a detector in an expanding Universe and in
Rindler space, and for the latter case we suggest a new expression for the
local virtual energy density seen by an accelerated observer. In the
ultraviolet domain, that is when the space between the energy levels is larger
than the Hubble rate or the acceleration of the detector, the Lamb shift
quantitatively dominates over the thermal response rate.


title:
A new and improved template for the detection of gravitational waves
  from compact binary systems using Chebyshev polynomials

abstract:
  We introduce a new template for the detection of gravitational waves from
compact binary systems which is based on Chebyshev polynomials of the first
kind. As well as having excellent convergence properties, these polynomials are
also very closely related to the elusive minimax polynomial. In this study we
have limited ourselves to the test-mass regime, where we model a test particle
in a circular equatorial orbit around a Schwarzschild black hole. Our objective
is to model the numerical gravitational wave flux function, starting with the
post-Newtonian expansion from Black Hole Perturbation Theory. We introduce a
new Chebyshev approximation to the flux function, which due to a process called
Chebyshev economization gives a better model than either post-Newtonian or Pade
based methods. A graphical examination of the new flux function shows that it
gives an excellent fit to the numerical flux, but more importantly we find that
at the last stable orbit the error is reduced, < 1.8%, at all orders of
approximation. We also find that the templates constructed using the Chebyshev
approximation give better fitting factors, in general > 0.99, and smaller
errors, < 1/10%, in the estimation of the Chirp mass when compared to a
fiducial exact waveform, constructed using the numerical flux and the exact
expression for the orbital energy function, again at all orders of
approximation. We also show that in the test-mass case, the new Chebyshev
template is superior to both PN and Pade approximant templates, especially at
lower orders of approximation.


title:
The Lazarus Project. II. Spacelike extraction with the quasi-Kinnersley
  tetrad

abstract:
  The Lazarus project was designed to make the most of limited 3D binary
black-hole simulations, through the identification of perturbations at late
times, and subsequent evolution of the Weyl scalar $\Psi_4$ via the Teukolsky
formulation. Here we report on new developments, employing the concept of the
``quasi-Kinnersley'' (transverse) frame, valid in the full nonlinear regime, to
analyze late-time numerical spacetimes that should differ only slightly from
Kerr. This allows us to extract the essential information about the background
Kerr solution, and through this, to identify the radiation present. We
explicitly test this procedure with full numerical evolutions of Bowen-York
data for single spinning black holes, head-on and orbiting black holes near the
ISCO regime. These techniques can be compared with previous Lazarus results,
providing a measure of the numerical-tetrad errors intrinsic to the method, and
give as a by-product a more robust wave extraction method for numerical
relativity.


title:
Energy in Reboucas-Tiomno-Korotkii-Obukhov and Godel-type Space-times in
  Bergmann-Thomson's Formulations

abstract:
  This paper has been removed by arXiv administrators because it overlaps
gr-qc/0303009, hep-th/0405047, gr-qc/0412120, and others.
  This paper also has excessive overlap with the following papers also written
by the authors or their collaborators: gr-qc/0607119, gr-qc/0607103,
gr-qc/0607115, and others.


title: Gravity from Local Lorentz Violation

abstract:
  In general relativity, gravitational waves propagate at the speed of light,
and so gravitons are massless. The masslessness can be traced to symmetry under
diffeomorphisms. However, another elegant possibility exists: masslessness can
instead arise from spontaneous violation of local Lorentz invariance. We
construct the corresponding theory of gravity. It reproduces the
Einstein-Hilbert action of general relativity at low energies and temperatures.
Detectable signals occur for sensitive experiments, and potentially profound
implications emerge for our theoretical understanding of gravity.


title:
Analogue quantum gravity phenomenology from a two-component
  Bose-Einstein condensate

abstract:
  We present an analogue spacetime model that reproduces the salient features
of the most common ansatz for quantum gravity phenomenology. We do this by
investigating a system of two coupled Bose-Einstein condensates. This system
can be tuned to have two "phonon" modes (one massive, one massless) which share
the same limiting speed in the hydrodynamic approximation [Phys. Rev. D72
(2005) 044020, gr-qc/0506029; cond-mat/0409639]. The system nevertheless
possesses (possibly non-universal) Lorentz violating terms at very high
energies where "quantum pressure" becomes important. We investigate the
physical interpretation of the relevant fine-tuning conditions, and discuss the
possible lessons and hints that this analogue spacetime could provide for the
phenomenology of real physical quantum gravity. In particular we show that the
effective field theory of quasi-particles in such an emergent spacetime does
not exhibit the so called "naturalness problem".


