title: Lectures on Loop Quantum Gravity

abstract:
  Quantum General Relativity (QGR), sometimes called Loop Quantum Gravity, has
matured over the past fifteen years to a mathematically rigorous candidate
quantum field theory of the gravitational field. The features that distinguish
it from other quantum gravity theories are 1) background independence and 2)
minimality of structures. Background independence means that this is a
non-perturbative approach in which one does not perturb around a given,
distinguished, classical background metric, rather arbitrary fluctuations are
allowed, thus precisely encoding the quantum version of Einstein's radical
perception that gravity is geometry. Minimality here means that one explores
the logical consequences of bringing together the two fundamental principles of
modern physics, namely general covariance and quantum theory, without adding
any experimentally unverified additional structures. The approach is purposely
conservative in order to systematically derive which basic principles of
physics have to be given up and must be replaced by more fundamental ones. QGR
unifies all presently known interactions in a new sense by quantum mechanically
implementing their common symmetry group, the four-dimensional diffeomorphism
group, which is almost completely broken in perturbative approaches. These
lectures offer a problem -- supported introduction to the subject.


title:
Spin 0 and spin 1/2 quantum relativistic particles in a constant
  gravitational field

abstract:
  The Klein-Gordon and Dirac equations in a semi-infinite lab ($x > 0$), in the
background metric $\ds^2 = u^2(x) (-\dt^2 + \dx^2) + \dy^2 + \dz^2$, are
investigated. The resulting equations are studied for the special case $ u(x) =
1 + g x$. It is shown that in the case of zero transverse-momentum, the square
of the energy eigenvalues of the spin-1/2 particles are less than the squares
of the corresponding eigenvalues of spin-0 particles with same masses, by an
amount of $mg\hbar c$. Finally, for nonzero transverse-momentum, the energy
eigenvalues corresponding to large quantum numbers are obtained, and the
results for spin-0 and spin-1/2 particles are compared to each other.


title:
What does Quantum Field Theory in Curved Spacetime Have to Say about the
  Dark Energy?

abstract:
  The issue of the vacuum energy of quantum fields is briefly reviewed. It is
argued that this energy is normally either much too large or much too small to
account for the dark energy, However, there are a few proposals in which it
would be of the order needed to effect the dynamics of the present day
universe. Backreaction models are reviewed, and the question of whether quantum
effects can react against a cosmological constant is discussed.


title:
New exact cosmological solutions to Einstein's gravity minimally coupled
  to a Quintessence field

abstract:
  A linear relationship between the Hubble expansion parameter and the time
derivative of the scalar field is assumed in order to derive exact analytic
cosmological solutions to Einstein's gravity with two fluids: a barotropic
perfect fluid of ordinary matter, together with a self-interacting scalar field
fluid accounting for the dark energy in the universe. A priori assumptions
about the functional form of the self-interaction potential or about the scale
factor behavior are not neccessary. These are obtained as outputs of the
assumed linear relationship between the Hubble expansion parameter and the time
derivative of the scalar field. As a consequence only a class of exponential
potentials and their combinations can be treated. The relevance of the
solutions found for the description of the cosmic evolution are discussed in
some detail. The possibility to have superaccelerated expansion within the
context of normal quintessence models is also discussed.


title:
Comparison of filters for detecting gravitational wave bursts in
  interferometric detectors

abstract:
  Filters developed in order to detect short bursts of gravitational waves in
interferometric detector outputs are compared according to three main points.
Conventional Receiver Operating Characteristics (ROC) are first built for all
the considered filters and for three typical burst signals. Optimized ROC are
shown for a simple pulse signal in order to estimate the best detection
efficiency of the filters in the ideal case, while realistic ones obtained with
filters working with several ``templates'' show how detection efficiencies can
be degraded in a practical implementation. Secondly, estimations of biases and
statistical errors on the reconstruction of the time of arrival of pulse-like
signals are then given for each filter. Such results are crucial for future
coincidence studies between Gravitational Wave detectors but also with neutrino
or optical detectors. As most of the filters require a pre-whitening of the
detector noise, the sensitivity to a non perfect noise whitening procedure is
finally analysed. For this purpose lines of various frequencies and amplitudes
are added to a Gaussian white noise and the outputs of the filters are studied
in order to monitor the excess of false alarms induced by the lines. The
comparison of the performances of the different filters finally show that they
are complementary rather than competitive.


title: Shear-Free Gravitational Waves in an Anisotropic Universe

abstract:
  We study gravitational waves propagating through an anisotropic Bianchi I
dust-filled universe (containing the Einstein-de-Sitter universe as a special
case). The waves are modeled as small perturbations of this background
cosmological model and we choose a family of null hypersurfaces in this
space-time to act as the histories of the wavefronts of the radiation. We find
that the perturbations we generate can describe pure gravitational radiation if
and only if the null hypersurfaces are shear-free. We calculate the
gauge-invariant small perturbations explicitly in this case. How these differ
from the corresponding perturbations when the background space-time is
isotropic is clearly exhibited.


title: Structure of Malicious Singularities

abstract:
  We investigate spacetimes with their singular boundaries as noncommutative
spaces. Such a space is defined by a noncommutative algebra on a transformation
groupoid $\Gamma = E \times G$, where $E$ is the total space of the frame
bundle over spacetime with its singular boundary, and $G$ its structural group.
There is a bijective correspondence between unitary representations of the
groupoid $\Gamma $ and the systems of imprimitivity of the group $G$. This
allows us to apply the Mackey theorem, and deduce from it some information
concerning singular fibres of the groupoid. A subgroup $K$ of $G$, from which
-- according to the Mackey theorem -- the representation is induced to the
whole of $G$, can be regarded as measuring the "richness" of the singularity
structure.


title: Critical phenomena in gravitational collapse (Physics Reports)

abstract:
  In general relativity black holes can be formed from regular initial data
that do not contain a black hole already. The space of regular initial data for
general relativity therefore splits naturally into two halves: data that form a
black hole in the evolution and data that do not. The spacetimes that are
evolved from initial data near the black hole threshold have many properties
that are mathematically analogous to a critical phase transition in statistical
mechanics.
  Solutions near the black hole threshold go through an intermediate attractor,
called the critical solution. The critical solution is either time-independent
(static) or scale-independent (self-similar). In the latter case, the final
black hole mass scales as $(p-p_*)^\gamma$ along any one-parameter family of
data with a regular parameter $p$ such that $p=p_*$ is the black hole threshold
in that family. The critical solution and the critical exponent $\gamma$ are
universal near the black hole threshold for a given type of matter.
  We show how the essence of these phenomena can be understood using dynamical
systems theory and dimensional analysis. We then review separately the analogy
with critical phase transitions in statistical mechanics, and aspects specific
to general relativity, such as spacetime singularities. We examine the evidence
that critical phenomena in gravitational collapse are generic, and give an
overview of their rich phenomenology.


title: The rotational modes of relativistic stars: Numerical results

abstract:
  We study the inertial modes of slowly rotating, fully relativistic compact
stars. The equations that govern perturbations of both barotropic and
non-barotropic models are discussed, but we present numerical results only for
the barotropic case. For barotropic stars all inertial modes are a hybrid
mixture of axial and polar perturbations. We use a spectral method to solve for
such modes of various polytropic models. Our main attention is on modes that
can be driven unstable by the emission of gravitational waves. Hence, we
calculate the gravitational-wave growth timescale for these unstable modes and
compare the results to previous estimates obtained in Newtonian gravity (i.e.
using post-Newtonian radiation formulas). We find that the inertial modes are
slightly stabilized by relativistic effects, but that previous conclusions
concerning eg. the unstable r-modes remain essentially unaltered when the
problem is studied in full general relativity.


title: On "many black hole" space-times

abstract:
  We analyze the horizon structure of families of space times obtained by
evolving initial data sets containing apparent horizons with several connected
components. We show that under certain smallness conditions the outermost
apparent horizons will also have several connected components. We further show
that, again under a smallness condition, the maximal globally hyperbolic
development of the many black hole initial data constructed by Chrusciel and
Delay, or of hyperboloidal data of Isenberg, Mazzeo and Pollack, will have an
event horizon, the intersection of which with the initial data hypersurface is
not connected. This justifies the "many black hole" character of those
space-times.


title: On optical black holes in moving dielectrics

abstract:
  We study the optical paths of the light rays propagating inside a nonlinear
moving dielectric media. For the rapidly moving dielectrics we show the
existence of a distinguished surface which resembles, as far as the light
propagation is concerned, the event horizon of a black hole. Our analysis
clarifies the physical conditions under which electromagnetic analogues of the
gravitational black holes can eventually be obtained in laboratory.


title:
Massive charged scalar field in a Reissner-Nordstrom black hole
  background: quasinormal ringing

abstract:
  We compute characteristic (quasinormal) frequencies corresponding to decay of
a massive charged scalar field in a Reissner-Nordstrom black hole background.
It proves that, contrary to the behavior at very late times, at the stage of
quasinormal ringing the neutral perturbations will damp slower than the charged
ones. In the limit of the extremal black hole the damping rate of charged and
neutral perturbations coincides. Possible connection of this with the critical
collapse in a massive scalar electrodynamics is discussed.


title: Analysis of the Anomalous Brillet and Hall Experimental Result

abstract:
  The persistent, second order, anomalous signal found in the Brillet and Hall
experiment is derived by applying 4D differential geometry in the rotating
earth frame. By incorporating the off diagonal time-space components of the
rotating frame metric directly into the analysis, rather than arbitrarily
transforming them away, one finds a signal dependence on the surface speed of
the earth due to rotation about its axis. This leads to a Brillet-Hall signal
prediction in remarkably close agreement with experiment. No signal is
predicted from the speed of the earth in solar or galactic orbit, as the
associated metric for gravitational orbit has no off diagonal component. To
corroborate this result, a repetition by other experimentalists of the
Brillet-Hall experiment, in which the test apparatus turns with respect to the
earth surface, is urged.


title: Neutrino asymmetry in general relativistic rotating radiative stars

abstract:
  Neutrino asymmetry in general relativistic radiative spacetime exterior to
spinning stars is investigating by making use of Newmann-Penrose (NP) spin
coefficient formalism. It is shown that neutrino current depends on the
direction of rotation of the star. The solution is obtained in test field
approximation where the neutrinos do not generate gravitational fields.


title: How Are Black Holes Quantized?

