title: On the length expectation values in quantum Regge calculus

abstract:
  Regge calculus configuration superspace can be embedded into a more general
superspace where the length of any edge is defined ambiguously depending on the
4-tetrahedron containing the edge. Moreover, the latter superspace can be
extended further so that even edge lengths in each the 4-tetrahedron are not
defined, only area tensors of the 2-faces in it are. We make use of our
previous result concerning quantisation of the area tensor Regge calculus which
gives finite expectation values for areas. Also our result is used showing that
quantum measure in the Regge calculus can be uniquely fixed once we know
quantum measure on (the space of the functionals on) the superspace of the
theory with ambiguously defined edge lengths. We find that in this framework
quantisation of the usual Regge calculus is defined up to a parameter. The
theory may possess nonzero (of the order of Plank scale) or zero length
expectation values depending on whether this parameter is larger or smaller
than a certain value. Vanishing length expectation values means that the theory
is becoming continuous, here {\it dynamically} in the originally discrete
framework.


title:
Test particles behavior in the framework of a lagrangian geometric
  theory with propagating torsion

abstract:
  Working in the lagrangian framework, we develop a geometric theory in vacuum
with propagating torsion; the antisymmetric and trace parts of the torsion
tensor, considered as derived from local potential fields, are taken and, using
the minimal action principle, their field equations are calculated. Actually
these will show themselves to be just equations for propagating waves giving
torsion a behavior similar to that of metric which, as known, propagates
through gravitational waves. Then we establish a principle of minimal
substitution to derive test particles equation of motion, obtaining, as result,
that they move along autoparallels. We then calculate the analogous of the
geodesic deviation for these trajectories and analyze their behavior in the
nonrelativistic limit, showing that the torsion trace potential $\phi$ has a
phenomenology which is indistinguishable from that of the gravitational
newtonian field; in this way we also give a reason for why there have never
been evidence for it.


title: General Aspects of the de Sitter phase

abstract:
  We present a detailed discussion of the inflationary scenario in the context
of inhomogeneous cosmologies. After a review of the fundamental features
characterizing the inflationary model, as referred to a homogeneous and
isotropic Universe, we develop a generalization in view of including small
inhomogeneous corrections in the theory. A second step in our discussion is
devoted to show that the inflationary scenario provides a valuable dynamical
``bridge'' between a generic Kasner-like regime and a homogeneous and isotropic
Universe in the horizon scale. This result is achieved by solving the
Hamilton-Jacobi equation for a Bianchi IX model in the presence of a
cosmological space-dependent term. In this respect, we construct a
quasi-isotropic inflationary solution based on the expansion of the Einstein
equations up to first-two orders of approximation, in which the isotropy of the
Universe is due to the dominance of the scalar field kinetic term; the first
order of approximation corresponds to the inhomogeneous corrections and is
driven by the matter evolution. We show how such a quasi-isotropic solution
contains a certain freedom in fixing the space functions involved in the
problem. The main physical issue of this analysis corresponds to outline the
impossibility for the classical origin of density perturbations, due to the
exponential decay of the matter term during the de Sitter phase.


title:
Some Implications of the Density Matrix Deformation in Statistical
  Mechanics of the Early Universe

abstract:
  This work is an extension of the study into statistical mechanics of the
early Universe that has been the subject in prior works of the author, the
principal approach being the density matrix deformation. In the work it is
demonstrated that the previously derived exponential ansatz may be successfully
applied to the derivation of the free and average energy deformation as well as
entropy deformation. Based on the exponential ansatz, the derivation of a
statistical-mechanical Liouville equation as a deformation of the
quantum-mechanical counterpart is presented. It is shown that deformed
Liouville equation will possess nontrivial components as compared to the normal
equation in two cases: for the original singularity (i.e. early Universe) and
for black hole, that is in complete agreement with the results obtained by the
author with coworkers in earlier works devoted to the deformation in quantum
mechanics at Planck scale. In conclusion some possible applications of the
proposed methods are given, specifically for investigation into thermodynamics
of black holes.


title: Remarks on Schwinger Pair Production by Charged Black Holes

abstract:
  We introduce a canonical method for pair production by electromagnetic
fields. The canonical method in the space-dependent gauge provides
pair-production rate even for inhomogeneous fields. Further, the instanton
action including all corrections leads to an accurate formula for the
pair-production rate. We discuss various aspects of the canonical method and
clarify terminology for pair production. We study pair production by charged
black holes first by finding states of the field equation that describe pair
production and then by applying the canonical method.


title:
Spin Foam Models of n-dimensional Quantum Gravity and Non-Archimedean
  and Non-Commutative Formulations

abstract:
  This paper is twofold. First of all a complete unified picture of
$n$-dimensional quantum gravity is proposed in the following sense: In spin
foam models of quantum gravity the evaluation of spin networks play a very
important role. These evaluations correspond to amplitudes which contribute in
a state sum model of quantum gravity. In \cite{fk}, the evaluation of spin
networks as integrals over internal spaces was described. This evaluation was
restricted to evaluations of spin networks in $n$-dimensional Euclidean quantum
gravity. Here we propose that a similar method can be considered to include
Lorentzian quantum gravity. We therefore describe the the evaluation of spin
networks in the Lorentzian framework of spin foam models. We also include a
limit of the Euclidean and Lorentzian spin foam models which we call Newtonian.
This Newtonian limit was also considered in \cite{jm}.
  Secondly, we propose an alternative formulation of spin foam models of
quantum gravity with its corresponding evaluation of spin networks. This
alternative formulation is a non-archimedean or $p$-adic spin foam model. The
interest on this description is that it is based on a discrete space-time,
which is the expected situation we might have at the Planck length; this
description might lead us to an alternative regularisation of quantum gravity.
Moreover a non-commutative formulation follows from the non-archimedean one.


title:
On the equation of motion of compact binaries in Post-Newtonian
  approximation

abstract:
  A third post-Newtonian (3 PN) equation of motion for two spherical compact
stars in a harmonic coordinate has been derived based on the surface integral
approach and the strong field point particle limit. The strong field point
particle limit enables us to incorporate a notion of a self-gravitating regular
star into general relativity. The resulting 3 PN equation of motion is Lorentz
invariant, unambiguous, and conserves an energy of the binary orbital motion.


title: Brane cosmology with a van der Waals equation of state

abstract:
  The evolution of a Universe confined onto a 3-brane embedded in a
five-dimensional space-time is investigated where the cosmological fluid on the
brane is modeled by the van der Waals equation of state. It is shown that the
Universe on the brane evolves in such a manner that three distinct periods
concerning its acceleration field are attained: (a) an initial accelerated
epoch where the van der Waals fluid behaves like a scalar field with a negative
pressure; (b) a past decelerated period which has two contributions, one of
them is related to the van der Waals fluid which behaves like a matter field
with a positive pressure, whereas the other contribution comes from a term of
the Friedmann equation on the brane which is inversely proportional to the
scale factor to the fourth power and can be interpreted as a radiation field,
and (c) a present accelerated phase due to a cosmological constant on the
brane.


title:
Symmetries of the Energy-Momentum Tensor of Cylindrically Symmetric
  Static Spacetimes

abstract:
  We investigate matter symmetries of cylindrically symmetric static
spacetimes. These are classified for both cases when the energy-momentum tensor
is non-degenerate and also when it is degenerate. It is found that the
non-degenerate energy-momentum tensor gives either three, four, five, six,
seven or ten independent matter collineations in which three are isometries and
the rest are proper. The worth mentioning cases are those where we obtain the
group of matter collineations finite-dimensional even the energy-momentum
tensor is degenerate. These are either three, four, five or ten. Some examples
are constructed satisfying the constraints on the energy-momentum tensor.


