title:
Scalar field self-force effects on orbits about a Schwarzschild black
  hole

abstract:
  For a particle of mass mu and scalar charge q, we compute the effects of the
scalar field self-force upon circular orbits, upon slightly eccentric orbits
and upon the innermost stable circular orbit of a Schwarzschild black hole of
mass M. For circular orbits the self force is outward and causes the angular
frequency at a given radius to decrease. For slightly eccentric orbits the self
force decreases the rate of the precession of the orbit. The effect of the self
force moves the radius of the innermost stable circular orbit inward by
0.122701 q^2/mu, and it increases the angular frequency of the ISCO by the
fraction 0.0291657 q^2/mu M.


title: Polygon model from first order gravity

abstract:
  The gauge fixed polygon model of 2+1 gravity with zero cosmological constant
and arbitrary number of spinless point particles is reconstructed from the
first order formalism of the theory in terms of the triad and the spin
connection. The induced symplectic structure is calculated and shown to agree
with the canonical one in terms of the variables.


title: On the gravitational energy of the Bonnor spacetime

abstract:
  In the paper we consider the energy and its flux in the Bonnor spacetime. We
construct some non-local expressions from the Einstein canonical
energy-momentum pseudotensor of the gravitational field which show that the
gravitational energy and its flux in this spacetime are different from zero and
do not vanish even outside of the material source (a stationary beam of the
null dust) of this spacetime.


title: Dynamics of dissipative gravitational collapse

abstract:
  The Misner and Sharp approach to the study of gravitational collapse is
extended to the dissipative case in, both, the streaming out and the diffusion
approximations. The role of different terms in the dynamical equation are
analyzed in detail. The dynamical equation is then coupled to a causal
transport equation in the context of Israel--Stewart theory. The decreasing of
the inertial mass density of the fluid, by a factor which depends on its
internal thermodynamics state, is reobtained, at any time scale. In accordance
with the equivalence principle, the same decreasing factor is obtained for the
gravitational force term. Prospective applications of this result to some
astrophysical scenarios are discussed.


title: Perturbation theory in covariant canonical quantization

abstract:
  I investigate a new idea of perturbation theory in covariant canonical
quantization. I present preliminary results for a toy model of a harmonic
oscillator with a quartic perturbation, and show that this method reproduces
the quantized spectrum of standard quantum theory. This result indicates that
when the exact solutions to classical equations are not known, covariant
canonical quantization via perturbation theory could be a viable approximation
scheme for finding observables, and suggests a physically interesting way of
extending the scope of covariant canonical quantization in quantum gravity


title:
Initial data for Einstein's equations with superposed gravitational
  waves

abstract:
  A method is presented to construct initial data for Einstein's equations as a
superposition of a gravitational wave perturbation on an arbitrary stationary
background spacetime. The method combines the conformal thin sandwich formalism
with linear gravitational waves, and allows detailed control over
characteristics of the superposed gravitational wave like shape, location and
propagation direction. It is furthermore fully covariant with respect to
spatial coordinate changes and allows for very large amplitude of the
gravitational wave.


title: Linear derivative Cartan formulation of General Relativity

abstract:
  Beside diffeomorphism invariance also manifest SO(3,1) local Lorentz
invariance is implemented in a formulation of Einstein Gravity (with or without
cosmological term) in terms of initially completely independent vielbein and
spin connection variables and auxiliary two-form fields. In the systematic
study of all possible embeddings of Einstein gravity into that formulation with
auxiliary fields, the introduction of a ``bi-complex'' algebra possesses
crucial technical advantages. Certain components of the new two-form fields
directly provide canonical momenta for spatial components of all Cartan
variables, whereas the remaining ones act as Lagrange multipliers for a large
number of constraints, some of which have been proposed already in different,
less radical approaches. The time-like components of the Cartan variables play
that role for the Lorentz constraints and others associated to the vierbein
fields. Although also some ternary ones appear, we show that relations exist
between these constraints, and how the Lagrange multipliers are to be
determined to take care of second class ones. We believe that our formulation
of standard Einstein gravity as a gauge theory with consistent local Poincare
algebra is superior to earlier similar attempts.


title:
New Numerical Methods to Evaluate Homogeneous Solutions of the Teukolsky
  Equation

abstract:
  We discuss a numerical method to compute the homogeneous solutions of the
Teukolsky equation which is the basic equation of the black hole perturbation
method. We use the formalism developed by Mano, Suzuki and Takasugi, in which
the homogeneous solutions of the radial Teukolsky equation are expressed in
terms of two kinds of series of special functions, and the formulas for the
asymptotic amplitudes are derived explicitly.Although the application of this
method was previously limited to the analytical evaluation of the homogeneous
solutions, we find that it is also useful for numerical computation. We also
find that so-called "renormalized angular momentum parameter", $\nu$, can be
found only in the limited region of $\omega$ for each $l,m$ if we assume $\nu$
is real (here, $\omega$ is the angular frequency, and $l$ and $m$ are degree
and order of the spin-weighted spheroidal harmonics respectively). We also
compute the flux of the gravitational waves induced by a compact star in a
circular orbit on the equatorial plane around a rotating black hole. We find
that the relative error of the energy flux is about $10^{-14}$ which is much
smaller than the one obtained by usual numerical integration methods.


title: Rigidity of cosmic acceleration in a class of k-essence cosmologies

abstract:
  We study the structural stability of a cosmic acceleration (inflation) in a
class of k-essence cosmologies against changes in the shape of the potential.
Those models may be viewed as generalized tachyon cosmologies and this analysis
extends previous results on the structural stability of cosmic acceleration in
tachyon cosmologies. The study considers both phantom and non-phantom cases.
The concepts of rigidity and fragility are defined through a condition on the
functional form of the Hubble factor. Given the known result of the existence
of inflationary (non-phantom) and super-inflationary (phantom) attractors we
formulate the question of their structural stability. We find that those
attractors are rigid in the sense that they never change as long as the
conditions for inflation or super-inflation are met.


title: Approaching Space Time Through Velocity in Doubly Special Relativity

abstract:
  We discuss the definition of velocity as dE/dp, where E,p are the energy and
momentum of a particle, in Doubly Special Relativity (DSR). If this definition
matches dx/dt appropriate for the space-time sector, then space-time can in
principle be built consistently with the existence of an invariant length
scale. We show that, within different possible velocity definitions, a
space-time compatible with momentum-space DSR principles can not be derived.


title:
Surface-integral expressions for the multipole moments of post-Newtonian
  sources and the boosted Schwarzschild solution

abstract:
  New expressions for the multipole moments of an isolated post-Newtonian
source, in the form of surface integrals in the outer near-zone, are derived.
As an application we compute the ``source'' quadrupole moment of a
Schwarzschild solution boosted to uniform velocity, at the third post-Newtonian
(3PN) order. We show that the consideration of this boosted Schwarzschild
solution (BSS) is enough to uniquely determine one of the ambiguity parameters
in the recent computation of the gravitational wave generation by compact
binaries at 3PN order: zeta=-7/33. We argue that this value is the only one for
which the Poincar\'e invariance of the 3PN wave generation formalism is
realized. As a check, we confirm the value of zeta by a different method, based
on the far-zone expansion of the BSS at fixed retarded time, and a calculation
of the relevant non-linear multipole interactions in the external metric at the
3PN order.


title:
Scalar self-force on a static particle in Schwarzschild using the
  massive field approach

abstract:
  We use the recently developed massive field approach to calculate the scalar
self-force on a static particle in a Schwarzschild spacetime. In this approach
the scalar self-force is obtained from the difference between the (massless)
scalar field, and an auxiliary massive scalar field combined with a certain
limiting process. By applying this approach to a static particle in
Schwarzschild we show that the scalar self-force vanishes in this case. This
result conforms with a previous analysis by Wiseman .


title: Relativistic numerical models for stationary superfluid Neutron Stars

abstract:
  We have developed a theoretical model and a numerical code for stationary
rotating superfluid neutron stars in full general relativity. The underlying
two-fluid model is based on Carter's covariant multi-fluid hydrodynamic
formalism. The two fluids, representing the superfluid neutrons on one hand,
and the protons and electrons on the other, are restricted to uniform rotation
around a common axis, but are allowed to have different rotation rates. We have
performed extensive tests of the numerical code, including quantitative
comparisons to previous approximative results for these models. The results
presented here are the first ``exact'' calculations of such models in the sense
that no approximations (other than that inherent in a discretized numerical
treatment) are used. Using this code we reconfirm the existence of
prolate-oblate shaped configurations. We studied the dependency of the Kepler
rotation limit and of the mass-density relation on the relative rotation rate.
We further demonstrate how one can simulate a (albeit fluid) neutron-star
``crust'' by letting one fluid extend further outwards than the other, which
results in interesting cases where the Kepler limit is actually determined by
the outermost but slower fluid.


title:
Second Order Gauge Invariant Perturbation Theory -- Perturbative
  curvatures in the two-parameter case --

abstract:
  Based on the gauge invariant variables proposed in our previous paper [K.
Nakamura, Prog. Theor. Phys. vol.110 (2003), 723.], some formulae of the
perturbative curvatures of each order are derived. We follow the general
framework of the second order gauge invariant perturbation theory on arbitrary
background spacetime to derive these formulae. These perturbative curvatures do
have the same form as the definitions of gauge invariant variables for
arbitrary perturbative fields which are previously proposed. As a result, we
explicitly see that any perturbative Einstein equations are given in terms of
gauge invarinat form. We briefly discuss physical situations to which this
framework should be applied.


title: Quasinormal modes in time-dependent black hole background

abstract:
  We have studied the evolution of the massless scalar field propagating in
time-dependent charged Vaidya black hole background. A generalized tortoise
coordinate transformation were used to study the evolution of the massless
scalar field. It is shown that, for the slowest damped quasinormal modes, the
approximate formulae in stationary Reissner-Nordstr\"{o}m black hole turn out
to be a reasonable prescription, showing that results from quasinormal mode
analysis are rather robust.


