title: High Order Relativistic Corrections To Keplerian Motion

abstract:
  The first terms of the general solution for an asymptotically flat stationary
axisymmetric vacuum spacetime endowed with an equatorial symmetry plane are
calculated from the corresponding Ernst potential up to seventh order in the
radial pseudospherical coordinate. The metric is used to determine the
influence of high order multipoles in the perihelion precession of an
equatorial orbit and in the node line precession of a non-equatorial orbit with
respect to a geodesic circle. Both results are written in terms of invariant
quantities such as the Geroch-Hansen multipoles and the energy and angular
momentum of the orbit.


title: Unruh response functions for scalar fields in de Sitter space

abstract:
  We calculate the response functions of a freely falling Unruh detector in de
Sitter space coupled to scalar fields of different coupling to the curvature,
including the minimally coupled massless case. Although the responses differ
strongly in the infrared as a consequence of the amplification of superhorizon
modes, the energy levels of the detector are thermally populated.


title: Black Hole Excision with Multiple Grid Patches

abstract:
  When using black hole excision to numerically evolve a black hole spacetime
with no continuous symmetries, most 3+1 finite differencing codes use a
Cartesian grid. It's difficult to do excision on such a grid, because the
natural $r = \text{constant}$ excision surface must be approximated either by a
very different shape such as a contained cube, or by an irregular and
non-smooth "LEGO(tm) sphere" which may introduce numerical instabilities into
the evolution. In this paper I describe an alternate scheme, which uses
multiple $\{r \times (\text{angular coordinates}) \}$ grid patches, each patch
using a different (nonsingular) choice of angular coordinates. This allows
excision on a smooth $r = \text{constant}$ 2-sphere.
  I discuss the key design choices in such a multiple-patch scheme, including
the choice of ghost-zone versus internal-boundary treatment of the interpatch
boundaries, the number and shape of the patches, the details of how the ghost
zones are "synchronized" by interpolation from neighboring patches, the tensor
basis for the Einstein equations in each patch, and the handling of non-tensor
field variables such as the BSSN $\tilde{\Gamma}^i$.
  I present sample numerical results from a prototype implementation of this
scheme. This code simulates the time evolution of the (asymptotically flat)
spacetime around a single (excised) black hole, using 4th-order finite
differencing in space and time. Using Kerr initial data with $J/m^2 = 0.6$, I
present evolutions to $t \gtsim 1500m$. The lifetime of these evolutions
appears to be limited only by outer boundary instabilities, not by any excision
instabilities or by any problems inherent to the multiple-patch scheme.


title: Research of Gravitation in Flat Minkowski Space

abstract:
  In this paper it is introduced and studied an alternative theory of
gravitation in flat Minkowski space. Using an antisymmetric tensor, which is
analogous to the tensor of electromagnetic field, a non-linear connection is
introduced. It is very convenient for studying the perihelion/periastron shift,
deflection of the light rays near the Sun and the frame dragging together with
geodetic precession, i.e. effects where angles are involved. Although the
corresponding results are obtained in rather different way, they are the same
as in the General Relativity. The results about the barycenter of two bodies
are also the same as in the General Relativity. Comparing the derived equations
of motion for the $n$-body problem with the Einstein-Infeld-Hoffmann equations,
it is found that they differ from the EIH equations by Lorentz invariant terms
of order $c^{-2}$.


title: Transition from big crunch to big bang in brane cosmology

abstract:
  We consider branes $N=I\times\so$, where $\so$ is an $n$\ndash dimensional
space form, not necessarily compact, in a Schwarzschild-AdS_{(n+2)} bulk $\mc
N$. The branes have a big crunch singularity. If a brane is an ARW space, then,
under certain conditions, there exists a smooth natural transition flow through
the singularity to a reflected brane $\hat N$, which has a big bang singularity
and which can be viewed as a brane in a reflected Schwarzschild-AdS_{(n+2)}
bulk $\hat{\mc N}$. The joint branes $N\uu \hat N$ can thus be naturally
embedded in $R^2\times \so$, hence there exists a second possibility of
defining a smooth transition from big crunch to big bang by requiring that
$N\uu\hat N$ forms a $C^\infty$-hypersurface in $R^2\times \so$. This last
notion of a smooth transition also applies to branes that are not ARW spaces,
allowing a wide range of possible equations of state.


title:
How to reach a few percent level in determining the Lense-Thirring
  effect?

abstract:
  In this paper we discuss and compare a node-only LAGEOS-LAGEOS II combination
and a node-only LAGEOS-LAGEOS II-Ajisai-Jason1 combination for the
determination of the Lense-Thirring effect. The new combined EIGEN-CG01C Earth
gravity model has been adopted. The second combination cancels the first three
even zonal harmonics along with their secular variations but introduces the
non-gravitational perturbations of Jason1. The first combination is less
sensitive to the non-conservative forces but is sensitive to the secular
variations of the uncancelled even zonal harmonics of low degree J4 and J6
whose impact grows linearly in time.


title: Analog model for an expanding universe

abstract:
  Over the last few years numerous papers concerning analog models for gravity
have been published. It was shown that the dynamical equation of several
systems (e.g. Bose-Einstein condensates with a sink or a vortex) have the same
wave equation as light in a curved-space (e.g. black holes). In the last few
months several papers were released which deal with simulations of the
universe.
  In this article the de-Sitter universe will be compared with a freely
expanding three-dimensional spherical Bose-Einstein condensate. Initially the
condensate is in a harmonic trap, which suddenly will be switched off. At the
same time a small perturbation will be injected in the center of the condensate
cloud.
  The motion of the perturbation in the expanding condensate will be discussed,
and after some transformations the similarity to an expanding universe will be
shown.


title: A New Waveform Consistency Test for Gravitational Wave Inspiral Searches

abstract:
  Searches for binary inspiral signals in data collected by interferometric
gravitational wave detectors utilize matched filtering techniques. Although
matched filtering is optimal in the case of stationary Gaussian noise, data
from real detectors often contains "glitches" and episodes of excess noise
which cause filter outputs to ring strongly. We review the standard \chi^2
statistic which is used to test whether the filter output has appropriate
contributions from several different frequency bands. We then propose a new
type of waveform consistency test which is based on the time history of the
filter output. We apply one such test to the data from the first LIGO science
run and show that it cleanly distinguishes between true inspiral waveforms and
large-amplitude false signals which managed to pass the standard \chi^2 test.


title: Determinant-Gravity: Cosmological implications

abstract:
  We analyze the action $\int d^4x \sqrt{\det||{\cal B} g_{\mu\nu}+ {\cal C}
  R_{\mu\nu}}||$ as a possible alternative or addition to the Einstein gravity.
Choosing a particular form of ${\cal B}(R)= \sqrt {R}$ we can restore the
Einstein gravity and, if ${\cal B}=m^2$, we obtain the cosmological constant
term. Taking ${\cal B} = m^2 + {\cal B}_1 R$ and expanding the action in $
1/m^2$, we obtain as a leading term the Einstein Lagrangian with a cosmological
constant proportional to $m^4$ and a series of higher order operators. In
general case of non-vanishing ${\cal B}$ and ${\cal C}$ new cosmological
solutions for the Robertson-Walker metric are obtained.


title:
Variable Speed of Light Cosmology and Bimetric Gravity: An Alternative
  to Standard Inflation

abstract:
  A scalar-tensor bimetric gravity model of early universe cosmology is
reviewed. The metric frame with a variable speed of light (VSL) and a constant
speed of gravitational waves is used to describe a Friedmann-Robertson-Walker
universe. The Friedmann equations are solved for a radiation dominated equation
of state and the power spectrum is predicted to be scale invariant with a
scalar mode spectral index $n_s=0.97$. The scalar modes are born in a ground
state superhorizon and the fluctuation modes are causally connected by the VSL
mechanism. The cosmological constant is equated to zero and there is no
significant dependence on the scalar field potential energy. A possible way of
distinguishing the metric gravity model from standard inflationary models is
discussed.


title: Quantum Gravity Phenomenology and Lorentz Violation

abstract:
  If quantum gravity violates Lorentz symmetry, the prospects for observational
guidance in understanding quantum gravity improve considerably. This article
briefly reviews previous work on Lorentz violation (LV) and discusses aspects
of the effective field theory framework for parametrizing LV effects. Current
observational constraints on LV are then summarized, focusing on effects in QED
at order E/M_Planck.


title:
Geodesic motion in the Kundt spacetimes and the character of envelope
  singularity

abstract:
  We investigate geodesics in specific Kundt type N (or conformally flat)
solutions to Einstein's equations. Components of the curvature tensor in
parallelly transported tetrads are then explicitly evaluated and analyzed. This
elucidates some interesting global properties of the spacetimes, such as an
inherent rotation of the wave-propagation direction, or the character of
singularities. In particular, we demonstrate that the characteristic envelope
singularity of the rotated wave-fronts is a (non-scalar) curvature singularity,
although all scalar invariants of the Riemann tensor vanish there.


title: Note on the luminosity distance

abstract:
  We re-derive a formula relating the areal and luminosity distances, entirely
in the framework of the classical Maxwell theory, assuming a geometric-optics
type condition.


title:
Einstein boundary conditions for the Einstein equations in the
  conformal-traceless decomposition

abstract:
  In relation to the BSSN formulation of the Einstein equations, we write down
the boundary conditions that result from the vanishing of the projection of the
Einstein tensor normally to a timelike hypersurface. Furthermore, by setting up
a well-posed system of propagation equations for the constraints, we show
explicitly that there are three constraints that are incoming at the boundary
surface and that the boundary equations are linearly related to them. This
indicates that such boundary conditions play a role in enforcing the
propagation of the constraints in the region interior to the boundary.
Additionally, we examine the related problem for a strongly hyperbolic
first-order reduction of the BSSN equations and determine the characteristic
fields that are prescribed by the three boundary conditions, as well as those
that are left arbitrary.