title: Intersecting hypersurfaces, topological densities and Lovelock Gravity

abstract:
  Intersecting hypersurfaces in classical Lovelock gravity are studied
exploiting the description of the Lovelock Lagrangian as a sum of dimensionally
continued Euler densities. We wish to present an interesting geometrical
approach to the problem. The analysis allows us to deal most efficiently with
the division of space-time into a honeycomb network of cells produced by an
arbitrary arrangement of membranes of matter. We write the gravitational action
as bulk terms plus integrals over each lower dimensional intersection.
  The spin connection is discontinuous at the shared boundaries of the cells,
which are spaces of various dimensionalities. That means that at each
intersection there are more than one spin connections.
  We introduce a multi-parameter family of connections which interpolate
between the different connections at each intersection. The parameters live
naturally on a simplex. We can then write the action including all the
intersection terms in a simple way. The Lagrangian of Lovelock gravity is
generalized so as to live on the simplices as well. Each intersection term of
the action is then obtained as an integral over an appropriate simplex.
  Lovelock gravity and the associated topological (Euler) density are used as
an example of a more general formulation. In this example one finds that
singular sources up to a certain co-dimensionality naturally carry matter
without introducing conical or other singularities in spacetime geometry.


title: The Laser Astrometric Test of Relativity Mission

abstract:
  This paper discusses new fundamental physics experiment to test relativistic
gravity at the accuracy better than the effects of the 2nd order in the
gravitational field strength. The Laser Astrometric Test Of Relativity (LATOR)
mission uses laser interferometry between two micro-spacecraft whose lines of
sight pass close by the Sun to accurately measure deflection of light in the
solar gravity. The key element of the experimental design is a redundant
geometry optical truss provided by a long-baseline (100 m) multi-channel
stellar optical interferometer placed on the International Space Station. The
geometric redundancy enables LATOR to measure the departure from Euclidean
geometry caused by the solar gravity field to a very high accuracy. LATOR will
not only improve the value of the parameterized post-Newtonian (PPN) parameter
gamma to unprecedented levels of accuracy of 1 part in 1e8, it will also reach
ability to measure effects of the next post-Newtonian order (1/c^4) of light
deflection resulting from gravity's intrinsic non-linearity. The solar
quadrupole moment parameter, J2, will be measured with high precision, as well
as a variety of other relativistic. LATOR will lead to very robust advances in
the tests of fundamental physics: this mission could discover a violation or
extension of general relativity, or reveal the presence of an additional long
range interaction in the physical law. There are no analogs to the LATOR
experiment; it is unique and is a natural culmination of solar system gravity
experiments.


title: Gravitational Waves in Generalised Brans-Dicke Theory

abstract:
  We have solved cosmological gravitational Wave(GW)equation in the frame work
of Generalised Brans-Dicke(GBD) theory for all epochs of the Universe.The
solutions are expressed in terms of the present value of the Brans-Dicke
coupling parameter $\omega(\phi)$.It is seen that the solutions represent
travelling growing modes for negative values of $\omega_{0}$ for all epochs of
the Universe.


title: Dirac Equation in Standard Cosmological Models

abstract:
  The time equation associated to the Dirac Equation (DE) is studied for the
radiation-dominated Friedmann-Robertson-Walker (FRW) universe. The results are
analysed for small and large values of time. We also incorporate the
corrections of the paper studied by Zecca [1] for the matter-dominated FRW
universe.


title: Some Mathematical Issues Pertaining to Translational Gauge Theories

abstract:
  Some mathematical aspects of using the translation group as an internal
symmetry group in a gauge field theory are presented and discussed. The
traditional manner in which gravitation can be accounted for by the
introduction of a global frame field on a parallelizable spacetime is reviewed.
It is then discussed in the more general context of a global frame field on the
bundle of linear frames. In the process, the elements of variational field
theory for physical fields defined on G-structures are set down. It is
suggested that it is probably more proper to attribute gravitation to a
reduction of the bundle of linear frames to {e} -- at least over a generic
submanifold of spacetime -- than to a reduction to the Lorentz group since the
Lorentz group is more intrinsic to electromagnetism and gravitation has the
character of a "residual" symmetry of spacetime at the astrophysical level.


title:
Applying the q-algebras U'_q(so_n) to quantum gravity: towards
  q-deformed analog of SO(n) spin networks

abstract:
  Nonstandard q-deformed algebras U'_q(so_n), proposed a decade ago for the
needs of representation theory, essentially differ from the standard
Drinfeld-Jimbo quantum deformation of the algebras U(so_n) and possess with
regard to the latter a number of important advantages. We discuss possible
application of the q-algebras U'_q(so_n), within two different contexts of
quantum/q-deformed gravity: one concerns q-deforming of D-dimensional (D >= 3)
euclidean gravity, the other applies to 2+1 anti-De Sitter quantum gravity
(with space surface of genus g) in the approach of Nelson and Regge.


title: Purely magnetic spacetimes

abstract:
  Spacetimes in which the electric part of the Weyl tensor vanishes (relative
to some timelike unit vector field) are said to be purely magnetic. Examples of
purely magnetic spacetimes are known and are relatively easy to construct, if
no restrictions are placed on the energy-momentum tensor. However it has long
been conjectured that purely magnetic vacuum spacetimes (with or without a
cosmological constant) do not exist. The history of this conjecture is reviewed
and some advances made in the last year are described briefly. A generalisation
of this conjecture first suggested for type D vacuum spacetimes by Ferrando and
Saez is stated and proved in a number of special cases. Finally an approach to
a general proof of the conjecture is described using the Newman-Penrose
formalism based on a canonical null tetrad of the Weyl tensor.


title: Anisotropy in Bianchi-type brane cosmologies

abstract:
  The behavior near the initial singular state of the anisotropy parameter of
the arbitrary type, homogeneous and anisotropic Bianchi models is considered in
the framework of the brane world cosmological models. The matter content on the
brane is assumed to be an isotropic perfect cosmological fluid, obeying a
barotropic equation of state. To obtain the value of the anisotropy parameter
at an arbitrary moment an evolution equation is derived, describing the
dynamics of the anisotropy as a function of the volume scale factor of the
Universe. The general solution of this equation can be obtained in an exact
analytical form for the Bianchi I and V types and in a closed form for all
other homogeneous and anisotropic geometries. The study of the values of the
anisotropy in the limit of small times shows that for all Bianchi type
space-times filled with a non-zero pressure cosmological fluid, obeying a
linear barotropic equation of state, the initial singular state on the brane is
isotropic. This result is obtained by assuming that in the limit of small times
the asymptotic behavior of the scale factors is of Kasner-type. For brane
worlds filled with dust, the initial values of the anisotropy coincide in both
brane world and standard four-dimensional general relativistic cosmologies.


title: On the log correction to the black hole area law

abstract:
  Various approaches to black hole entropy yield the area law with logarithmic
corrections, many involving a coefficient 1/2, and some involving 3/2. It is
pointed out here that the standard quantum geometry formalism is not consistent
with 3/2 and favours 1/2.


title: Vacuum C-metric and the Gravitational Stark Effect

abstract:
  We study the vacuum C-metric and its physical interpretation in terms of the
exterior spacetime of a uniformly accelerating spherically - symmetric
gravitational source. Wave phenomena on the linearized C-metric background are
investigated. It is shown that the scalar perturbations of the linearized
C-metric correspond to the gravitational Stark effect. This effect is studied
in connection with the Pioneer anomaly.


title: Momentum and Angular Momentum in the Expanding Universe

abstract:
  A new approach has been used to evaluate the momentum and angular momentum of
the isotropic and homogeneous cosmological models. It is shown that the results
obtained for momentum exactly coincide with those already available in the
literature. However, the angular momentum expression coincides only for the
closed Friedmann model.


title: Force and Momentum in an Evolving Axisymmetric Universe Model

abstract:
  We take an axisymmetric rotating universe model by crossing with a time
dependent factor and evaluate its force and momentum in this evolving universe.
It is concluded that it behaves exactly like a Friedmann model. We also extend
this conclusion to the most general cosmological model.


title:
Effects of Force and Energy in an Evolving Universe with a Gravitational
  Source

abstract:
  Two models are given by crossing the Friedmann metrics with Schwarzschild and
Kerr metrics. In these evolving universes with a gravitational source, the
force four-vector and the corresponding potentials are evaluated.