title: Generalizing Quantum Mechanics for Quantum Gravity

abstract:
  `How do our ideas about quantum mechanics affect our understanding of
spacetime?' This familiar question leads to quantum gravity. The complementary
question is also important: `How do our ideas about spacetime affect our
understanding of quantum mechanics?' This short abstract of a talk given at the
Gafka2004 conference contains a very brief summary of some of the author's
papers on generalizations of quantum mechanics needed for quantum gravity. The
need for generalization is motivated. The generalized quantum theory framework
for such generalizations is described and illustrated for usual quantum
mechanics and a number of examples to which it does not apply. These include
spacetime alternatives extended over time, time-neutral quantum theory, quantum
field theory in fixed background spacetime not foliable by spacelike surfaces,
and systems with histories that move both forward and backward in time. A fully
four-dimensional, sum-over-histories generalized quantum theory of cosmological
geometries is briefly described. The usual formulation of quantum theory in
terms of states evolving unitarily through spacelike surfaces is an
approximation to this more general framework that is appropriate in the late
universe for coarse-grained descriptions of geometry in which spacetime behaves
classically. This abstract is unlikely to be clear on its own, but references
are provided to the author's works where the ideas can be followed up.


title: Imprints of Spacetime Topology in the Hawking-Unruh Effect

abstract:
  The Unruh and Hawking effects are investigated on certain families of
topologically non-trivial spacetimes using a variety of techniques. First we
present the Bogolubov transformation between Rindler and Minkowski
quantizations on two flat spacetimes with topology ${\R}^3\times{S^1}$ (M_0 and
M_-) for massive Dirac spinors. The two inequivalent spin structures on each
are considered. Results show modifications to the Minkowski space Unruh effect.
This provides a flat space model for the Hawking effect on Kruskal and RP^3
geon black hole spacetimes which is the subject of the rest of this part.
  Secondley we present the expectation values of the stress tensor for massive
scalar and spinor fields on $M_0$ and $M_-$, and for massive scalar fields on
Minkowski space with a single infinite plane boundary, in the Minkowski-like
vacua.
  Finally we investigate particle detector models. We investigate Schlicht's
regularization of the Wightman function and extend it to an arbitrary spacetime
dimension, to quotient spaces of Minkowski space, to non-linear couplings, to a
massless Dirac field, and to conformally flat spacetimes. Secondly we present
some detector responses, including the time dependent responses of inertial and
uniformly accelerated detectors on $M_-$ and $M$ with boundary with motion
perpendicular to the boundary. Responses are also considered for static
observers in the exterior of the RP^3 geon and comoving observers in RP^3 de
Sitter space, via those in the associated GEMS.


title: Phase space solutions in scalar-tensor cosmological models

abstract:
  An analysis of the solutions for the field equations of generalized
scalar-tensor theories of gravitation is performed through the study of the
geometry of the phase space and the stability of the solutions, with special
interest in the Brans-Dicke model. Particularly, we believe to be possible to
find suitable forms of the Brans-Dicke parameter omega and potential V of the
scalar field, using the dynamical systems approach, in such a way that they can
be fitted in the present observed scenario of the Universe.


title: Improved approximate inspirals of test-bodies into Kerr black holes

abstract:
  We present an improved version of the approximate scheme for generating
inspirals of test-bodies into a Kerr black hole recently developed by
Glampedakis, Hughes and Kennefick. Their original "hybrid" scheme was based on
combining exact relativistic expressions for the evolution of the orbital
elements (the semi-latus rectum p and eccentricity e) with approximate,
weak-field, formula for the energy and angular momentum fluxes, amended by the
assumption of constant inclination angle, iota, during the inspiral. Despite
the fact that the resulting inspirals were overall well-behaved, certain
pathologies remained for orbits in the strong field regime and for orbits which
are nearly circular and/or nearly polar. In this paper we eliminate these
problems by incorporating an array of improvements in the approximate fluxes.
Firstly, we add certain corrections which ensure the correct behaviour of the
fluxes in the limit of vanishing eccentricity and/or 90 degrees inclination.
Secondly, we use higher order post-Newtonian formulae, adapted for generic
orbits. Thirdly, we drop the assumption of constant inclination. Instead, we
first evolve the Carter constant by means of an approximate post-Newtonian
expression and subsequently extract the evolution of iota. Finally, we improve
the evolution of circular orbits by using fits to the angular momentum and
inclination evolution determined by Teukolsky based calculations. As an
application of the improved scheme we provide a sample of generic Kerr
inspirals and for the specific case of nearly circular orbits we locate the
critical radius where orbits begin to decircularise under radiation reaction.
These easy-to-generate inspirals should become a useful tool for exploring LISA
data analysis issues and may ultimately play a role in source detection.


title: Bounce Conditions in f(R) Cosmologies

abstract:
  We investigate the conditions for a bounce to occur in
Friedmann-Robertson-Walker cosmologies for the class of fourth order gravity
theories. The general bounce criterion is determined and constraints on the
parameters of three specific models are given in order to obtain bounces
solutions. It is found that unlike the case of General Relativity, a bounce
appears to be possible in open and flat cosmologies.