title:
Potential for ill-posedness in several 2nd-order formulations of the
  Einstein equations

abstract:
  Second-order formulations of the 3+1 Einstein equations obtained by
eliminating the extrinsic curvature in terms of the time derivative of the
metric are examined with the aim of establishing whether they are well posed,
in cases of somewhat wide interest, such as ADM, BSSN and generalized
Einstein-Christoffel. The criterion for well-posedness of second-order systems
employed is due to Kreiss and Ortiz. By this criterion, none of the three cases
are strongly hyperbolic, but some of them are weakly hyperbolic, which means
that they may yet be well posed but only under very restrictive conditions for
the terms of order lower than second in the equations (which are not studied
here). As a result, intuitive transferences of the property of well-posedness
from first-order reductions of the Einstein equations to their originating
second-order versions are unwarranted if not false.


title: Cartan Normal Conformal Connections from Pairs of 2nd Order PDE's

abstract:
  We explore the different geometric structures that can be constructed from
the class of pairs of 2nd order PDE's that satisfy the condition of a vanishing
generalized W\"{u}nschmann invariant. This condition arises naturally from the
requirement of a vanishing torsion tensor. In particular, we find that from
this class of PDE's we can obtain all four-dimensional conformal Lorentzian
metrics as well as all Cartan normal conformal O(4,2) connections.
  To conclude, we briefly discuss how the conformal Einstein equations can be
imposed by further restricting our class of PDE's to those satisfying
additional differential conditions.


title: The de Broglie-Bohm Interpretation of Evaporating Black-Holes

abstract:
  In this work we apply the de Broglie-Bohm interpretation of quantum mechanics
to the quantized spherically symmetric black-hole coupled to a massless scalar
field. The wave-functional used was first obtained by Tomimatsu using the
standard ADM quantization and a gauge that places the observer close to the
black-hole horizon. Using the causal interpretation, we compute quantum
trajectories determined by the initial conditions. We show that the quantum
trajectories for the black-hole mass can either increase or decrease with time.
The quantum trajectories that show increasing mass represent the usual
black-hole behavior of continuous energy absorption. The mass-decreasing
quantum trajectories are a purely quantum mechanical phenomena. They can be
physically interpreted as describing a black-hole that evaporates.


title:
Conservation of the stress tensor in perturbative interacting quantum
  field theory in curved spacetimes

abstract:
  We propose additional conditions (beyond those considered in our previous
papers) that should be imposed on Wick products and time-ordered products of a
free quantum scalar field in curved spacetime. These conditions arise from a
simple ``Principle of Perturbative Agreement'': For interaction Lagrangians
$L_1$ that are such that the interacting field theory can be constructed
exactly--as occurs when $L_1$ is a ``pure divergence'' or when $L_1$ is at most
quadratic in the field and contains no more than two derivatives--then
time-ordered products must be defined so that the perturbative solution for
interacting fields obtained from the Bogoliubov formula agrees with the exact
solution. The conditions derived from this principle include a version of the
Leibniz rule (or ``action Ward identity'') and a condition on time-ordered
products that contain a factor of the free field $\phi$ or the free
stress-energy tensor $T_{ab}$. The main results of our paper are (1) a proof
that in spacetime dimensions greater than 2, our new conditions can be
consistently imposed in addition to our previously considered conditions and
(2) a proof that, if they are imposed, then for {\em any} polynomial
interaction Lagrangian $L_1$ (with no restriction on the number of derivatives
appearing in $L_1$), the stress-energy tensor $\Theta_{ab}$ of the interacting
theory will be conserved. Our work thereby establishes (in the context of
perturbation theory) the conservation of stress-energy for an arbitrary
interacting scalar field in curved spacetimes of dimension greater than 2. Our
approach requires us to view time-ordered products as maps taking classical
field expressions into the quantum field algebra rather than as maps taking
Wick polynomials of the quantum field into the quantum field algebra.


title: Petrov classification of perturbed spacetimes: the Kasner example

abstract:
  In this paper we consider vacuum Kasner spacetimes, focusing on those that
can be parametrized as linear perturbations of the special Petrov type D case.
For these quasi-D Kasner models we first investigate the modification to the
principal null directions, then a Teukolsky Master Equation for fields of any
spin, considering in particular the quasi-D models as curvature perturbations
of the type D background. Considering the speciality index and the principal
null directions and comparing the results for the exact solutions and those for
the perturbative ones, this simple Kasner example allows us to clarify that
perturbed spacetime do not retain in general the speciality character of the
background. There are four distinct principal null directions, although they
are not necessarily first order perturbations of the background principal null
directions, as our example of the quasi-D Kasner models shows.
  For the quasi-D Kasner models the use of a Teukolsky Master Equation, a
classical tool for studying black hole perturbations, allows us to show, from a
completely new point of view, the well known absence of gravitational waves in
Kasner spacetimes. This result, used together with an explicit expression of
the electric Weyl tensor in terms of Weyl scalars, provides an example of the
fact that the presence of transverse curvature terms does not necessarily imply
the presence of gravitational waves.


title: Modified Gravitational Theory and Galaxy Rotation Curves

abstract:
  The nonsymmetric gravitational theory predicts an acceleration law that
modifies the Newtonian law of attraction between particles. For weak fields a
fit to the flat rotation curves of galaxies is obtained in terms of the mass
(mass-to-light ratio M/L) of galaxies. The fits assume that the galaxies are
not dominated by exotic dark matter. The equations of motion for test particles
reduce for weak gravitational fields to the GR equations of motion and the
predictions for the solar system and the binary pulsar PSR 1913+16 agree with
the observations. The gravitational lensing of clusters of galaxies can be
explained without exotic dark matter.


title: Energy conservation for dynamical black holes

abstract:
  An energy conservation law is described, expressing the increase in
mass-energy of a general black hole in terms of the energy densities of the
infalling matter and gravitational radiation. For a growing black hole, this
first law of black-hole dynamics is equivalent to an equation of Ashtekar &
Krishnan, but the new integral and differential forms are regular in the limit
where the black hole ceases to grow. An effective gravitational-radiation
energy tensor is obtained, providing measures of both ingoing and outgoing,
transverse and longitudinal gravitational radiation on and near a black hole.
Corresponding energy-tensor forms of the first law involve a preferred time
vector which plays the role for dynamical black holes which the stationary
Killing vector plays for stationary black holes. Identifying an energy flux,
vanishing if and only if the horizon is null, allows a division into
energy-supply and work terms, as in the first law of thermodynamics. The energy
supply can be expressed in terms of area increase and a newly defined surface
gravity, yielding a Gibbs-like equation, with a similar form to the so-called
first law for stationary black holes.


title: Coupled oscillators as models of phantom and scalar field cosmologies

abstract:
  We study a toy model for phantom cosmology recently introduced in the
literature and consisting of two oscillators, one of which carries negative
kinetic energy. The results are compared with the exact phase space picture
obtained for similar dynamical systems describing, respectively, a massive
canonical scalar field conformally coupled to the spacetime curvature, and a
conformally coupled massive phantom. Finally, the dynamical system describing
exactly a minimally coupled phantom is studied and compared with the toy model.


title: Lisa

abstract:
  The extreme weakness of the gravitational interaction has as one of its
consequences that appreciable intensities of gravitational waves (GW) can only
be generated in large size astrophysical and cosmological sources. Earth based
detectors face unsurmountable problems to be sensitive to signals at
frequencies below 10 Hz due to seismic vibrations. In order to see lower
frequency signals, a space based detector is the natural solution. LISA (Laser
Interferometer Space Antenna) is a joint ESA-NASA project aimed at detecting
GWs in a range of frequencies between 10^{-4} Hz and 10^{-1} Hz, and consists
in a constellation of three spacecraft in heliocentric orbit, whose GW-induced
armlength variations are monitored by high precision interferometry. This
article reviews the main features and scientific goals of the LISA mission, as
well as a shorter description of its precursor tecnological mission LPF (LISA
Pathfinder).


title: Dynamical Evolution of a Cylindrical Shell with Rotational Pressure

abstract:
  We prepare a general framework for analyzing the dynamics of a cylindrical
shell in the spacetime with cylindrical symmetry. Based on the framework, we
investigate a particular model of a cylindrical shell-collapse with rotational
pressure, accompanying the radiation of gravitational waves and massless
particles. The model has been introduced previously but has been awaiting for
proper analysis. Here the analysis is put forward: It is proved that, as far as
the weak energy condition is satisfied outside the shell, the collapsing shell
bounces back at some point irrespective of the initial conditions, and escapes
from the singularity formation.
  The behavior after the bounce depends on the sign of the shell pressure in
the z-direction. When the pressure is non-negative, the shell continues to
expand without re-contraction. On the other hand, when the pressure is negative
(i.e. it has a tension), the behavior after the bounce can be more complicated
depending on the details of the model. However, even in this case, the shell
never reaches the zero-radius configuration.


title: Integral equations, Kerr-Schild fields and gravitational sources

abstract:
  Kerr-Schild solutions to the vacuum Einstein equations are considered from
the viewpoint of integral equations. We show that, for a class of Kerr-Schild
fields, the stress-energy tensor can be regarded as a total divergence in
Minkowski spacetime. If one assumes that Minkowski coordinates cover the entire
manifold (no maximal extension), then Gauss' theorem can be used to reveal the
nature of any sources present. For the Schwarzschild and Vaidya solutions the
fields are shown to result from a delta-function point source. For the
Reissner-Nordstrom solution we find that inclusion of the gravitational fields
removes the divergent self-energy familiar from classical electromagnetism. For
more general solutions a complex structure is seen to arise in a natural,
geometric manner with the role of the unit imaginary fulfilled by the spacetime
pseudoscalar. The Kerr solution is analysed leading to a novel picture of its
global properties. Gauss' theorem reveals the presence of a disk of tension
surrounded by the matter ring singularity. Remarkably, the tension profile over
this disk has a simple classical interpretation. It is also shown that the
matter in the ring follows a light-like path, as one expects for the endpoint
of rotating, collapsing matter. Some implications of these results for
physically-realistic black holes are discussed.