title: Matter Collineations of Some Static Spherically Symmetric Spacetimes

abstract:
  We derive matter collineations for some static spherically symmetric
spacetimes and compare the results with Killing, Ricci and Curvature
symmetries. We conclude that matter and Ricci collineations are not, in
general, the same.


title: Relativistic Hydrodynamic Evolutions with Black Hole Excision

abstract:
  We present a numerical code designed to study astrophysical phenomena
involving dynamical spacetimes containing black holes in the presence of
relativistic hydrodynamic matter. We present evolutions of the collapse of a
fluid star from the onset of collapse to the settling of the resulting black
hole to a final stationary state. In order to evolve stably after the black
hole forms, we excise a region inside the hole before a singularity is
encountered. This excision region is introduced after the appearance of an
apparent horizon, but while a significant amount of matter remains outside the
hole. We test our code by evolving accurately a vacuum Schwarzschild black
hole, a relativistic Bondi accretion flow onto a black hole, Oppenheimer-Snyder
dust collapse, and the collapse of nonrotating and rotating stars. These
systems are tracked reliably for hundreds of M following excision, where M is
the mass of the black hole. We perform these tests both in axisymmetry and in
full 3+1 dimensions. We then apply our code to study the effect of the stellar
spin parameter J/M^2 on the final outcome of gravitational collapse of rapidly
rotating n = 1 polytropes. We find that a black hole forms only if J/M^2<1, in
agreement with previous simulations. When J/M^2>1, the collapsing star forms a
torus which fragments into nonaxisymmetric clumps, capable of generating
appreciable ``splash'' gravitational radiation.


title: Comoving suppression mechanism and cosmological constant problem

abstract:
  In this paper, we assume that the observer is fixed in a comoving frame of
reference with $g_{00}=\frac{\lambda}{\Lambda}$, where $\lambda$ and $\Lambda$
denote the comoving parameter and the cosmological constant, respectively. By
using the {\it comoving suppression mechanism} and {\it Mach's principle} (the
latter of which is used to determine the comoving parameter $\lambda$), we
calculate the vacuum energy density of quantum fluctuation field in the
above-mentioned comoving frame of reference. It is shown that in such a
comoving frame of reference, the cosmological constant will greatly decrease by
many orders of magnitude (if Mach's principle is applied to this calculation,
then it will be shown that $\Lambda$ is reduced by about 120 orders of
magnitude). Additionally, we briefly discuss the related topics such as the
varying observed speed of light ($\frac{{\rm d}c}{{\rm d}t}={\mathcal
O}(10^{-9}{\rm m/s}^{2})$) and the mystery of anomalous acceleration ($\sim
10^{-9}{\rm m/s}^{2}$) acquired by the Pioneer 10/11, Galileo and Ulysses
spacecrafts.


title: Propagation of Light in Doubly Special Relativity

abstract:
  In an attempt to clarify what is the velocity of a particle in doubly special
relativity, we solve Maxwell's equations invariant under the position-space
nonlinear Lorentz transformation proposed by Kimberly, Magueijo, and Medeiros.
We show that only the amplitude of the Maxwell wave, not the phase, is affected
by the nonlinearity of the transformation. Thus, although the Maxwell wave
appears to have infinitely large energy near the Planck time, the wave velocity
is the same as the conventional light velocity. Surprisingly, the velocity of
the Maxwell wave is not the same as the maximum signal velocity determined by
the null geodesic condition, which is infinitely large near the Planck time and
monotonically decreases in time to the conventional light velocity when time
approaches infinity. This implies that, depending on the position of the
particle in question, the light cone determined by Maxwell's equations may be
inside or outside the null cone determined by the null geodesic equation, which
may lead to the causality problem.


title: Non-Static Spherically Symmetric Perfect Fluid Solutions

abstract:
  We investigate solutions of Einstein field equations for the non-static
spherically symmetric perfect fluid case using different equations of state.
The properties of an exact spherically symmetric perfect fluid solutions are
obtained which contain shear. We obtain three different solutions out of these
one turns out to be an incoherent dust solution and the other two are stiff
matter solutions.


title: Force Behaviour in Radiation-Dominated Friedmann Universe

abstract:
  We consider radiation-dominated Friedmann universe and evaluate its force
four-vector and momentum. We analyse and compare the results with the already
evaluated for the matter-dominated Friedmann model. It turns out that the
results are physically acceptable.


title:
Non-trivial, static, geodesically complete space-times with a negative
  cosmological constant II. $n\ge 5$

abstract:
  We show that the recent work of Lee [23] implies existence of a large class
of new singularity-free strictly static Lorentzian vacuum solutions of the
Einstein equations with a negative cosmological constant. This holds in all
space-time dimensions greater than or equal to four, and leads both to strictly
static solutions and to black hole solutions. The construction allows in
principle for metrics (whether black hole or not) with Yang-Mills-dilaton
fields interacting with gravity through a Kaluza-Klein coupling.


title: Phenomenology of Space Time Fluctuations

abstract:
  Quantum gravitational effects may induce stochastic fluctuations in the
structure of space-time, to produce a characteristic foamy structure. It has
been known for some time now that these fluctuations may have observable
consequences for the propagation of cosmic ray particles over cosmological
distances. While invoked as a possible explanation for the detection of the
puzzling cosmic rays with energies in excess of the threshold for photopion
production (the so-called super-GZK particles), we demonstrate here that lower
energy observations may provide strong constraints on the role of a fluctuating
space-time structure. We note also that the same fluctuations, if they exist,
imply that some decay reactions normally forbidden by elementary conservation
laws, become kinematically allowed, inducing the decay of particles that are
seen to be stable in our universe. Due to the strength of the prediction, we
are led to consider this finding as the most severe constraint on the classes
of models that may describe the effects of gravity on the structure of
space-time. We also propose and discuss several potential loopholes of our
approach, that may affect our conclusions. In particular, we try to identify
the situations in which despite a fluctuating energy-momentum of the particles,
the reactions mentioned above may not take place.


title: Thin shells around traversable wormholes

abstract:
  Applying the Darmois-Israel thin shell formalism, we construct static and
dynamic thin shells around traversable wormholes. Firstly, by applying the
cut-and-paste technique we apply a linearized stability analysis to thin-shell
wormholes in the presence of a generic cosmological constant. We find that for
large positive values of the cosmological constant, i.e., the Schwarzschild-de
Sitter solution, the regions of stability significantly increase relatively to
the Schwarzschild case, analyzed by Poisson and Visser. Secondly, we construct
static thin shell solutions by matching an interior wormhole solution to a
vacuum exterior solution at a junction surface. In the spirit of minimizing the
usage of exotic matter we analyze the domains in which the weak and null energy
conditions are satisfied at the junction surface. The characteristics and
several physical properties of the surface stresses are explored, namely, we
determine regions where the sign of tangential surface pressure is positive and
negative (surface tension). An equation governing the behavior of the radial
pressure across the junction surface is deduced. Specific dimensions of the
wormhole, namely, the throat radius and the junction interface radius, are
found by taking into account the traversability conditions, and estimates for
the traversal time and velocity are also determined.


title:
Canonical Reduction of Gravity: from General Covariance to Dirac
  Observables and post-Minkowskian Background-Independent Gravitational Waves

abstract:
  The status of canonical reduction for metric and tetrad gravity in
space-times of the Christodoulou-Klainermann type, where the ADM energy rules
the time evolution, is reviewed. Since in these space-times there is an
asymptotic Minkowski metric at spatial infinity, it is possible to define a
Hamiltonian linearization in a completely fixed (non harmonic) 3-orthogonal
gauge without introducing a background metric. Post-Minkowskian
background-independent gravitational waves are obtained as solutions of the
linearized Hamilton equations.