title: Dark Matter Prediction from Canonical Quantum Gravity with Frame Fixing

abstract:
  We show how, in canonical quantum cosmology, the frame fixing induces a new
energy density contribution having features compatible with the (actual) cold
dark matter component of the Universe. First we quantize the closed
Friedmann-Robertson-Walker (FRW) model in a sinchronous reference and determine
the spectrum of the super-Hamiltonian in the presence of ultra-relativistic
matter and a perfect gas contribution. Then we include in this model small
inhomogeneous (spherical) perturbations in the spirit of the Lemaitre-Tolman
cosmology. The main issue of our analysis consists in outlining that, in the
classical limit, the non-zero eigenvalue of the super-Hamiltonian can make
account for the present value of the dark matter critical parameter.
Furthermore we obtain a direct correlation between the inhomogeneities in our
dark matter candidate and those one appearing in the ultra-relativistic matter.


title: Patch dualities and remarks on nonstandard cosmologies

abstract:
  In this paper we establish dualities between inflationary, cyclic/ekpyrotic,
and phantom cosmologies within the patch formalism approximating high-energy
effects in scenarios with extra dimensions. The exact dualities relating the
four-dimensional spectra are broken in favour of their braneworld counterparts;
the dual solutions display new interesting features because of the modification
of the effective Friedmann equation on the brane. We then address some
qualitative issues about phantomlike cosmologies without phantom matter.


title:
Thermoelastic-damping noise from sapphire mirrors in a
  fundamental-noise-limited interferometer

abstract:
  We report the first high-precision interferometer using large sapphire
mirrors, and we present the first direct, broadband measurements of the
fundamental thermal noise in these mirrors. Our results agree well with the
thermoelastic-damping noise predictions of Braginsky, et al. [Phys. Lett. A
264, 1(1999)] and Cerdonio, et al.[Phys. Rev. D 63, 082003 (2001)], which have
been used to predict the astrophysical reach of advanced interferometric
gravitational wave detectors.


title: From Ginzburg-Landau to Hilbert-Einstein via Yamabe

abstract:
  In this work, based on some mathematical results obtained by Yamabe, Osgood,
Phillips and Sarnak, we demonstrate that in dimensions three and higher the
famous Ginzburg-Landau equations used in theory of phase transitions can be
obtained (without any approximations) by minimization of the Riemannian-type
Hilbert-Einstein action functional for pure gravity in the presence of
cosmological term. We use this observation in order to bring to completion the
work by Lifshitz (done in 1941) on group-theoretical refinements of the Landau
theory of phase transitions. In addition, this observation allows us to develop
a systematic extension to higher dimensions of known string-theoretic path
integral methods developed for calculation of observables in two dimensional
conformal field theories.


title:
Testing quantum superpositions of the gravitational field with
  Bose-Einstein condensates

abstract:
  We consider the gravity field of a Bose-Einstein condensate in a quantum
superposition. The gravity field then is also in a quantum superposition which
is in principle observable. Hence we have ``quantum gravity'' far away from the
so-called Planck scale.


title: A dynamical symmetry of the spherical dust collapse

abstract:
  By linearly scaling the initial data set (mass and kinetic energy functions)
together with the initial area radius of a collapsing dust sphere, we find a
symmetry of the collapse dynamics. That is, the linear transformation defines
an equivalence class of data sets which lead to the same end result as well as
its evolution all through. In particular, the density and shear remain
invariant initially as well as during the collapse. What the transformation is
exhibiting is an interesting scaling relationship between mass, kinetic energy
and the size of the collapsing dust sphere.


title: Braneworld Cosmological Models

abstract:
  The main cosmological models on the brane are presented. A generic equation
is given, from which the Friedmann equations of the Randall-Sundrum, induced
gravity, Gauss-Bonnet and the combined induced gravity and Gauss-Bonnet
cosmological models are obtained. We discuss the modifications they bring to
the standard cosmology and the main features of their inflationary dynamics.


title: Inhomogenized sudden future singularities

abstract:
  We find that sudden future singularities may also appear in spatially
inhomogeneous Stephani models of the universe. They are temporal pressure
singularities and may appear independently of the spatial finite density
singularities already known to exist in these models. It is shown that the main
advantage of the homogeneous sudden future singularities which is the
fulfillment of the strong and weak energy conditions may not be the case for
inhomogeneous models.


title: General relativity principle and uniqueness in Einstein equations

abstract:
  The issue of implementing the principle of general relativity in Einstein
equations has been widely discussed, since Kretschmann's well-known criticism
stated that general covariance of the Einstein equations is not suffice to
express the principle of general relativity (the equivalence of all the
coordinate systems). This failure is usually rooted in the fact that metric in
Einstein equations is not univocally determined by the matter distribution. We
show that the condition of univocal determination of the metric by the matter
distribution is stronger than the requirement of equivalence of all coordinate
systems. In order to separate the uniqueness problem in Einstein equations from
the issue of the principle of general relativity, we define the "equivalence
group" instead of the notion of covariance group which is empty of physical
content. Moreover, we have complemented in a positive way Kretschmann's
objection by supplementing Einstein equations with a sufficient condition for
the equivalence of all the coordinate systems.


title:
Time travel paradoxes, path integrals, and the many worlds
  interpretation of quantum mechanics

abstract:
  We consider two approaches to evading paradoxes in quantum mechanics with
closed timelike curves (CTCs). In a model similar to Politzer's, assuming pure
states and using path integrals, we show that the problems of paradoxes and of
unitarity violation are related; preserving unitarity avoids paradoxes by
modifying the time evolution so that improbable events bewcome certain. Deutsch
has argued, using the density matrix, that paradoxes do not occur in the "many
worlds interpretation". We find that in this approach account must be taken of
the resolution time of the device that detects objects emerging from a wormhole
or other time machine. When this is done one finds that this approach is viable
only if macroscopic objects traversing a wormhole interact with it so strongly
that they are broken into microscopic fragments.


title: Non-Riemannian geometry of turbulent acoustic flows and analog gravity

abstract:
  Non-Riemannian geometry of acoustic non-relativistic turbulent flows is
irrotationally perturbed generating a acoustic geometry model with acoustic
metric and acoustic Cartan contortion. The contortion term is due to
nonlinearities in the turbulent fluid. The acoustic curvature and acoustic
contortion are given by Dirac delta distributions. Violation of Lorentz
invariance due to turbulence is considered and analog gravity is suggested to
be linked to planar acoustic domain walls.


title:
On Detection of Black Hole Quasi-Normal Ringdowns: Detection Efficiency
  and Waveform Parameter Determination in Matched Filtering

abstract:
  Gravitational radiation from a slightly distorted black hole with ringdown
waveform is well understood in general relativity. It provides a probe for
direct observation of black holes and determination of their physical
parameters, masses and angular momenta (Kerr parameters). For ringdown searches
using data of gravitational wave detectors, matched filtering technique is
useful. In this paper, we describe studies on problems in matched filtering
analysis in realistic gravitational wave searches using observational data.
Above all, we focus on template constructions, matches or signal-to-noise
ratios (SNRs), detection probabilities for Galactic events, and accuracies in
evaluation of waveform parameters or black hole hairs. We have performed
matched filtering analysis for artificial ringdown signals which are generated
with Monte-Carlo technique and injected into the TAMA300 observational data. It
is shown that with TAMA300 sensitivity, the detection probability for Galactic
ringdown events is about 50% for black holes of masses greater than $20
M_{\odot}$ with SNR $> 10$. The accuracies in waveform parameter estimations
are found to be consistent with the template spacings, and resolutions for
black hole masses and the Kerr parameters are evaluated as a few % and $\sim 40
%$, respectively. They can be improved up to $< 0.9 %$ and $< 24 %$ for events
of ${\rm SNR} \ge 10$ by using fine-meshed template bank in the hierarchical
search strategy.


title: A dynamical evolution model on the black hole horizon

abstract:
  This paper demonstrates a dynamical evolution model of the black hole (BH)
horizon. The result indicates that a kinetic area-cells model of the BH's
horizon can model the evolution of BH due to the Hawking radiation, and this
area-cell system can be considered as an interacting geometrical particle
system. Thus the evolution turns into a problem of statistical physics. In the
present work, this problem is treated in the framework of non-equilibrium
statistics. It is proposed that each area-cell possesses the energy like a
microscopic black hole, and has the gravitational interaction with the other
area-cells. We consider both a non-interaction ideal system, and a system with
small nearest-neighbor interactions, and obtain an analytic expression of the
expected value of the horizon area of a dynamical BH. We find that, after a
long enough evolution, a dynamical BH with the Hawking radiation can be in
equilibrium with a finite temperature radiation field. However, we also find
that, the system has a critical point, and when the temperature of the
radiation field surrounding the BH approaches the critical temperature of the
BH, a critical slowing down phenomenon occurs.


title: Rotation Effects and The Gravito-Magnetic Approach

abstract:
  Gravito-electromagnetism is somewhat ubiquitous in relativity. In fact, there
are many situations where the effects of gravitation can be described by
formally introducing "gravito-electric" and "gravito-magnetic" fields, starting
from the corresponding potentials, in analogy with the electromagnetic theory
(see also A. Tartaglia's contribution to these proceedings). The "many faces of
gravito-electromagnetism" are related to rotation effects in both approximated
and full theory approaches. Here we show that, by using a 1+3 splitting,
relativistic dynamics can be described in terms of gravito-electromagnetic
(GEM) fields in full theory. On the basis of this formalism, we introduce a
"gravito-magnetic Aharonov-Bohm effect", which allows to interpret some
rotation effects as gravito-magnetic effects. Finally, we suggest a way for
measuring the angular momentum of celestial bodies by studying the
gravito-magnetic effects on the propagation of electromagnetic signals.


title: A Numerical Study of Boson Stars

abstract:
  We present a numerical study of general relativistic boson stars in both
spherical symmetry and axisymmetry. We consider both time-independent problems,
involving the solution of equilibrium equations for rotating boson stars, and
time-dependent problems, focusing on black hole critical behaviour associated
with boson stars.
  The study of the critical phenomena that arise at the threshold of black hole
formation has been a subject of intense interest among relativists and applied
mathematicians over the past decade. Type I critical phenomena were previously
observed in the dynamics of spherically symmetric boson stars by Hawley and
Choptuik. We extend this work and show that, contrary to previous claims, the
subcritical end-state is well described by a stable boson star executing a
large amplitude oscillation with a frequency in good agreement with that
predicted for the fundamental normal mode of the end-state star from linear
perturbation theory.
  We then extend our studies of critical phenomena to the axisymmetric case,
studying two distinct classes of parametrized families of initial data whose
evolution generates families of spacetimes that ``interpolate'' between those
than contain a black hole and those that do not. In both cases we find strong
evidence for a Type I transition at threshold, and are able to demonstrate
scaling of the lifetime for near-critical configurations of the type expected
for such a transition. This is the first time that Type I critical solutions
have been simulated in axisymmetry.