title: A squeezed state source using radiation pressure induced rigidity

abstract:
  We propose an experiment to extract ponderomotive squeezing from an
interferometer with high circulating power and low mass mirrors. In this
interferometer, optical resonances of the arm cavities are detuned from the
laser frequency, creating a mechanical rigidity that dramatically suppresses
displacement noise. After taking into account imperfection of optical elements,
laser noise, and other technical noise consistent with existing laser and
optical technologies and typical laboratory environments, we expect the output
light from the interferometer to have measurable squeezing of ~5 dB, with a
frequency-independent squeeze angle for frequencies below 1 kHz. This squeeze
source is well suited for injection into a gravitational-wave interferometer,
leading to improved sensitivity from reduction in the quantum noise.
Furthermore, this design provides an experimental test of quantum-limited
radiation pressure effects, which have not previously been tested.


title: A Systematic Derivation of the Riemannian Barrett-Crane Intertwiner

abstract:
  The Barrett-Crane intertwiner for the Riemannian general relativity is
systematically derived by solving the quantum Barrett-Crane constraints
corresponding to a tetrahedron (except for the non-degeneracy condition). It
was shown by Reisenberger that the Barrett-Crane intertwiner is the unique
solution. The systematic derivation can be considered as an alternative proof
of the uniqueness. The new element in the derivation is the rigorous imposition
of the cross-simplicity constraint.


title: Chaplygin traversable wormholes

abstract:
  The generalized Chaplygin gas (GCG) is a candidate for the unification of
dark energy and dark matter, and is parametrized by an exotic equation of state
given by $p_{ch}=-A/\rho_{ch}^{\alpha}$, where $A$ is a positive constant and
$0<\alpha \leq 1$. In this paper, exact solutions of spherically symmetric
traversable wormholes supported by the GCG are found, possibly arising from a
density fluctuation in the GCG cosmological background. To be a solution of a
wormhole, the GCG equation of state imposes the following generic restriction
$A<(8\pi r_0^2)^{-(1+\alpha)}$, where $r_0$ is the wormhole throat radius,
consequently violating the null energy condition. The spatial distribution of
the exotic GCG is restricted to the throat neighborhood, and the physical
properties and characteristics of these Chaplygin wormholes are further
analyzed. Four specific solutions are explored in some detail, namely, that of
a constant redshift function, a specific choice for the form function, a
constant energy density, and finally, isotropic pressure Chaplygin wormhole
geometries.


title: Braneworld black holes as gravitational lenses

abstract:
  Black holes acting as gravitational lenses produce, besides the primary and
secondary weak field images, two infinite sets of relativistic images. These
images can be studied using the strong field limit, an analytic method based on
a logarithmic asymptotic approximation of the deflection angle. In this work,
braneworld black holes are analyzed as gravitational lenses in the strong field
limit and the feasibility of observation of the images is discussed.


title:
The volume operator for spin networks with planar or cylindrical
  symmetry

abstract:
  This paper constructs a kinematic basis for spin networks with planar or
cylindrical symmetry, by exploiting the fact that the basis elements are
representations of an O(3) subgroup of O(4). The action of the volume operator
on this basis gives a difference equation for the eigenvalues and eigenvectors
of the volume operator. For basis elements of low spin, the difference equation
can be solved readily on a computer. For higher spins, I solve for the
eigenvalues using a WKBJ method. This paper considers only the case where the
gravitational wave can have both polarizations. The single polarization case is
considered in a spearate paper.


title:
The volume operator for singly polarized gravity waves with planar or
  cylindrical symmetry

abstract:
  A previous paper constructed a kinematic basis for spin networks with planar
or cylindrical symmetry and arbitrary polarization. This paper imposes a
constraint which limits the gravitational wave to a single polarization. The
spectrum of the constraint contains a physically reasonable number of zero
eigenvalues, and the zero eigenvectors can be constructed explicitly.
Commutation of the constraint with the Hamiltonian is expected to lead to a
further constraint. This new constraint is not investigated in this paper, but
I argue it will be non-local, relating states at two or more neighboring
vertices.


title:
Phenomenological implications of an alternative Hamiltonian constraint
  for quantum cosmology

abstract:
  In this paper we review a model based on loop quantum cosmology that arises
from a symmetry reduction of the self dual Plebanski action. In this
formulation the symmetry reduction leads to a very simple Hamiltonian
constraint that can be quantized explicitly in the framework of loop quantum
cosmology. We investigate the phenomenological implications of this model in
the semi-classical regime and compare those with the known results of the
standard Loop Quantum Cosmology.