title: Conserved currents in $D$-dimensional gravity and brane cosmology

abstract:
  In $D$-dimentional gravity on arbitrary curved backgrounds using proven
methods conserved currents, divergences of antisymmetrical tensor densities
(superpotentials), are constructed. These superpotentials have two remarkable
properties: they depend in an essential way on second derivatives in the
Lagrangian and are independent on divergences added to it. The conserved
currents are thus particulary well adapted to the case of perturbations in
Gauss-Bonett cosmological brane theories.


title: Bianchi IX Chaoticity: BKL Map and Continuous Flow

abstract:
  We analyze the Bianchi IX dynamics (Mixmaster) in view of its stochastic
properties; in the present paper we address either the original approach due to
Belinski, Khalatnikov and Lifshitz (BKL) as well as a Hamiltonian one relying
on the Arnowitt--Deser--Misner (ADM) reduction. We compare these two frameworks
and show how the BKL map is related to the geodesic flow associated with the
ADM dynamics. In particular, the link existing between the \textit{anisotropy
parameters} and the \textit{Kasner indices} is outlined.


title: Renormalization for spin foam models of quantum gravity

abstract:
  We give an introductory account to the renormalization of models without
metric background. We sketch the application to certain discrete models of
quantum gravity such as spin foam models.


title: Towards the deformation quantization of linearized gravity

abstract:
  We present a first attempt to apply the approach of deformation quantization
to linearized Einstein's equations. We use the analogy with Maxwell equations
to derive the field equations of linearized gravity from a modified Maxwell
Lagrangian which allows the construction of a Hamiltonian in the standard way.
The deformation quantization procedure for free fields is applied to this
Hamiltonian. As a result we obtain the complete set of quantum states and its
discrete spectrum.


title: Spacetime G-structures II: geometry of the ground states

abstract:
  This article is a continuation of a previous work that dealt with the
topological obstructions to the reductions of the bundle of linear frames on a
spacetime manifold for a particular chain of subgroups of GL(4). In this
article, the corresponding geometrical information, such as connections,
torsion, curvature, and automorphisms of the reductions will be discussed. The
details are elaborated upon for a certain sequence of reductions of GL(M) when
M is a four-dimensional spacetime manifold.


title:
Unified Field Theory From Enlarged Transformation Group. The Consistent
  Hamiltonian

abstract:
  A theory has been presented previously in which the geometrical structure of
a real four-dimensional space time manifold is expressed by a real orthonormal
tetrad, and the group of diffeomorphisms is replaced by a larger group. The
group enlargement was accomplished by including those transformations to
anholonomic coordinates under which conservation laws are covariant statements.
Field equations have been obtained from a variational principle which is
invariant under the larger group. These field equations imply the validity of
the Einstein equations of general relativity with a stress-energy tensor that
is just what one expects for the electroweak field and associated currents. In
this paper, as a first step toward quantization, a consistent Hamiltonian for
the theory is obtained. Some concluding remarks are given concerning the need
for further development of the theory. These remarks include discussion of a
possible method for extending the theory to include the strong interaction.


title:
On the Possibility of Measuring the Lense--Thirring Effect with a
  Lageos-Lageos II-Optis Mission

abstract:
  The possibility of performing post-Newtonian gravitoelectromagnetic
measurements with a joint LAGEOS-LAGEOS II-OPTIS space-based mission is
investigated


title: Radiation tails and boundary conditions for black hole evolutions

abstract:
  In numerical computations of Einstein's equations for black hole spacetimes,
it will be necessary to use approximate boundary conditions at a finite
distance from the holes. We point out here that ``tails,'' the inverse
power-law decrease of late-time fields, cannot be expected for such
computations. We present computational demonstrations and discussions of
features of late-time behavior in an evolution with a boundary condition.


title: Observables in 3-dimensional quantum gravity and topological invariants

abstract:
  In this paper we report some results on the expectation values of a set of
observables introduced for 3-dimensional Riemannian quantum gravity with
positive cosmological constant, that is, observables in the Turaev-Viro model.
Instead of giving a formal description of the observables, we just formulate
the paper by examples. This means that we just show how an idea works with
particular cases and give a way to compute 'expectation values' in general by a
topological procedure.


title:
Scalar and spinor perturbation to the most generalised Kerr-NUT
  space-time

abstract:
  We study the scalar and spinor perturbation to Kerr-NUT space-time, that is,
Klein-Gordan and Dirac equation therein. The equations are invariant under
duality transformation between the gravitational electric (M) and magnetic (l)
charge, radial and angular coordinate, and radial and angular component of the
field. We solve the equations separating into radial and angular parts.
Moreover, if sets of Klein-Gordan and Dirac equation and corresponding
solutions are known for Kerr space-time, under duality transformation, those in
dual Kerr space-time are shown to be achieved. A few examples of solution are
shown. We comment about the horizon and singularity conditions.


title: Neutrino asymmetry in presence of gravitational interaction

abstract:
  Propagation of fermions in curved space-time generates a gravitational
interaction due to the coupling between spin of the fermion and space-time
curvature. This gravitational interaction, which is an axial-vector appears as
the CPT violating term in the Lagrangian, can generate the neutrino asymmetry
in Universe. If the back-ground metric is spherically asymmetric, say, of
rotating black hole, the axisymmetric space-time of an expanding Universe, this
interaction as well as the neutrino asymmetry is non-zero.


title:
The Gravitomagnetic measurement of the angular momentum of celestial
  bodies

abstract:
  The asymmetry in the time delay for light rays propagating on opposite sides
of a spinning body is analyzed. A frequency shift in the perceived signals is
found. A practical procedure is proposed for evidencing the asymmetry, allowing
for a measurement of the specific angular momentum of the rotating mass. Orders
of magnitude are discussed.


title: The infinite curvature limit of AdS/CFT

abstract:
  Some kinematical speculations on the infinite curvature limit of the
conjectured duality of Maldacena between ten-dimensional strings living in
$AdS_5\times S_5$ and a ordinary four-dimensional quantum field theory, namely
${\cal{N}}=4$ super Yang-Mills with gauge group SU(N) are given.


title:
Late Time Analysis for Maximal Slicing of Reissner-Nordstr\"om Puncture
  Evolutions

abstract:
  We perform an analytic late time analysis for maximal slicing of the
Reissner-Nordstr\"om black hole spacetime. In particular, we discuss the
collapse of the lapse in terms of its late time behavior at the throat and at
the event horizon for the even and the puncture lapse. In the latter case we
also determine the value of the lapse at the puncture. Furthermore, in the
limit of late times slice stretching effects are studied as they arise for
maximal slicing of puncture evolutions. We perform numerical experiments for a
Schwarzschild black hole with puncture lapse and find agreement with the
analytical results.


title:
Physical and Geometric Interpretations of the Riemann Tensor, Ricci
  Tensor, and Scalar Curvature

abstract:
  Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and
Scalar Curvature are described. Also, the physical meanings of the Einstein
Tensor and Einstein's Equations are discussed. Finally a derivation of
Newtonian Gravity from Einstein's Equations is given.


title:
A boundary value problem for the five-dimensional stationary rotating
  black holes

abstract:
  We study the boundary value problem for the stationary rotating black hole
solutions to the five-dimensional vacuum Einstein equation. Assuming the two
commuting rotational symmetry and the sphericity of the horizon topology, we
show that the black hole is uniquely characterized by the mass, and a pair of
the angular momenta.


title: The double torus as a 2D cosmos: groups, geometry and closed geodesics

abstract:
  The double torus provides a relativistic model for a closed 2D cosmos with
topology of genus 2 and constant negative curvature. Its unfolding into an
octagon extends to an octagonal tessellation of its universal covering, the
hyperbolic space H^2. The tessellation is analysed with tools from hyperbolic
crystallography. Actions on H^2 of groups/subgroups are identified for SU(1,
1), for a hyperbolic Coxeter group acting also on SU(1, 1), and for the
homotopy group \Phi_2 whose extension is normal in the Coxeter group. Closed
geodesics arise from links on H^2 between octagon centres. The direction and
length of the shortest closed geodesics is computed.