title: A Time-Like Naked Singularity

abstract:
  We construct a class of spherically symmetric collapse models in which a
naked singularity may develop as the end state of collapse. The matter
distribution considered has negative radial and tangential pressures, but the
weak energy condition is obeyed throughout. The singularity forms at the center
of the collapsing cloud and continues to be visible for a finite time. The
duration of visibility depends on the nature of energy distribution. Hence the
causal structure of the resulting singularity depends on the nature of the mass
function chosen for the cloud. We present a general model in which the naked
singularity formed is timelike, neither pointlike nor null. Our work represents
a step toward clarifying the necessary conditions for the validity of the
Cosmic Censorship Conjecture.


title: Doing without the Equivalence Principle

abstract:
  In Einstein's general relativity, geometry replaces the concept of force in
the description of the gravitation interaction. Such an approach rests on the
universality of free-fall--the weak equivalence principle--and would break down
without it. On the other hand, the teleparallel version of general relativity,
a gauge theory for the translation group, describes the gravitational
interaction by a force similar to the Lorentz force of electromagnetism, a
non-universal interaction. It is shown that, similarly to the Maxwell's
description of electromagnetism, the teleparallel gauge approach provides a
consistent theory for gravitation even in the absence of the weak equivalence
principle.


title: Space-time Curvature of Classical Electromagnetism

abstract:
  The space-time curvature carried by electromagnetic fields is discovered and
a new unification of geometry and electromagnetism is found. Curvature is
invariant under charge reversal symmetry. Electromagnetic field equations are
examined with De Rham co homology theory. Radiative electromagnetic fields must
be exact and co exact to preclude unobserved massless topological charges.
Weyl's conformal tensor, here called ``the gravitational field'', is decomposed
into a divergence-free non-local piece with support everywhere and a local
piece with the same support as the matter. By tuning a local gravitational
field to a Maxwell field the electromagnetic field's local gravitational field
is discovered. This gravitational field carries the electromagnetic field's
polarization or phase information, unlike Maxwell's stress-energy tensor. The
unification assumes Einstein's equations and derives Maxwell's equations from
curvature assumptions. Gravity forbids magnetic monopoles! This unification is
stronger than the Einstein-Maxwell equations alone, as those equations must
produce the electromagnetic field's local gravitational field and not just any
conformal tensor. Charged black holes are examples. Curvature of radiative null
electromagnetic fields is characterized.


title: Experimental Design for the LATOR Mission

abstract:
  This paper discusses experimental design for the Laser Astrometric Test Of
Relativity (LATOR) mission. LATOR is designed to reach unprecedented accuracy
of 1 part in 10^8 in measuring the curvature of the solar gravitational field
as given by the value of the key Eddington post-Newtonian parameter \gamma.
This mission will demonstrate the accuracy needed to measure effects of the
next post-Newtonian order (~G^2) of light deflection resulting from gravity's
intrinsic non-linearity. LATOR will provide the first precise measurement of
the solar quadrupole moment parameter, J2, and will improve determination of a
variety of relativistic effects including Lense-Thirring precession. The
mission will benefit from the recent progress in the optical communication
technologies -- the immediate and natural step above the standard radio-metric
techniques. The key element of LATOR is a geometric redundancy provided by the
laser ranging and long-baseline optical interferometry. We discuss the mission
and optical designs, as well as the expected performance of this proposed
mission. LATOR will lead to very robust advances in the tests of Fundamental
physics: this mission could discover a violation or extension of general
relativity, or reveal the presence of an additional long range interaction in
the physical law. There are no analogs to the LATOR experiment; it is unique
and is a natural culmination of solar system gravity experiments.


title:
Entropy in the NUT-Kerr-Newman Black Holes Due to an Arbitrary Spin
  Field

abstract:
  Membrane method is used to compute the entropy of the NUT-Kerr-Newman black
holes. It is found that even though the Euler characteristic is greater than
two, the Bekenstein-Hawking area law is still satisfied. The formula $S=\chi
A/8$ relating the entropy and the Euler characteristic becomes inapplicable for
non-extreme four dimensional NUT-Kerr-Newman black holes.


title: Cosmological dynamics of R^n gravity

abstract:
  A detailed analysis of dynamics of cosmological models based on $R^{n}$
gravity is presented. We show that the cosmological equations can be written as
a first order autonomous system and analyzed using the standard techniques of
dynamical system theory. In absence of perfect fluid matter, we find exact
solutions whose behavior and stability are analyzed in terms of the values of
the parameter $n$. When matter is introduced, the nature of the (non-minimal)
coupling between matter and higher order gravity induces restrictions on the
allowed values of $n$. Selecting such intervals of values and following the
same procedure used in the vacuum case, we present exact solutions and analyze
their stability for a generic value of the parameter $n$. From this analysis
emerges the result that for a large set of initial conditions an accelerated
expansion is an attractor for the evolution of the $R^n$ cosmology. When matter
is present a transient almost-Friedman phase can also be present before the
transition to an accelerated expansion.


title:
Collision of plane gravitational and electromagnetic waves in a
  Minkowski background: solution of the characteristic initial value problem

abstract:
  We consider the collisions of plane gravitational and electromagnetic waves
with distinct wavefronts and of arbitrary polarizations in a Minkowski
background. We first present a new, completely geometric formulation of the
characteristic initial value problem for solutions in the wave interaction
region for which initial data are those associated with the approaching waves.
We present also a general approach to the solution of this problem which
enables us in principle to construct solutions in terms of the specified
initial data. This is achieved by re-formulating the nonlinear dynamical
equations for waves in terms of an associated linear problem on the spectral
plane. A system of linear integral ``evolution'' equations which solve this
spectral problem for specified initial data is constructed. It is then
demonstrated explicitly how various colliding plane wave space-times can be
constructed from given characteristic initial data.


title: Higher dimensional black holes in external magnetic fields

abstract:
  We apply a Harrison transformation to higher dimensional asymptotically flat
black hole solutions, which puts them into an external magnetic field. First,
we magnetize the Schwarzschild-Tangherlini metric in arbitrary spacetime
dimension n>=4. The thus generated exact solution of the Einstein-Maxwell
equations describes a static black hole immersed in a Melvin "fluxbrane", and
generalizes previous results by Ernst for the case n=4. The magnetic field
deforms the shape of the event horizon, but the total area (as a function of
the mass) and the thermodynamics remain unaffected. The amount of flux through
a one-dimensional loop on the horizon exhibits a maximum for a finite value of
the magnetic field strength, and decreases for larger values. In the
Aichelburg-Sexl ultrarelativistic limit, the magnetized black hole becomes an
impulsive gravitational wave propagating in the Melvin background. Furthermore,
we discuss possible applications of a similar Harrison transformation to
rotating black objects. This enables us to magnetize the Myers-Perry hole and
the (dipole) Emparan-Reall ring at least in the special case when the vector
potential is parallel to a nonrotating Killing field. In particular, dipole
rings may be held in equilibrium even when their spin vanishes, thus
demonstrating (infinite) non-uniqueness of magnetized static uncharged black
holes in five dimensions. Physical properties of such rings are discussed.


title: Spacetime in String Theory

abstract:
  We give a brief overview of the nature of spacetime emerging from string
theory. This is radically different from the familiar spacetime of Einstein's
relativity. At a perturbative level, the spacetime metric appears as ``coupling
constants" in a two dimensional quantum field theory. Nonperturbatively (with
certain boundary conditions), spacetime is not fundamental but must be
reconstructed from a holographic, dual theory.


title:
Late-time phantom universe in ${\bf SO(1,1)}$ dark energy model with
  exponential potential

abstract:
  We discuss the late-time property of universe and phantom field in the
SO(1,1) dark energy model for the potential $V=V_0e^{-\beta\Phi^\alpha}$ with
$\alpha$ and $\beta$ two positive constants. We assume in advance some
conditions satisfied by the late-time field to simplify equations, which are
confirmed to be correct from the eventual results. For $\alpha<2$, the filed
falls exponentially off and the phantom equation of state rapidly approaches
-1. When $\alpha=2$, the kinetic energy $\rho_k$ and the coupling energy
$\rho_c$ become comparable but there is always $\rho_k<-\rho_c$ so that the
phantom property of field proceeds to hold. The analysis on the perturbation to
the late-time field $\Phi$ illustrates the square effective mass of the
perturbation field is always positive and thus the phantom is stable. The
universe considered currently may evade the future sudden singularity and will
evolve to de Sitter expansion phase.


title:
Detecting a stochastic background of gravitational waves by correlating
  n detectors

abstract:
  We discuss the optimal detection strategy for a stochastic background of
gravitational waves in the case n detectors are available. In literature so
far, only two cases have been considered: 2- and n-point correlators. We
generalize these analysises to m-point correlators (with m<n) built out of the
n detector signals, obtaining the result that the optimal choice is to combine
2-point correlators. Correlating n detectors in this optimal way will improve
the (suitably defined) signal-to-noise ratio with respect to the n=2 case by a
factor equal to the fourth root of n(n-1)/2. Finally we give an estimation of
how this could improve the sensitivity for a network of multi-mode spherical
antennas.


title: Unruh model for the Einstein-Rosen charge: Squealing Wormholes?

abstract:
  We present two kinds of acoustic models for the massless electric charge
conceived by Einstein and Rosen in the form of a bridge (wormhole throat). It
is found that the first kind of modelling requires a thin layer of exotic
matter at the bridge. We also derive an acoustic equation that exclusively
characterizes the model. Using a second kind of model, it is demonstrated that
the Einstein-Rosen charge has a sonic Hawking-Unruh temperature proportional to
+-1/$beta$, where $beta$ is the size of the charge. This suggests that
(squealing!) wormholes can also be formally accommodated into Unruh's fluid
model.