title:
Sub-SQL Sensitivity via Optical Rigidity in Advanced LIGO Interferometer
  with Optical Losses

abstract:
  The ``optical springs'' regime of the signal-recycled configuration of laser
interferometric gravitational-wave detectors is analyzed taking in account
optical losses in the interferometer arm cavities. This regime allows to obtain
sensitivity better than the Standard Quantum Limits both for a free test mass
and for a conventional harmonic oscillator. The optical losses restrict the
gain in sensitivity and achievable signal-to-noise ratio. Nevertheless, for
parameters values planned for the Advanced LIGO gravitational-wave detector,
this restriction is insignificant.


title:
The deterministic nature of conservative post-Newtonian accurate
  dynamics of compact binaries with leading order spin-orbit interaction

abstract:
  We formally show that the conservative second post-Newtonian (PN) accurate
dynamics of spinning compact binaries moving in eccentric orbits, when spin
effects are restricted to the leading order spin-orbit interaction cannot be
chaotic for the following two distinct cases: (i) the binary consists of
compact objects of arbitrary mass, where only one of them is spinning with an
arbitrary spin and (ii) the binary consists of equal mass compact objects,
having two arbitrary spins. We rest our arguments on the recent determination
of PN accurate Keplerian-type parametric solutions to the above cases,
indicating that the PN accurate dynamics is integrable in these two situations.
We compare predictions of our case (i) with those from a numerical
investigation of an equivalent scenario that observed chaos in the associated
dynamics. We also present possible reasons for the discrepancies.


title: Electromagnetic Mass in $(n+2)$ Dimensional Space-times

abstract:
  Einstein-Maxwell field equations correspoding to higher dimensional
description of static spherically symmetric space-time have been solved under
two specific set of conditions, viz., (i) $\rho \ne 0$, $\nu^\prime= 0$ and
(ii) $\rho=0$, $ \nu^\prime\ne 0$ where $\rho$ and $\nu$ represent the mass
density and metric potential. The solution sets thus obtained satisfy the
criteria of being electromagnetic mass model such that the gravitational mass
vanishes for the vanishing charge density $\sigma$ and also the space-time
becomes flat. Physical features related to other parameters also have been
discussed.


title:
Conserved Matter Superenergy Currents for Hypersurface Orthogonal
  Killing Vectors

abstract:
  We show that for hypersurface orthogonal Killing vectors, the corresponding
Chevreton superenergy currents will be conserved and proportional to the
Killing vectors. This holds for four-dimensional Einstein-Maxwell spacetimes
with an electromagnetic field that is sourcefree and inherits the symmetry of
the spacetime. A similar result also holds for the trace of the Chevreton
tensor. The corresponding Bel currents have previously been proven to be
conserved and our result can be seen as giving further support to the concept
of conserved mixed superenergy currents. The analogous case for a scalar field
has also previously been proven to give conserved currents and we show, for
completeness, that these currents also are proportional to the Killing vectors.


title:
Induced matter: Curved N-manifolds encapsulated in Riemann-flat N+1
  dimensional space

abstract:
  Liko and Wesson have recently introduced a new 5-dimensional induced matter
solution of the Einstein equations, a negative curvature Robertson-Walker space
embedded in a Riemann flat 5-dimensional manifold. We show that this solution
is a special case of a more general theorem prescribing the structure of
certain N+1-dimensional Riemann flat spaces which are all solutions of the
Einstein equations. These solutions encapsulate N-dimensional curved manifolds.
Such spaces are said to "induce matter" in the sub-manifolds by virtue of their
geometric structure alone. We prove that the N-manifold can be any maximally
symmetric space.


title:
Utilization of electromagnetic detector for selection and detection of
  high-frequency relic gravitational waves

abstract:
  It is shown that coupling system between fractal membranes and a Gaussian
beam passing through a static magnetic field has strong selection capability
for the stochastic relic gravitational wave background. The relic GW components
propagating along the positive direction of the symmetrical axis of the
Gaussian beam might generate an optimal electromagnetic perturbation while the
perturbation produced by the relic GW components propagating along the negative
and perpendicular directions to the symmetrical axis will be much less than the
former.The influence of the random fluctuation of the relic GWs to such effect
can be neglected and the influence of the random fluctuation of the relic GWs
to such effect can be neglected.


title: Reality Conditions for Spin Foams

abstract:
  An idea of reality conditions in the context of spin foams (Barrett-Crane
models) is developed. The square of areas are the most elementary observables
in the case of spin foams. This observation implies that simplest reality
conditions in the context of the Barrett-Crane models is that the all possible
scalar products of the bivectors associated to the triangles of a four simplex
be real. The continuum generalization of this is the area metric reality
constraint: the area metric is real iff a non-degenerate metric is real or
imaginary. Classical real general relativity (all signatures) can be extracted
from complex general relativity by imposing the area metric reality constraint.
The Plebanski theory can be modified by adding a Lagrange multiplier to impose
the area metric reality condition to derive classical real general relativity.
I discuss the SO(4,C) BF model and SO(4,C) Barrett-Crane model. It appears that
the spin foam models in 4D for all the signatures are the projections of the
SO(4,C) spin foam model using the reality constraints on the bivectors.