abstract:
  Some approaches to quantization of the horizon area of black holes are
discussed. The maximum entropy of a quantized surface is demonstrated to be
proportional to the surface area in the classical limit. This result is valid
for a rather general class of approaches to surface quantization. In the case
of rotating black holes no satisfactory solution for the quantization problem
has been found up to now.


title:
Quasi-Equatorial Gravitational Lensing by Spinning Black Holes in the
  Strong Field Limit

abstract:
  Spherically symmetric black holes produce, by strong field lensing, two
infinite series of relativistic images, formed by light rays winding around the
black hole at distances comparable to the gravitational radius. In this paper,
we address the relevance of the black hole spin for the strong field lensing
phenomenology, focusing on trajectories close to the equatorial plane for
simplicity. In this approximation, we derive a two-dimensional lens equation
and formulae for the position and the magnification of the relativistic images
in the strong field limit. The most outstanding effect is the generation of a
non trivial caustic structure. Caustics drift away from the optical axis and
acquire finite extension. For a high enough black hole spin, depending on the
source extension, we can practically observe only one image rather than two
infinite series of relativistic images. In this regime, additional non
equatorial images may play an important role in the phenomenology.


title:
Particle production in time-dependent gravitational fields: the
  expanding mass shell

abstract:
  We compute the production of particles from the gravitational field of an
expanding mass shell. Contrary to the situation of Hawking radiation and the
production of cosmological perturbations during cosmological inflation, the
example of an expanding mass shell has no horizon and no singularity. We apply
the method of `ray-tracing', first introduced by Hawking, and calculate the
energy spectrum of the produced particles. The result depends on three
parameters: the expansion velocity of the mass shell, its radius, and its mass.
Contrary to the situation of a collapsing mass shell, the energy spectrum is
non-thermal. Invoking time reversal we reproduce Hawking's thermal spectrum in
a certain limit.


title:
Power laws, scale invariance, and generalized Frobenius series:
  Applications to Newtonian and TOV stars near criticality

abstract:
  We present a self-contained formalism for analyzing scale invariant
differential equations. We first cast the scale invariant model into its
equidimensional and autonomous forms, find its fixed points, and then obtain
power-law background solutions. After linearizing about these fixed points, we
find a second linearized solution, which provides a distinct collection of
power laws characterizing the deviations from the fixed point. We prove that
generically there will be a region surrounding the fixed point in which the
complete general solution can be represented as a generalized Frobenius-like
power series with exponents that are integer multiples of the exponents arising
in the linearized problem. This Frobenius-like series can be viewed as a
variant of Liapunov's expansion theorem. As specific examples we apply these
ideas to Newtonian and relativistic isothermal stars and demonstrate (both
numerically and analytically) that the solution exhibits oscillatory power-law
behaviour as the star approaches the point of collapse. These series solutions
extend classical results. (Lane, Emden, and Chandrasekhar in the Newtonian
case; Harrison, Thorne, Wakano, and Wheeler in the relativistic case.) We also
indicate how to extend these ideas to situations where fixed points may not
exist -- either due to ``monotone'' flow or due to the presence of limit
cycles. Monotone flow generically leads to logarithmic deviations from scaling,
while limit cycles generally lead to discrete self-similar solutions.


title:
Plane-Symmetric Inhomogeneous Bulk Viscous Cosmological Models with
  Variable $\Lambda$

abstract:
  A plane-symmetric non-static cosmological model representing a bulk viscous
fluid distribution has been obtained which is inhomogeneous and anisotropic and
a particular case of which is gravitationally radiative. Without assuming any
{\it adhoc} law, we obtain a cosmological constant as a decreasing function of
time. The physical and geometric features of the models are also discussed.


title: Holography, Time and Quantum Mechanics

abstract:
  In this talk we entertain the possibility that the synthesis of general
covariance and quantum mechanics requires an extension of the basic kinematical
setup of quantum mechanics. According to the holographic principle, regions of
spacetime bounded by a finite area carry finite entropy. When we in addition
assume that the origin of the entropy is a finite dimensional Hilbert space,
and apply this to cosmological solutions using a suitable notion of
complementarity, we find as a consequence that gravitational effects can lead
to dynamical variation in the dimensionality of such Hilbert spaces. This
happens generally in cosmological settings like our own universe.


title: Horizon Dynamics of a BTZ Black Hole

abstract:
  It has been suggested in the literature that, given a black hole spacetime, a
relativistic membrane can provide an effective description of the horizon
dynamics. In this paper, we explore such a framework in the context of a
2+1-dimensional BTZ black hole. Following this membrane prescription, we are
able to translate the horizon dynamics (now described by a string) into the
convenient form of a 1+1-dimensional Klein-Gordon equation. We proceed to
quantize the solutions and construct a thermodynamic partition function.
Ultimately, we are able to extract the quantum-corrected entropy, which is
shown to comply with the BTZ form of the Bekenstein-Hawking area law. We also
substantiate that the leading-order correction is proportional to the logarithm
of the area.


title:
Creation of Dirac Particles in the Presence of a Constant Electric Field
  in an Anisotropic Bianchi I Universe

abstract:
  In this article we compute the density of Dirac particles created by a
cosmological anisotropic Bianchi I universe in the presence of a constant
electric field. We show that the particle distribution becomes thermal when one
neglects the electric interaction.


title:
Non-trivial, static, geodesically complete, vacuum space-times with a
  negative cosmological constant

abstract:
  We construct a large class of new singularity-free static Lorentzian
four-dimensional solutions of the vacuum Einstein equations with a negative
cosmological constant. The new families of metrics contain space-times with, or
without, black hole regions. Two uniqueness results are also established.


title:
Role of the Dilatonic potential to the Quantum stabilization of
  dilatonic Anti-de Sitter Universe

abstract:
  Quantum effects lead to the annihilation of AdS Universe when dilaton is
absent. We consider here the role of the form for the dilatonic potential in
the quantum creation of a dilatonic AdS Universe and its stabilization. Using
the conformal anomaly for dilaton coupled scalar, the anomaly induced action
and the equations of motion are obtained. Using numerical methods the solutions
of the full theory which correspond to quantum-corrected AdS Universe are given
for a particular case of dilatonic potential.


title: Conformally Flat Spherically Symmetric Cosmological Models-Revisited

abstract:
  Conformally flat spherically symmetric cosmological models representing a
charged perfect fluid as well as a bulk viscous fluid distribution have been
obtained. The cosmological constant \Lambda is found positive and is a
decreasing function of time which is consistent with the recent supernovae
observations. The physical and geometrical properties of the models are
discussed.


title: Totally Asymmetric Torsion on Riemann-Cartan Manifold

abstract:
  A relativistic theory constructed on Riemann-Cartan manifold with a derived
totally antisymmetric torsion is proposed. It follows the coincidence of the
autoparallel curve and metric geodesic. The totally antisymmetric torsion
naturally appears in the theory without any ad hoc imposed on.


title: Can an observer really catch up with light

abstract:
  Given a null geodesic $\gamma_0(\lambda)$ with a point $r$ in $(p,q)$
conjugate to $p$ along $\gamma_0(\lambda)$, there will be a variation of
$\gamma_0(\lambda)$ which will give a time-like curve from $p$ to $q$. This is
a well-known theory proved in the famous book\cite{2}. In the paper we prove
that the time-like curves coming from the above-mentioned variation have a
proper acceleration which approaches infinity as the time-like curve approaches
the null geodesic. This means no observer can be infinitesimally near the light
and begin at the same point with the light and finally catch the light. Only
separated from the light path finitely, does the observer can begin at the same
point with the light and finally catch the light.


title: Shadows of a maximal acceleration

abstract:
  A quantum mechanical upper limit on the value of particle accelerations, or
maximal acceleration (MA), is applied to compact stars. A few MA fermions are
at most present in canonical white dwarfs and neutron stars. They drastically
alter a star's stability conditions.


title: Polymer and Fock representations for a Scalar field

abstract:
  In loop quantum gravity, matter fields can have support only on the
`polymer-like' excitations of quantum geometry, and their algebras of
observables and Hilbert spaces of states can not refer to a classical,
background geometry. Therefore, to adequately handle the matter sector, one has
to address two issues already at the kinematic level. First, one has to
construct the appropriate background independent operator algebras and Hilbert
spaces. Second, to make contact with low energy physics, one has to relate this
`polymer description' of matter fields to the standard Fock description in
Minkowski space. While this task has been completed for gauge fields, important
gaps remained in the treatment of scalar fields. The purpose of this letter is
to fill these gaps.


title:
On the possibility of measuring relativistic gravitational effects with
  a LAGEOS-LAGEOS II-OPTIS-mission

abstract:
  In this paper we wish to preliminary investigate if it would be possible to
use the orbital data from the proposed OPTIS mission together with those from
the existing geodetic passive SLR LAGEOS and LAGEOS II satellites in order to
perform precise measurements of some general relativistic
gravitoelectromagnetic effects, with particular emphasis on the Lense-Thirring
effect.


title: All Static Circularly Symmetric Perfect Fluid Solutions of 2+1 Gravity

abstract:
  Via a straightforward integration of the Einstein equations with cosmological
constant, all static circularly symmetric perfect fluid 2+1 solutions are
derived. The structural functions of the metric depend on the energy density,
which remains in general arbitrary. Spacetimes for fluids fulfilling linear and
polytropic state equations are explicitly derived; they describe, among others,
stiff matter, monatomic and diatomic ideal gases, nonrelativistic degenerate
fermions, incoherent and pure radiation. As a by--product, we demonstrate the
uniqueness of the constant energy density perfect fluid within the studied
class of metrics. A full similarity of the perfect fluid solutions with
constant energy density of the 2+1 and 3+1 gravities is established.


title: Cold dark matter and primordial superheavy particles

abstract:
  The hypothesis that cold dark matter consists of primordial superheavy
particles, the decay of short lifetime component of which led to the observable
mass of matter while long living component survived up to modern times
manifesting its presence in high energetic cosmic rays particles is
investigated.


title: Inflation and Oscillations of Universe in 4D Dilatonic Gravity

abstract:
  We investigate the inflation of Universe in a model of four dimensional
dilatonic gravity with a massive dilaton field $\Phi$. The dilaton plays
simultaneously the roles of an inflation field and a quintessence field. It
yields a sequential {\em hyper}-inflation with a graceful exit to asymptotic de
Sitter space-time, which is an attractor, and is approached as
$\exp(-\sqrt{3\Lambda^{obs}} ct/2)$. The time duration of the inflation is
reciprocal to the the mass of the dilaton: $\Delta t_{infl}\sim
m_{{}_\Phi}^{-1}$. The typical number of e-folds in the simplest model of this
type is shown to be realistic without fine tuning.