title:
Palatini approach to 1/R gravity and its implications to the late
  Universe

abstract:
  By applying the Palatini approach to the 1/R-gravity model it is possible to
explain the present accelerated expansion of the Universe. Investigation of the
late Universe limiting case shows that: (i) due to the curvature effects the
energy-momentum tensor of the matter field is not covariantly conserved; (ii)
however, it is possible to reinterpret the curvature corrections as sources of
the gravitational field, by defining a modified energy-momentum tensor; (iii)
with the adoption of this modified energy-momentum tensor the Einstein's field
equations are recovered with two main modifications: the first one is the
weakening of the gravitational effects of matter whereas the second is the
emergence of an effective varying "cosmological constant"; (iv) there is a
transition in the evolution of the cosmic scale factor from a power-law scaling
$a\propto t^{11/18}$ to an asymptotically exponential scaling $a\propto
\exp(t)$; (v) the energy density of the matter field scales as $\rho_m\propto
(1/a)^{36/11}$; (vi) the present age of the Universe and the
decelerated-accelerated transition redshift are smaller than the corresponding
ones in the $\Lambda$CDM model.


title:
Spectrum of quantized black hole, correspondence principle, and
  holographic bound

abstract:
  An equidistant spectrum of the horizon area of a quantized black hole does
not follow from the correspondence principle or from general statistical
arguments. On the other hand, such a spectrum obtained in loop quantum gravity
(LQG) either does not comply with the holographic bound, or demands a special
choice of the Barbero-Immirzi parameter for the horizon surface, distinct from
its value for other quantized surfaces. The problem of distinguishability of
edges in LQG is discussed, with the following conclusion. Only under the
assumption of partial distinguishability of the edges, the microcanonical
entropy of a black hole can be made both proportional to the horizon area and
satisfying the holographic bound.


title: Smooth globally hyperbolic splittings and temporal functions

abstract:
  Geroch's theorem about the splitting of globally hyperbolic spacetimes is a
central result in global Lorentzian Geometry. Nevertheless, this result was
obtained at a topological level, and the possibility to obtain a metric (or, at
least, smooth) version has been controversial since its publication in 1970. In
fact, this problem has remained open until a definitive proof, recently
provided by the authors. Our purpose is to summarize the history of the
problem, explain the smooth and metric splitting results (including
smoothability of time functions in stably causal spacetimes), and sketch the
ideas of the solution.


title:
The 2.5PN gravitational wave polarisations from inspiralling compact
  binaries in circular orbits

abstract:
  Using the multipolar post-Minkowskian and matching formalism we compute the
gravitational waveform of inspiralling compact binaries moving in
quasi-circular orbits at the second and a half post-Newtonian (2.5PN)
approximation to general relativity. The inputs we use include notably the
mass-type quadrupole at the 2.5PN order, the mass octupole and current
quadrupole at the 2PN order, the mass $2^5$-pole and current $2^4$-pole at 1PN.
The non-linear hereditary terms come from the monopole-quadrupole multipole
interactions or tails, present at the 1.5PN, 2PN and 2.5PN orders, and the
quadrupole-quadrupole interaction arising at the 2.5PN level. In particular,
the specific effect of non-linear memory is computed using a simplified model
of binary evolution in the past. The ``plus'' and ``cross'' wave polarisations
at the 2.5PN order are obtained in ready-to-use form, extending the 2PN results
calculated earlier by Blanchet, Iyer, Will and Wiseman.


title: Some minor examples on discrete geometry

abstract:
  Assuming a minimum value for area measurement, the emergence of quantum
mechanics can be easily motivated from naive consideration of gravitational
force. Here we provide some pedagogical examples and extensions.
  At the same time, the role of Planck mass is shown to be of some theoretical
influence even at low energies.


title: 2D $R^2$ gravity in weak coupling limit

abstract:
  2D $R^2$ quantum gravity in infinitely large invariant volume is considered.
In weak coupling limit the dynamics is reduced to quantum mechanics of a single
degree of freedom. The correspondent two - point Green function is calculated
explicitly in Gaussian approximation.


title: Quantum general relativity and the classification of smooth manifolds

abstract:
  The gauge symmetry of classical general relativity under space-time
diffeomorphisms implies that any path integral quantization which can be
interpreted as a sum over space-time geometries, gives rise to a formal
invariant of smooth manifolds. This is an opportunity to review results on the
classification of smooth, piecewise-linear and topological manifolds. It turns
out that differential topology distinguishes the space-time dimension d=3+1
from any other lower or higher dimension and relates the sought-after path
integral quantization of general relativity in d=3+1 with an open problem in
topology, namely to construct non-trivial invariants of smooth manifolds using
their piecewise-linear structure. In any dimension d<=5+1, the classification
results provide us with triangulations of space-time which are not merely
approximations nor introduce any physical cut-off, but which rather capture the
full information about smooth manifolds up to diffeomorphism. Conditions on
refinements of these triangulations reveal what replaces block-spin
renormalization group transformations in theories with dynamical geometry. The
classification results finally suggest that it is space-time dimension rather
than absence of gravitons that renders pure gravity in d=2+1 a `topological'
theory.


title:
Higher Dimensional Szekeres' Space-time in Brans-Dicke Scalar Tensor
  Theory

abstract:
  The generalized Szekeres family of solution for quasi-spherical space-time of
higher dimensions are obtained in the scalar tensor theory of gravitation.
Brans-Dicke field equations expressed in Dicke's revised units are exhaustively
solved for all the subfamilies of the said family. A particular group of
solutions may also be interpreted as due to the presence of the so-called
C-field of Hoyle and Narlikar and for a chosen sign of the coupling parameter.
The models show either expansion from a big bang type of singularity or a
collapse with the turning point at a lower bound. There is one particular case
which starts from the big bang, reaches a maximum and collapses with the in
course of time to a crunch.


title:
Extremal limit for charged and rotating 2+1-dimensional black holes and
  Bertotti-Robinson geometry

abstract:
  We consider 2+1--dimensional analogues of the Bertotti-Robinson (BR)
spacetimes in the sense that the coefficient at the angular part is a constant.
We show that such BR-like solutions are either pure static or uncharged
rotating. We trace the origin of the inconsistency between a charge and
rotation, considering the BR-like spacetime as a result of the limiting
transition of a non-extremal black hole to the extremal state. We also find
that the quasilocal energy and angular momentum of such BR-like spacetimes
calculated within the boundary $l=const$ ($l$ is the proper distance) are
constants independent of the position of the boundary.


title:
Concept of temperature in multi-horizon spacetimes: Analysis of
  Schwarzschild-De Sitter metric

abstract:
  In case of spacetimes with single horizon, there exist several
well-established procedures for relating the surface gravity of the horizon to
a thermodynamic temperature. Such procedures, however, cannot be extended in a
straightforward manner when a spacetime has multiple horizons. In particular,
it is not clear whether there exists a notion of global temperature
characterizing the multi-horizon spacetimes. We examine the conditions under
which a global temperature can exist for a spacetime with two horizons using
the example of Schwarzschild-De Sitter (SDS) spacetime. We systematically
extend different procedures (like the expectation value of stress tensor,
response of particle detectors, periodicity in the Euclidean time etc.) for
identifying a temperature in the case of spacetimes with single horizon to the
SDS spacetime. This analysis is facilitated by using a global coordinate chart
which covers the entire SDS manifold. We find that all the procedures lead to a
consistent picture characterized by the following features: (a) In general, SDS
spacetime behaves like a non-equilibrium system characterized by two
temperatures. (b) It is not possible to associate a global temperature with SDS
spacetime except when the ratio of the two surface gravities is rational (c)
Even when the ratio of the two surface gravities is rational, the thermal
nature depends on the coordinate chart used. There exists a global coordinate
chart in which there is global equilibrium temperature while there exist other
charts in which SDS behaves as though it has two different temperatures. The
coordinate dependence of the thermal nature is reminiscent of the flat
spacetime in Minkowski and Rindler coordinate charts. The implications are
discussed.


title: Some mathematical problems in numerical relativity

abstract:
  The main goal of numerical relativity is the long time simulation of highly
nonlinear spacetimes that cannot be treated by perturbation theory. This
involves analytic, computational and physical issues. At present, the major
impasses to achieving global simulations of physical usefulness are of an
analytic/computational nature. We present here some examples of how analytic
insight can lend useful guidance for the improvement of numerical approaches.


title: Quasinormal Modes and Gravitational Radiation in Black Hole Spacetimes

abstract:
  Black holes play a fundamental role in modern physics. They have
characteristic oscillation modes, called quasinormal modes. Past studies have
shown that these modes are important to our understanding of the dynamics of
astrophysical black holes. Recent studies indicate that they are important as a
link between gravitation and quantum mechanics. Thus, the investigation of
these modes is a timeliness topic.
  Quasinormal modes dominate almost every process involving black holes, in
particular gravitational wave emission during, for example, the collision
between two black holes. It may be possible to create black holes at future
accelerators, according to recent theories advocating the existence of extra
dimensions in our universe. It is therefore important to study in depth the
gravitational radiation emitted in high energy collision between two black
holes in several dimensions, and also to make a theoretical study of
gravitational waves in higher dimensions.
  In this thesis we shall make a thorough study of the quasinormal modes of
black holes in several kinds of background spacetimes. We shall investigate the
gravitational radiation given away when highly energetic particles collide with
black holes, and also when two black holes collide with each other. Finally, we
shall study the properties of gravitational waves in higher dimensions, for
instance, we generalize Einstein's quadrupole formula.


title: The Relative Motion of Membranes

abstract:
  The relative classical motion of membranes is governed by an equation of the
form D(hessian D separation)=riemann times separation times momentum. This is a
generalization of the geodesic deviation equation and can be derived from a
simple lagrangian. Quantum mechanically the picture is less clear. Some
quantizations of the classical equations are attempted so that the question as
to whether the Universe started with a quantum fluctuation can be addressed.


title: Viscous Cosmology, Entropy, and the Cardy-Verlinde Formula

abstract:
  The holographic principle in a radiation dominated universe, as discussed
first by Verlinde (2000), is extended so as to incorporate the case of a
bulk-viscous cosmic fluid. This corresponds to a non-conformally invariant
theory. Generalization of the Cardy-Verlinde entropy formula to the viscous
case appears to be formally possible, although on physical grounds one may
question some elements in this type of theory, especially the manner in which
the Casimir energy is evaluated. Also, we consider the observation made by Youm
(2002),namely that the entropy of the universe is no longer expressible in the
conventional Cardy-Verlinde form if one relaxes the radiation dominance
equation of state for the fluid and instead merely assumes that the pressure is
proportional to the energy density. We show that Youm's generalized entropy
formula remains valid when the cosmic fluid is no longer ideal, but endowed
with a constant bulk viscosity. In the introductory part of this article, we
take a general point of view and survey the essence of cosmological theory
applied to a fluid containing both a constant shear viscosity and a constant
bulk viscosity.