title: Revisiting the Light Cone of the Goedel Universe

abstract:
  The structure of a light cone in the Goedel universe is studied. We derive
the intrinsic cone metric, calculate the rotation coefficients of the ray
congruence forming the cone, determine local differential invariants up to
second order, describe the crossover (keel) singularities and give a first
discussion of its focal points. Contrary to many rotation coefficients, some
inner differential invariants attain simple finite standard values at focal
singularities.


title: Cauchy hypersurfaces as levels of time and temporal functions

abstract:
  This paper has been withdrawn because the new one gr-qc/0512095 includes all
its results (as well as those in gr-qc/0507018), in a clearer way.


title:
Non-symmetric trapped surfaces in the Schwarzschild and Vaidya
  spacetimes

abstract:
  Marginally trapped surfaces (MTSs) are commonly used in numerical relativity
to locate black holes. For dynamical black holes, it is not known generally if
this procedure is sufficiently reliable. Even for Schwarzschild black holes,
Wald and Iyer constructed foliations which come arbitrarily close to the
singularity but do not contain any MTSs. In this paper, we review the Wald-Iyer
construction, discuss some implications for numerical relativity, and
generalize to the well known Vaidya spacetime describing spherically symmetric
collapse of null dust. In the Vaidya spacetime, we numerically locate
non-spherically symmetric trapped surfaces which extend outside the standard
spherically symmetric trapping horizon. This shows that MTSs are common in this
spacetime and that the event horizon is the most likely candidate for the
boundary of the trapped region.


title:
The Midpoint Rule as a Variational--Symplectic Integrator. I.
  Hamiltonian Systems

abstract:
  Numerical algorithms based on variational and symplectic integrators exhibit
special features that make them promising candidates for application to general
relativity and other constrained Hamiltonian systems. This paper lays part of
the foundation for such applications. The midpoint rule for Hamilton's
equations is examined from the perspectives of variational and symplectic
integrators. It is shown that the midpoint rule preserves the symplectic form,
conserves Noether charges, and exhibits excellent long--term energy behavior.
The energy behavior is explained by the result, shown here, that the midpoint
rule exactly conserves a phase space function that is close to the Hamiltonian.
The presentation includes several examples.


title:
Formalism for Testing Theories of Gravity Using Lensing by Compact
  Objects. I: Static, Spherically Symmetric Case

abstract:
  We are developing a general, unified, and rigorous analytical framework for
using gravitational lensing by compact objects to test different theories of
gravity beyond the weak-deflection limit. In this paper we present the
formalism for computing corrections to lensing observables for static,
spherically symmetric gravity theories in which the corrections to the
weak-deflection limit can be expanded as a Taylor series in one parameter,
namely the gravitational radius of the lens object. We take care to derive
coordinate-independent expressions and compute quantities that are directly
observable. We compute first- and second-order corrections to the image
positions, magnifications, and time delays. Interestingly, we find that the
first-order corrections to the total magnification and centroid position vanish
in all gravity theories that agree with general relativity in the
weak-deflection limit, but they can remain nonzero in modified theories that
disagree with GR in the weak-deflection limit. For the Reissner-Nordstrom
metric and a related metric from heterotic string theory, our formalism reveals
an intriguing connection between lensing observables and the condition for
having a naked singularity, which could provide an observational method for
testing the existence of such objects. We apply our formalism to the Galactic
black hole and predict that the corrections to the image positions are at the
level of 10 micro-arcseconds, while the correction to the time delay is a few
hundredths of a second. These corrections would be measurable today if a pulsar
were found to be lensed by the Galactic black hole; and they should be readily
detectable with planned missions like MAXIM.


title: Gravity tests and the Pioneer anomaly

abstract:
  Experimental tests of gravity performed in the solar system show a good
agreement with general relativity. The latter is however challenged by the
Pioneer anomaly which might be pointing at some modification of gravity law at
ranges of the order of the size of the solar system. We introduce a metric
extension of general relativity which, while preserving the equivalence
principle, modifies the coupling between curvature and stress tensors and,
therefore, the metric solution in the solar system. The ``post-Einsteinian
extension'' replaces Newton gravitation constant by two running coupling
constants, which depend on the scale and differ in the sectors of traceless and
traced tensors, so that the metric solution is characterized by two gravitation
potentials. The extended theory has the capability to preserve compatibility
with gravity tests while accounting for the Pioneer anomaly. It can also be
tested by new experiments or, maybe, by having a new look at data of already
performed experiments.