title: On General Plane Fronted Waves. Geodesics

abstract:
  A general class of Lorentzian metrics, $M_0 x R^2$, $ds^2 = <.,.> + 2 du dv +
H(x,u) du^2$, with $(M_0, <.,.>$ any Riemannian manifold, is introduced in
order to generalize classical exact plane fronted waves. Here, we start a
systematic study of their main geodesic properties: geodesic completeness,
geodesic connectedness and multiplicity, causal character of connecting
geodesics. These results are independent of the possibility of a full
integration of geodesic equations. Variational and geometrical techniques are
applied systematically.
  In particular, we prove that the asymptotic behavior of $H(x,u)$ with $x$ at
infinity determines many properties of geodesics. Essentially, a subquadratic
growth of $H$ ensures geodesic completeness and connectedness, while the
critical situation appears when $H(x,u)$ behaves in some direction as $|x|^2$,
as in the classical model of exact gravitational waves


title:
Capture and Critical Scattering of a Long Cosmic String by a Rotating
  Black Hole

abstract:
  The capture of a straight, infinitely long cosmic string by a rotating black
hole with rotation parameter $a$ is considered. We assume that a string is
moving with velocity $v$ and that initially the string is parallel to the axis
of rotation of the black hole and has the impact parameter $b$. The string can
be either scattered or captured by the black hole. We demonstrate that there
exists a critical value of the impact parameter $b_c(v,a)$ which separates
these two regimes. Using numerical simulations we obtain the critical impact
parameter curve for different values of the rotation parameter $a$. We show
that for the prograde motion of the string this curve lies below the curve for
the retrograde motion. Moreover, for ultrarelativistic strings moving in the
prograde direction and nearly extremal black holes the critical impact
parameter curve is found to be a multiply valued function of $v$. We obtain
real time profiles of the scattered strings in the regime close to the
critical. We also study critical scattering and capture of strings by the
rotating black hole in the relativistic and ultrarelativistic regime and
especially such relativistic effects as coil formation and wrapping effect.


title: Gravitational collapse of null strange quark fluid and cosmic censorship

abstract:
  We study gravitational collapse of the general spherically symmetric null
strange quark fluid having the equation of state, $p = (\rho - 4B)/n$, where
$B$ is the bag constant. An interesting feature that emerges is that the
initial data set giving rise to naked singularity in the Vaidya collapse of
null fluid gets covered due to the presence of strange quark matter component.
Its implication to the Cosmic Censorship Conjecture is discussed.


title: Exponential Potentials on the Brane

abstract:
  In this paper we study the cosmological dynamics of Randall-Sundrum
braneworld type scenarios in which the five-dimensional Weyl tensor has a
non-vanishing projection onto the three-brane where matter fields are confined.
Using dynamical systems techniques, we study how the state space of
Friedmann-Lemaitre-Robertson-Walker (FLRW) and Bianchi type I scalar field
models with an exponential potential is affected by the bulk Weyl tensor,
focusing on the differences that appear with respect to standard general
relativity and also Randall-Sundrum cosmological scenarios without the Weyl
tensor contribution.


title: Scale-Invariant Gravity: Particle Dynamics

abstract:
  A new and universal method for implementing scale invariance, called best
matching, is presented. It extends to scaling the method introduced by Bertotti
and the author to create a fully relational dynamics that satisfies Mach's
principle. The method is illustrated here in the context of non-relativistic
gravitational particle dynamics.. It leads to far stronger predictions than
general Newtonian dynamics. The energy and angular momentum of an `island
universe' must be exactly zero and its size, measured by its moment of inertia,
cannot change. This constancy is enforced because the scale invariance requires
all potentials to be homogeneous of degree -2. It is remarkable that one can
nevertheless exactly recover the standard observed Newtonian laws and forces,
which are merely accompanied by an extremally weak universal force like the one
due to Einstein's cosmological constant. In contrast to Newtonian and
Einsteinian dynamics, both the gravitational constant G and the strength of the
cosmological force are uniquely determined by the matter distribution of the
universe. Estimates of their values in agreement with observations are
obtained. Best matching implements a dynamics of pure shape for which the
action is a dimensionless number. If the universe obeys such scale invariant
law, steadily increasing inhomogeneity, not expansion of the universe, causes
the Hubble red shift. The application of best matching to geometrodynamics is
treated in a companion paper.


title: Scale-Invariant Gravity: Geometrodynamics

abstract:
  We present a scale-invariant theory, conformal gravity, which closely
resembles the geometrodynamical formulation of general relativity (GR). While
previous attempts to create scale-invariant theories of gravity have been based
on Weyl's idea of a compensating field, our direct approach dispenses with this
and is built by extension of the method of best matching w.r.t scaling
developed in the parallel particle dynamics paper by one of the authors. In
spatially-compact GR, there is an infinity of degrees of freedom that describe
the shape of 3-space which interact with a single volume degree of freedom. In
conformal gravity, the shape degrees of freedom remain, but the volume is no
longer a dynamical variable. Further theories and formulations related to GR
and conformal gravity are presented.
  Conformal gravity is successfully coupled to scalars and the gauge fields of
nature. It should describe the solar system observations as well as GR does,
but its cosmology and quantization will be completely different.


title: Transition from inspiral to plunge for eccentric equatorial Kerr orbits

abstract:
  Ori and Thorne have discussed the duration and observability (with LISA) of
the transition from circular, equatorial inspiral to plunge for stellar-mass
objects into supermassive ($10^{5}-10^{8}M_{\odot}$) Kerr black holes. We
extend their computation to eccentric Kerr equatorial orbits. Even with orbital
parameters near-exactly determined, we find that there is no universal length
for the transition; rather, the length of the transition depends sensitively --
essentially randomly -- on initial conditions. Still, Ori and Thorne's
zero-eccentricity results are essentially an upper bound on the length of
eccentric transitions involving similar bodies (e.g., $a$ fixed). Hence the
implications for observations are no better: if the massive body is
$M=10^{6}M_{\odot}$, the captured body has mass $m$, and the process occurs at
distance $d$ from LISA, then $S/N \lesssim (m/10
M_{\odot})(1\text{Gpc}/d)\times O(1)$, with the precise constant depending on
the black hole spin. For low-mass bodies ($m \lesssim 7 M_\odot$) for which the
event rate is at least vaguely understood, we expect little chance (probably
[much] less than 10%, depending strongly on the astrophysical assumptions) of
LISA detecting a transition event with $S/N>5$ during its run; however, even a
small infusion of higher-mass bodies or a slight improvement in LISA's noise
curve could potentially produce $S/N>5$ transition events during LISA's
lifetime.


title: A new class of obstructions to the smoothness of null infinity

abstract:
  Expansions of the gravitational field arising from the development of
asymptotically Euclidean, time symmetric, conformally flat initial data are
calculated in a neighbourhood of spatial and null infinities up to order 6. To
this ends a certain representation of spatial infinity as a cylinder is used.
This set up is based on the properties of conformal geodesics. It is found that
these expansions suggest that null infinity has to be non-smooth unless the
Newman-Penrose constants of the spacetime, and some other higher order
quantities of the spacetime vanish. As a consequence of these results it is
conjectured that similar conditions occur if one were to take the expansions to
even higher orders. Furthermore, the smoothness conditions obtained suggest
that if a time symmetric initial data which is conformally flat in a
neighbourhood of spatial infinity yields a smooth null infinity, then the
initial data must in fact be Schwarzschildean around spatial infinity.


title: Purely gravito-magnetic vacuum space-times

abstract:
  It is shown that there are no vacuum space-times (with or without
cosmological constant) for which the Weyl-tensor is purely gravito-magnetic
with respect to a normal and timelike congruence of observers.


title:
Elastic Stars in General Relativity: I. Foundations and Equilibrium
  Models

abstract:
  The aim of this paper is twofold. First, we set up the theory of elastic
matter sources within the framework of general relativity in a self-contained
manner. The discussion is primarily based on the presentation of Carter and
Quintana but also includes new methods and results as well as some
modifications that in our opinion make the theory more modern and transparent.
For instance, the equations of motion for the matter are shown to take a neat
form when expressed in terms of the relativistic Hadamard elasticity tensor.
Using this formulation we obtain simple formulae for the speeds of elastic wave
propagation along eigendirections of the pressure tensor. Secondly, we apply
the theory to static spherically symmetric configurations using a specific
equation of state and consider models either having an elastic crust or core.


title:
Gravitational radiation reaction in compact binary systems: Contribution
  of the quadrupole-monopole interaction

abstract:
  The radiation reaction in compact spinning binaries on eccentric orbits due
to the quadrupole-monopole interaction is studied. This contribution is of
second post-Newtonian order. As result of the precession of spins the magnitude
$L$ of the orbital angular momentum is not conserved. Therefore a proper
characterization of the perturbed radial motion is provided by the energy $E$
and angular average $\bar{L}$. As powerful computing tools, the generalized
true and eccentric anomaly parametrizations are introduced. Then the secular
losses in energy and magnitude of orbital angular momentum together with the
secular evolution of the relative orientations of the orbital angular momentum
and spins are found for eccentric orbits by use of the residue theorem. The
circular orbit limit of the energy loss agrees with Poisson's earlier result.


title: Numerical Relativity and Compact Binaries

abstract:
  Numerical relativity is the most promising tool for theoretically modeling
the inspiral and coalescence of neutron star and black hole binaries, which, in
turn, are among the most promising sources of gravitational radiation for
future detection by gravitational wave observatories. In this article we review
numerical relativity approaches to modeling compact binaries. Starting with a
brief introduction to the 3+1 decomposition of Einstein's equations, we discuss
important components of numerical relativity, including the initial data
problem, reformulations of Einstein's equations, coordinate conditions, and
strategies for locating and handling black holes on numerical grids. We focus
on those approaches which currently seem most relevant for the compact binary
problem. We then outline how these methods are used to model binary neutron
stars and black holes, and review the current status of inspiral and
coalescence simulations.