title:
How Many Templates for GW Chirp Detection? The Minimal-Match Issue
  Revisited

abstract:
  In a recent paper dealing with maximum likelihood detection of gravitational
wave chirps from coalescing binaries with unknown parameters we introduced an
accurate representation of the no-signal cumulative distribution of the
supremum of the whole correlator bank. This result can be used to derive a
refined estimate of the number of templates yielding the best tradeoff between
detector's performance (in terms of lost signals among those potentially
detectable) and computational burden.


title: BI action for gravitational and electroweak fields

abstract:
  This note suggests a generalization of the Born--Infeld action (1932) on case
of electroweak and gravitational fields in four-dimensional spacetime. The
action is constructed from Dirac matrices, $\gamma_a$, and dimensionless
covariant derivatives, $\pi_{a} = - i\ell \nabla_{a}$, where $\ell$ is of order
of magnitude of Planck's length. By a postulate, the action possesses
additional symmetry with respect to global transformations of the Lorentz group
imposed on pairs ($\gamma_{a}$, $\pi_{a}$). It's shown, that parameter of the
Lorentz group is associated with a constant value of the electroweak potential
at spatial infinity. It follows, that in linear and quadratic in $\ell^2$
approximation, action for gravitational field coincides with Einstein-Hilbert
(EH) and Gauss-Bonnet (GB).


title: Wormhole phase in the RST model

abstract:
  We show that the RST model describing the exactly soluble black hole model
can have a dynamical wormhole solution along with an appropriate boundary
condition. The necessary exotic matter which is usually negative energy density
is remarkably produced by the quantization of the infalling matter fields. Then
the asymptotic geometry in the past is two-dimensional anti-de Sitter(AdS$_2$),
which implies the exotic matter is negative. As time goes on, the wormhole
eventually evolves into the black hole and its Hawking radiation appears. The
throat of the static RST wormhole is lower-bounded but in the presence of
infalling matter it collapses to a black hole.


title:
A first-principles derivation of York scaling and the Lichnerowicz-York
  equation

abstract:
  The only efficient and robust method of generating consistent initial data in
general relativity is the conformal technique initiated by Lichnerowicz and
perfected by York. In the spatially compact case, the complete scheme consists
of the Arnowitt-Deser-Misner (ADM) Hamiltonian and momentum constraints, the
ADM Euler-Lagrange equations, York's constant-mean-curvature (CMC) condition,
and a lapse-fixing equation (LFE) that ensures propagation of the CMC condition
by the Euler-Lagrange equations. The Hamiltonian constraint is rewritten as the
Lichnerowicz-York equation for the conformal factor (psi) of the physical
metric (psi)^4(g_{ij}) given an initial unphysical 3-metric (g_{ij}). The CMC
condition and LFE introduce a distinguished foliation (definition of
simultaneity) on spacetime, and separate scaling laws for the canonical momenta
and their trace are used. In this article, we derive all these features in a
single package by seeking a gauge theory of geometrodynamics (evolving
3-geometries) invariant under both three-dimensional diffeomorphisms and
volume-preserving conformal transformations.


title: Refined algebraic quantisation with the triangular subgroup of SL(2,R)

abstract:
  We investigate refined algebraic quantisation with group averaging in a
constrained Hamiltonian system whose gauge group is the connected component of
the lower triangular subgroup of SL(2,R). The unreduced phase space is
T^*R^{p+q} with p>0 and q>0, and the system has a distinguished classical
o(p,q) observable algebra. Group averaging with the geometric average of the
right and left invariant measures, invariant under the group inverse, yields a
Hilbert space that carries a maximally degenerate principal unitary series
representation of O(p,q). The representation is nontrivial iff (p,q) is not
(1,1), which is also the condition for the classical reduced phase space to be
a symplectic manifold up to a singular subset of measure zero. We present a
detailed comparison to an algebraic quantisation that imposes the constraints
in the sense H_a Psi = 0 and postulates self-adjointness of the o(p,q)
observables. Under certain technical assumptions that parallel those of the
group averaging theory, this algebraic quantisation gives no quantum theory
when (p,q) = (1,2) or (2,1), or when p>1, q>1 and p+q is odd.


title:
Post-1-Newtonian equations of motion for systems of arbitrarily
  structured bodies

abstract:
  We give a surface integral derivation of post-1-Newtonian translational
equations of motion for a system of arbitrarily structured bodies, including
the coupling to all the bodies' mass and current multipole moments. The
derivation requires only that the post-1-Newtonian vacuum field equations are
satisfied in weak-field regions between the bodies; the bodies' internal
gravity can be arbitrarily strong. The derivation extends previous results of
Damour, Soffel and Xu (DSX) for weakly self-gravitating bodies for which the
post-1-Newtonian field equations are satisfied everywhere. The derivation
consists of a number of steps: (i) The definition of each body's current and
mass multipole moments and center-of-mass worldline in terms of the behavior of
the metric in a weak-field region surrounding the body. (ii) The definition for
each body of a set of gravitoelectric and gravitomagnetic tidal moments, again
in terms of the behavior of the metric in a weak-field region surrounding the
body. For the special case of weakly self-gravitating bodies, our definitions
of these multipole and tidal moments agree with definitions given previously by
DSX. (iii) The derivation of a formula, for any given body, of the second time
derivative of its mass dipole moment in terms of its other multipole and tidal
moments and their time derivatives. This formula was obtained previously by DSX
for weakly self-gravitating bodies. (iv) A derivation of the relation between
the tidal moments acting on each body and the multipole moments and
center-of-mass worldlines of all the other bodies. A formalism to compute this
relation was developed by DSX; we simplify their formalism and compute the
relation explicitly. (v) The deduction from the previous steps of the explicit
translational equations of motion, whose form has not been previously derived.


title: Understanding Quantum Theory in Terms of Geometry

abstract:
  Understanding quantum theory in terms of a geometric picture sounds great.
There are different approaches to this idea. Here we shall present a geometric
picture of quantum theory using the de-Broglie--Bohm causal interpretation of
quantum mechanics. We shall show that it is possible to understand the key
character of de-Broglie--Bohm theory, the quantum potential, as the conformal
degree of freedom of the space--time metric. In this way, gravity should give
the causal structure of the space--time, while quantum phenomena determines the
scale. Some toy models in terms of tensor and scalar--tensor theories will be
presented. Then a few essential physical aspects of the idea including the
effect on the black holes, the initial Big--Bang singularity and non locality
are investigated. We shall formulate a quantum equivalence principle according
to which gravitational effects can be removed by going to a freely falling
frame while quantum effects can be eliminated by choosing an appropriate scale.
And we shall see that the best framework for both quantum and gravity is Weyl
geometry. Then we shall show how one can get the de-Broglie--Bohm quantum
theory out of a Weyl covariant theory. Extension to the case of many particle
systems and spinning particles is discussed at the end.


title: Long-Range Behavior in Quantum Gravity

abstract:
  Quantum gravity effects of zeroth order in the Planck constant are
investigated in the framework of the low-energy effective theory. A special
emphasis is placed on establishing the correspondence between classical and
quantum theories, for which purpose transformation properties of the
\hbar^0-order radiative contributions to the effective gravitational field
under deformations of a reference frame are determined. Using the
Batalin-Vilkovisky formalism it is shown that the one-loop contributions
violate the principle of general covariance, in the sense that the quantities
which are classically invariant under such deformations take generally
different values in different reference frames. In particular, variation of the
scalar curvature under transitions between different reference frames is
calculated explicitly. Furthermore, the long-range properties of the two-point
correlation function of the gravitational field are examined. Using the
Schwinger-Keldysh formalism it is proved that this function is finite in the
coincidence limit outside the region of particle localization. In this limit,
the leading term in the long-range expansion of the correlation function is
calculated explicitly, and the relative value of the root mean square
fluctuation of the Newton potential is found to be 1/\sqrt{2}. It shown also
that in the case of a macroscopic gravitating body, the terms violating general
covariance, and the field fluctuation are both suppressed by a factor 1/N,
where N is the number of particles in the body. This leads naturally to a
macroscopic formulation of the correspondence between classical and quantum
theories of gravitation. As an application of the obtained results, the secular
precession of a test particle orbit in the field of a black hole is determined.


title: Can the galactic rotation curves be explained in brane world models?

abstract:
  We consider solutions with conformal symmetry of the static, spherically
symmetric gravitational field equations in the vacuum in the brane world
scenario. By assuming that the vector field generating the symmetry is
non-static, the general solution of the field equations on the brane can be
obtained in an exact parametric form, with the conformal factor taken as
parameter. As a physical application of the obtained solutions we consider the
behavior of the angular velocity of a test particle moving in a stable circular
orbit. In this case the tangential velocity can be expressed as a function of
the conformal factor and some integration constants only. For a specific range
of the integration constants, the tangential velocity of the test particle
tends, in the limit of large radial distances, to a constant value. This
behavior is specific to the galactic rotation curves, and is explained usually
by invoking the hypothesis of the dark matter. The limiting value of the
angular velocity of the test particle can be obtained as a function of the
baryonic mass and radius of the galaxy. The behavior of the dark radiation and
dark pressure terms is also considered in detail, and it is shown that they can
be expressed in terms of the rotational velocity of a test particle. Hence all
the predictions of the present model can be tested observationally. Therefore
the existence of the non-local effects, generated by the free gravitational
field of the bulk in a conformally symmetric brane, may provide an explanation
for the dynamics of the neutral hydrogen clouds at large distances from the
galactic center.