title: A New Approach in Quantum Gravity and its Cosmological Implications

abstract:
  This work concerns a new reformulation of quantum geometrodynamics, which
allows to overcome a fundamental ambiguity contained in the canonical approach
to quantum gravity: the possibility of performing a (3+1)-slicing of
space-time, when the metric tensor is in a quantum regime. Our formulation
provides also a procedure to solve the problems connected to the so called
"frozen formalism". In particular we fix the reference frame (i.e. the lapse
function and the shift vector) by introducing the so called "kinematical
action"; as a consequence, the new hamiltonian constraints become parabolic, so
arriving to evolutive (Schroedinger-like) equations for the quantum dynamics.
The kinematical action can be interpreted as the action of a pressureless, but,
in general, non geodesic perfect fluid, so in the semi classical limit our
theory leads to the dynamics of the gravitational field coupled to a dust which
represents the material reference frame we have introduced fixing the slicing.
We also investigate the cosmological implications of the presence of the dust,
which, in the WKB limit of a cosmological problem, makes account for a "dark
matter" component and could play, at present time, a dynamical role.


title:
Experimental limits for low-frequency space-time fluctuations from
  ultrastable optical resonators

abstract:
  It has been suggested that space-time might undergo fluctuations because of
its intrinsic quantum nature. These fluctuations would pose a fundamental limit
to the ability of measuring distances with arbitrary precision, beyond any
limitations due to standard quantum mechanics. Laser interferometers have
recently been proposed as being suited for a search for the existence of
space-time fluctuations. Here we present results of a search for space-time
fluctuations of very low fluctuation frequencies, in the range from 1 microHz
to 0.5 Hz. Rigid optical interferometers made out of sapphire and operated at
cryogenic temperature were used. We find an upper limit of 1.10^-24 Hz^-1 for
the normalized distance noise spectral density at 6 microHz, and of 1.10^-28
Hz^-1 above 5 mHz, and establish an experimental limit for the parameter of a
recently proposed random-walk hypothesis.


title: Numerical Models of Spin-Orbital Coupling in Neutron Star Binaries

abstract:
  We present a new numerical scheme for solving the initial value problem for
quasiequilibrium binary neutron stars allowing for arbitrary spins. We
construct sequences of circular-orbit binaries of varying separation, keeping
the rest mass and circulation constant along each sequence. The spin angular
frequency of the stars is shown to vary along the sequence, a result that can
be derived analytically in the PPN limit. This spin effect, in addition to
leaving an imprint on the gravitational waveform emitted during binary
inspiral, is measurable in the electromagnetic signal if one of the stars is a
pulsar visible from Earth.


title:
A theory of evolving natural constants embracing Einstein's theory of
  general relativity and Dirac's large number hypothesis

abstract:
  Taking a hint from Dirac's large number hypothesis, we note the existence of
cosmic combined conservation laws that work to cosmologically long time. We
thus modify or generalize Einstein's theory of general relativity with fixed
gravitation constant $G$ to a theory for varying $G$, which can be applied to
cosmology without inconsistency, where a tensor arising from the variation of G
takes the place of the cosmological constant term. We then develop on this
basis a systematic theory of evolving natural constants $m_{e},m_{p},e,\hslash
,k_{B}$ by finding out their cosmic combined counterparts involving factors of
appropriate powers of $G$ that remain truly constant to cosmologically long
time. As $G$ varies so little in recent centuries, so we take these natural
constants to be constant.


title:
Metric Perturbation Approach to Gravitational Waves in Isotropic
  Cosmologies

abstract:
  Gravitational waves in isotropic cosmologies were recently studied using the
gauge-invariant approach of Ellis-Bruni. We now construct the linearised metric
perturbations of the background Robertson-Walker space-time which reproduce the
results obtained in that study. The analysis carried out here also facilitates
an easy comparison with Bardeen.


title: Surface embedding, topology and dualization for spin networks

abstract:
  Spin networks are graphs derived from 3nj symbols of angular momentum. The
surface embedding, the topology and dualization of these networks are
considered. Embeddings into compact surfaces include the orientable sphere S^2
and the torus T, and the not orientable projective space P^2 and Klein's bottle
K. Two families of 3nj graphs admit embeddings of minimal genus into S^2 and
P^2. Their dual 2-skeletons are shown to be triangulations of these surfaces.


title: Optimal filtering of the LISA data

abstract:
  The LISA time-delay-interferometry responses to a gravitational-wave signal
are rewritten in a form that accounts for the motion of the LISA constellation
around the Sun; the responses are given in closed analytic forms valid for any
frequency in the band accessible to LISA. We then present a complete procedure,
based on the principle of maximum likelihood, to search for stellar-mass binary
systems in the LISA data. We define the required optimal filters, the
amplitude-maximized detection statistic (analogous to the F statistic used in
pulsar searches with ground-based interferometers), and discuss the false-alarm
and detection probabilities. We test the procedure in numerical simulations of
gravitational-wave detection.


title: Loop quantization from a lattice gauge theory perspective

abstract:
  We present an interpretation of loop quantization in the framework of lattice
gauge theory. Within this context the lack of appropriate notions of effective
theories and renormalization group flow exhibit loop quantization as an
incomplete framework. This interpretation includes a construction of embedded
spin foam models which does not rely on the choice of any auxiliary structure
(e.g. triangulation) and has the following straightforward consequences: (1)
The values of the coupling constants need to be those of an UV-attractive fixed
point (2) The kinematics of canonical loop quantization and embedded spin foam
models are compatible (3) The weights assigned to embedded spin foams are
independent of the 2-polyhedron used to regularize the path integral, $|J|_x =
|J|_{x'}$ (4) An area spectrum with edge contributions proportional to $l_{\rm
PL}^2 (j+1 / 2)$ is not compatible with embedded spin foam models and/or
canonical loop quantization


title: Comparison of area spectra in loop quantum gravity

abstract:
  We compare two area spectra proposed in loop quantum gravity in different
approaches to compute the entropy of the Schwarzschild black hole. We describe
the black hole in general microcanonical and canonical area ensembles for these
spectra. We show that in the canonical ensemble, the results for all
statistical quantities for any spectrum can be reproduced by a heuristic
picture of Bekenstein up to second order. For one of these spectra - the
equally-spaced spectrum - in light of a proposed connection of the black hole
area spectrum to the quasinormal mode spectrum and following hep-th/0304135, we
present explicit calculations to argue that this spectrum is completely
consistent with this connection. This follows without requiring a change in the
gauge group of the spin degrees of freedom in this formalism from SU(2) to
SO(3). We also show that independent of the area spectrum, the degeneracy of
the area observable is bounded by $C A\exp(A/4)$, where $A$ is measured in
Planck units and $C$ is a constant of order unity.


title: Kerr black holes in horizon-generating form

abstract:
  New coordinates are given which describe non-degenerate Kerr black holes in
dual-null foliations based on the outer (or inner) horizons, generalizing the
Kruskal form for Schwarzschild black holes. The construction involves an area
radius for the transverse surfaces and a generalization of the Regge-Wheeler
radial function, both functions of the original radial coordinate only.


title:
Smoothness of time functions and the metric splitting of globally
  hyperbolic spacetimes

abstract:
  The folk questions in Lorentzian Geometry, which concerns the smoothness of
time functions and slicings by Cauchy hypersurfaces, are solved by giving
simple proofs of: (a) any globally hyperbolic spacetime $(M,g)$ admits a smooth
time function $\tau$ whose levels are spacelike Cauchy hyperfurfaces and, thus,
also a smooth global splitting $M= \R \times {\cal S}$, $g= - \beta(\tau,x)
d\tau^2 + \bar g_\tau $, (b) if a spacetime $M$ admits a (continuous) time
function $t$ (i.e., it is stably causal) then it admits a smooth (time)
function $\tau$ with timelike gradient $\nabla \tau$ on all $M$.