title: Warped space-time for phonons moving in a perfect nonrelativistic fluid

abstract:
  We construct a kinematical analogue of superluminal travel in the ``warped''
space-times curved by gravitation, in the form of ``super-phononic'' travel in
the effective space-times of perfect nonrelativistic fluids. These warp-field
space-times are most easily generated by considering a solid object that is
placed as an obstruction in an otherwise uniform flow. No violation of any
condition on the positivity of energy is necessary, because the effective
curved space-times for the phonons are ruled by the Euler and continuity
equations, and not by the Einstein field equations.


title: Leibnizian, Galilean and Newtonian structures of spacetime

abstract:
  The following three geometrical structures on a manifold are studied in
detail: (1) Leibnizian: a non-vanishing 1-form $\Omega$ plus a Riemannian
metric $\h$ on its annhilator vector bundle. In particular, the possible
dimensions of the automorphism group of a Leibnizian G-structure are
characterized. (2) Galilean: Leibnizian structure endowed with an affine
connection $\nabla$ (gauge field) which parallelizes $\Omega$ and $\h$. Fixed
any vector field of observers Z ($\Omega (Z) = 1$), an explicit Koszul--type
formula which reconstruct bijectively all the possible $\nabla$'s from the
gravitational ${\cal G} = \nabla_Z Z$ and vorticity $\omega = rot Z/2$ fields
(plus eventually the torsion) is provided. (3) Newtonian: Galilean structure
with $\h$ flat and a field of observers Z which is inertial (its flow preserves
the Leibnizian structure and $\omega = 0$). Classical concepts in Newtonian
theory are revisited and discussed.


title:
Conserved charges in gravitational theories: contribution from scalar
  fields

abstract:
  In order to illustrate a recently derived covariant formalism for computing
asymptotic symmetries and asymptotically conserved superpotentials in gauge
theories, the case of gravity with minimally coupled scalar fields is
considered and the matter contribution to the asymptotically conserved
superpotentials is computed.


title: On localizing topological algebras

abstract:
  Through the subsequent discussion we consider a certain particular sort of
(topological) algebras, which may substitute the `` structure sheaf algebras''
in many--in point of fact, in all--the situations of a geometrical character
that occur, thus far, in several mathematical disciplines, as for instance,
differential and/or algebraic geometry, complex (geometric) analysis etc. It is
proved that at the basis of this type of algebras lies the sheaf-theoretic
notion of (functional) localization, which, in the particular case of a given
topological algebra, refers to the respective ``Gel'fand transform algebra''
over the spectrum of the initial algebra. As a result, one further considers
the so-called ``geometric topological algebras'', having special cohomological
properties, in terms of their ``Gel'fand sheaves'', being also of a particular
significance for (abstract) differential-geometric applications; yet, the same
class of algebras is still ``closed'', with respect to appropriate inductive
limits, a fact which thus considerably broadens the sort of the topological
algebras involved, hence, as we shall see, their potential applications as
well.


title: Radiating fluid spheres in the effective variables approximation

abstract:
  We study the evolution of spherically symmetric radiating fluid distributions
using the effective variables method, implemented {\it ab initio} in
Schwarzschild coordinates. To illustrate the procedure and to establish some
comparison with the original method, we integrate numerically the set of
equations at the surface for two different models. The first model is derived
from the Schwarzschild interior solution. The second model is inspired in the
Tolman VI solution.


title: Induced gravitation as nonlinear electrodynamics effect

abstract:
  The effect of induced Riemann geometry in nonlinear electrodynamics is
considered. The possibility for description of real gravitation by this effect
is discussed.


title: A note on Schwarzschild black hole thermodynamics in a magnetic universe

abstract:
  We prove that the thermodynamic properties of a Schwarzschild black hole are
unaffected by an external magnetic field passing through it. Apart from the
background substraction prescription, this result is obtained also by using a
counterterm method.


title:
Charged black holes: Wave equations for gravitational and
  electromagnetic perturbations

abstract:
  A pair of wave equations for the electromagnetic and gravitational
perturbations of the charged Kerr black hole are derived. The perturbed
Einstein-Maxwell equations in a new gauge are employed in the derivation. The
wave equations refer to the perturbed Maxwell spinor $\Phi_0$ and to the shear
$\sigma$ of a principal null direction of the Weyl curvature. The whole
construction rests on the tripod of three distinct derivatives of the first
curvature $\kappa$ of a principal null direction.


title:
Perturbative Solutions of the Extended Constraint Equations in General
  Relativity

abstract:
  The extended constraint equations arise as a special case of the conformal
constraint equations that are satisfied by an initial data hypersurface $Z$ in
an asymptotically simple spacetime satisfying the vacuum conformal Einstein
equations developed by H. Friedrich. The extended constraint equations consist
of a quasi-linear system of partial differential equations for the induced
metric, the second fundamental form and two other tensorial quantities defined
on $Z$, and are equivalent to the usual constraint equations that $Z$ satisfies
as a spacelike hypersurface in a spacetime satisfying Einstein's vacuum
equation. This article develops a method for finding perturbative,
asymptotically flat solutions of the extended constraint equations in a
neighbourhood of the flat solution on Euclidean space. This method is
fundamentally different from the `classical' method of Lichnerowicz and York
that is used to solve the usual constraint equations.


title: Cosmic Evolution in Generalised Brans-Dicke Theory

abstract:
  We have studied the Generalised Brans-Dicke theory and obtained exact
solutions of a(t),phi(t),and omega(t) for different epochs of the cosmic
evolution .We discuss how inflation,decceleration,cosmic acceleration can
result from this solution.The time variation of G(t) is also examined.


title: CYK Tensors, Maxwell Field and Conserved Quantities for Spin-2 Field

abstract:
  Starting from an important application of Conformal Yano--Killing tensors for
the existence of global charges in gravity, some new observations at $\scri^+$
are given. They allow to define asymptotic charges (at future null infinity) in
terms of the Weyl tensor together with their fluxes through $\scri^+$. It
occurs that some of them play a role of obstructions for the existence of
angular momentum.
  Moreover, new relations between solutions of the Maxwell equations and the
spin-2 field are given. They are used in the construction of new conserved
quantities which are quadratic in terms of the Weyl tensor. The obtained
formulae are similar to the functionals obtained from the
  Bel--Robinson tensor.


title: Relativistic Dyson Rings and Their Black Hole Limit

abstract:
  In this Letter we investigate uniformly rotating, homogeneous and
axisymmetric relativistic fluid bodies with a toroidal shape. The corresponding
field equations are solved by means of a multi-domain spectral method, which
yields highly accurate numerical solutions. For a prescribed, sufficiently
large ratio of inner to outer coordinate radius, the toroids exhibit a
continuous transition to the extreme Kerr black hole. Otherwise, the most
relativistic configuration rotates at the mass-shedding limit. For a given
mass-density, there seems to be no bound to the gravitational mass as one
approaches the black-hole limit and a radius ratio of unity.


title:
Gravitational waves from black hole binary inspiral and merger: The span
  of third post-Newtonian effective-one-body templates

abstract:
  We extend the description of gravitational waves emitted by binary black
holes during the final stages of inspiral and merger by introducing in the
third post-Newtonian (3PN) effective-one-body (EOB) templates seven new
``flexibility'' parameters that affect the two-body dynamics and gravitational
radiation emission. The plausible ranges of these flexibility parameters,
notably the parameter characterising the fourth post-Newtonian effects in the
dynamics, are estimated. Using these estimates, we show that the currently
available standard 3PN bank of EOB templates does ``span'' the space of signals
opened up by all the flexibility parameters, in that their maximized mutual
overlaps are larger than 96.5%. This confirms the effectualness of 3PN EOB
templates for the detection of binary black holes in gravitational-wave data
from interferometric detectors. The possibility to drastically reduce the
number of EOB templates using a few ``universal'' phasing functions is
suggested.


title: Determinism and the gravitational Planck constant

abstract:
  A discussion is given of the uncertainty principle in view of the
introduction of a Gravitational Planck Constant. The need for such a
gravitational constant is shown first. A reduced electromagnetic Planck
constant and the analogous reduced gravitational Planck constant are defined as
h/e^2 and H/m^2 respectively. An attempt is made to reconcile the quantum
uncertainty concepts with a deterministic view of the physical world. This
conclusion is achieved trough the detailed analysis of the measurement
procedures of physical quantities.


title:
Non-Existence of Black Hole Solutions to Static, Spherically Symmetric
  Einstein-Dirac Systems - a Critical Discussion

abstract:
  This short note compares different methods to prove that Einstein-Dirac
systems have no static, spherically symmetric solutions.


title: Fresh inflation with increasing cosmological parameter

abstract:
  I study a fresh inflationary model with an increasing F-cosmological
parameter. The model provides sufficiently e-folds to solve the
flatness/horizon problem and the density fluctuations agree with experimental
values. The temperature increases during fresh inflation and reach its maximum
value when inflation ends. I find that entropy perturbations always remain
below $10^{-4}$ during fresh inflation and become negligible when fresh
inflation ends. Hence, the adiabatic fluctuations dominate the primordial
spectrum at the end of fresh inflation.


title: On Fast Travel through spherically symmetric spacetimes

abstract:
  In a static spacetime, the Killing time can be used to measure the time
required for signals or objects to propagate between two of its orbits. By
further restricting to spherically symmetric cases, one obtains a natural
association between these orbits and timelike lines in Minkowski space. We
prove a simple theorem to the effect that in any spacetime satisfying the weak
energy condition the above signaling time is, in this sense, no faster than
that for a corresponding signal in Minkowski space. The theorem uses a
ormalization of Killing time appropriate to an observer at infinity. We then
begin an investigation of certain related but more local questions by studying
particular families of spacetimes in detail. Here we are also interested in
restrictions imposed by the dominant energy condition. Our examples suggest
that signaling in spacetimes satisfying this stronger energy condition may be
significantly slower than the fastest spacetimes satisfying only the weak
energy condition.


title:
On the possibility of measuring the Earth's gravitomagnetic force in a
  new laboratory experiment

abstract:
  In this paper we propose, in a preliminary way, a new Earth-based laboratory
experiment aimed to the detection of the gravitomagnetic field of the Earth. It
consists of the measurement of the difference of the circular frequencies of
two rotators moving along identical circular paths, but in opposite directions,
on a horizontal friction-free plane in a vacuum chamber placed at South Pole.
The accuracy of our knowledge of the Earth's rotation from VLBI and the
possibility of measuring the rotators'periods over many revolutions should
allow for the feasibility of the proposed experiment.