title: Minisuperspace Model for Revised Canonical Quantum Gravity

abstract:
  We present a reformulation of the canonical quantization of gravity, as
referred to the minisuperspace; the new approach is based on fixing a Gaussian
(or synchronous) reference frame and then quantizing the system via the
reconstruction of a suitable constraint; then the quantum dynamics is re-stated
in a generic coordinates system and it becomes dependent on the lapse function.
The analysis follows a parallelism with the case of the non-relativistic
particle and leads to the minisuperspace implementation of the so-called {\em
kinematical action} as proposed in \cite{M02} (here almost coinciding also with
the approach presented in \cite{KT91}). The new constraint leads to a
Schr\"odinger equation for the system. i.e. to non-vanishing eigenvalues for
the super-Hamiltonian operator; the physical interpretation of this feature
relies on the appearance of a ``dust fluid'' (non-positive definite) energy
density, i.e. a kind of ``materialization'' of the reference frame. As an
example of minisuperspace model, we consider a Bianchi type IX Universe, for
which some dynamical implications of the revised canonical quantum gravity are
discussed. We also show how, on the classical limit, the presence of the dust
fluid can have relevant cosmological issues. Finally we upgrade our analysis by
its extension to the generic cosmological solution, which is performed in the
so-called long-wavelength approximation. In fact, near the Big-Bang, we can
neglect the spatial gradients of the dynamical variables and arrive to
implement, in each space point, the same minisuperspace paradigm valid for the
Bianchi IX model.


title:
Mixmaster Chaoticity as Semiclassical Limit of the Canonical Quantum
  Dynamics

abstract:
  Within a cosmological framework, we provide a Hamiltonian analysis of the
Mixmaster Universe dynamics on the base of a standard Arnowitt-Deser-Misner
approach, showing how the chaotic behavior characterizing the evolution of the
system near the cosmological singularity can be obtained as the semiclassical
limit of the canonical quantization of the model in the same dynamical
representation. The relation between this intrinsic chaotic behavior and the
indeterministic quantum dynamics is inferred through the coincidence between
the microcanonical probability distribution and the semiclassical quantum one.


title:
On the impossibility of using the longitude of the ascending node of
  GP-B for measuring the Lense-Thirring effect

abstract:
  The possibility of analyzing the node Omega of the GP-B satellite in order to
measure also the Lense-Thirring effect on its orbit is examined. This feature
is induced by the general relativistic gravitomagnetic component of the Earth
gravitational field. The GP-B mission has been launched in April 2004 and is
aimed mainly to the measurement of the gravitomagnetic precession of four
gyroscopes carried onboard at a claimed accuracy of 1% or better. The aliasing
effect of the solid Earth and ocean components of the solar K_1 tidal
perturbations would make the measurement of the Lense-Thirring effect on the
orbit unfeasible. Indeed, the science period of the GP-B mission amounts to
almost one year. During this time span the Lense-Thirring shift on the GP-B
node would be 164 milliarcseconds (mas), while the tidal perturbations on its
node would have a period of the order of 10^3 years and amplitudes of the order
of 10^5 mas.


title:
Energy and Momentum Densities Associated with Solutions Exhibiting
  Directional Type Singularities

abstract:
  We obtain the energy and momentum densities of a general static axially
symmetric vacuum space-time described by the Weyl metric, using Landau-Lifshitz
and Bergmann-Thomson energy-momentum complexes. These two definitions of the
energy-momentum complex do not provide the same energy density for the
space-time under consideration, while give the same momentum density. We show
that, in the case of Curzon metric which is a particular case of the Weyl
metric, these two definitions give the same energy only when $R \to \infty$.
Furthermore, we compare these results with those obtained using Einstein,
Papapetrou and M{\o}ller energy momentum complexes.


title: Black ring formation in particle systems

abstract:
  It is known that the formation of apparent horizons with non-spherical
topology is possible in higher-dimensional spacetimes. One of these is the
black ring horizon with $S^1\times S^{D-3}$ topology where $D$ is the spacetime
dimension number. In this paper, we investigate the black ring horizon
formation in systems with $n$-particles. We analyze two kinds of system: the
high-energy $n$-particle system and the momentarily-static $n$-black-hole
initial data. In the high-energy particle system, we prove that the black ring
horizon does not exist at the instant of collision for any $n$. But there
remains a possibility that the black ring forms after the collision and this
result is not sufficient. Because calculating the metric of this system after
the collision is difficult, we consider the momentarily-static $n$-black-hole
initial data that can be regarded as a simplified $n$-particle model and
numerically solve the black ring horizon that surrounds all the particles. Our
results show that there is the minimum particle number that is necessary for
the black ring formation and this number depends on $D$. Although many particle
number is required in five-dimensions, $n=4$ is sufficient for the black ring
formation in the $D\ge 7$ cases. The black ring formation becomes easier for
larger $D$. We provide a plausible physical interpretation of our results and
discuss the validity of Ida and Nakao's conjecture for the horizon formation in
higher-dimensions. Finally we briefly discuss the probable methods of producing
the black rings in accelerators.


title: Negative energies and time reversal in Quantum Field Theory

abstract:
  The theoretical and phenomenological status of negative energies is reviewed
in Quantum Field theory leading to the conclusion that hopefully their
rehabilitation might only be completed in a modified general relativistic model


title: FRW Quantum Cosmology with a Generalized Chaplygin Gas

abstract:
  Cosmologies with a Chaplygin gas have recently been explored with the
objective of explaining the transition from a dust dominated epoch towards an
accelerating expansion stage. We consider the hypothesis that the transition to
the accelerated period involves a quantum mechanical process. Three physically
admissible cases are possible. In particular, we identify a minisuperspace
configuration with two Lorentzian sectors, separated by a classically forbidden
region. The Hartle-Hawking and Vilenkin wave functions are computed, together
with the transition amplitudes towards the accelerating epoch. Furthermore, it
is found that for specific initial conditions, the parameters characterizing
the generalized Chaplygin gas become related through an expression involving an
integer $n$. We also introduce a phenomenological association between some
brane-world scenarios and a FRW minisuperspace cosmology with a generalized
Chaplygin gas. The aim is to promote a discussion and subsequent research on
the quantum creation of brane cosmologies from such a perspective. Results
suggest that the brane tension would become related with generalized Chaplygin
gas parameters through another expression involving an integer.


title:
The inverse mean curvature flow in Robertson-Walker spaces and its
  application to cosmology

abstract:
  We consider the inverse mean curvature flow in Robertson-Walker spacetimes
that satisfy the Einstein equations and have a big crunch singularity and prove
that under natural conditions the rescaled inverse mean curvature flow provides
a smooth transition from big crunch to big bang. We also construct an example
showing that in general the transition flow is only of class $C^3$.


title:
On alternative approaches to Lorentz violation in loop quantum gravity
  inspired models

abstract:
  Recent claims point out that possible violations of Lorentz symmetry
appearing in some semiclassical models of extended matter dynamics motivated by
loop quantum gravity can be removed by a different choice of canonically
conjugated variables. In this note we show that such alternative is
inconsistent with the choice of variables in the underlying quantum theory
together with the semiclassical approximation, as long as the correspondence
principle is maintained. A consistent choice will violate standard Lorentz
invariance. Thus, to preserve a relativity principle in this framework, the
linear realization of Lorentz symmetry should be extended or superseded.


title: Can higher order curvature theories explain rotation curves of galaxies?

abstract:
  Higher order curvature gravity has recently received a lot of attention due
to the fact that it gives rise to cosmological models which seem capable of
solving dark energy and quintessence issues without using "ad hoc" scalar
fields. In this letter, a gravitational potential is obtained which differs
from the Newtonian one because of a repulsive correction increasing with
distance. We evaluate the rotation curve of our Galaxy and compare it with the
observed data in order both to test the viability of these theories and to
estimate the scalelength of the correction. It is remarkable that the Milky Way
rotation curve is well fitted without the need of any dark matter halo and a
similar result tentatively holds also for other galaxies.


title: New and Recent Trends in Modern Cosmology

abstract:
  Non Conventional treatments in modern cosmology, in both Steady State and Big
Bang, are given. The motivation behind these treatments is to solve some of the
problems of the conventional treatments in cosmology. For this aim, different
geometric structures and alternative field theories, used to construct world
models, are given. A brief review of Absolute parallelism (AP) geometry and its
parameterized version(PAP), as a wider geometry than the Riemannian one, is
presented. World models constructed using alternative field theories,
constructed in the AP geometry, are discussed and compared. Some points about
using topology in the field of cosmology are commented. A new path equation,
admitted by the PAP geometry, is used to get the effect of spin-gravity
interaction on the cosmological parameters.


title:
Scalar field and electromagnetic perturbations on Locally Rotationally
  Symmetric spacetimes

abstract:
  We study scalar field and electromagnetic perturbations on Locally
Rotationally Symmetric (LRS) class II spacetimes, exploiting a recently
developed covariant and gauge-invariant perturbation formalism. From the
Klein-Gordon equation and Maxwell's equations, respectively, we derive
covariant and gauge-invariant wave equations for the perturbation variables and
thereby find the generalised Regge-Wheeler equations for these LRS class II
spacetime perturbations. As illustrative examples, the results are discussed in
detail for the Schwarzschild and Vaidya spacetime, and briefly for some classes
of dust Universes.


title: Properties of Information Carrying Waves in Cosmology

abstract:
  Recently we studied the effects of information carrying waves propagating
through isotropic cosmologies. By information carrying we mean that the waves
have an arbitrary dependence on a function. We found that the waves introduce
shear and anisotropic stress into the universe. We then constructed explicit
examples of pure gravity wave perturbations for which the presence of this
anisotropic stress is essential and the null hypersurfaces playing the role of
the histories of the wave-fronts in the background space-time are shear-free.
Motivated by this result we now prove that these two properties are true for
all information carrying waves in isotropic cosmologies.


title:
Slice Stretching Effects for Maximal Slicing of a Schwarzschild Black
  Hole

abstract:
  Slice stretching effects such as slice sucking and slice wrapping arise when
foliating the extended Schwarzschild spacetime with maximal slices. For
arbitrary spatial coordinates these effects can be quantified in the context of
boundary conditions where the lapse arises as a linear combination of odd and
even lapse. Favorable boundary conditions are then derived which make the
overall slice stretching occur late in numerical simulations. Allowing the
lapse to become negative, this requirement leads to lapse functions which
approach at late times the odd lapse corresponding to the static Schwarzschild
metric. Demanding in addition that a numerically favorable lapse remains
non-negative, as result the average of odd and even lapse is obtained. At late
times the lapse with zero gradient at the puncture arising for the puncture
evolution is precisely of this form. Finally, analytic arguments are given on
how slice stretching effects can be avoided. Here the excision technique and
the working mechanism of the shift function are studied in detail.