title:
Regularization of spherically symmetric evolution codes in numerical
  relativity

abstract:
  The lack of regularity of geometric variables at the origin is often a source
of serious problem for spherically symmetric evolution codes in numerical
relativity. One usually deals with this by restricting the gauge and solving
the hamiltonian constraint for the metric. Here we present a generic algorithm
for dealing with the regularization of the origin that can be used directly on
the evolution equations and that allows very general gauge choices. Our
approach is similar in spirit to the one introduced by Arbona and Bona for the
particular case of the Bona-Masso formulation. However, our algorithm is more
general and can be used with a wide variety of evolution systems.


title: Multipole Moments of Isolated Horizons

abstract:
  To every axi-symmetric isolated horizon we associate two sets of numbers,
$M_n$ and $J_n$ with $n = 0, 1, 2, ...$, representing its mass and angular
momentum multipoles. They provide a diffeomorphism invariant characterization
of the horizon geometry. Physically, they can be thought of as the `source
multipoles' of black holes in equilibrium. These structures have a variety of
potential applications ranging from equations of motion of black holes and
numerical relativity to quantum gravity.


title:
Elastic Stars in General Relativity: III. Stiff ultrarigid exact
  solutions

abstract:
  We present an equation of state for elastic matter which allows for purely
longitudinal elastic waves in all propagation directions, not just principal
directions. The speed of these waves is equal to the speed of light whereas the
transversal type speeds are also very high, comparable to but always strictly
less than that of light. Clearly such an equation of state does not give a
reasonable matter description for the crust of a neutron star, but it does
provide a nice causal toy model for an extremely rigid phase in a neutron star
core, should such a phase exist. Another reason for focusing on this particular
equation of state is simply that it leads to a very simple recipe for finding
stationary rigid motion exact solutions to the Einstein equations. In fact, we
show that a very large class of stationary spacetimes with constant Ricci
scalar can be interpreted as rigid motion solutions with this matter source. We
use the recipe to derive a static spherically symmetric exact solution with
constant energy density, regular centre and finite radius, having a nontrivial
parameter that can be varied to yield a mass-radius curve from which stability
can be read off. It turns out that the solution is stable down to a tenuity R/M
slightly less than 3. The result of this static approach to stability is
confirmed by a numerical determination of the fundamental radial oscillation
mode frequency. We also present another solution with outwards decreasing
energy density. Unfortunately, this solution only has a trivial scaling
parameter and is found to be unstable.


title: A brief remark on Unruh effect and causality

abstract:
  Unruh effect states that the vacuum of a quantum field theory on Minkovski
space-time looks like a thermal state for an eternal uniformly accelerated
observer. Adaptation to the non eternal case causes a serious problem: if the
thermalization of the vacuum depends on the lifetime of the observer, then in
principle the latest is able to deduce its lifetime from the measurement of the
temperature. This short note aims at underlining that time-energy uncertainty
relation allows to adapt Unruh effect to non-eternal observers without breaking
causality. In particular we show that our adaptation - the diamonds's
temperature- of Bisognano-Wichman approach to Unruh effect is causally
acceptable. This note is self-contained but it is fully meaningful as a
complement to gr-qc/0212074 as well as a comment on gr-qc/0306022.


title: Quantum Gravity Momentum Representation and Maximum Invariant Energy

abstract:
  We use the idea of the symmetry between the spacetime coordinates x^\mu and
the energy-momentum p^\mu in quantum theory to construct a momentum space
quantum gravity geometry with a metric s_{\mu\nu} and a curvature
P^\lambda_{\mu\nu\rho}. For a closed maximally symmetric momentum space with a
constant 3-curvature, the volume of the p-space admits a cutoff with an
invariant maximum momentum a. A Wheeler-DeWitt-type wave equation is obtained
in the momentum space representation. The vacuum energy density and the
self-energy of a charged particle are shown to be finite, and modifications of
the electromagnetic radiation density and the entropy density of a system of
particles occur for high frequencies.


title: Boyer-Finley equation and systems of hydrodynamic type

abstract:
  We reduce Boyer-Finley equation to a family of compatible systems of
hydrodynamic type, with characteristic speeds expressed in terms of spaces of
rational functions. The systems of hydrodynamic type are then solved by the
generalized hodograph method, providing solutions of the Boyer-Finley equation
including functional parameters.


title:
Squeezed Light for the Interferometric Detection of High Frequency
  Gravitational Waves

abstract:
  The quantum noise of the light field is a fundamental noise source in
interferometric gravitational wave detectors. Injected squeezed light is
capable of reducing the quantum noise contribution to the detector noise floor
to values that surpass the so-called Standard-Quantum-Limit (SQL). In
particular, squeezed light is useful for the detection of gravitational waves
at high frequencies where interferometers are typically shot-noise limited,
although the SQL might not be beaten in this case. We theoretically analyze the
quantum noise of the signal-recycled laser interferometric gravitational-wave
detector GEO600 with additional input and output optics, namely
frequency-dependent squeezing of the vacuum state of light entering the dark
port and frequency-dependent homodyne detection. We focus on the frequency
range between 1 kHz and 10 kHz, where, although signal recycled, the detector
is still shot-noise limited. It is found that the GEO600 detector with present
design parameters will benefit from frequency dependent squeezed light.
Assuming a squeezing strength of -6 dB in quantum noise variance, the
interferometer will become thermal noise limited up to 4 kHz without further
reduction of bandwidth. At higher frequencies the linear noise spectral density
of GEO600 will still be dominated by shot-noise and improved by a factor of
10^{6dB/20dB}~2 according to the squeezing strength assumed. The interferometer
might reach a strain sensitivity of 6x10^{-23} above 1 kHz (tunable) with a
bandwidth of around 350 Hz. We propose a scheme to implement the desired
frequency dependent squeezing by introducing an additional optical component to
GEO600s signal-recycling cavity.


title:
Effective connections and fields associated with shear-free null
  congruences

abstract:
  A special subclass of shear-free null congruences (SFC) is studied, with
tangent vector field being a repeated principal null direction of the Weyl
tensor. We demonstrate that this field is parallel with respect to an effective
affine connection which contains the Weyl nonmetricity and the skew symmetric
torsion. On the other hand, a Maxwell-like field can be directly associated
with any special SFC, and the electric charge for bounded singularities of this
field turns to be ``self-quantized''. Two invariant differential operators are
introduced which can be thought of as spinor analogues of the Beltrami
operators and both nullify the principal spinor of any special SFC.


title: Price's law, mass inflation, and strong cosmic censorship

abstract:
  Two aspects of the widely accepted heuristic picture of the final state of
gravitational collapse are the so-called Price law tails, describing the
asymptotics of the exterior region of the black hole that forms, and
Israel-Poisson's mass inflation scenario, describing the internal structure of
the black hole. (The latter scenario, if valid, would indicate that the maximal
development of initial data is extendible as a C^0 metric, putting into
question the validity of Penrose's strong cosmic censorship conjecture.) In
this talk, I shall discuss a series of rigorous results proving both Price's
law and the mass inflation scenario in an appropriate spherically symmetric
setting. The proof of Price's law is joint work with I. Rodnianski.


title:
The Pauli Exclusion Principle and SU(2) Versus SO(3) in Loop Quantum
  Gravity

abstract:
  Recent attempts to resolve the ambiguity in the loop quantum gravity
description of the quantization of area has led to the idea that $j=1$ edges of
spin-networks dominate in their contribution to black hole areas as opposed to
$j=1/2$ which would naively be expected. This suggests that the true gauge
group involved might be SO(3) rather than SU(2) with attendant difficulties. We
argue that the assumption that a version of the Pauli principle is present in
loop quantum gravity allows one to maintain SU(2) as the gauge group while
still naturally achieving the desired suppression of spin-1/2 punctures. Areas
come from $j=1$ punctures rather than $j=1/2$ punctures for much the same
reason that photons lead to macroscopic classically observable fields while
electrons do not.


title: Normal forces in stationary spacetimes

abstract:
  For geodesic motion of a particle in a stationary spacetime the $U_0$
component of particle 4-velocity is constant and is considered to be a
conserved mechanical energy. We show that this concept of a conserved
mechanical energy can be extended to particles that move under the influence of
a ``normal force,'' a force that, in the stationary frame, is orthogonal to the
motion of the particle. We illustrate the potential usefulness of the concept
with a simple example.