title: Expanding the Area of Gravitational Entropy

abstract:
  I describe how gravitational entropy is intimately connected with the concept
of gravitational heat, expressed as the difference between the total and free
energies of a given gravitational system. From this perspective one can compute
these thermodyanmic quantities in settings that go considerably beyond
Bekenstein's original insight that the area of a black hole event horizon can
be identified with thermodynamic entropy. The settings include the outsides of
cosmological horizons and spacetimes with NUT charge. However the
interpretation of gravitational entropy in these broader contexts remains to be
understood.


title:
On Consistence of Matter Coupling in GL(3,R) Gauge Formulation of
  Gravity

abstract:
  A covariant scheme for matter coupling with a GL(3,R) gauge formulation of
gravity is studied. We revisit a known Yang-Mills type construction, where
quadratical power of cosmological constant have to be considered in consistence
with vacuum Einstein's gravity. Then, matter coupling with gravity is
introduced and some constraints on fields and background appear. Finally we
elucidate that introduction of auxiliary fields decreases the number of these
constraints.


title: On black hole solutions in model with anisotropic fluid

abstract:
  A family of spherically symmetric solutions in the model with 1-component
anisotropic fluid is considered. The metric of the solution depends on a
parameter q > 0 relating radial pressure and the density and contains n -1
parameters corresponding to Ricci-flat ``internal space'' metrics. For q = 1
and certain equations of state the metric coincides with the metric of black
brane solutions in the model with antisymmetric form. A family of black hole
solutions corresponding to natural numbers q = 1,2, ... is singled out. Certain
examples of solutions (e.g. containing for q =1 Reissner-Nordstr\"{o}m, M2 and
M5 black brane metrics) are considered. The post-Newtonian parameters beta and
gamma corresponding to the 4-dimensional section of the metric are calculated.


title: Measuring the general relativistic curvature of wave-fronts

abstract:
  Einstein's general theory of relativity predicts that an initially plane
wave-front will curve because of gravity. This effect can now be measured using
Very Long Baseline Interferometry (VLBI). A wave-front from a distant point
source will curve as it passes the gravitational field of the Sun. We propose
an experiment to directly measure this curvature, using four VLBI stations on
earth, separated by intercontinental distances. Expressed as a time delay, the
size of the effect is a few hundred picoseconds and may be measureable with
present technology.


title: Closed timelike curves in general relativity

abstract:
  Many solutions of Einstein's field equations contain closed timelike curves
(CTC). Some of these solutions refer to ordinary materials in situations which
might occur in the laboratory, or in astrophysics. It is argued that, in
default of a reasonable interpretation of CTC, general relativity does not give
a satisfactory account of all phenomena within its terms of reference.


title: The Pioneer riddle, the quantum vacuum and the acceleration of light

abstract:
  It is shown that the same phenomenological Newtonian model recently proposed
by the author to explain the cosmological evolution of the fine structure
constant suggests furthermore an explanation of the unmodelled acceleration
$a_P\simeq 8.5\times 10^{-10}m/s^2$ of the Pioneer 10/11 spaceships reported by
Anderson {\em et al} in 1998. In the view presented here, it is argued that the
permittivity and permeability of empty space are decreasing adiabatically, and
the light is accelerating therefore, as a consequence of the progressive
attenuation of the quantum vacuum due to the combined effect of its
gravitational interaction with all the expanding universe and the fourth
Heisenberg relation. It is suggested that the spaceships do not have any extra
acceleration (but follow the unchanged Newton laws), the observed effect being
due to an adiabatic acceleration of the light equal to $a_P$, which has the
same observational radio signature as the anomalous acceleration of the
Pioneers.


title:
Do static sources respond to massive scalar particles from the Hawking
  radiation as uniformly accelerated ones do in the inertial vacuum?

abstract:
  We revisit the recently found equivalence for the response of a static scalar
source interacting with a {\em massless} Klein-Gordon field when the source is
(i) static in Schwarzschild spacetime, in the Unruh vacuum associated with the
Hawking radiation and (ii) uniformly accelerated in Minkowski spacetime, in the
inertial vacuum, provided that the source's proper acceleration is the same in
both cases. It is shown that this equivalence is broken when the massless
Klein-Gordon field is replaced by a {\em massive} one.


title: Relativistic Elasticity

abstract:
  Relativistic elasticity on an arbitrary spacetime is formulated as a
Lagrangian field theory which is covariant under spacetime diffeomorphisms.
This theory is the relativistic version of classical elasticity in the
hyperelastic, materially frame-indifferent case and, on Minkowski space,
reduces to the latter in the non-relativistic limit . The field equations are
cast into a first -- order symmetric hyperbolic system. As a consequence one
obtains local--in--time existence and uniqueness theorems under various
circumstances.


title: Quantum Radiation from a 5-Dimensional Rotating Black Hole

abstract:
  We study a massless scalar field propagating in the background of a
five-dimensional rotating black hole. We showed that in the Myers-Perry metric
describing such a black hole the massless field equation allows the separation
of variables. The obtained angular equation is a generalization of the equation
for spheroidal functions. The radial equation is similar to the radial
Teukolsky equation for the 4-dimensional Kerr metric. We use these results to
quantize the massless scalar field in the space-time of the 5-dimensional
rotating black hole and to derive expressions for energy and angular momentum
fluxes from such a black hole.


title: Analytic Evaluation of the Decay Rate for Accelerated Proton

abstract:
  We evaluate the decay rate of the uniformly accelerated proton. We obtain an
analytic expression for inverse beta decay process caused by the acceleration.
We evaluate the decay rate both from the inertial frame and from the
accelerated frame where we should consider thermal radiation by Unruh effect.
We explicitly check that the decay rates obtained in both frame coincide with
each other.


title: Quintessence and cosmic acceleration

abstract:
  A cosmological model with perfect fluid and self-interacting quintessence
field is considered in the framework of the spatially flat
Friedmann-Robertson-Walker (FRW) geometry. By assuming that all physical
quantities depend on the volume scale factor of the Universe, the general
solution of the gravitational field equations can be expressed in an exact
parametric form. The quintessence field is a free parameter. With an
appropriate choice of the scalar field a class of exact solutions is obtained,
with an exponential type scalar field potential fixed via the gravitational
field equations. The general physical behavior of the model is consistent with
the recent cosmological scenario favored by supernova Type Ia observations,
indicating an accelerated expansion of the Universe.


title:
Mass formulae for spherically symmetric stellar configurations in five
  dimensional space-time

abstract:
  An expression is derived where the mass is connected to an integral over the
pressure of gravitating matter in the frame work of five dimensional(5D)
space-time.


title: Perturbations of rotating cosmological black holes

abstract:
  Charged, rotating black hole solutions of Einstein's gravitational equations
are investigated in the presence of a cosmological constant. A pair of wave
equations governing the electromagnetic and gravitational perturbations are
derived.


title:
Improvement on the metric reconstruction scheme in the
  Regge-Wheeler-Zerilli formalism

abstract:
  We study master variables in the Regge-Wheeler-Zerilli formalism. We show
that a specific choice of new variables is suitable for studying perturbation
theory from the viewpoint of radiation reaction calculations. With explicit
definition of the improved master variables in terms of components of metric
perturbations, we present the master equations, with source terms, and metric
reconstruction formulas. In the scheme using these new variables, we do not
need any time and radial integrations except for solving the master equation.
We also show that the master variable for even parity modes which satisfies the
same homogeneous equation as the odd parity case, obtained via
  Chandrasekhar transformation, does not have the good property in this sense.


title: How Does Naked Singularity Look?

abstract:
  There are non-radial null geodesics emanating from the shell focusing
singularity formed at the symmetric center in a spherically symmetric dust
collapse. In this article, assuming the self-similarity in the region filled
with the dust fluid, we study these singular null geodesics in detail. We see
the time evolution of the angular diameter of the central naked singularity and
show that it might be bounded above by the value corresponding to the circular
null geodesic in the Schwarzschild spacetime. We also investigate the angular
frequency of a physical field which propagates along the singular null geodesic
and find that it depends on the impact parameter. Further, we comment on the
non-uniformity of the topology of the central naked singularity.


title:
The Hamilton Operator and Quantum Vacuum for Nonconformal Scalar Fields
  in the Homogeneous and Isotropic Space

abstract:
  The diagonalization of the metrical and canonical Hamilton operators of a
scalar field with an arbitrary coupling, with a curvature in N-dimensional
homogeneous isotropic space is considered in this paper. The energy spectrum of
the corresponding quasiparticles is obtained and then the modified
energy-momentum tensor is constructed; the latter coincides with the metrical
energy-momentum tensor for conformal scalar field. Under the diagonalization of
corresponding Hamilton operator the energies of relevant particles of a
nonconformal field are equal to the oscillator frequencies, and the density of
such particles created in a nonstationary metric is finite. It is shown that
the modified Hamilton operator can be constructed as a canonical Hamilton
operator under the special choice of variables.


title:
Existence of CMC and constant areal time foliations in T^2 symmetric
  spacetimes with Vlasov matter

abstract:
  The global structure of solutions of the Einstein equations coupled to the
Vlasov equation is investigated in the presence of a two-dimensional symmetry
group. It is shown that there exist global CMC and areal time foliations. The
proof is based on long-time existence theorems for the partial differential
equations resulting from the Einstein-Vlasov system when conformal or areal
coordinates are introduced.


title:
An elliptical tiling method to generate a 2-dimensional set of templates
  for gravitational wave search

abstract:
  Searching for a signal depending on unknown parameters in a noisy background
with matched filtering techniques always requires an analysis of the data with
several templates in parallel in order to ensure a proper match between the
filter and the real waveform. The key feature of such an implementation is the
design of the filter bank which must be small to limit the computational cost
while keeping the detection efficiency as high as possible. This paper presents
a geometrical method which allows one to cover the corresponding physical
parameter space by a set of ellipses, each of them being associated to a given
template. After the description of the main characteristics of the algorithm,
the method is applied in the field of gravitational wave (GW) data analysis,
for the search of damped sine signals. Such waveforms are expected to be
produced during the de-excitation phase of black holes -- the so-called
'ringdown' signals -- and are also encountered in some numerically computed
supernova signals.