title: New galactic open cluster candidates from DSS and 2MASS imagery

abstract:
  An inspection of the DSS and 2MASS images of selected Milky Way regions has
led to the discovery of 66 stellar groupings whose morphologies,
color-magnitude diagrams, and stellar density distributions suggest that these
objects are possible open clusters that do not yet appear to be listed in any
catalogue. For 24 of these groupings, which we consider to be the most likely
to be candidates, we provide extensive descriptions on the basis of 2MASS
photometry and their visual impression on DSS and 2MASS. Of these cluster
candidates, 9 have fundamental parameters determined by fitting the
color-magnitude diagrams with solar metallicity Padova isochrones. An
additional 10 cluster candidates have distance moduli and reddenings derived
from K magnitudes and (J-K) color indices of helium-burning red clump stars. As
an addendum, we also provide a list of a number of apparently unknown galactic
and extragalactic objects that were also discovered during the survey.


title:
Measurement of radiation-pressure-induced optomechanical dynamics in a
  suspended Fabry-Perot cavity

abstract:
  We report on experimental observation of radiation-pressure induced effects
in a high-power optical cavity. These effects play an important role in next
generation gravitational wave (GW) detectors, as well as in quantum
non-demolition (QND) interferometers. We measure the properties of an optical
spring, created by coupling of an intense laser field to the pendulum mode of a
suspended mirror; and also the parametric instability (PI) that arises from the
nonlinear coupling between acoustic modes of the cavity mirrors and the cavity
optical mode. Specifically, we measure an optical rigidity of $K = 3 \times
10^4$ N/m, and PI value $R = 3$.


title: Path and Path Deviation Equations in Kaluza-Klein Type Theories

abstract:
  Path and path deviation equations for charged, spinning and spinning charged
objects in different versions of Kaluza-Klein (KK) theory using a modified
Bazanski Lagrangian have been derived. The significance of motion in five
dimensions, especially for a charged spinning object, has been examined. We
have also extended the modified Bazanski approach to derive the path and path
deviation equations of a test particle in a version of non-symmetric KK theory.


title: Cylindrically Symmetric Solution in Teleparallel Theory of Gravitation

abstract:
  The field equations of a special class of teleparallel theory of gravitation
and electromagnetic fields have been applied to tetrad space having cylindrical
symmetry with four unknown functions of radial coordinate $r$ and azimuth angle
$\theta$. The vacuum stress-energy momentum tensor with one assumption
concerning its specific form generates one non-trivial exact analytic solution.
This solution is characterized by a constant magnetic field parameter $B_0$. If
$B_0=0$ then, the solution will reduces to the flat spacetime. The energy
content is calculated using the superpotential given in the framework of
teleparallel geometry. The energy contained in a sphere is found to be
different from the pervious results.


title: A Note on the Asymptotic Limit of the Four Simplex

abstract:
  Recently the asymptotic limit of the Barrett-Crane models has been studied by
Barrett and Steele. Here by a direct study, I show that we can extract the
bivectors which satisfy the essential Barrett-Crane constraints from the
asymptotic limit. Because of this the Schlaffi identity is implied by the
asymptotic limit, rather than to be imposed as a constraint.


title: Gravitational solution to the Pioneer 10/11 anomaly

abstract:
  A fully relativistic modified gravitational theory including a fifth force
skew symmetric field is fitted to the Pioneer 10/11 anomalous acceleration. The
theory allows for a variation with distance scales of the gravitational
constant G, the fifth force skew symmetric field coupling strength omega and
the mass of the skew symmetric field mu=1/lambda. A fit to the available
anomalous acceleration data for the Pioneer 10/11 spacecraft is obtained for a
phenomenological representation of the "running" constants and values of the
associated parameters are shown to exist that are consistent with fifth force
experimental bounds. The fit to the acceleration data is consistent with all
current satellite, laser ranging and observations for the inner planets.


title: Spin Foams for the SO(4,C) BF theory and the SO(4,C) General Relativity

abstract:
  The Spin Foam Model for the SO(4,C) BF theory is discussed. The Barrett-Crane
intertwiner for the SO(4,C) general relativity is systematically derived. The
SO(4,C) Barret-Crane interwiner is unique. The propagators of the SO(4,C)
Barrett-Crane model are discussed. The asymptotic limit of the SO(4,C) general
relativity is discussed. The asymptotic limit is controlled by the SO(4,C)
Regge calculus.


title:
A Note on Particles and Scalar Fields in Higher Dimensional Nutty
  Spacetimes

abstract:
  In this note, we study the integrability of geodesic flow in the background
of a very general class of spacetimes with NUT-charge(s) in higher dimensions.
This broad set encompasses multiply NUT-charged solutions, electrically and
magnetically charged solutions, solutions with a cosmological constant, and
time dependant bubble-like solutions. We also derive first-order equations of
motion for particles in these backgrounds. Separability turns out to be
possible due to the existence of non-trivial irreducible Killing tensors.
Finally, we also examine the Klein-Gordon equation for a scalar field in these
spacetimes and demonstrate complete separability.