title:
Generation of Cosmological Seed Magnetic Fields from Inflation with
  Cutoff

abstract:
  Inflation has the potential to seed the galactic magnetic fields observed
today. However, there is an obstacle to the amplification of the quantum
fluctuations of the electromagnetic field during inflation: namely the
conformal invariance of electromagnetic theory on a conformally flat underlying
geometry. As the existence of a preferred minimal length breaks the conformal
invariance of the background geometry, it is plausible that this effect could
generate some electromagnetic field amplification. We show that this scenario
is equivalent to endowing the photon with a large negative mass during
inflation. This effective mass is negligibly small in a radiation and matter
dominated universe. Depending on the value of the free parameter of the theory,
we show that the seed required by the dynamo mechanism can be generated. We
also show that this mechanism can produce the requisite galactic magnetic field
without resorting to a dynamo mechanism.


title: Gravity and the Quantum

abstract:
  The goal of this article is to present a broad perspective on quantum gravity
for \emph{non-experts}. After a historical introduction, key physical problems
of quantum gravity are illustrated. While there are a number of interesting and
insightful approaches to address these issues, over the past two decades
sustained progress has primarily occurred in two programs: string theory and
loop quantum gravity. The first program is described in Horowitz's contribution
while my article will focus on the second. The emphasis is on underlying ideas,
conceptual issues and overall status of the program rather than mathematical
details and associated technical subtleties.


title: Discrete symmetries and general relativity, the dark side of gravity

abstract:
  None of the previous versions of this article is the one published in Int
Journ Mod Phys A which can be found on the journal server. A more recent and
living review of the DArk Gravity Theory can be found in gr-qc/0610079 .


title: Bianchi type I universe with viscous fluid: A qualitative analysis

abstract:
  The nature of cosmological solutions for a homogeneous, anisotropic Universe
given by a Bianchi type-I (BI) model in the presence of a Cosmological constant
$\Lambda$ is investigated by taking into account dissipative process due to
viscosity. The system in question is thoroughly studied both analytically and
numerically. It is shown the viscosity, as well as the $\Lambda$ term exhibit
essential influence on the character of the solutions. In particular a negative
$\Lambda$ gives rise to an ever-expanding Universe, whereas, a suitable choice
of initial conditions plus a positive $\Lambda$ can result in a
singularity-free oscillatory mode of expansion. For some special cases it is
possible to obtain oscillations in the exponential mode of expansion of the BI
model even with a negative $\Lambda$, where oscillations arise by virtue of
viscosity.


title: Experimental signatures of gravitational wave bursters

abstract:
  Gravitational wave bursters are sources which emit repeatedly bursts of
gravitational waves, and have been recently suggested as potentially
interesting candidates for gravitational wave (GW) detectors. Mechanisms that
could give rise to a GW burster can be found for instance in highly magnetized
neutron stars (the magnetars which explain the phenomenon of soft gamma
repeaters), in accreting neutron stars and in hybrid stars with a quark core.
We point out that these sources have very distinctive experimental signatures.
In particular, as already observed in the gamma-ray bursts from soft gamma
repeaters, the energy spectrum of the events is a power-law, dN\sim
E^{-\gamma}dE with \gamma\simeq 1.6, and they have a distribution of waiting
times (the times between one outburst and the next) significantly different
from the distribution of uncorrelated events. We discuss possible detection
strategies that could be used to search for these events in existing
gravitational wave detectors.


title: Why Solve the Hamiltonian Constraint in Numerical Relativity?

abstract:
  The indefinite sign of the Hamiltonian constraint means that solutions to
Einstein's equations must achieve a delicate balance--often among numerically
large terms that nearly cancel. If numerical errors cause a violation of the
Hamiltonian constraint, the failure of the delicate balance could lead to
qualitatively wrong behavior rather than just decreased accuracy. This issue is
different from instabilities caused by constraint-violating modes. Examples of
stable numerical simulations of collapsing cosmological spacetimes exhibiting
local mixmaster dynamics with and without Hamiltonian constraint enforcement
are presented.


title: Dynamical Charged N-body Equilibrium in Circular Dilaton Gravity

abstract:
  We extend the problem of $(1+1)$ circular dilaton gravity to include charged
particles. We examine the two (charged) particle case in detail and find an
exact equilibrium solution. We then extend this to $N-$particles and obtain a
solution for this case as well. This class of solutions corresponds to
$N$-particles of the same mass, spaced evenly around the circle with charges
chosen so that the electric field satisfies $E^{2}=$constant. We discuss the
relation of these solutions to the previous uncharged equilibrium solutions and
examine the behavior when the number of particles is large. We comment on the
challenges in further generalizing the solutions we obtain.


title:
Resonant Interaction Between a Weak Gravitational Wave and a Microwave
  Beam in the Double Polarized States Through a Static Magnetic Field

abstract:
  We investigate the resonant interaction to the weak gravitational waves in a
coupling electromagnetic system, which consists of a Gaussian beam with the
double polarized transverse electric modes, a static magnetic field and the
fractal membranes. We find that under the syncroresonance condition a
high-frequency GW (HFGW) of h=10^-30,v_g=3GHz may produce the perturbative
photon flux (PPF) of 2.15*10/s in a surface of 0.01m^2. The PPF can be pumped
out from the background photon fluxes and one might obtain the amplified signal
photon flux of 2.15*10^4s^-1 by cascade fractal membranes. It appears to be
worthwhile to study this effect for the detection of the high-frequency relic
GWs in quintessential inflationary models and the HFGWs expected by possible
laboratory schemes.


title:
Scalar fields on SL(2,R) and H^2 x R geometric spacetimes and linear
  perturbations

abstract:
  Using appropriate harmonics, we study the future asymptotic behavior of
massless scalar fields on a class of cosmological vacuum spacetimes. The
spatial manifold is assumed to be a circle bundle over a higher genus surface
with a locally homogeneous metric. Such a manifold corresponds to the
SL(2,R)-geometry (Bianchi VIII type) or the H^2 x R-geometry (Bianchi III
type). After a technical preparation including an introduction of suitable
harmonics for the circle-fibered Bianchi VIII to separate variables, we derive
systems of ordinary differential equations for the scalar field. We present
future asymptotic solutions for these equations in a special case, and find
that there is a close similarity with those on the circle-fibered Bianchi III
spacetime. We discuss implications of this similarity, especially to
(gravitational) linear perturbations. We also point out that this similarity
can be explained by the "fiber term dominated behavior" of the two models.


title:
Finite differencing second order systems describing black hole
  spacetimes

abstract:
  Keeping Einstein's equations in second order form can be appealing for
computational efficiency, because of the reduced number of variables and
constraints. Stability issues emerge, however, which are not present in first
order formulations. We show that a standard discretization of the second order
``shifted'' wave equation leads to an unstable semi-discrete scheme if the
shift parameter is too large. This implies that discretizations obtained using
integrators such as Runge-Kutta, Crank-Nicholson, leap-frog are unstable for
any fixed value of the Courant factor. We argue that this situation arises in
numerical relativity, particularly in simulations of spacetimes containing
black holes, and discuss several ways of circumventing this problem. We find
that the first order reduction in time based on ``ADM'' type variables is very
effective.


title:
Self-consistent invariant dynamics of scalar perturbations in the
  inflationary cosmology

abstract:
  The gauge-independent invariant approach to investigation of the linear
scalar perturbations of inflaton and gravitational fields is developed in
self-consistent way. This approach allows to compare various gauges used by
other researchers and to find unambiguous selection criteria of physical and
coordinate effects. We have shown that the so-called longitudinal gauge
commonly used for studying the gravitational instability leads to
overestimation of physical effects due to the presence of nonphysical proper
time perturbations. Equation of invariant dynamics (EID) is derived. The
general long-wave solution of EID for an arbitrary potential U(phi) has been
obtained. We have also found analytical solutions for all wave lengths at all
stages of the universe evolution in the framework of simplest potential
U(phi)=m^2*phi^2/2. We have constructed the analytical expressions for the
energy density perturbations spectrum Delta(k,t) at all possible k and t.
Amplitude of the long-wave spectrum in the case of the transition from short
waves to long ones occurs at the inflationary stage is almost flat, i.e. has
the Harrison-Zeldovich form, for arbitrary potential U(phi).


title: On Structure and History of Space-time with Variable Speed of Light

abstract:
  We apply the variable speed of light into general relativity in order to
solve the problems we met in the standard cosmology. We're surprised to find
that, the results from the general relativity in cosmology are exactly the same
as those we got from Newtonian dynamics. The relation between the Newtonian
dynamics and the relativistic dynamics can be demonstrated with the variable
speed of light. With this approach, some problems in the standard cosmology
such as the flatness problem and the horizon problem doesn't arise any more.
All the cosmological results and the physical results are reasonable and
natural. There are no any difficulties in the standard cosmology.


title: Full causal bulk viscous LRS Bianchi I with time varying constants

abstract:
  In this paper we study the evolution of a LRS Bianchi I Universe, filled with
a bulk viscous cosmological fluid in the presence of time varying constants
"but" taking into account the effects of a c-variable into the curvature
tensor. We find that the only physical models are those which ``constants'' $G$
and $c$ are growing functions on time $t$, while the cosmological constant
$\Lambda$ is a negative decreasing function. In such solutions the energy
density obeys the ultrastiff matter equation of state i.e. $\omega=1$.


title: Braneworld Cosmology

abstract:
  We present a general formalism for studying an inflationary scenario in the
two-brane system. We explain the gradient expansion method and obtain the
4-dimensional effective action. Based on this effective action, we give a basic
equations for the background homogeneous universe and the cosmological
perturbations. As an application, we propose a born-again braneworld scenario.


title: On The Higher Codimension Braneworld

abstract:
  We study a codimension 2 braneworld in the Einstein-Gauss-Bonnet gravity. In
the linear regime, we show the conventional Einstein gravity can be recovered
on the brane. While, in the nonlinear regime, we find corrections due to the
thickness and the bulk geometry.