title: Status of non-Riemannian cosmology

abstract:
  We provide a brief chronological guide to the literature on non-Riemannian
cosmological models. Developments in this field are traced back to the early
seventies and are given in table form.


title: Shortcuts to Spherically Symmetric Solutions: A Cautionary Note

abstract:
  Spherically symmetric solutions of generic gravitational models are
optimally, and legitimately, obtained by expressing the action in terms of the
two surviving metric components. This shortcut is not to be overdone, however:
a one-function ansatz invalidates it, as illustrated by the incorrect solutions
of [1].


title: On state sums, internalisation and unification

abstract:
  In this mostly expository article, elements of higher category theory
essential to the construction of a class of four dimensional quantum geometric
models are reviewed. These models improve current state sum models for Quantum
Gravity, such as the Barrett-Crane model, in that they appear, for instance, to
remove degeneracies which swamp the partition function. Much work remains to be
done before a complete construction is reached, but the crucial categorical
notion of internalisation already illuminates the idea that a full unified
model may result from few, albeit as yet poorly understood, additional
principles. In particular, a spacetime and matter duality principle is employed
through an understanding of the role of pseudomonoidal objects in categorified
cohomology.


title:
The Chrono'Geometrical Structure of Special and General Relativity:
  Towards a Background-Independent Description of the Gravitational Field and
  Elementary Particles

abstract:
  Since the main open problem of contemporary physics is to find a unified
description of the four interactions, we present a possible scenario which,
till now only at the classical level, is able to englobe experiments ranging
from experimental space gravitation to atomic and particle physics. After a
reformulation of special relativistic physics in a form taking into account the
non-dynamical chrono-geometrical structure of Minkowski space-time
(parametrized Minkowski theories and rest-frame instant form) and in particular
the conventionality of simultaneity (re-phrased as a gauge freedom), a model of
canonical metric and tetrad gravity is proposed in a class of space-times where
the deparametrization to Minkowski space-time is possible. In them it is
possible to give a post-Minkowskian background-independent description of the
gravitational field and of matter. The study of the dynamical
chrono-geometrical structure of these space-times allows to face
interpretational problems like the physical identification of point-events (the
Hole Argument), the distinction between inertial (gauge) and tidal (Dirac
observables) effects, the dynamical nature of simultaneity in general
relativity and to find background-independent gravitational waves. These
developments are possible at the Hamiltonian level due to a systematic use of
Dirac-Bergmann theory of constraints. Finally there is a proposal for a new
coordinate- and background-independent quantization scheme for gravity.


title: Overview of the BlockNormal Event Trigger Generator

abstract:
  In the search for unmodeled gravitational wave bursts, there are a variety of
methods that have been proposed to generate candidate events from time series
data. Block Normal is a method of identifying candidate events by searching for
places in the data stream where the characteristic statistics of the data
change. These change-points divide the data into blocks in which the
characteristics of the block are stationary. Blocks in which these
characteristics are inconsistent with the long term characteristic statistics
are marked as Event-Triggers which can then be investigated by a more
computationally demanding multi-detector analysis.


title: Gravitational Waves from Chaotic Dynamical System

abstract:
  To investigate how chaos affects gravitational waves, we study the
gravitational waves from a spinning test particle moving around a Kerr black
hole, which is a typical chaotic system. To compare the result with those in
non-chaotic dynamical system, we also analyze a spinless test particle, which
orbit can be complicated in the Kerr back ground although the system is
integrable. We estimate the emitted gravitational waves by the multipole
expansion of a gravitational field. We find a striking difference in the energy
spectra of the gravitational waves. The spectrum for a chaotic orbit of a
spinning particle, contains various frequencies, while some characteristic
frequencies appear in the case of a spinless particle.


title: On the Riemann Extension of the Schwarzschild Metric

abstract:
  Some solutions of the Einstein equations for the eight-dimensional Riemann
extension of the classical four-dimensional Schwarzschild metric are
considered.


title: Bouncing universes and their perturbations: remarks on a toy model

abstract:
  Friedmann-Lemaitre universes driven by a scalar field, spatially closed and
bouncing, were recently studied by Martin and Peter in [1], with the conclusion
that the spectrum of their large scale matter perturbations was generically
modified when going through the bounce. In this Note we give the properties of
the scalar field potentials which underly such models.


title: Light Tides and the Kennedy-Thorndike experiments

abstract:
  We model the system Earth-Moon-Sun from the point of view of a frame of
reference co-moving with the Earth and we derive a detailed prediction of the
outcome of future Kennedy-Thorndike's type experiments to be seen as light
tides.


title: Phasing of gravitational waves from inspiralling eccentric binaries

abstract:
  We provide a method for analytically constructing high-accuracy templates for
the gravitational wave signals emitted by compact binaries moving in
inspiralling eccentric orbits. By contrast to the simpler problem of modeling
the gravitational wave signals emitted by inspiralling {\it circular} orbits,
which contain only two different time scales, namely those associated with the
orbital motion and the radiation reaction, the case of {\it inspiralling
eccentric} orbits involves {\it three different time scales}: orbital period,
periastron precession and radiation-reaction time scales. By using an improved
`method of variation of constants', we show how to combine these three time
scales, without making the usual approximation of treating the radiative time
scale as an adiabatic process. We explicitly implement our method at the 2.5PN
post-Newtonian accuracy. Our final results can be viewed as computing new
`post-adiabatic' short period contributions to the orbital phasing, or
equivalently, new short-period contributions to the gravitational wave
polarizations, $h_{+,\times}$, that should be explicitly added to the
`post-Newtonian' expansion for $h_{+,\times}$, if one treats radiative effects
on the orbital phasing of the latter in the usual adiabatic approximation. Our
results should be of importance both for the LIGO/VIRGO/GEO network of ground
based interferometric gravitational wave detectors (especially if Kozai
oscillations turn out to be significant in globular cluster triplets), and for
the future space-based interferometer LISA.


title: LISA Source Confusion

abstract:
  The Laser Interferometer Space Antenna (LISA) will detect thousands of
gravitational wave sources. Many of these sources will be overlapping in the
sense that their signals will have a non-zero cross-correlation. Such overlaps
lead to source confusion, which adversely affects how well we can extract
information about the individual sources. Here we study how source confusion
impacts parameter estimation for galactic compact binaries, with emphasis on
the effects of the number of overlaping sources, the time of observation, the
gravitational wave frequencies of the sources, and the degree of the signal
correlations. Our main findings are that the parameter resolution decays
exponentially with the number of overlapping sources, and super-exponentially
with the degree of cross-correlation. We also find that an extended mission
lifetime is key to disentangling the source confusion as the parameter
resolution for overlapping sources improves much faster than the usual square
root of the observation time.


title: Clock Synchronization and Navigation in the Vicinity of the Earth

abstract:
  Clock synchronization is the backbone of applications such as high-accuracy
satellite navigation, geolocation, space-based interferometry, and
cryptographic communication systems. The high accuracy of synchronization
needed over satellite-to-ground and satellite-to-satellite distances requires
the use of general relativistic concepts. The role of geometrical optics and
antenna phase center approximations are discussed in high accuracy work. The
clock synchronization problem is explored from a general relativistic point of
view, with emphasis on the local measurement process and the use of the tetrad
formalism as the correct model of relativistic measurements. The treatment
makes use of J. L. Synge's world function of space-time as a basic coordinate
independent geometric concept. A metric is used for space-time in the vicinity
of the Earth, where coordinate time is proper time on the geoid. The problem of
satellite clock syntonization is analyzed by numerically integrating the
geodesic equations of motion for low-Earth orbit (LEO), geosynchronous orbit
(GEO), and highly elliptical orbit (HEO) satellites. Proper time minus
coordinate time is computed for satellites in these orbital regimes. The
frequency shift as a function of time is computed for a signal observed on the
Earth's geoid from a LEO, GEO, and HEO satellite. Finally, the problem of
geolocation in curved space-time is briefly explored using the world function
formalism.


title:
An unification of general theory of relativity with Dirac's large number
  hypothesis

abstract:
  Taking a hint from Dirac's large number hypothesis, we note the existence of
cosmologically combined conservation laws that work to cosmologically long
time. We thus modify Einstein's theory of general relativity with fixed
gravitation constant $G$ to a theory for varying $G$, with a tensor term
arising naturally from the derivatives of $G$ in place of the cosmological
constant term usually introduced \textit{ad hoc}. The modified theory, when
applied to cosmology, is consistent with Dirac's large number hypothesis, and
gives a theoretical Hubble's relation not contradicting the observational data.
For phenomena of duration and distance short compared with that of the
universe, our theory reduces to Einstein's theory with $G$ being constant
outside the gravitating matter, and thus also passes the crucial tests of
Einstein's theory.


title: Bouncing universes and their perturbations : a simple model revisited

abstract:
  We reconsider the toy model studied in [1] of a spatially closed
Friedmann-Lemaitre universe, driven by a massive scalar field, which deflates
quasi-exponentially, bounces and then enters a period of standard inflation. We
find that the equations for the matter density perturbations can be solved
analytically, at least at lowest order in some "slow-roll" parameter. We can
therefore give, in that limit, the explicit spectrum of the post-bounce
perturbations in terms of their pre-bounce initial spectrum. Our result is
twofold. If the pre-bounce growing and decaying modes are of the same order of
magnitude at the bounce, then the spectrum of the pre-bounce growing modes is
carried over to the post-bounce decaying modes ("mode inversion"). On the other
hand, if, more likely, the pre-bounce growing modes dominate, then resolution
at next order indicates that their spectrum is nicely carried over, with
reduced amplitude, to the post-bounce growing modes.


title:
Algebraic and differential Rainich conditions for symmetric trace-free
  tensors of higher rank

abstract:
  We study Rainich-like conditions for symmetric and trace-free tensors T. For
arbitrary even rank we find a necessary and sufficient differential condition
for a tensor to satisfy the source free field equation. For rank 4, in a
generic case, we combine these conditions with previously obtained algebraic
conditions to obtain a complete set of algebraic and differential conditions on
T for it to be a superenergy tensor of a Weyl candidate tensor satisfying the
Bianchi vacuum equations. By a result of Bell and Szekeres this implies that in
vacuum, generically, T must be the Bel-Robinson tensor of the spacetime. For
the rank 3 case we derive a complete set of necessary algebraic and
differential conditions for T to be the superenergy tensor of a massless spin
3/2 field satisfying the source free field equation.