title: Scalar waves in a wormhole topology

abstract:
  Global monochromatic solutions of the scalar wave equation are obtained in
flat wormholes of dimensions 2+1 and 3+1. The solutions are in the form of
infinite series involving cylindirical and spherical wave functions and they
are elucidated by the multiple scattering method. Explicit solutions for some
limiting cases are illustrated as well. The results presented in this work
constitute instances of solutions of the scalar wave equation in a spacetime
admitting closed timelike curves.


title: Energy of a Charged Wormhole

abstract:
  This paper has been removed by arXiv administrators because it overlaps
gr-qc/0102077 and others.
  This paper also has excessive overlap with the following papers also written
by the authors or their collaborators: gr-qc/0603027, gr-qc/0606022,
gr-qc/0512080, gr-qc/0603108, gr-qc/0601141, gr-qc/0603063, gr-qc/0608050,
gr-qc/0607095, gr-qc/0607011, gr-qc/0607083, and others.


title:
Deformed Special Relativity as an effective theory of measurements on
  quantum gravitational backgrounds

abstract:
  In this article we elaborate on a recently proposed interpretation of DSR as
an effective measurement theory in the presence of non-negligible (albeit
small) quantum gravitational fluctuations. We provide several heuristic
arguments to explain how such a new theory can emerge and discuss the possible
observational consequences of this framework.


title: Einstein Bianchi equations with sources

abstract:
  In this article, dedicated to one of the best specialist of the FOSH systems,
we couple the Bianchi equations with the equations satisfied by the dynamical
acceleration of a charged fluid and the derivatives of the associated Maxwell
field.


title:
Dynamical evolution and leading order gravitational wave emission of
  Riemann-S binaries

abstract:
  An approximate strategy for studying the evolution of binary systems of
extended objects is introduced. The stars are assumed to be polytropic
ellipsoids. The surfaces of constant density maintain their ellipsoidal shape
during the time evolution. The equations of hydrodynamics then reduce to a
system of ordinary differential equations for the internal velocities, the
principal axes of the stars and the orbital parameters. The equations of motion
are given within Lagrangian and Hamiltonian formalism. The special case when
both stars are axially symmetric fluid configurations is considered. Leading
order gravitational radiation reaction is incorporated, where the quasi-static
approximation is applied to the internal degrees of freedom of the stars. The
influence of the stellar parameters, in particular the influence of the
polytropic index $n$, on the leading order gravitational waveforms is studied.


title:
An alternative explanation of the conflict between 1/R gravity and solar
  system tests

abstract:
  Recently the 1/R gravity has been proposed in order to explain the
accelerated expansion of the universe. However, it was argued that the 1/R
gravity conflicts with solar system tests. While this statement is true if one
views the 1/R gravity as an effective theory, we find that this difficulty
might be avoided if one treats the 1/R term as a correction to the scalar
curvature term in the high curvature limit $R \gg \mu^2$.


title: Cosmic acceleration in a model of scalar-tensor gravitation

abstract:
  In this paper we consider a model of scalar-tensor theory of gravitation in
which the scalar field, $\phi$ determines the gravitational coupling G and has
a Lagrangian of the form, $\mathcal{L}_{\phi} =-V(\phi)\sqrt{1 -
\partial_{\mu}\phi\partial^{\mu}\phi}$. We study the cosmological consequence
of this theory in the matter dominated era and show that this leads to a
transition from an initial decelerated expansion to an accelerated expansion
phase at the present epoch. Using observational constraints, we see that the
effective equation of state today for the scalar field turns out to be
$p_{\phi}=w_{\phi}{\rho}_{\phi}$, with $w_{\phi}=-0.88$ and that the transition
to an accelerated phase happened at a redshift of about 0.3.


title: On the relation between ADM and Bondi energy-momenta

abstract:
  When a spacetime takes Bondi radiating metric, and is vacuum and
asymptotically flat at spatial infinity which ensures the positive mass
theorem, we prove that the standard ADM energy-momentum is the past limit of
the Bondi energy-momentum. We also derive a formula relating the ADM
energy-momentum of any asymptotically flat spacelike hypersurface to the Bondi
energy-momentum of any null hypersurface. The formula indicates that the Bondi
mass is always less than the ADM total energy if the system has {\it news}.
  The assumed asymptotic flatness precludes gravitational radiation. We
therefore study further the relation between the ADM total energy and the Bondi
mass when gravitational radiation emits. We find that in this case the ADM
total energy is no longer the past limit of the Bondi mass. They differ by
certain quantity relating to the {\it news} of the system.


title:
On the relation between ADM and Bondi energy-momenta - radiative spatial
  infinity

abstract:
  In a vacuum spacetime equips with the Bondi's radiating metric which is
asymptotically flat at spatial infinity including gravitational radiation ({\bf
Condition D}), we establish the relation between the ADM total linear momentum
and the Bondi momentum. The relation between the ADM total energy and the Bondi
mass in this case was established earlier in [12].