title:
A Strange Detail Concerning the Variational Principle of General
  Relativity Theory

abstract:
  A mathematical complication due to an unnecessary formal assumption
concerning the variational principle of general relativity theory, which
apparently bothered Einstein and Hilbert, is shown and cleared up. Some
historical confusion seems caused by the impossibility to use the conventional
Euler-Lagrange formalism directly there, which even otherwise is nothing but
one of various possible procedures to apply the superior principle of least
action. Correspondingly to the absence of any direct calculation in the
literature so far, only a numerical modification in parts - explicitly taken
into account now after once mentioned by Hilbert without implementation - would
allow to compute the fundamental Einstein tensor density from these authors'
initial formulae, which must not be taken literally. Nevertheless adhering to a
merely symbolic Euler-Lagrange formalism, this needs a clear distinction
between 'component differentiation' and 'tensor differentiation' defined here.
Various corresponding solutions are shown including the probably most natural
one. Two of them are additionally verified in the detailed supplementary
material appended to the electronic edition of the note.


title: Nonstandard spin 2 field theory

abstract:
  It is usually accepted that General Relativity is the only consistent theory
which can be obtained starting from the linear Fiertz-Pauli Lagrangian. It is
the aim of the present paper to study whether, under certain requirements, a
different and consistent theory can be found. These requirements will be the
common ones encountered in flat field theory: removal of the non physical
degrees of freedom and conservation of the energy momentum currents determined
by Noether's Theorem. It will be shown that imposing certain constraint
(related to the elimination of the undesired components of the reducible
representation) on the field manifold, a consistent theory (at least to first
order in nonlinearties) is achieved. The theory obtained proceeding this way is
characterizd, to the lowest nonlinear order, by certain parameter epsilon.
General Relativity's corresponding term is found to be a limit case when the
parameter tends to zero. So, epsilon measures at this level the size of the
breaking of the global symmetry appearing in General Relativity i.e.
diff.invariance. It remains as open questions the matters of the theory's
solvability to all orders and the appearence of it's quantized version.


title: Vanishing Scalar Invariant Spacetimes in Higher Dimensions

abstract:
  We study manifolds with Lorentzian signature and prove that all scalar
curvature invariants of all orders vanish in a higher-dimensional Lorentzian
spacetime if and only if there exists an aligned non-expanding, non-twisting,
geodesic null direction along which the Riemann tensor has negative boost
order.


title: Higher Order Corrections to Black Hole Entropy

abstract:
  A scheme for calculating corrections to all orders to the entropy of any
thermodynamic system due to statistical fluctuations around equilibrium has
been developed. It is then applied to the BTZ black hole, AdS-Schwarzschild
black Hole and Schwarzschild black Hole in a cavity. The scheme that we present
is a model-independent scheme and hence universally applicable to all classical
black holes with positive specific heat. It has been seen earlier that the
microcanonical entropy of a system can be more accurately reproduced by
considering a logarithmic correction to the canonical entropy function. The
higher order corrections will be a step further in calculating the
microcanonical entropy of a black hole.


title:
A Nonlinear Coupling Network to Simulate the Development of the r-mode
  Instablility in Neutron Stars II. Dynamics

abstract:
  Two mechanisms for nonlinear mode saturation of the r-mode in neutron stars
have been suggested: the parametric instability mechanism involving a small
number of modes and the formation of a nearly continuous Kolmogorov-type
cascade. Using a network of oscillators constructed from the eigenmodes of a
perfect fluid incompressible star, we investigate the transition between the
two regimes numerically. Our network includes the 4995 inertial modes up to n<=
30 with 146,998 direct couplings to the r-mode and 1,306,999 couplings with
detuning< 0.002 (out of a total of approximately 10^9 possible couplings).
  The lowest parametric instability thresholds for a range of temperatures are
calculated and it is found that the r-mode becomes unstable to modes with
13<n<15. In the undriven, undamped, Hamiltonian version of the network the rate
to achieve equipartition is found to be amplitude dependent, reminiscent of the
Fermi-Pasta-Ulam problem. More realistic models driven unstable by
gravitational radiation and damped by shear viscosity are explored next. A
range of damping rates, corresponding to temperatures 10^6K to 10^9K, is
considered. Exponential growth of the r-mode is found to cease at small
amplitudes, approximately 10^-4. For strongly damped, low temperature models, a
few modes dominate the dynamics. The behavior of the r-mode is complicated, but
its amplitude is still no larger than about 10^-4 on average. For high
temperature, weakly damped models the r-mode feeds energy into a sea of
oscillators that achieve approximate equipartition. In this case the r-mode
amplitude settles to a value for which the rate to achieve equipartition is
approximately the linear instability growth rate.


title: Weyl geometry approach to describe planetary systems

abstract:
  In the present work we show that planetary mean distances can be calculated
through considering the Weyl geometry. We interpret the Weyl gauge field as a
vector field associated with the hypercharge of the particles and apply the
gauge concept of the Weyl geometry. The results obtained are shown to agree
with the observed orbits of all the planets and of the asteroid belt in the
solar system, with some empty states.


title:
Quasinormal modes, Superradiance and Area Spectrum for 2+1 Acoustic
  Black Holes

abstract:
  We present an exact expression for the quasinormal modes of acoustic
disturbances in a rotating 2+1 dimensional sonic black hole (draining bathtub
fluid flow) in the low frequency limit and evaluate the adiabatic invariant
proposed by Kunstatter. We also compute,via Bohr-Sommerfeld quantization rule
the equivalent area spectrum for this acoustic black hole, and we compute the
superradiance phenomena for pure spinning 2+1 black holes.


title: Chen-Wu type model and the total energy of the universe

abstract:
  The inclusion of a $\Lambda $ term, today, in the relativistic field
equations is consequence of the evolution of an observational cosmology. In
this work we argue the "ansatz" $\Lambda = \beta H^2 +\frac{\alpha}{R^2}$ is
applicable to the total energy density of the universe, discuss some
cosmological consequences and compare the growing mode of the density contrast
with the corresponding mode of the standard model.


title: May gravitons be super-strong interacting particles?

abstract:
  A scheme, in which gravitons are super-strong interacting, is described. The
graviton background with the Planckian spectrum and a small effective
temperature is considered as a reservoir of gravitons. A cross-section of
interaction of a graviton with any particle is assumed to be a bilinear
function of its energies. Any pair of bodies are attracting not due to an
exchange with its own gravitons, but due to a pressure of external gravitons of
this background. A graviton pairing is necessary to obtain classical gravity.
Any divergencies are not possible in such the model because of natural smooth
cut-offs of the graviton spectrum from both sides. Some cosmological
consequences of this scheme are discussed, too. Also it is shown here that the
main conjecture of this approach may be verified at present on the Earth.


title: A Note on the Generalization of the GEMS Approach

abstract:
  This paper is a supplement of our earlier work JHEP 0410 (2004)
011[gr-qc/0409107].We map the vector potential of charged black holes into GEMS
and find that its effect on the thermal spectrum is the same as that on the
black hole side, i.e., it will induce a chemical potential in the thermal
spectrum which is the same as that in the charged black holes.We also argue
that the generalization of GEMS approach to non-stationary motions is not
possible.


title: Can a circulating light beam produce a time machine?

abstract:
  In a recent paper, Mallett found a solution of the Einstein equations in
which closed timelike curves (CTC's) are present in the empty space outside an
infinitely long cylinder of light moving in circular paths around an axis. Here
we show that, for physically realistic energy densities, the CTC's occur at
distances from the axis greater than the radius of the visible universe by an
immense factor. We then show that Mallett's solution has a curvature
singularity on the axis, even in the case where the intensity of the light
vanishes. Thus it is not the solution one would get by starting with Minkowski
space and establishing a cylinder of light.


title: Gauge pathologies in singularity-avoidant spacetime foliations

abstract:
  The family of generalized-harmonic gauge conditions, which is currently used
in Numerical Relativity for its singularity-avoidant behavior, is analyzed by
looking for pathologies of the corresponding spacetime foliation. The
appearance of genuine shocks, arising from the crossing of characteristic
lines, is completely discarded. Runaway solutions, meaning that the lapse
function can grow without bound at an accelerated rate, are instead predicted.
Black Hole simulations are presented, showing spurious oscillations due to the
well known slice stretching phenomenon. These oscillations are made to
disappear by switching the numerical algorithm to a high-resolution
shock-capturing one, of the kind currently used in Computational Fluid
Dynamics. Even with these shock-capturing algorithms, runaway solutions are
seen to appear and the resulting lapse blow-up is causing the simulations to
crash. As a side result, a new method is proposed for obtaining regular initial
data for Black Hole spacetimes, even inside the horizons.


title:
Minisuperspace, WKB, Quantum States of General Relativistic Extended
  Objects

abstract:
  The dynamics of relativistic thin shells is a recurrent topic in the
literature about the classical theory of gravitating systems and the still
ongoing attempts to obtain a coherent description of their quantum behavior.
Certainly, a good reason to make this system a preferred one for many models is
the clear, synthetic description given by Israel junction conditions. Using
some results from an effective Lagrangian approach to the dynamics of
spherically symmetric shells, we show a general way to obtain WKB states for
the system; a simple example is also analyzed.


title: Horizon Pretracking

abstract:
  We introduce horizon pretracking as a method for analysing numerically
generated spacetimes of merging black holes. Pretracking consists of following
certain modified constant expansion surfaces during a simulation before a
common apparent horizon has formed. The tracked surfaces exist at all times,
and are defined so as to include the common apparent horizon if it exists. The
method provides a way for finding this common apparent horizon in an efficient
and reliable manner at the earliest possible time. We can distinguish inner and
outer horizons by examining the distortion of the surface. Properties of the
pretracking surface such as its expansion, location, shape, area, and angular
momentum can also be used to predict when a common apparent horizon will
appear, and its characteristics. The latter could also be used to feed back
into the simulation by adapting e.g. boundary or gauge conditions even before
the common apparent horizon has formed.