title: The Geometric Origin of the Madelung Potential

abstract:
  Madelung's hydrodynamical forms of the Schrodinger equation and the
Klein-Gordon equation are presented. The physical nature of the quantum
potential is explored. It is demonstrated that the geometrical origin of the
quantum potential is in the scalar curvature of the of the metric that defines
the kinetic energy density for an extended particle and that the quantization
of circulation (Bohr-Sommerfeld) is a consequence of associating an
SO(2)-reduction of the Lorentz frame bundle with wave motion. The Madelung
equations are then cast in a basis-free form in terms of exterior differential
forms in such a way that they represent the equations for a timelike solution
to the conventional wave equations whose rest mass density satisfies a
differential equation of the "Klein-Gordon minus nonlinear term" type. The role
of non-zero vorticity is briefly examined.


title: Proper Time Foliations of Lorentz Manifolds

abstract:
  Some standard definitions and results concerning foliations of dimension one
and codimension one are introduced. A proper time foliation of Minkowski space
is defined and contrasted with the foliation that is defined by the time
coordinate. The extent to which a Lorentz structure on a manifold defines
foliations, and the issues concerning the extension of the proper time
foliation of Minkowski space to a Lorentz manifold are discussed, such as
proper time sections of a geodesic flow.


title: Charged multifluids in general relativity

abstract:
  The exact 1+3 covariant dynamical fluid equations for a multi-component
plasma, together with Maxwell's equations are presented in such a way as to
make them suitable for a gauge-invariant analysis of linear density and
velocity perturbations of the Friedmann-Robertson-Walker model. In the case
where the matter is described by a two component plasma where thermal effects
are neglected, a mode representing high-frequency plasma oscillations is found
in addition to the standard growing and decaying gravitational instability
picture. Further applications of these equations are also discussed.


title: Curvature of the universe and the dark energy potential

abstract:
  The flatness of an accelerating universe model (characterized by a dark
energy scalar field $\chi$) is mimicked from a curved model that is filled
with, apart from the cold dark matter component, a quintessencelike scalar
field $Q$. In this process, we characterize the original scalar potential
$V(Q)$ and the mimicked scalar potential $V(\chi)$ associated to the scalar
fields $Q$ and $\chi$, respectively. The parameters of the original model are
fixed through the mimicked quantities that we relate to the present
astronomical data, such that the equation state parameter $w_{_{\chi}}$ and the
dark energy density parameter $\Omega_{\chi}$.


title: Intrinsic instability of sonic white holes

abstract:
  Artificial black holes, such as sonic holes in Bose-Einstein condensates, may
give insights into the role of the physics at the event horizon beyond the
Planck scale. We show that sonic white holes give rise to a discrete spectrum
of instabilities that is insensitive to the analogue of trans-Planckian physics
for Bose-Einstein condensates.


title:
New Techniques for Analysing Axisymmetric Gravitational Systems. 1.
  Vacuum Fields

abstract:
  A new framework for analysing the gravitational fields in a stationary,
axisymmetric configuration is introduced. The method is used to construct a
complete set of field equations for the vacuum region outside a rotating
source. These equations are under-determined. Restricting the Weyl tensor to
type D produces a set of equations which can be solved, and a range of new
techniques are introduced to simplify the problem. Imposing the further
condition that the solution is asymptotically flat yields the Kerr solution
uniquely. The implications of this result for the no-hair theorem are
discussed. The techniques developed here have many other applications, which
are described in the conclusions.


title: Asymptotic dynamics of the exceptional Bianchi cosmologies

abstract:
  In this paper we give, for the first time, a qualitative description of the
asymptotic dynamics of a class of non-tilted spatially homogeneous (SH)
cosmologies, the so-called exceptional Bianchi cosmologies, which are of
Bianchi type VI$_{-1/9}$. This class is of interest for two reasons. Firstly,
it is generic within the class of non-tilted SH cosmologies, being of the same
generality as the models of Bianchi types VIII and IX. Secondly, it is the SH
limit of a generic class of spatially inhomogeneous $G_{2}$ cosmologies.
  Using the orthonormal frame formalism and Hubble-normalized variables, we
show that the exceptional Bianchi cosmologies differ from the non-exceptional
Bianchi cosmologies of type VI$_{h}$ in two significant ways. Firstly, the
models exhibit an oscillatory approach to the initial singularity and hence are
not asymptotically self-similar. Secondly, at late times, although the models
are asymptotically self-similar, the future attractor for the vacuum-dominated
models is the so-called Robinson-Trautman SH model instead of the vacuum SH
plane wave models.


title: Spin polarised magnetized cylinder in torsioned spacetime

abstract:
  A Spin-polarised cylindrically symmetric exact class of solutions endowed
with magnetic fields in Einstein-Cartan-Maxwell gravity is obtained.
Application of matching conditions to this interior solution having an exterior
as Einstein's vacuum solution shows that for this class of metrics the
Riemann-Cartan (RC) rotation vanishes which makes the solution static.
Therefore we end up with a magnetized static spin polarised cylinder where the
pressure along the symmetry axis is negative.


title:
Two and Three parametric regular generalizations of spherically
  symmetric and axially symmetric metrics

abstract:
  Regular generalizations of spherically and axially symmetric metrics and
their properties are considered. Newton gravity law generalizations are reduced
for null geodesic.


title: Unusual Features of Varying Speed of Light Cosmologies

abstract:
  We contrast features of simple varying speed of light (VSL) cosmologies with
inflationary universe models. We present new features of VSL cosmologies and
show that they face problems explaining the cosmological isotropy problem. We
also find that if c falls fast enough to solve the flatness and horizon
problems then the quantum wavelengths of massive particle states and the radii
of primordial black holes can grow to exceed the scale of the particle horizon.
This may provide VSL cosmologies with a self-reproduction property. The
constraint of entropy increase is also discussed. The new problems described in
the this letter provide a set of bench tests for more sophisticated VSL
theories to pass.


title:
Searching for Gravitational Waves from the Inspiral of Precessing Binary
  Systems: New Hierarchical Scheme using "Spiky" Templates

abstract:
  In a recent investigation of the effects of precession on the anticipated
detection of gravitational-wave inspiral signals from compact object binaries
with moderate total masses, we found that (i) if precession is ignored, the
inspiral detection rate can decrease by almost a factor of 10, and (ii)
previously proposed ``mimic'' templates cannot improve the detection rate
significantly (by more than a factor of 2). In this paper we propose a new
family of templates that can improve the detection rate by factors of 5--6 in
cases where precession is most important. Our proposed method for these new
``mimic'' templates involves a hierarchical scheme of efficient, two-parameter
template searches that can account for a sequence of spikes that appear in the
residual inspiral phase, after one corrects for the any oscillatory
modification in the phase. We present our results for two cases of compact
object masses (10 and 1.4 solar masses and 7 and 3 solar masses) as a function
of spin properties. Although further work is needed to fully assess the
computational efficiency of this newly proposed template family, we conclude
that these ``spiky templates'' are good candidates for a family of precession
templates used in realistic searches, that can improve detection rates of
inspiral events.


title: Quasinormal Modes, the Area Spectrum, and Black Hole Entropy

abstract:
  The results of canonical quantum gravity concerning geometric operators and
black hole entropy are beset by an ambiguity labelled by the Immirzi parameter.
We use a result from classical gravity concerning the quasinormal mode spectrum
of a black hole to fix this parameter in a new way. As a result we arrive at
the Bekenstein - Hawking expression of $A/4 l_P^2$ for the entropy of a black
hole and in addition see an indication that the appropriate gauge group of
quantum gravity is SO(3) and not its covering group SU(2).


title:
A Cosmologic Model Based on the Equivalence of Expansion and Light
  Retardation

abstract:
  Proceeding from a homogeneous and isotropic Friedmann universe a conceptional
problem concerning light propagation in an expanding universe is brought up. As
a possible solution of this problem it is suggested that light waves do not
scale with R(t). With the aid of a Generalized Equivalence Principle a
cosmologic model with variable "constants" c, H, and G is constructed. It is
shown that with an appropriate variation of the Boltzmann "constant" k the
thermal evolution of the universe is similar to the standard model. It is
further shown that this model explains the cosmological redshift as well as
certain problems of the standard model (horizon, flatness, accelerated
expansion of the universe).
  PACS numbers: 98.80.Bp, 98.80.Hw, 04.20.Cv.
  Keywords: cosmology, velocity of light, expansion.


title:
Conceptual tensions between quantum mechanics and general relativity:
  Are there experimental consequences?

abstract:
  One of the conceptual tensions between quantum mechanics (QM) and general
relativity (GR) arises from the clash between the spatial nonseparability} of
entangled states in QM, and the complete spatial separability of all physical
systems in GR, i.e., between the nonlocality implied by the superposition
principle, and the locality implied by the equivalence principle. Possible
experimental consequences of this conceptual tension will be discussed for
macroscopically entangled, coherent quantum fluids, such as superconductors,
superfluids, atomic Bose-Einstein condensates, and quantum Hall fluids,
interacting with tidal and gravitational radiation fields. A minimal-coupling
rule, which arises from the electron spin coupled to curved spacetime, leads to
an interaction between electromagnetic (EM) and gravitational (GR) radiation
fields mediated by a quantum Hall fluid. This suggests the possibility of a
quantum transducer action, in which EM waves are convertible to GR waves, and
vice versa.


title: Relativity theory of clocks and rulers

abstract:
  Special Relativity (SR) kinematics is derived from very intuitive
assumptions. Contrary to standard Einstein's derivation, no light signal is
used in the construction nor it is assumed to exist. Instead we postulate the
existence of two equivalence classes of physical objects: proportional clocks
and proportional rulers. Simple considerations lead to Lorentz kinematics as
one of three generic cases. The Lorentz case is characterized by the maximal
relative speed of physical objects. The two others are the Galilean and the
Euclidean cases.


title: Non-linear relativistic perturbation theory with two parameters

abstract:
  An underlying fundamental assumption in relativistic perturbation theory is
the existence of a parametric family of spacetimes that can be Taylor expanded
around a background. Since the choice of the latter is crucial, sometimes it is
convenient to have a perturbative formalism based on two (or more) parameters.
A good example is the study of rotating stars, where generic perturbations are
constructed on top of an axisymmetric configuration built by using the slow
rotation approximation. Here, we discuss the gauge dependence of non-linear
perturbations depending on two parameters and how to derive explicit higher
order gauge transformation rules.