title: False Vacuum Lumps with the Fermionic Core

abstract:
  Stable gravitating lumps with a false vacuum core surrounded by the true
vacuum in a scalar field potential exist in the presence of fermions at the
core. These objects may exist in the universe at various scales.


title:
Magneto-dilatonic Bianchi-I cosmology: isotropization and singularity
  problems

abstract:
  We study the evolution of Bianchi-I space-times filled with a global
unidirectional electromagnetic field $F_{mn}$ interacting with a massless
scalar dilatonic field according to the law \Psi(\phi) F^{mn} F_{mn} where
\Psi(\phi) > 0 is an arbitrary function. A qualitative study, among other
results, shows that (i) the volume factor always evolves monotonically, (ii)
there exist models becoming isotropic at late times and (iii) the expansion
generically starts from a singularity but there can be special models starting
from a Killing horizon preceded by a static stage. All these features are
confirmed for exact solutions found for the usually considered case \Psi =
e^{2\lambda\phi}, \lambda = const. In particular, isotropizing models are found
for |\lambda| > 1/\sqrt{3}. In the special case |\lambda| = 1, which
corresponds to models of string origin, the string metric behaviour is studied
and shown to be qualitatively similar to that of the Einstein frame metric.


title:
Lorentzian Gromov Hausdorff theory as a tool for quantum gravity
  kinematics

abstract:
  This thesis start by a review of different approaches to classical and
quantum gravity. The main theme is Lorentzian Gromov Hausdorff theory which is
an active diffeomorphism invariant theory on the space of Lorentz spaces (think
about globally hyperbolic spacetimes). It is argued why such theory might be of
significant importance for Lorentzian approaches to quantum gravity such as
causal set theory and Lorentzian dynamical triangulations


title: On the Frame Fixing in Quantum Gravity

abstract:
  We provide a discussion about the necessity to fix the reference frame before
quantizing the gravitational field. Our presentation is based on stressing how
the 3+1-slicing of the space time becomes an ambiguous procedure as referred to
a quantum 4-metric.


title: Dark energy and matter from a five-dimensional Chern-Simons cosmology

abstract:
  A Friedman-Robertson-Walker cosmology arising from a five-dimensional
Chern-Simons (CS) theory for the group S0(1,5) coupled to matter is considered
as an alternative model for dark energy and matter. The four-dimensional
reduction describes an accelerating universe having a time dependent Newton's
coupling G and a positive cosmological constant. Five dimensional matter gives
rise to what we interprete as four dimensional ordinary plus dark matter and a
dark energy is provided by a cosmological constant term plus a fluid arising
from the CS coupling. The case of five dust is studied in detail, leading to
acceptable limits for most of the cosmological parameters considered, in the
context of an open non-flat universe. Nevertheless, a value for ${\dot G}/G $
which is two orders of magnitude higher than recent bounds is predicted.


title:
Are classically singular spacetimes quantum mechanically singular as
  well?

abstract:
  Are the classical singularities of general relativistic spacetimes, normally
defined by the incompleteness of classical particle paths, still singular if
quantum mechanical particles are used instead? This is the question we will
attempt to answer for particles obeying the quantum mechanical wave equations
for scalar, null vector and spinor particles. The analysis will be restricted
to certain static general relativistic spacetimes that classically contain the
mildest true classical singularities, quasiregular singularities.


title: Some fundamental issues in General Relativity and their resolution

abstract:
  The purpose of this article is to draw attention to some fundamental issues
in General Relativity. It is argued that these deep issues cannot be resolved
within the standard approach to general relativity that considers {\em every}
solution of Einstein's field equations to be of relevance to some, hypothetical
or not, physical situation. Hence, to resolve the considered problems of the
standard approach to general relativity, one must go beyond it. A possible
approach, a theory of everything, is outlined in the present article and will
be developed in details subsequently.


title: Geometrical Incompatibility of Quantum Measurements

abstract:
  The problem of quantization of general relativity is considered in the
framework of noncommutative differential geometry. Operator analogues for
interval, scalar curvature, values of the Einstein tensor are proposed. Quantum
measurements of these observables lead to a paradox: different procedures of
measurements can supply non equivalent geometrical pictures of space-time. A
concrete example of such situation is provided.


title: Einstein-Aether Waves

abstract:
  Local Lorentz invariance violation can be realized by introducing extra
tensor fields in the action that couple to matter. If the Lorentz violation is
rotationally invariant in some frame, then it is characterized by an
``aether'', i.e. a unit timelike vector field. General covariance requires that
the aether field be dynamical. In this paper we study the linearized theory of
such an aether coupled to gravity and find the speeds and polarizations of all
the wave modes in terms of the four constants appearing in the most general
action at second order in derivatives. We find that in addition to the usual
two transverse traceless metric modes, there are three coupled aether-metric
modes.


title: Translational Invariance and Noncommutative Field Theories

abstract:
  Implications of noncommutative field theories with commutator of the
coordinates of the form $[x^{\mu},x^{\nu}]=i \Lambda_{\quad \omega}^{\mu
\nu}x^{\omega}$with nilpotent structure constants are investigated. It is shown
that a free quantum field theory is not affected by noncommutativity, but that
invariance under translations is broken and hence the energy-momentum
conservation is not respected. The new energy-momentum law is expressed by a
Poincar\'e-invariant equation and the resulting kinematics is developed and
applied to the astrophysical puzzle related with the observed violation of the
GZK cutoff.


title:
Binary-pulsar tests of strong-field gravity and gravitational radiation
  damping

abstract:
  This talk reviews the constraints imposed by binary-pulsar data on gravity
theories, focusing on ``tensor-scalar'' ones which are the best motivated
alternatives to general relativity. We recall that binary-pulsar tests are
qualitatively different from solar-system experiments, because of
nonperturbative strong-field effects which can occur in compact objects like
neutron stars, and because one can observe the effect of gravitational
radiation damping. Some theories which are strictly indistinguishable from
general relativity in the solar system are ruled out by binary-pulsar
observations. During the last months, several impressive new experimental data
have been published. Today, the most constraining binary pulsar is no longer
the celebrated (Hulse-Taylor) PSR B1913+16, but the neutron star-white dwarf
system PSR J1141-6545. In particular, in a region of the ``theory space'',
solar-system tests were known to give the tightest constraints; PSR J1141-6545
is now almost as powerful. We also comment on the possible scalar-field effects
for the detection of gravitational waves with future interferometers. The
presence of a scalar partner to the graviton might be detectable with the LISA
space experiment, but we already know that it would have a negligible effect
for LIGO and VIRGO, so that the general relativistic wave templates can be used
securely for these ground interferometers.


title: A class of nonunitary models of Newtonian gravity and its unicity

abstract:
  A class of non-Markoffian nonunitary models for Newtonian gravity is
characterized as following from some rather natural hypotheses. One of such
models was previously obtained as the Newtonian limit of a classically stable
version of higher derivative gravity. They give rise to a mass threshold around
$10^{11}$ proton masses for gravity induced localization, to a breaking of
linearity and to the possible identification of thermodynamic and von Neumann
entropies.


title: A perspective on Quantum Gravity Phenomenology

abstract:
  I give a brief overview of some Quantum-Gravity-Phenomenology research lines,
focusing on studies of cosmic rays and gamma-ray bursts that concern the fate
of Lorentz symmetry in quantum spacetime. I also stress that the most valuable
phenomenological analyses should not mix too many conjectured new features of
quantum spacetime, and from this perspective it appears that it should be
difficult to obtain reliable guidance on the quantum-gravity problem from the
analysis of synchrotron radiation from the Crab nebula and from the analysis of
phase coherence of light from extragalactic sources. Forthcoming observatories
of ultra-high-energy neutrinos should provide several opportunities for clean
tests of some simple hypothesis for the short-distance structure of spacetime.
In particular, these neutrino studies, and some related cosmic-ray studies,
should provide access to the regime $E>\sqrt{m E_p}$.