title: Spinning test particles and clock effect in Schwarzschild spacetime

abstract:
  We study the behaviour of spinning test particles in the Schwarzschild
spacetime. Using Mathisson-Papapetrou equations of motion we confine our
attention to spatially circular orbits and search for observable effects which
could eventually discriminate among the standard supplementary conditions
namely the Corinaldesi-Papapetrou, Pirani and Tulczyjew. We find that if the
world line chosen for the multipole reduction and whose unit tangent we denote
as $U$ is a circular orbit then also the generalized momentum $P$ of the
spinning test particle is tangent to a circular orbit even though $P$ and $U$
are not parallel four-vectors. These orbits are shown to exist because the spin
induced tidal forces provide the required acceleration no matter what
supplementary condition we select. Of course, in the limit of a small spin the
particle's orbit is close of being a circular geodesic and the (small)
deviation of the angular velocities from the geodesic values can be of an
arbitrary sign, corresponding to the possible spin-up and spin-down alignment
to the z-axis. When two spinning particles orbit around a gravitating source in
opposite directions, they make one loop with respect to a given static observer
with different arrival times. This difference is termed clock effect. We find
that a nonzero gravitomagnetic clock effect appears for oppositely orbiting
both spin-up or spin-down particles even in the Schwarzschild spacetime. This
allows us to establish a formal analogy with the case of (spin-less) geodesics
on the equatorial plane of the Kerr spacetime. This result can be verified
experimentally.


title: Spinning test particles and clock effect in Kerr spacetime

abstract:
  We study the motion of spinning test particles in Kerr spacetime using the
Mathisson-Papapetrou equations; we impose different supplementary conditions
among the well known Corinaldesi-Papapetrou, Pirani and Tulczyjew's and analyze
their physical implications in order to decide which is the most natural to
use. We find that if the particle's center of mass world line, namely the one
chosen for the multipole reduction, is a spatially circular orbit (sustained by
the tidal forces due to the spin) then the generalized momentum $P$ of the test
particle is also tangent to a spatially circular orbit intersecting the center
of mass line at a point. There exists one such orbit for each point of the
center of mass line where they intersect; although fictitious, these orbits are
essential to define the properties of the spinning particle along its physical
motion. In the small spin limit, the particle's orbit is almost a geodesic and
the difference of its angular velocity with respect to the geodesic value can
be of arbitrary sign, corresponding to the spin-up and spin-down possible
alignment along the z-axis. We also find that the choice of the supplementary
conditions leads to clock effects of substantially different magnitude. In
fact, for co-rotating and counter-rotating particles having the same spin
magnitude and orientation, the gravitomagnetic clock effect induced by the
background metric can be magnified or inhibited and even suppressed by the
contribution of the individual particle's spin. Quite surprisingly this
contribution can be itself made vanishing leading to a clock effect
undistiguishable from that of non spinning particles. The results of our
analysis can be observationally tested.


title: The Pioneer anomaly as acceleration of the clocks

abstract:
  This work proposes an explanation of the Pioneer anomaly, the unmodelled and
as yet unexplained blueshift detected in the microwave signal of the Pioneer 10
and other spaceships by Anderson {\it et al} in 1998. What they observed is
similar to the effect that would have either (i) an anomalous acceleration
$a_{\rm P}$ of the ship towards the Sun or (ii) an acceleration of the clocks
$a_{\rm t}=a_{\rm P}/c$. The second alternative is investigated here, with a
phenomenological model in which the anomaly is an effect of the background
gravitational potential $\Psi (t)$ that pervades all the universe and is
increasing because of the expansion. It is shown that $2a_{\rm t}={\rm d}\Psi
/{\rm d}t ={\rm d}^2\tau_{\rm clocks} /{\rm d}t^2$, evaluated at present time
$t_0$, where $t$ and $\tau_{\rm clocks}$ are the coordinate time and the time
measured by the clocks, respectively. The result of a simple estimate gives the
value $a_{\rm t}\simeq 1.8\times 10^{-18}{s}^{-1}$, while Anderson {\it et al}
suggested $a_{\rm t}= (2.9\pm 0.4)\times 10^{-18}{s}^{-1}$ on the basis of
their observations. The calculation are performed near the Newtonian limit but
in the frame of general relativity.


title: Freely falling observers

abstract:
  We show that the field equations of the Schwarzschild geometry are invariant
under passive Lorentz transformations to a freely falling system. We decompose
the field equations with respect to the accelerated system and find that the
force of gravity is not transformed away but dynamically compensated.


title: A brief commentary on black hole entropy

abstract:
  It is commonplace, in the literature, to find that the Bekenstein-Hawking
entropy has been endowed with having an explicit statistical interpretation. In
the following essay, we discuss why such a viewpoint warrants a certain degree
of caution.


title: Energy conditions, traversable wormholes and dust shells

abstract:
  Firstly, we review the pointwise and averaged energy conditions, the quantum
inequality and the notion of the ``volume integral quantifier'', which provides
a measure of the ``total amount'' of energy condition violating matter.
Secondly, we present a specific metric of a spherically symmetric traversable
wormhole in the presence of a generic cosmological constant, verifying that the
null and the averaged null energy conditions are violated, as was to be
expected. Thirdly, a pressureless dust shell is constructed around the interior
wormhole spacetime by matching the latter geometry to a unique vacuum exterior
solution. In order to further minimize the usage of exotic matter, we then find
regions where the surface energy density is positive, thereby satisfying all of
the energy conditions at the junction surface. An equation governing the
behavior of the radial pressure across the junction surface is also deduced.
Lastly, taking advantage of the construction, specific dimensions of the
wormhole, namely, the throat radius and the junction interface radius, and
estimates of the total traversal time and maximum velocity of an observer
journeying through the wormhole, are also found by imposing the traversability
conditions.


title: Wormhole throats in $R^{m}$ gravity

abstract:
  We consider wormhole geometries subject to a gravitational action consisting
of non-linear powers of the Ricci scalar. Specifically, wormhole throats are
studied in the case where Einstein gravity is supplemented with a Ricci-squared
and inverse Ricci term. In this modified theory it is found that static
wormhole throats respecting the weak energy condition can exist. The analysis
is done locally in the vicinity of the throat, which eliminates certain
restrictions on the models introduced by considering the global topology.


title: Spinning Up Asymptotically Flat Spacetimes

abstract:
  We present a method for constructing stationary, asymptotically flat,
rotating solutions of Einstein's field equations. One of the spun-up solutions
has quasilocal mass but no global mass. It has an ergosphere but no event
horizon. The angular momentum is constant everywhere beyond the ergosphere. The
energy-momentum content of this solution can be interpreted as a rotating
string-fluid.


title: Warped products and FRW cosmology

abstract:
  We study the Friedmann-Robertson-Walker cosmological model to investigate
non-smooth curvatures associated with multiple discontinuities involved in the
evolution of the universe, by exploiting Lorentzian warped product scheme.
Introducing double discontinuities occurred at the radiation-matter and
matter-lambda phase transitions, we also discuss non-smooth features of the
spatially flat Friedmann-Robertson-Walker universe.


title: New Regular Solutions with Axial Symmetry in Einstein-Yang-Mills Theory

abstract:
  We construct new regular solutions in Einstein-Yang-Mills theory. They are
static, axially symmetric and asymptotically flat. They are characterized by a
pair of integers (k,n), where k is related to the polar angle and $n$ to the
azimuthal angle. The known spherically and axially symmetric EYM solutions have
k=1. For k>1 new solutions arise, which form two branches. They exist above a
minimal value of n, that increases with k. The solutions on the lower mass
branch are related to certain solutions of Einstein-Yang-Mills-Higgs theory,
where the nodes of the Higgs field form rings.


title: Improved WKB analysis of cosmological perturbations

abstract:
  Improved Wentzel-Kramers-Brillouin (WKB)-type approximations are presented in
order to study cosmological perturbations beyond the lowest order. Our methods
are based on functions which approximate the true perturbation modes over the
complete range of the independent (Langer) variable, from sub-horizon to
super-horizon scales, and include the region near the turning point. We employ
both a perturbative Green's function technique and an adiabatic (or
``semiclassical'') expansion (for a linear turning point) in order to compute
higher order corrections. Improved general expressions for the WKB scalar and
tensor power spectra are derived for both techniques. We test our methods on
the benchmark of power-law inflation, which allows comparison with exact
expressions for the perturbations, and find that the next-to-leading order
adiabatic expansion yields the amplitude of the power spectra with excellent
accuracy, whereas the next-to-leading order with the perturbative Green's
function method does not improve the leading order result significantly.
However, in more general cases, either or both methods may be useful.


title: Fundamentals of the LISA Stable Flight Formation

abstract:
  The joint NASA-ESA mission LISA relies crucially on the stability of the
three spacecraft constellation. Each of the spacecraft is in heliocentric
orbits forming a stable triangle. The principles of such a formation flight
have been formulated long ago and analysis performed, but seldom presented if
ever, even to LISA scientists. We nevertheless need these details in order to
carry out theoretical studies on the optical links, simulators etc. In this
article, we present in brief, a model of the LISA constellation, which we
believe will be useful for the LISA community.


title:
Invariant operator due to F. Klein quantizes H. Poincare's dodecahedral
  3-manifold

abstract:
  The eigenmodes of the Poincar\'e dodecahedral 3-manifold $M$ are constructed
as eigenstates of a novel invariant operator. The topology of $M$ is
characterized by the homotopy group $\pi_1(M)$, given by loop composition on
$M$, and by the isomorphic group of deck transformations $deck(\tilde{M})$,
acting on the universal cover $\tilde{M}$. ($\pi_1(M)$, $\tilde{M}$) are known
to be the binary icosahedral group ${\cal H}_3$ and the sphere $S^3$
respectively.
  Taking $S^3$ as the group manifold $SU(2,C)$ it is shown that
$deck(\tilde{M}) \sim {\cal H}^r_3$ acts on $SU(2,C)$ by right multiplication.
A semidirect product group is constructed from ${\cal H}^r_3$ as normal
subgroup and from a second group ${\cal H}^c_3$ which provides the icosahedral
symmetries of $M$. Based on F. Klein's fundamental icosahedral ${\cal
H}_3$-invariant, we construct a novel hermitian ${\cal H}_3$-invariant
polynomial (generalized Casimir) operator ${\cal K}$. Its eigenstates with
eigenvalues $\kappa$ quantize a complete orthogonal basis on Poincar\'{e}'s
dodecahedral 3-manifold. The eigenstates of lowest degree $\lambda=12$ are 12
partners of Klein's invariant polynomial. The analysis has applications in
cosmic topology \cite{LA},\cite{LE}. If the Poincar\'{e} 3-manifold $M$ is
assumed to model the space part of a cosmos, the observed temperature
fluctuations of the cosmic microwave background must admit an expansion in
eigenstates of ${\cal K}$.