title: Thick domain wall spacetimes with and without reflection symmetry

abstract:
  We show that the spacetimes of domain wall solutions to the coupled
Einstein-scalar field equations with a given scalar field potential fall into
two classes, depending on whether or not reflection symmetry on the wall is
imposed. Solutions with reflection symmetry are dynamic, while the asymmetric
ones are static. Asymmetric walls are asymptotically flat on one side and
reduce to the Taub spacetime on the other. Examples of asymmetric thick walls
in D-dimensional spacetimes are given, and results on the thin-wall limit of
the dynamic, symmetric walls are extended to the asymmetric case. The
particular case of symmetric, static spacetimes is considered and a new family
of solutions, including previously known BPS walls, is presented.


title: The Emergent Universe: inflationary cosmology with no singularity

abstract:
  Observations indicate that the universe is effectively flat, but they do not
rule out a closed universe. The role of positive curvature is negligible at
late times, but can be crucial in the early universe. In particular, positive
curvature allows for cosmologies that originate as Einstein static universes,
and then inflate and later reheat to a hot big bang era. These cosmologies have
no singularity, no "beginning of time", and no horizon problem. If the initial
radius is chosen to be above the Planck scale, then they also have no quantum
gravity era, and are described by classical general relativity throughout their
history.


title:
Density matrix and dynamical aspects of Quantum Mechanics with
  Fundamental Length

abstract:
  In this paper Quantum Mechanics with Fundamental Length is built as a
deformation of Quantum Mechanics. To this aim an approach is used which does
not take into account commutator deformation as usually it is done, but density
matrix deformation. The corresponding deformed density matrix, which is called
density pro-matrix is given explicitly. It properties have been investigated as
well as some dynamical aspects of the theory. In particular, the deformation of
Liouville equation is analyzed in detail. It was shown that Liouville equation
in Quantum Mechanics appears as a low energy limit of deformed Liouville
equation in Quantum Mechanics with Fundamental Length. Some implications of
obtained results are presented as well as their application to the calculation
of black hole entropy.


title: Resource Letter GrW-1: Gravitational Waves

abstract:
  This Resource Letter provides a guide to the literature on the physics and
astrophysics of gravitational waves. Journals, books, reports, archives, and
websites are provided as basic resources and for current research frontiers in
detectors, data analysis, and astrophysical source modeling.


title: Clifford Space as the Arena for Physics

abstract:
  A new theory is considered according to which extended objects in
$n$-dimensional space are described in terms of multivector coordinates which
are interpreted as generalizing the concept of centre of mass coordinates.
While the usual centre of mass is a point, by generalizing the latter concept,
we associate with every extended object a set of $r$-loops, $r=0,1,..., n-1$,
enclosing oriented $(r+1)$-dimensional surfaces represented by Clifford numbers
called $(r+1)$-vectors or multivectors. Superpositions of multivectors are
called polyvectors or Clifford aggregates and they are elements of Clifford
algebra. The set of all possible polyvectors forms a manifold, called
$C$-space. We assume that the arena in which physics takes place is in fact not
Minkowski space, but $C$-space. This has many far reaching physical
implications, some of which are discussed in this paper. The most notable is
the finding that although we start from the constrained relativity in $C$-space
we arrive at the unconstrained Stueckelberg relativistic dynamics in Minkowski
space which is a subspace of $C$-space.


title: Causality and Conjugate Points in General Plane Waves

abstract:
  Let $M = M_0 \times \R^2$ be a pp--wave type spacetime endowed with the
metric $<\cdot,\cdot>_z = <\cdot,\cdot>_x + 2 du dv + H(x,u) du^2$, where
$(M_0, <\cdot,\cdot>_x) $ is any Riemannian manifold and $H(x,u)$ an arbitrary
function. We show that the behaviour of $H(x,u)$ at spatial infinity determines
the causality of $M$, say: (a) if $-H(x,u)$ behaves subquadratically (i.e,
essentially $-H(x,u) \leq R_1(u) |x|^{2-\epsilon} $ for some $\epsilon >0$ and
large distance $|x|$ to a fixed point) and the spatial part $(M_0,
<\cdot,\cdot>_x) $ is complete, then the spacetime $M$ is globally hyperbolic,
(b) if $-H(x,u)$ grows at most quadratically (i.e, $-H(x,u) \leq R_1(u)
|x|^{2}$ for large $|x|$) then it is strongly causal and (c) $M$ is always
causal, but there are non-distinguishing examples (and thus, non-strongly
causal), even when $-H(x,u) \leq R_1(u) |x|^{2+\epsilon} $, for small $\epsilon
>0$.
  Therefore, the classical model $M_0 = \R^2$, $H(x,u) = \sum_{i,j} h_{ij}(u)
x_i x_j (\not\equiv 0)$, which is known to be strongly causal but not globally
hyperbolic, lies in the critical quadratic situation with complete $M_0$. This
must be taken into account for realistic applications. In fact, we argue that
$-H$ will be subquadratic (and the spacetime globally hyperbolic) if $M$ is
asymptotically flat. The relation of these results with the notion of
astigmatic conjugacy and the existence of conjugate points is also discussed.


title:
Detecting gravitational waves from precessing binaries of spinning
  compact objects: Adiabatic limit

abstract:
  Black-hole (BH) binaries with single-BH masses m=5--20 Msun, moving on
quasicircular orbits, are among the most promising sources for first-generation
ground-based gravitational-wave (GW) detectors. Until now, the development of
data-analysis techniques to detect GWs from these sources has been focused
mostly on nonspinning BHs. The data-analysis problem for the spinning case is
complicated by the necessity to model the precession-induced modulations of the
GW signal, and by the large number of parameters needed to characterize the
system, including the initial directions of the spins, and the position and
orientation of the binary with respect to the GW detector. In this paper we
consider binaries of maximally spinning BHs, and we work in the
adiabatic-inspiral regime to build families of modulated detection templates
that (i) are functions of very few physical and phenomenological parameters,
(ii) model remarkably well the dynamical and precessional effects on the GW
signal, with fitting factors on average >~ 0.97, but (iii) might require
increasing the detection thresholds, offsetting at least partially the gains in
the fitting factors. Our detection-template families are quite promising also
for the case of neutron-star--black-hole binaries, with fitting factors on
average ~ 0.93. For these binaries we also suggest (but do not test) a further
template family, which would produce essentially exact waveforms written
directly in terms of the physical spin parameters.


title: Quantum speedmeter and laser interferometric gravitational-wave antennae

abstract:
  A new topology of laser interferometric gravitational-wave antenna is
considered. It is based on two schemes: {\em quantum speedmeter} and {\em
zero-area Sagnac interferometer} and allows to obtain sensitivity better than
the Standard Quantum Limit in wide band without any large-scale modifications
of the standard topology of the laser interferometric antennae.


title: Kerr Black Hole as a Quantum Rotator

abstract:
  It has been proposed by Bekenstein and others that the horizon area of a
black hole conforms, upon quantization, to a discrete and uniformly spaced
spectrum. In this paper, we consider the area spectrum for the highly
non-trivial case of a rotating (Kerr) black hole solution. Following a prior
work by Barvinsky, Das and Kunstatter, we are able to express the area spectrum
in terms of an integer-valued quantum number and an angular-momentum operator.
Moreover, by using an analogy between the Kerr black hole and a quantum
rotator, we are able to quantize the angular-momentum sector. We find the area
spectrum to be $A_{n,J_{cl}}=8\pi\hbar(n+J_{cl}+1/2)$, where $n$ and $J_{cl}$
are both integers. The quantum number $J_{cl}$ is related to but distinct from
the eigenvalue $j$ of the angular momentum of the black hole. Actually, it
represents the ``classical'' angular momentum and, for $J_{cl}\gg 1$,
$J_{cl}\approx j$.


title: Stochastic Gravity: A Primer with Applications

abstract:
  Stochastic semiclassical gravity of the 90's is a theory naturally evolved
from semiclassical gravity of the 70's and 80's. It improves on the
semiclassical Einstein equation with source given by the expectation value of
the stress-energy tensor of quantum matter fields in curved spacetimes by
incorporating an additional source due to their fluctuations. In stochastic
semiclassical gravity the main object of interest is the noise kernel, the
vacuum expectation value of the (operator-valued) stress-energy bi-tensor, and
the centerpiece is the (stochastic) Einstein-Langevin equation. We describe
this new theory via two approaches: the axiomatic and the functional. The
axiomatic approach is useful to see the structure of the theory from the
framework of semiclassical gravity. The functional approach uses the
Feynman-Vernon influence functional and the Schwinger-Keldysh close-time-path
effective action methods which are convenient for computations. It also brings
out the open systems concepts and the statistical and stochastic contents of
the theory such as dissipation, fluctuations, noise and decoherence. We then
describe the application of stochastic gravity to the backreaction problems in
cosmology and black hole physics. Intended as a first introduction to this
subject, this article places more emphasis on pedagogy than completeness.


title:
Universal one-way light speed from a universal light speed over closed
  paths

abstract:
  This paper gives two complete and elementary proofs that if the speed of
light over closed paths has a universal value $c$, then it is possible to
synchronize clocks in such a way that the one-way speed of light is c. The
first proof is an elementary version of a recent proof. The second provides
high precision experimental evidence that it is possible to synchronize clocks
in such a way that the one-way speed of light has a universal value. We also
discuss an old incomplete proof by Weyl which is important from an historical
perspective.


title: 2D-gravity and the Hamilton-Jacobi formalism

abstract:
  Hamilton-Jacobi formalism is used to study 2D-gravity and its SL(2, R) hidden
symmetry. If the contribution of the surface term is considered the obtained
results coincide with those given by the Dirac and Faddeev-Jackiw approaches.


title: A class of homogeneous scalar-tensor cosmologies with a radiation fluid

abstract:
  We present a new class of exact homogeneous cosmological solutions with a
radiation fluid for all scalar-tensor theories. The solutions belong to Bianchi
type $VI_{h}$ cosmologies. Explicit examples of nonsingular homogeneous
scalar-tensor cosmologies are also given.