title: The Initial Value Problem Using Metric and Extrinsic Curvature

abstract:
  The initial value problem is introduced after a thorough review of the
essential geometry. The initial value equations are put into elliptic form
using both conformal transformations and a treatment of the extrinsic curvature
introduced recently. This use of the metric and the extrinsic curvature is
manifestly equivalent to the author's conformal thin sandwich formulation.
Therefore, the reformulation of the constraints as an elliptic system by use of
conformal techniques is complete.


title: Generalized Tomonaga-Schwinger equation from the Hadamard formula

abstract:
  A generalized Tomonaga--Schwinger equation, holding on the entire boundary of
a {\em finite} spacetime region, has recently been considered as a tool for
studying particle scattering amplitudes in background-independent quantum field
theory. The equation has been derived using lattice techniques under
assumptions on the existence of the continuum limit. Here I show that in the
context of continuous euclidean field theory the equation can be directly
derived from the functional integral formalism, using a technique based on
Hadamard's formula for the variation of the propagator.


title:
The holographic solution - Why general relativity must be understood in
  terms of strings

abstract:
  This paper is a significantly expanded version of gr-qc/0306066. It discusses
the geometric properties of the so called holographic solution, an exact,
spherically symmetric solution to the Einstein field equations with zero
cosmological constant. The holographic solution can be regarded as the simplest
solution of the field equations including matter. Its interior matter-density
follows an inverse square law: e = 1 / (8 pi r2). The interior principle
pressures are P_r = - e in the radial direction and P_tan = 0 in the tangential
direction. This is the equation of state of a radial arrangement of strings.
The interior string type matter state is densely packed, each string occupying
a transverse extension of exactly one Planck area, and bounded by a membrane
consisting out of tangential pressure. The membrane's energy density is zero,
as expected from string theory. Despite its simple structure, the results that
can be derived from this solution are far from trivial. It is not possible to
give a fair account of all relevant results in a 20-line abstract. The reader
is referred to the abstract in the paper, which summarizes some of the more
important results. The author appreciates any comments, critique or suggestions
of new material.


title:
On the thermodynamic origin of the Hawking entropy and a measurement of
  the Hawking temperature

abstract:
  In the spherically symmetric case the Einstein field equations take on their
simplest form for a matter-density rho = 1 / (8 pi r^2), from which a radial
metric coefficient g_{rr} \propto r follows. The boundary of an object with
such an interior matter-density is situated slightly outside of its
gravitational radius. Its surface-redshift scales with z \propto \sqrt{r}, so
that any such large object is practically indistinguishable from a black hole,
as seen from exterior space-time. The interior matter has a well defined
temperature, T \propto 1 / \sqrt{r}. Under the assumption, that the interior
matter can be described as an ultra-relativistic gas, the object's total
entropy and its temperature at infinity can be calculated by microscopic
statistical thermodynamics. They are equal to the Hawking result up to a
possibly different constant factor. The simplest solution of the field
equations with rho = 1 / (8 pi r^2) is the so called holographic solution,
short "holostar". It has an interior string equation of state. The strings are
densely packed, explaining why the solution does not collapse to a singularity.
The holographic solution has been shown to be a very accurate model for the
universe as we see it today in Ref[7]. The factor relating the holostar's
temperature at infinity to the Hawking temperature can be expressed in terms
the holostar's interior (local) radiation temperature and its (local)
matter-density, allowing an experimental verification of the Hawking
temperature law. Using the recent experimental data for the CMBR-temperature
and the total matter-density in the universe measured by WMAP, the Hawking
formula is verified to an accuracy of 1%.


title:
Quantum Observables Algebras and Abstract Differential Geometry: The
  Topos-Theoretic Dynamics of Diagrams of Commutative Algebraic Localizations

abstract:
  We construct a sheaf-theoretic representation of quantum observables algebras
over a base category equipped with a Grothendieck topology, consisting of
epimorphic families of commutative observables algebras, playing the role of
local arithmetics in measurement situations. This construction makes possible
the adaptation of the methodology of Abstract Differential Geometry (ADG), a la
Mallios, in a topos-theoretic environment, and hence, the extension of the
"mechanism of differentials" in the quantum regime. The process of gluing
information, within diagrams of commutative algebraic localizations, generates
dynamics, involving the transition from the classical to the quantum regime,
formulated cohomologically in terms of a functorial quantum connection, and
subsequently, detected via the associated curvature of that connection.


title:
On the origin of the matter-antimatter asymmetry in self-gravitating
  systems at ultra-high temperatures

abstract:
  It is shown, that self-gravitating systems can be classified by a
dimensionless constant positive number $\kappa = S T / E$, which can be
determined from the (global) values for the entropy, temperature and (total)
energy. The Kerr-Newman black hole family is characterized by $\kappa$ in the
range $0-1/2$, depending on the dimensionless ratios of angular momentum and
charge squared to the horizon area, $J/A$ and $Q^2/A$. By analyzing the most
general case of an ultra-relativistic ideal gas with non-zero chemical
potential it is shown, that $\kappa$ is an important parameter which determines
the (local) thermodynamic properties of an ultra-relativistic gas. $\kappa$
only depends on the chemical potential per temperature $u = \mu / T$ and on the
ratio of bosonic to fermionic degrees of freedom $r_F = f_B / f_F$. A gas with
zero chemical potential has $\kappa = 4/3$. Whenever $\kappa < 4/3$ the gas
must acquire a non-zero chemical potential. This non-zero chemical potential
induces a natural matter-antimatter asymmetry, whenever microscopic statistical
thermodynamics can be applied. The recently discovered holographic solution
describes a compact self gravitating black hole type object with an interior,
well defined matter state. One can associate a local - possibly
observer-dependent - value of $\kappa$ to the interior matter, which lies in
the range $2/3-1$ (for the uncharged case). This finding is used to construct
an alternative scenario of baryogenesis in the context of the holographic
solution, based on quasi-equilibrium thermodynamics.


title: Are we living in a string-dominated universe?

abstract:
  The holographic solution is a new exact solution to the Einstein field
equations. It describes a compact self-gravitating object with properties
similar to a black hole. Its entropy and temperature at infinity are
proportional to the Hawking result. Instead of an event horizon, the
holographic solution has a real spherical boundary membrane, situated roughly
two Planck distances outside of the object's gravitational radius. The interior
matter-state is singularity free. It consists out of string type matter, which
is densely packed. Each string has a transverse extension of exactly one Planck
area. This dense package of strings might be the reason, why the solution does
not collapse to a singularity. The local string tension is inverse proportional
to the average string length. This purely classical result has its almost exact
correspondence in a recent result in string theory. The holographic solution
suggest, that string theory is relevant also on cosmological scales. The large
scale phenomena in the universe can be explained naturally in a string context.
Due to the zero active gravitational mass-density of the strings the Hubble
constant in a string dominated universe is related to its age by H t = 1. The
WMAP measurements have determined H t \approx 1.02 \pm 0.02 experimentally. The
nearly unaccelerated expansion in a string dominated universe is compatible
with the recent supernova measurements. Under the assumption, that the cold
dark matter (CDM) consists out of strings, the ratio of CDM to baryonic matter
is estimated as \Omega_CDM / \Omega_b \approx 6.45. Some arguments are given,
which suggest that the universe might be constructed hierarchically out of its
most basic building blocks: strings and membranes.


title: Cosmological constant and vacuum energy

abstract:
  The general thermodynamic analysis of the quantum vacuum, which is based on
our knowledge of the vacua in condensed-matter systems, is consistent with the
Einstein earlier view on the cosmological constant. In the equilibrium
Universes the value of the cosmological constant is regulated by matter. In the
empty Universe, the vacuum energy is exactly zero, lambda=0. The huge
contribution of the zero point motion of the quantum fields to the vacuum
energy is exactly cancelled by the higher-energy degrees of freedom of the
quantum vacuum. In the equilibrium Universes homogeneously filled by matter,
the vacuum is disturbed, and density of the vacuum energy becomes proportional
to the energy density of matter. This consideration applies to any equilibrium
vacuum irrespective of whether the vacuum is false or true, and is valid both
in the Einstein general theory of relativity and within the special theory of
relativity, i.e. in the world without gravity.

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


title: Non-singular G2 stiff fluid cosmologies

abstract:
  In this paper we analyse Abelian diagonal orthogonally transitive spacetimes
with spacelike orbits for which the matter content is a stiff perfect fluid.
The Einstein equations are cast in a suitable form for determining their
geodesic completeness. A sufficient condition on the metric of these spacetimes
is obtained, that is fairly easy to check and to implement in exact solutions.
These results confirm that non-singular spacetimes are abundant among stiff
fluid cosmologies.


title:
False vacuum decay via Coleman - de Luccia instanton in the theory with
  quasi-exponential potential

abstract:
  The necessary and sufficient condition for the false vacuum decay in a de
Sitter universe via Coleman - de Luccia instanton is applied on the scalar
field with quasi - exponential potential.


title: A spatially-VSL gravity model with 1-PN limit of GRT

abstract:
  A scalar gravity model is developed according the 'geometric conventionalist'
approach introduced by Poincare (Einstein 1921, Poincare 1905, Reichenbach
1957, Gruenbaum1973). In principle this approach allows an alternative
interpretation and formulation of General Relativity Theory (GRT), with
distinct i) physical congruence standard, and ii) gravitation dynamics
according Hamilton-Lagrange mechanics, while iii) retaining empirical
indistinguishability with GRT. In this scalar model the congruence standards
have been expressed as gravitationally modified Lorentz Transformations
(Broekaert 2002). The first type of these transformations relate quantities
observed by gravitationally 'affected' (natural geometry) and 'unaffected'
(coordinate geometry) observers and explicitly reveal a spatially variable
speed of light (VSL). The second type shunts the unaffected perspective and
relates affected observers, recovering i) the invariance of the locally
observed velocity of light, and ii) the local Minkowski metric (Broekaert
2003). In the case of a static gravitation field the model retrieves the
phenomenology implied by the Schwarzschild metric. The case with proper source
kinematics is now described by introduction of a 'sweep velocity' field w: The
model then provides a hamiltonian description for particles and photons in full
accordance with the first Post-Newtonian approximation of GRT (Weinberg 1972,
Will 1993).