abstract:
  Binary black hole spacetimes with a helical Killing vector, which are
discussed as an approximation for the early stage of a binary system, are
studied in a projection formalism. In this setting the four dimensional
Einstein equations are equivalent to a three dimensional gravitational theory
with a $SL(2,\mathbb{C})/SO(1,1)$ sigma model as the material source. The sigma
model is determined by a complex Ernst equation. 2+1 decompositions of the
3-metric are used to establish the field equations on the orbit space of the
Killing vector. The two Killing horizons of spherical topology which
characterize the black holes, the cylinder of light where the Killing vector
changes from timelike to spacelike, and infinity are singular points of the
equations. The horizon and the light cylinder are shown to be regular
singularities, i.e. the metric functions can be expanded in a formal power
series in the vicinity. The behavior of the metric at spatial infinity is
studied in terms of formal series solutions to the linearized Einstein
equations. It is shown that the spacetime is not asymptotically flat in the
strong sense to have a smooth null infinity under the assumption that the
metric tends asymptotically to the Minkowski metric. In this case the metric
functions have an oscillatory behavior in the radial coordinate in a
non-axisymmetric setting, the asymptotic multipoles are not defined. The
asymptotic behavior of the Weyl tensor near infinity shows that there is no
smooth null infinity.


title: Phantom Cosmology with Non-minimally Coupled Real Scalar Field

abstract:
  We find that the expansion of the universe is accelerating by analyzing the
recent observation data of type $\textsc{I}a$ supernova(SN-Ia) .It indicates
that the equation of state of the dark energy might be smaller than -1,which
leads to the introduction of phantom models featured by its negative kinetic
energy to account for the regime of equation of state parameter $w<-1$.In this
paper the possibility of using a non-minimally coupled real scalar field as
phantom to realize the equation of state parameter $w<-1$ is discussed.The main
equations which govern the evolution of the universe are obtained.Then we
rewrite them with the observable quantities.


title: Some aspects of the scalar-tensor theory

abstract:
  The scalar-tensor theory of gravitation has been and still is one of the most
widely discussed "alternative theories" to General Relativity (GR). Despite
nearly half a century of its age, it continues to attract renewed interests of
not only theorists but also experimentalists when we now face such issues like
the accelerating universe and possible time-variability of the fine-structure
constant, both viewed as something beyond the standard GR. It appears that the
theory provides realistic results sometimes even beyond what is expected from
the quintessence approach aimed primarily to be more phenomenological. It seems
nevertheless as if some of the unique aspects of this theory are not fully
understood, even leading to occasional confusions. I try in my lectures, partly
using the contents of our book (Y.F. and K. Maeda, Scalar-tensor theory of
gravitation, Cambridge University Press, 2003), to discuss some of the most
crucial concepts starting from elementary introduction to the theory.
Particular emphases will be placed on the unique features of the nonminimal
coupling term, the roles of the conformal transformations together with the
choice of a physical conformal frame and the value of the coupling strength to
the matter. Readers are advised to refer to the references for more details.


title: Inertial effects of an accelerating black hole

abstract:
  We consider the static vacuum C metric that represents the gravitational
field of a black hole of mass $m$ undergoing uniform translational acceleration
$A$ such that $mA<1/(3\sqrt{3})$. The influence of the inertial acceleration on
the exterior perturbations of this background are investigated. In particular,
we find no evidence for a direct spin-acceleration coupling.


title: Problems in field theoretical approach to gravitation

abstract:
  We consider gravitational self interaction in the lowest approximation and
assume that graviton interacts with gravitational energy-momentum tensor in the
same way as it interacts with particles. We show that, using gravitational
vertex with a preferred gravitational energy-momentum tensor, it is possible to
obtain a metric necessary for explaining perihelion precession. The preferred
gravitational energy-momentum tensor gives positive gravitational energy
density of Newtonian center. We show also that, employing "improvement"
technique, any gravitational energy-momentum tensor can be made suitable for
using in gravitational wave equation for obtaining metric which explains
perihelion precession. Yet the "improvement" leads to negative gravitational
energy density of the Newtonian center.


title: Algebraic stability analysis of constraint propagation

abstract:
  The divergence of the constraint quantities is a major problem in
computational gravity today. Apparently, there are two sources for constraint
violations. The use of boundary conditions which are not compatible with the
constraint equations inadvertently leads to 'constraint violating modes'
propagating into the computational domain from the boundary. The other source
for constraint violation is intrinsic. It is already present in the initial
value problem, i.e. even when no boundary conditions have to be specified. Its
origin is due to the instability of the constraint surface in the phase space
of initial conditions for the time evolution equations. In this paper, we
present a technique to study in detail how this instability depends on gauge
parameters. We demonstrate this for the influence of the choice of the time
foliation in context of the Weyl system. This system is the essential
hyperbolic part in various formulations of the Einstein equations.


title:
Classical model of elementary particle with Bertotti-Robinson core and
  extremal black holes

abstract:
  We discuss the question, whether the Reissner-Nordstr\"{o}m RN) metric can be
glued to another solutions of Einstein-Maxwell equations in such a way that (i)
the singularity at r=0 typical of the RN metric is removed (ii), matching is
smooth. Such a construction could be viewed as a classical model of an
elementary particle balanced by its own forces without support by an external
agent. One choice is the Minkowski interior that goes back to the old Vilenkin
and Fomin's idea who claimed that in this case the bare delta-like stresses at
the horizon vanish if the RN metric is extremal. However, the relevant entity
here is the integral of these stresses over the proper distance which is
infinite in the extremal case. As a result of the competition of these two
factors, the Lanczos tensor does not vanish and the extremal RN cannot be glued
to the Minkowski metric smoothly, so the elementary-particle model as a ball
empty inside fails. We examine the alternative possibility for the extremal RN
metric - gluing to the Bertotti-Robinson (BR) metric. For a surface placed
outside the horizon there always exist bare stresses but their amplitude goes
to zero as the radius of the shell approaches that of the horizon. This limit
realizes the Wheeler idea of "mass without mass" and "charge without charge".
We generalize the model to the extremal Kerr-Newman metric glued to the
rotating analog of the BR metric.


title:
Tracing the geometry around a massive, axisymmetric body to measure,
  through gravitational waves, its mass moments and electromagnetic moments

abstract:
  The geometry around a rotating massive body, which carries charge and
electrical currents, could be described by its multipole moments (mass moments,
mass-current moments, electric moments, and magnetic moments). When a small
body is orbiting this massive body, it will move on geodesics, at least for a
time interval that is short with respect to the characteristic time of the
binary due to gravitational radiation. By monitoring the waves emitted by the
small body we are actually tracing the geometry of the central object, and
hence, in principle, we can infer all its multipole moments. This paper is a
generalization of previous similar results by Ryan. The fact that the
electromagnetic moments of spacetime can be measured demonstrates that one can
obtain information about the electromagnetic field purely from gravitational
wave analysis. Additionally, these measurements could be used as a test of the
no-hair theorem for black holes.


title: Symmetries at stationary Killing horizons

abstract:
  It has often been suggested (especially by Carlip) that spacetime symmetries
in the neighborhood of a black hole horizon may be relevant to a statistical
understanding of the Bekenstein-Hawking entropy. A prime candidate for this
type of symmetry is that which is exhibited by the Einstein tensor. More
precisely, it is now known that this tensor takes on a strongly constrained
(block-diagonal) form as it approaches any stationary, non-extremal Killing
horizon. Presently, exploiting the geometrical properties of such horizons, we
provide a particularly elegant argument that substantiates this highly
symmetric form for the Einstein tensor. It is, however, duly noted that, on
account of a "loophole", the argument does fall just short of attaining the
status of a rigorous proof.


title: Causal sites as quantum geometry

abstract:
  We propose a structure called a causal site to use as a setting for quantum
geometry, replacing the underlying point set. The structure has an interesting
categorical form, and a natural "tangent 2-bundle," analogous to the tangent
bundle of a smooth manifold. Examples with reasonable finiteness conditions
have an intrinsic geometry, which can approximate classical solutions to
general relativity. We propose an approach to quantization of causal sites as
well.


title:
A source of a quasi--spherical space--time: The case for the M--Q
  solution

abstract:
  We present a physically reasonable source for an static, axially--symmetric
solution to the Einstein equations. Arguments are provided, supporting our
belief that the exterior space--time produced by such source, describing a
quadrupole correction to the Schwarzschild metric, is particularly suitable
(among known solutions of the Weyl family) for discussing the properties of
quasi--spherical gravitational fields.


title: Preheating and Dark Sector of Universe

abstract:
  Regarding long life particles produced during preheating after inflation as
dark matter, we find that its back reaction on the field $\phi$ could lock
$\phi$ in a false vacuum up to today. This false vacuum can drive the
accelerated expansion of universe at late time and play the role of dark
energy. When the number density of dark matter particles is dilute to some
value, the field $\phi$ becomes tachyonic and rolls to its true minima rapidly,
and the acceleration of universe ceases. We discuss the constraints on the
parameters of model from the observations of dark energy and dark matter halos
on subgalactic scale.


title:
Quasinormal modes and stability of the rotating acoustic black hole:
  numerical analysis

abstract:
  The study of the quasinormal modes (QNMs) of the 2+1 dimensional rotating
draining bathtub acoustic black hole, the closest analogue found so far to the
Kerr black hole, is performed. Both the real and imaginary parts of the
quasinormal (QN) frequencies as a function of the rotation parameter B are
found through a full non-linear numerical analysis. Since there is no change in
sign in the imaginary part of the frequency as B is increased we conclude that
the 2+1 dimensional rotating draining bathtub acoustic black hole is stable
against small perturbations.

categories: gr-qc astro-ph hep-ph hep-th physics.flu-dyn


title: Quasinormal modes of charged black holes in string theory

abstract:
  Both scalar and Dirac quasinormal modes in Garfinkle-Horowitz-Strominger
black hole spacetime are studied by using the WKB approximation and the
P\"{o}schl-Teller approximation. For scalar field, we find that the QNMs with
higher dilatons decay more rapidly than that with lower ones. However, this is
not the case for mass $m$. Fields with higher mass will decay more slowly. The
similar behaviors appear in the case of Dirac field. We also find that QNM
frequencies evaluated by using WKB approximation and P\"{o}schl-Teller
approximation have a good agreement with each other when mode number $n$ is
small.


title: Electromagnetic Magic: The Relativistically Rotating Disk

abstract:
  A closed form analytic solution is found for the electromagnetic field of the
charged uniformly rotating conducting disk for all values of the tip speed $v$
up to $c$. For $v=c$ it becomes the Magic field of the Kerr-Newman black hole
with $G$ set to zero.
  The field energy, field angular momentum and gyromagnetic ratio are
calculated and compared with those of the electron.
  A new mathematical expression that sums products of 3 Legendre functions each
of a different argument, is demonstrated.


title:
Some comments about a recent paper on the measurement of the general
  relativistic Lense-Thirring effect in the gravitational field of the Earth
  with the laser-ranged LAGEOS and LAGEOS II satellites

abstract:
  In this brief note some comments about the observable used in a recently
published paper on the measurement of the general relativistic Lense-Thirring
in the gravitational field of the Earth are presented. It turns out that, among
other things, the authors might have yielded an optimistic evaluation of the
error budget because of an underestimation of the impact of the secular
variations of the even zonal harmonics of the geopotential. More realistic
evaluations point towards a 15-45% error at 1-3sigma level, respectively.