title:
Gravitational Radiation from the radial infall of highly relativistic
  point particles into Kerr black holes

abstract:
  In this paper, we consider the gravitational radiation generated by the
collision of highly relativistic particles with rotating Kerr black holes. We
use the Sasaki-Nakamura formalism to compute the waveform, energy spectra and
total energy radiated during this process. We show that the gravitational
spectrum for high-energy collisions has definite characteristic universal
features, which are independent of the spin of the colliding objects. We also
discuss possible connections between these results and the black hole-black
hole collision at the speed of light process. With these results at hand, we
predict that during the high speed collision of a non-rotating hole with a
rotating one, about 35% of the total energy can get converted into
gravitational waves. Thus, if one is able to produce black holes at the Large
Hadron Collider, as much as 35% of the partons' energy should be emitted during
the so called balding phase. This energy will be missing, since we don't have
gravitational wave detectors able to measure such amplitudes. The collision at
the speed of light between one rotating black hole and a non-rotating one or
two rotating black holes turns out to be the most efficient gravitational wave
generator in the Universe.


title:
Inflation and Transition to a Slowly Accelerating Phase from S.S.B. of
  Scale Invariance

abstract:
  We consider the effects of adding a scale invariant $R^{2}$ term to the
action of the scale invariant model (SIM) studied previously by one of us
(E.I.G., Mod. Phys. Lett. A14, 1043 (1999)). The SIM belongs to the general
class of theories, where an integration measure independent of the metric is
introduced. To implement scale invariance (S.I.), a dilaton field is
introduced. The integration of the equations of motion associated with the new
measure gives rise to the spontaneous symmetry breaking (S.S.B) of S.I.. After
S.S.B. of S.I. in the model with the $R^{2}$ term, it is found that a non
trivial potential for the dilaton is generated. This potential contains two
flat regions: one associated with the Planck scale and with an inflationary
phase, while the other flat region is associated to a very small vacuum energy
(V.E.) and is associated to the present slowly accelerated phase of the
universe (S.A.PH). The smallness of the V.E. in the S.A.PH. is understood
through the see saw mechanism introduced in S.I.M.


title: Singularity-free cosmological solutions in string theories

abstract:
  Singularity-free cosmological solutions may be obtained from the string
action at tree level if the dimension of the space-time is greater than 10 and
if brane configurations are taken into account. The behaviour of the dilaton
field in this case is also regular. Asymptotically a radiative phase is
attained indicating a smooth transition to the standard cosmological model.


title: Neutrino Oscillation as Coupled vibration

abstract:
  Neutrino oscillation is visualized as coupled vibrations. Unlike existing
models describing neutrino oscillations, our model involving a single
fundamental mass parameter $m$ and first discussed in the context of a possible
boson oscillation demonstrates that for a self consistent theory there should
be three types of bosons paired with maximal mixing. The argument is easily
extended to neutrinos (fermions) with the exception that in the case of boson
oscillation means periodic variation of particle number, whereas in the case of
fermions the particle number does not change, only the mass oscillates. The
fermionic vacuum is not really empty but filled with zero energy fermions. The
oscillation length calculated perturbatively conforms to the experimental
findings. Also there is no fermionic number violation in our model.


title: Covariant Charges in Chern-Simons AdS_3 Gravity

abstract:
  We try to give hereafter an answer to some open questions about the
definition of conserved quantities in Chern-Simons theory, with particular
reference to Chern-Simons AdS_3 Gravity. Our attention is focused on the
problem of global covariance and gauge invariance of the variation of Noether
charges. A theory which satisfies the principle of covariance on each step of
its construction is developed, starting from a gauge invariant Chern-Simons
Lagrangian and using a recipe developed in gr-qc/0110104 and gr-qc/0107074 to
calculate the variation of conserved quantities. The problem to give a
mathematical well-defined expression for the infinitesimal generators of
symmetries is pointed out and it is shown that the generalized Kosmann lift of
spacetime vector fields leads to the expected numerical values for the
conserved quantities when the solution corresponds to the BTZ black hole. The
fist law of black holes mechanics for the BTZ solution is then proved and the
transition between the variation of conserved quantities in Chern-Simons AdS_3
Gravity theory and the variation of conserved quantities in General Relativity
is analysed in detail.


title: Naked Singularities in Higher Dimensional Gravitational Collapse

abstract:
  Spherically symmetric inhomogeneous dust collapse has been studied in higher
dimensional space-time and the factors responsible for the appearance of a
naked singularity are analyzed in the region close to the centre for the
marginally bound case. It is clearly demonstrated that in the former case naked
singularities do not appear in the space-time having more than five dimension,
which appears to a strong result. The non-marginally bound collapse is also
examined in five dimensions and the role of shear in developing naked
singularities in this space-time is discussed in details. The five dimensional
space-time is chosen in the later case because we have exact solution in closed
form only in five dimension and not in any other case.


title:
Solutions to the Lorentz force equation with fixed charge-to-mass ratio
  in globally hyperbolic spacetimes

abstract:
  We extend the classical Avez-Seifert theorem to trajectories of charged test
particles with fixed charge-to-mass ratio. In particular, given two events
x_{0} and x_{1}, with x_{1} in the chronological future of x_{0}, we find an
interval I=]-R,R[ such that for any q/m in I there is a timelike connecting
solution of the Lorentz force equation. Moreover, under the assumption that
there is no null geodesic connecting x_0 and x_1, we prove that to any value of
|q/m| there correspond at least two connecting timelike solutions which
coincide only if they are geodesics.


title: Bounds on Stringy Quantum Gravity from Low Energy Existing Data

abstract:
  We show that existing low energy experiments, searching for the breaking of
local Lorentz invariance, set bounds upon string theory inspired quantum
gravity models that induce corrections to the propagation of fields. In the
D-particle recoil model we find M > 1.2 x 10^5 M_P and v < 2 x 10^{-27}c for
the mass and recoil speed of the D-particle, respectively. These bounds are
\~10^8 times stronger than the latest astrophysical bounds. These results
indicate that the stringy scenario for modified dispersion relations is as
vulnerable to these types of tests as the loop quantum gravity schemes.


title: Gravitational Collapse in Higher Dimension

abstract:
  Spherically symmetric inhomogeneous dust collapse has been studied in higher
dimensional space-time and appearance of naked singularity has been analyzed
both for non-marginal and marginally bound cases. It has been shown that naked
singularity is possible for any arbitrary dimension in non-marginally bound
case. For marginally bound case we have examined the radial null geodesics from
the singularity and found that naked singularity is possible upto five
dimension.


title:
Dynamics of Density Fluctuations in the
  Einstein-Yang-Mills-Maxwell-Inflaton System: I. Initial Value Problem

abstract: This paper has been withdrawn.


title:
Gravitational redshifts in electromagnetic bursts occuring near
  Schwarzschild horizon

abstract:
  It was suggested earlier that the gravitational redshift formula can be
invalid when the effect of the backscattering is strong. It is demonstrated
here numerically, for an exemplary electromagnetic pulse that is: i) initially
located very close to the horizon of a Schwarzschild black hole and ii)
strongly backscattered, that a mean frequency does not obey the standard
redshift formula. Redshifts appear to depend on the frequency and there
manifests a backscatter-induced blueshift in the outgoing radiation.


title: Stationary structure of relativistic superfluid neutron stars

abstract:
  We describe recent progress in the numerical study of the structure of
rapidly rotating superfluid neutron star models in full general relativity. The
superfluid neutron star is described by a model of two interpenetrating and
interacting fluids, one representing the superfluid neutrons and the second
consisting of the remaining charged particles (protons, electrons, muons). We
consider general stationary configurations where the two fluids can have
different rotation rates around a common rotation axis. The previously
discovered existence of configurations with one fluid in a prolate shape is
confirmed.


title: Positivity of relativistic spin network evaluations

abstract:
  Let G be a compact Lie group. Using suitable normalization conventions, we
show that the evaluation of GxG-symmetric spin networks is non-negative
whenever the edges are labeled by representations of the form V\otimes V^*
where V is a representation of G, and the intertwiners are generalizations of
the Barrett--Crane intertwiner. This includes in particular the relativistic
spin networks with symmetry group Spin(4) or SO(4). We also present a
counterexample, using the finite group S_3, to the stronger conjecture that all
spin network evaluations are non-negative as long as they can be written using
only group integrations and index contractions. This counterexample applies in
particular to the product of five 6j-symbols which appears in the spin foam
model of the S_3-symmetric BF-theory on the two-complex dual to a triangulation
of the sphere S^3 using five tetrahedra. We show that this product is negative
real for a particular assignment of representations to the edges.


title:
The computation of the Conformal Killing Vectors of an 1+(n-1)
  decomposable metric

abstract:
  A generalisation of a known theorem concerning the computation of the
conformal algebra in 1+(n-1) decomposable spaces is presented. It is shown that
the general form of Conformal Vector Fields (CVF) is the sum of a gradient CVF
and a Killing or Homothetic (n-1)-vector. A simple criterion is established
which enables one to check if a 1+(n-1) decomposable spacetime admits proper
CVF. As an example, the complete conformal algebra of a G\"odel-type spacetime
is computed.


title: The gravitomagnetic clock effect and its possible observation

abstract:
  The general relativistic gravitomagnetic clock effect involves a coupling
between the orbital motion of a test particle and the rotation of the central
mass and results in a difference in the proper periods of two counter-revolving
satellites. It is shown that at O(c^-2) this effect has a simple analogue in
the electromagnetic case. Moreover, in view of a possible measurement of the
clock effect in the gravitational field of the Earth, we investigate the
influence of some classical perturbing forces of the terrestrial space
environment on the orbital motion of test bodies along opposite trajectories.


title: Cosmological Deformation of Lorentzian Spin Foam Models

abstract:
  We study the quantum deformation of the Barrett-Crane Lorentzian spin foam
model which is conjectured to be the discretization of Lorentzian Plebanski
model with positive cosmological constant and includes therefore as a
particular sector quantum gravity in de-Sitter space. This spin foam model is
constructed using harmonic analysis on the quantum Lorentz group. The
evaluation of simple spin networks are shown to be non commutative integrals
over the quantum hyperboloid defined as a pile of fuzzy spheres. We show that
the introduction of the cosmological constant removes all the infrared
divergences: for any fixed triangulation, the integration over the area
variables is finite for a large class of normalization of the amplitude of the
edges and of the faces.


title: Diffeomorphisms and spin foam models

abstract:
  We study the action of diffeomorphisms on spin foam models. We prove that in
3 dimensions, there is a residual action of the diffeomorphisms that explains
the naive divergences of state sum models. We present the gauge fixing of this
symmetry and show that it explains the original renormalization of
Ponzano-Regge model. We discuss the implication this action of diffeomorphisms
has on higher dimensional spin foam models and especially the finite ones.