title: Mach's Principle and a Variable Speed of Light

abstract:
  Ernst Mach (1838-1916) suggested that the origin of gravitational interaction
could depend on the presence of all masses in the universe. A corresponding
hypothesis of Sciama (1953) on the gravitational constant, c^2/G = \sum
m_i/r_i, is linked to Dicke's (1957) proposal of an electromagnetic origin of
gravitation, a precursor of scalar-tensor-theories. In this an equivalent
description in terms of a variable speed of light (VSL) is given, and the
agreement with the four classical tests of general relativity is shown.
Moreover, VSL opens the possibility to write the total energy of a particle as
E=mc^2; this necessarily leads to the proportionality of inertial and
gravitating mass, the equivalence principle. Furthermore, a formula for c
depending on the mass distribution is given that reproduces Newton's law of
gravitation. This mass distribution allows to calculate a slightly variable
term that corresponds to the `constant' G. The present proposal may also supply
an alternative explanation to the flatness problem and the horizon problem in
cosmology.


title: Acceleration of a Spherical Brane-Universe

abstract:
  The model where the universe is considered as an expanding spherical 3-brane
allows us to explain its expansion rate without a dark energy component. In
this scenario the computed redshift that corresponds to the transition from
cosmic deceleration to acceleration is in a good agreement with observations.


title:
Canonical gauge-invariant variables for scalar perturbations in
  synchronous coordinates

abstract:
  Under an appropriate change of the perturbation variable Lifshitz-Khalatnikov
propagation equations for the scalar perturbation reduce to d'Alembert
equation. The change of variables is based on the Darboux transform.


title: Reference frames and rigid motions in relativity: Applications

abstract:
  The concept of rigid reference frame and of constricted spatial metric, given
in the previous work [\emph{Class. Quantum Grav.} {\bf 21}, 3067,(2004)] are
here applied to some specific space-times: In particular, the rigid rotating
disc with constant angular velocity in Minkowski space-time is analyzed, a new
approach to the Ehrenfest paradox is given as well as a new explanation of the
Sagnac effect. Finally the anisotropy of the speed of light and its measurable
consequences in a reference frame co-moving with the Earth are discussed.


title: What local supersymmetry can do for quantum cosmology

abstract:
  The canonical approach to Riemannian quantum gravity is reviewed with
reference to local supersymmetry, to the classical boundary-value problem
arising from the Hartle-Hawking quantum state, and particularly for
(anti-)self-dual geometries. Two examples of the boundary-value problem for the
Einstein equations, possibly with a cosmological constant \Lambda, are treated,
both of Bianchi-IX type. These close smoothly in the interior with a NUT or a
BOLT. The Hamiltonian approach to general relativity is described using
Ashtekar variables; for non-zero \Lambda and anti-self-dual Weyl tensor, the
classical solution corresponds, with the most naive choice of boundary data, to
the Chern-Simons functional of the boundary data, the classical action being
I_{CS}. Hence, one is led to the corresponding quantum states exp(\pm I_{CS}).
Apparently, the classical solutions have the undesirable feature that, in
general, the resulting Riemannian classical geometry, arising from the
Hamilton-Jacobi equation, does not close smoothly in the interior. The
canonical quantum theory of supergravity is also described, and may lead to
very streamlined (finite) calculations of loop amplitudes for N=1 supergravity
with gauged supermatter. If one uses Ashtekar/Jacobson variables for canonical
supergravity, then again (for \Lambda\neq 0) one arrives at a (supersymmetric)
Chern-Simons action and quantum state in the (anti-)self-dual case.


title: Spin precession in the Dvali-Gabadadze-Porrati braneworld scenario

abstract:
  In this letter we work out the secular precession of the spin of a gyroscope
in geodesic motion around a central mass in the framework of the
Dvali-Gabadadze-Porrati multidimensional gravity model. Such an effect, which
depends on the mass of the central body and on the orbit radius of the
gyroscope, contrary to the precessions of the orbital elements of the orbit of
a test body, is far too small to be detected.


title: Naked singularity resolution in cylindrical collapse

abstract:
  In this paper, we study the gravitational collapse of null dust in the
cylindrically symmetric spacetime. The naked singularity necessarily forms at
the symmetry axis. We consider the situation in which null dust is emitted
again from the naked singularity formed by the collapsed null dust and
investigate the back-reaction by this emission for the naked singularity. We
show a very peculiar but physically important case in which the same amount of
null dust as that of the collapsed one is emitted from the naked singularity as
soon as the ingoing null dust hits the symmetry axis and forms the naked
singularity. In this case, although this naked singularity satisfies the strong
curvature condition by Kr\'{o}lak (limiting focusing condition), geodesics
which hit the singularity can be extended uniquely across the singularity.
Therefore we may say that the collapsing null dust passes through the
singularity formed by itself and then leaves for infinity. Finally the
singularity completely disappears and the flat spacetime remains.