title:
Slice Stretching at the Event Horizon when Geodesically Slicing the
  Schwarzschild Spacetime with Excision

abstract:
  Slice-stretching effects are discussed as they arise at the event horizon
when geodesically slicing the extended Schwarzschild black-hole spacetime while
using singularity excision. In particular, for Novikov and isotropic spatial
coordinates the outward movement of the event horizon (``slice sucking'') and
the unbounded growth there of the radial metric component (``slice wrapping'')
are analyzed. For the overall slice stretching, very similar late time behavior
is found when comparing with maximal slicing. Thus, the intuitive argument that
attributes slice stretching to singularity avoidance is incorrect.


title: Wormhole solutions in 5D Kaluza-Klein theory as string-like objects

abstract:
  The detailed numerical and analytical approximate analysis of wormhole-like
solutions in 5D Kaluza-Klein gravity is given. It is shown that some part of
these solutions with $E \approx H, E>H$ relation between electric $E$ and
magnetic $H$ fields can be considered as a superthin and superlong
gravitational flux tube filled with electric and magnetic fields, namely
$\Delta-$strings. The solution behaviour near hypersurface $ds^2=0$ and the
model of electric charge on the basis of $\Delta-$string are discussed. The
comparison of the properties of $\Delta-$string and ordinary string in string
theory is carried out. Some arguments are given that fermionic degrees of
freedom can be build in on the $\Delta-$string. These degrees of freedom are
connected with quantum wormholes of spacetime foam. It is shown that the
natural theory for these spinor fields is supergravity.


title:
On the variable-charged black holes embedded into de Sitter space:
  Hawking's radiation

abstract:
  In this paper we study the Hawking evaporation of masses of variable-charged
Reissner-Nordstrom and Kerr-Newman, black holes embedded into the de Sitter
universe by considering the charge to be function of radial coordinate of the
spherically symmetric metric.


title:
On the variable-charged black holes in General Relativity: Hawking's
  radiation and naked singularities

abstract:
  In this paper we study the Hawking radiation in Reissner-Nordstrom and
Kerr-Newman black holes by considering the charge to be the function of radial
coordinate.


title: On big rip singularities

abstract:
  In this comment we discuss big rip singularities occurring in typical phantom
models by violation of the weak energy condition. After that, we compare them
with future late-time singularities arising in models where the scale factor
ends in a constant value and there is no violation of the strong energy
condition. In phantom models the equation of state is well defined along the
whole evolution, even at the big rip. However, both the pressure and the energy
density of the phantom field diverge. In contrast, in the second kind of model
the equation of state is not defined at the big rip because the pressure bursts
at a finite value of the energy density.


title: Renormalization Group approach to Inhomogeneous Cosmology

abstract:
  Soliton solutions are recovered as scale-invariant asymptotic states of
vacuum inhomogeneous cosmologies using renormalization group method. The
stability analysis of these states is also given.


title: Leibniz--Mach foundations for GR and fundamental physics

abstract:
  Consider the configuration space Q for some physical system, and a continuous
group of transformations G whose action on the configurations is declared to be
physically irrelevant. Implement G indirectly by adjoining 1 auxiliary g per
independent generator of G to Q, by writing the system's action in an arbitrary
G-frame (G-AF), and then passing to the quotient Q/G thanks to the constraints
encoded by g-variation. I show that this G-AF principle supercedes (and indeed
leads to a derivation of) the Barbour--Bertotti (BB) best matching principle.
My other consideration is that absolute external time is meaningless for the
universe as a whole. For various choices of Q and G, these lead to BB's
proposed absolute structure free replacement of Newtoninan mechanics, to Gauge
Theory and to the 3-space approach (TSA) formulation of GR. For the latter with
matter fields, I discuss the SR postulates, Principle of Equivalence (POE) and
simplicity postulates. I explain how a full enough set of fundamental matter
fields to describe nature can be accommodated in the TSA, and compare the TSA
with the `split spacetime formulation' of Kuchar. I explain the emergence of
broken and unbroken Gauge Theories as a consequence of the POE. I also consider
as further examples of the G-AF principle the further quotienting out of
conformal transformations (CT) or volume preserving CT. Depending on which
choices are made, this leads to York's initial value formulation (IVF) of GR,
new alternative foundations for it, or alternative theories of gravity built
out of similar conformal mathematics which nevertheless admit no GR-like
spacetime interpretation.


title:
Correlator Bank Detection of GW chirps. False-Alarm Probability,
  Template Density and Thresholds: Behind and Beyond the Minimal-Match Issue

abstract:
  The general problem of computing the false-alarm rate vs. detection-threshold
relationship for a bank of correlators is addressed, in the context of
maximum-likelihood detection of gravitational waves, with specific reference to
chirps from coalescing binary systems. Accurate (lower-bound) approximants for
the cumulative distribution of the whole-bank supremum are deduced from a class
of Bonferroni-type inequalities. The asymptotic properties of the cumulative
distribution are obtained, in the limit where the number of correlators goes to
infinity. The validity of numerical simulations made on small-size banks is
extended to banks of any size, via a gaussian-correlation inequality. The
result is used to estimate the optimum template density, yielding the best
tradeoff between computational cost and detection efficiency, in terms of
undetected potentially observable sources at a prescribed false-alarm level,
for the simplest case of Newtonian chirps.


title:
Noncompact Kaluza-Klein theory and inflationary cosmology: a complete
  formalism

abstract:
  A formalization of the recently introduced formalism for inflation is
developed from noncompact Kaluza-Klein theory. In particular, the case for a
single scalar field inflationary model is studied. We obtain that the scalar
potential, which assume different representations in different frames, has a
geometrical origin.


title: Gravitational Lensing by Galaxy Quantization States

abstract:
  We show how our theory of large-scale gravitational quantization explains the
large angle gravitational lensing by galaxies without requiring "dark matter".
A galaxy is treated as a collective system of billions of stars in each
quantization state with each star experiencing an average gravitational
environment analogous to that for nucleons in the atomic nucleus. Consequently,
each star is in an approximate finite depth square well type of gravitational
potential. The "effective potential" is shown to be about ten times greater
than the Newtonian gravitational potential, so the gravitational lensing
effects of a galaxy are about ten times greater also, in agreement with the
measured gravitational lensing.


title: Spherically symmetric perfect fluid in area-radial coordinates

abstract:
  We study the spherically symmetric collapse of a perfect fluid using
area-radial coordinates. We show that analytic mass functions describe a static
regular centre in these coordinates. In this case, a central singularity can
not be realized without an infinite discontinuity in the central density. We
construct mass functions involving fluid dynamics at the centre and investigate
the relationship between those and the nature of the singularities.


title: Reference Frame in General Relativity

abstract:
  A reference frame in event space is a smooth field of orthonormal bases.
Every reference frame is equipped by anholonomic coordinates. Using anholonomic
coordinates allows to find out relative speed of two observers and appropriate
Lorentz transformation.
  Synchronization of a reference frame is an anholonomic time coordinate.
Simple calculations show how synchronization influences time measurement in the
vicinity of the Earth.
  Measurement of Doppler shift from the star orbiting the black hole helps to
determine mass of the black hole. According observations of Sgr A, if non
orbiting observer estimates age of S2 about 10 Myr, this star is 0.297 Myr
younger.


title: Metric-Affine Manifold

abstract:
  We call a manifold with torsion and nonmetricity the metric-affine manifold.
The nonmetricity leads to a difference between the auto parallel line and the
extreme line, and to a change in the expression of the Frenet transport and
moving basis. The torsion leads to a change in the Killing equation. We also
need to add a similar equation for the connection.
  The analysis of the Frenet transport leads to the concept of the Cartan
transport and an introduction of the connection compatible with the metric
tensor. The dynamics of a particle follows to the Cartan transport. We need
additional physical constraints to make a nonmetricity observable.


title:
New Formulation of the First Law of Black Hole Thermodynamics: A Stringy
  Analogy

abstract:
  We consider the first laws of thermodynamics for a pair of systems made up of
the two horizons of a Kerr-Newman black hole. These two systems are constructed
in such a way that we only demand their ``horizon areas'' to be the sum and
difference of that of the outer and inner horizons of their prototype.
Remarkably, these two copies bear a striking resemblance to the right- and
left-movers in string theory and D-brane physics. Our reformulation of the
first law of black hole thermodynamics can be thought of as an analogy of
thermodynamics of effective string or D-brane models.


title: Scalar Gravitation and Extra Dimensions

abstract:
  Gunnar Nordstrom constructed the first relativistic theory of gravitation
formulated in terms of interactions with a scalar field. It was an important
precursor to Einstein's general theory of relativity a couple of years later.
He was also the first to introduce an extra dimension to our spacetime so that
gravitation would be just an aspect of electromagnetic interactions in five
dimensions. His scalar theory and generalizations thereof are here presented in
a bit more modern setting. Extra dimensions are of great interest in physics
today and can give scalar gravitational interactions with similar properties as
in Nordstrom's original theory.


title: Area Regge Calculus and Discontinuous Metrics

abstract:
  Taking the triangle areas as independent variables in the theory of Regge
calculus can lead to ambiguities in the edge lengths, which can be interpreted
as discontinuities in the metric. We construct solutions to area Regge calculus
using a triangulated lattice and find that on a spacelike hypersurface no such
discontinuity can arise. On a null hypersurface however, we can have such a
situation and the resulting metric can be interpreted as a so-called refractive
wave.


title:
Perturbations of the spherically symmetric collapsar in the relativistic
  theory of gravitation: axial perturbations. I

abstract:
  Horizon solutions for the axial perturbations of the spherically symmetric
metric are analyzed in the framework of the relativistic theory of gravitation.
The gravitational perturbations can not be absorbed by the horizon that results
in the excitation of the new type of the normal modes trapped by the
Regge-Wheeler potential. The obtained results demonstrate testable differences
between the collapsar and the black hole near-horizon physics.