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


title: Regularized dualities in patch cosmology

abstract:
  Following past investigations, we explore the symmetries of the
Hamilton-Jacobi cosmological equations in the generalized patch formalism
describing braneworld and tachyon scenarios. Dualities between different
patches are established and regular dual solutions, either contracting or
phantom-like, are constructed.


title: Quantum cosmology and the accelerated Universe

abstract:
  The quantized Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) model minimally
coupled to a free massless scalar field is studied and interpreted in the
Bohm-de Broglie framework. We analyze the quantum bohmian trajectories
corresponding to a certain class of gaussian packets, solutions of the
Wheeler-DeWitt equation. We show that these bohmian trajectories undergo an
accelerated expansion in the middle of its evolution due to the presence of
quantum cosmological effects in this period. It is shown that the
luminosity-redshift relation in the quantum cosmological model can be made
close to the corresponding relation coming from the classical model suplemented
by a cosmological constant, for $z<1$. In this way we have the posibility of
interpreting the present observations of high redshift supernovae as the
consequence of a quantum cosmological effect.


title:
Interpreting doubly special relativity as a modified theory of
  measurement

abstract:
  In this article we develop a physical interpretation for the deformed
(doubly) special relativity theories (DSRs), based on a modification of the
theory of measurement in special relativity. We suggest that it is useful to
regard the DSRs as reflecting the manner in which quantum gravity effects
induce Planck-suppressed distortions in the measurement of the "true" energy
and momentum. This interpretation provides a framework for the DSRs that is
manifestly consistent, non-trivial, and in principle falsifiable. However, it
does so at the cost of demoting such theories from the level of "fundamental"
physics to the level of phenomenological models -- models that should in
principle be derivable from whatever theory of quantum gravity one ultimately
chooses to adopt.


title:
Classical and Quantum Singularities of Levi-Civita Spacetimes with and
  without a Positive Cosmological Constant

abstract:
  Levi-Civita spacetimes have classical naked singularities. They also have
quantum singularities. Quantum singularities in general relativistic spacetimes
are determined by the behavior of quantum test particles. A static spacetime is
said to be quantum mechanically singular if the spatial portion of the wave
operator is not essentially self-adjoint on a $C_{0}^{\infty}$ domain in
$L^{2}$, a Hilbert space of square integrable functions. Here we summarize how
Weyl's limit point-limit circle criterion can be used to determine whether a
wave operator is essentially self-adjoint and how this test can then be applied
to scalar wave packets in Levi-Civita spacetimes with and without a
cosmological constant to help elucidate the physical properties of these
spacetimes.


title:
A new analytical method for self-force regularization II. Testing the
  efficiency for circular orbits

abstract:
  In a previous paper, based on the black hole perturbation approach, we
formulated a new analytical method for regularizing the self-force acting on a
particle of small mass $\mu$ orbiting a Schwarzschild black hole of mass $M$,
where $\mu\ll M$. In our method, we divide the self-force into the $\tilde
S$-part and $\tilde R$-part. All the singular behaviors are contained in the
$\tilde S$-part, and hence the $\tilde R$-part is guaranteed to be regular. In
this paper, focusing on the case of a scalar-charged particle for simplicity,
we investigate the precision of both the regularized $\tilde S$-part and the
$\tilde R$-part required for the construction of sufficiently accurate
waveforms for almost circular inspiral orbits. For the regularized $\tilde
S$-part, we calculate it for circular orbits to 18 post-Newtonian (PN) order
and investigate the convergence of the post-Newtonian expansion. We also study
the convergence of the remaining $\tilde{R}$-part in the spherical harmonic
expansion. We find that a sufficiently accurate Green function can be obtained
by keeping the terms up to $\ell=13$.


title:
The Hamiltonian of Asymptotically Friedmann-Lemaitre-Robertson-Walker
  Spacetimes

abstract:
  We obtain the correct hamiltonian which describes the dynamics of classes of
asymptotic open Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) spacetimes,
which includes Tolman geometries. We calculate the surface term that has to be
added to the usual hamiltonian of General Relativity in order to obtain an
improved hamiltonian with well defined functional derivatives. For asymptotic
flat FLRW spaces, this surface term is zero, but for asymptotic negative
curvature FLRW spaces it is not null in general. In the particular case of the
Tolman geometries, they vanish. The surface term evaluated on a particular
solution of Einstein's equations may be viewed as the ``energy'' of this
solution with respect to the FLRW spacetime they approach asymptotically. Our
results are obtained for a matter content described by a dust fluid, but they
are valid for any perfect fluid, including the cosmological constant.


title: The Bohm Interpretation of Quantum Cosmology

abstract:
  I make a review on the aplications of the Bohm-De Broglie interpretation of
quantum mechanics to quantum cosmology. In the framework of minisuperspaces
models, I show how quantum cosmological effects in Bohm's view can avoid the
initial singularity, isotropize the Universe, and even be a cause for the
present observed acceleration of the Universe. In the general case, we
enumerate the possible structures of quantum space and time.


title:
The post-Newtonian mean anomaly advance as further post-Keplerian
  parameter in pulsar binary systems

abstract:
  The post-Newtonian gravitoelectric secular rate of the mean anomaly M is
worked out for a two-body system in the framework of the General Theory of
Relativity. The possibility of using such an effect, which is different from
the well known decrease of the orbital period due to gravitational wave
emission, as a further post-Keplerian parameter in binary systems including one
pulsar is examined. The resulting effect is almost three times larger than the
periastron advance \dot\omega. E.g., for the recently discovered double pulsar
system PSR J0737-3039 A+B it would amount to -47.79 deg yr^-1. This implies
that it could be extracted from the linear part of a quadratic fit of the
orbital phase because the uncertainties both in the linear drift due to the
mean motion and in the quadratic shift due to the gravitational wave are
smaller. The availability of such additional post-Keplerian parameter would be
helpful in further constraining the General Theory of Relativity, especially
for such systems in which some of the other post-Keplerian parameters can be
measured with limited accuracy. Moreover, also certain pulsar-white dwarf
binary systems, characterized by circular orbits like PSR B1855+09 and a
limited number of measured post-Keplerian parameters, could be used for
constraining competing theories of gravity.


title:
Nonsingular multidimensional cosmologies with Lobachevsky spatial
  sections

abstract:
  Examples of nonsingular cosmological models are presented on the basis of
exact solutions to multidimensional gravity equations. These examples involve
pure imaginary scalar fields, or, in other terms, ``phantom'' fields with an
unusual sign of the kinetic term in the Lagrangian. We show that, with such
fields, hyperbolic nonsingular models with a cosmological bounce (unlike
spherical and spatially flat models) emerge without special relations among the
integration constants, i.e., without fine tuning. In such models, the
extra-dimension scale factors as well as scalar fields evolve smoothly between
different finite asymptotic values. Examples of theories which create phantom
scalar fields are obtained from string-inspired multidimensional field models
and from theories of gravity in integrable Weyl space-times.


title:
The graviton vacuum as a distributional state in kinematic Loop Quantum
  Gravity

abstract:
  The quantum behaviour of weak gravitational fields admits an adequate, albeit
approximate, description by those graviton states in which the expectation
values and fluctuations of the linearised gravitational field are small. Such
states must approximate corresponding states in full quantum gravity. We
analyse the nature of this approximation for the graviton vacuum state in the
context of kinematical Loop Quantum Gravity (LQG) wherein the constraints are
ignored. We identify the graviton vacuum state with kinematically
non-normalizable, distributional states in LQG by demanding that relations
between linearised operator actions on the former are mirrored by those of
their non-linear counterparts on the latter. We define a semi- norm on the
space of kinematical distributions and show that the identification is
approximate upto distributions which are small in this semi-norm. We argue that
our candidate states are annihilated by the linearised constraints (expressed
as operators in the full theory) to leading order in the parameter
characterising the approximation. This suggests the possibility, in a scheme
such as ours, of solving the full constraints order by order in this parameter.
The main drawback of our considerations is that they depend on certain
auxilliary constructions which, though mathematically well defined, do not
arise from physical insight. Our work is an attempt to implement an earlier
proposal of Iwasaki and Rovelli.


title: The art and science of black hole mergers

abstract:
  The merger of two black holes is one of the most extraordinary events in the
natural world. Made of pure gravity, the holes combine to form a single hole,
emitting a strong burst of gravitational radiation. Ground-based detectors are
currently searching for such bursts from holes formed in the evolution of
binary stars, and indeed the very first gravitational wave event detected may
well be a black-hole merger. The space-based LISA detector is being designed to
search for such bursts from merging massive black holes in the centers of
galaxies, events that would emit many thousands of solar masses of pure
gravitational wave energy over a period of only a few minutes. To assist
gravitational wave astronomers in their searches, and to be in a position to
understand the details of what they see, numerical relativists are performing
supercomputer simulations of these events. I review here the state of the art
of these simulations, what we have learned from them so far, and what
challenges remain before we have a full prediction of the waveforms to be
expected from these events.