title: Geometry, EFE's and Foundations for Brane Cosmology

abstract:
  I argue that GR Cauchy and Initial Value Problem mathematics is a valuable
source of ideas for braneworlds based on higher-dimensional Einstein field
equations.


title:
$R^2$ corrections to the cosmological dynamics of inflation in the
  Palatini formulation

abstract:
  We investigate the corrections to the inflationary cosmological dynamics due
to a $R^2$ term in the Palatini formulation which may arise as quantum
corrections to the effective Lagrangian in early universe. We found that the
standard Friedmann equation will not be changed when the scalar field is in the
potential energy dominated era. However, in the kinetic energy dominated era,
the standard Friedmann equation will be modified and in the case of closed and
flat universe, the Modified Friedmann equation will automatically require that
the initial kinetic energy density of the scalar field must be in sub-Planckian
scale.


title: Symmetries and assisted inflation in the DGP braneworld model

abstract:
  We present here the general transformation that leaves unchanged the form of
the field equations for perfect fluid cosmologies in the DGP braneworld model.
Specifically, a prescription for relating exact solutions with different
equations of state is provided, and the symmetries found can be used as
algorithms for generating new cosmological models from previously known ones.
We also present, implicitly, the first known exact DGP perfect fluid spacetime.
A particular case of the general transformation is used to illustrate the
crucial role played both by the number of scalar fields and the extra
dimensional effects in the occurrence of inflation. In particular, we see that
assisted inflation does not proceed at all times for one of the two possible
ways in which the brane can be embedded into the bulk.


title: Neutrino mixing contribution to the cosmological constant

abstract:
  We show that the non-perturbative vacuum structure associated with neutrino
mixing leads to a non-zero contribution to the value of the cosmological
constant. Such a contribution comes from the specific nature of the mixing
phenomenon. Its origin is completely different from the one of the ordinary
contribution of a massive spinor field. We estimate this neutrino mixing
contribution by using the natural cut--off appearing in the quantum field
theory formalism for neutrino mixing and oscillation.


title:
Regularization parameters for the self-force of a scalar particle in a
  general orbit about a Schwarzschild black hole

abstract:
  The interaction of a charged particle with its own field results in the
"self-force" on the particle, which includes but is more general than the
radiation reaction force. In the vicinity of the particle in curved spacetime,
one may follow Dirac and split the retarded field of the particle into two
parts, (1) the singular source field, ~q/r, and (2) the regular remainder
field. The singular source field exerts no force on the particle, and the
self-force is entirely caused by the regular remainder. We describe an
elementary multipole decomposition of the singular source field which allows
for the calculation of the self-force on a scalar-charged particle orbiting a
Schwarzschild black hole.


title:
Slowly Rotating General Relativistic Superfluid Neutron Stars with
  Relativistic Entrainment

abstract:
  Neutron stars that are cold enough should have two or more
superfluids/supercondutors in their inner crusts and cores. The implication of
superfluidity/superconductivity for equilibrium and dynamical neutron star
states is that each individual particle species that forms a condensate must
have its own, independent number density current and equation of motion that
determines that current. An important consequence of the quasiparticle nature
of each condensate is the so-called entrainment effect, i.e. the momentum of a
condensate is a linear combination of its own current and those of the other
condensates. We present here the first fully relativistic modelling of slowly
rotating superfluid neutron stars with entrainment that is accurate to the
second-order in the rotation rates. The stars consist of superfluid neutrons,
superconducting protons, and a highly degenerate, relativistic gas of
electrons. We use a relativistic $\sigma$ - $\omega$ mean field model for the
equation of state of the matter and the entrainment. We determine the effect of
a relative rotation between the neutrons and protons on a star's total mass,
shape, and Kepler, mass-shedding limit.


title: Cosmology in Flat Space-Time

abstract:
  Flat space-time has not heretofore been thought a suitable locus in which to
construct model universes because of the presumed necessity of incorporating
gravitation in such models and because of the historical lack of a theory of
gravitation in flat space-time. It is here shown that a Lorentz-invariant
theory of gravitation can be formulated by incorporating in it the mass-energy
relation. Such a theory correctly predicts the well-known relativistic effects
(advance of perihelion, gravitational refraction, gravitational red shift, echo
delay of sun-grazing radio signals, and others). The equations of motion,
properly stated, are also seen to be identical to those of electromagnetism and
lead to the correct prediction of gravitational radiation. Therefore Milne's
kinematic model of the universe, mappable into his dynamical (or Newtonian)
model, offers a unique alternative to the general relativistic models which are
encumbered with both theoretically and observationally objectionable features.


title: Back Reaction from Trace Anomaly in RN-blackholes Evaporation

abstract:
  A model is proposed to describe a transition from a charged black hole of
mass $M$ and charge $Q$ to one of mass $\bar{M}$ and charge $\bar{Q}$. The
basic equations are derived from the non-vacuum Einstein field equations
sourced by the Coulomb field and by a null scalar field with a nonvanishing
trace anomaly. It is shown that the nonvanishing trace of the energy-momentum
tensor prevents the formation of a naked singularity.


title: Quantum long-range interactions in general relativity

abstract:
  We consider one-loop effects in general relativity which result in quantum
long-range corrections to the Newton law, as well as to the gravitational
spin-dependent and velocity-dependent interactions. Some contributions to these
effects can be interpreted as quantum corrections to the Schwarzschild and Kerr
metric.


title: Covariant Lyapunov Exponents for the Mixmaster

abstract:
  The dynamics of the Mixmaster Universe is analized in a covariant picture via
Misner--Chitre-like variables for an ADM Hamiltonian approach. The system
outcomes as isomorphic to a billiard on the Lobachevsky plane and Lyapunov
exponents are calculated explicitly.


title: Measuring random force noise for LISA aboard the LISA Pathfinder mission

abstract:
  The LTP (LISA Testflight Package), to be flown aboard the ESA / NASA LISA
Pathfinder mission, aims to demonstrate drag-free control for LISA test masses
with acceleration noise below 30 fm/s^2/Hz^1/2 from 1-30 mHz. This paper
describes the LTP measurement of random, position independent forces acting on
the test masses. In addition to putting an overall upper limit for all source
of random force noise, LTP will measure the conversion of several key
disturbances into acceleration noise and thus allow a more detailed
characterization of the drag-free performance to be expected for LISA.


title:
Travelling Magnetic Waves due to Plasma Surrounding a Slow Rotating
  Compact Gravitational Source

abstract:
  The magnetic field due to an axially symmetric, hot and highly conducting
plasma, taken as an ideal magnetohydrodynamic fluid, surrounding a slow
rotating compact gravitational object is studied within the context of
Einstein-Maxwell field equations. It is assumed that whereas the plasma is
effected by the background spacetime it does not effect the spacetime itself.
The Einstein-Maxwell equations are then solved for the magnetic field in a
comoving frame with the background spacetime described by the slow rotating
Kerr black hole spacetime. It is found that the solutions are magnetic waves
travelling along the azimuthal angle with velocity equal to the angular
velocity of a free falling intertial frame. These general solutions, when
applied to various particular cases of physical interest, show that for a fixed
value of the azimuthal angle the magnetic field is completely induced by the
dragging of the background spacetime.


title: Spin and Anholonomy in General Relativity

abstract:
  In the general case, torsion couples to the spin current of the Dirac field.
In General Relativity, the apparent torsion field to which the spin current of
the Dirac field couples is a mere manifestation of the tetrad anholonomy. Seen
from the tetrad frame itself, it has for components the anholonomy
coefficients. The latter represent mechanical characteristics of the frame. In
the teleparallel equivalent of General Relativity, this coefficient turns out
to be the only torsion present.


title:
Special relativity with two invariant scales: Motivation, Fermions,
  Bosons, Locality, and Critique

abstract:
  We present a Master equation for description of fermions and bosons for
special relativities with two invariant scales, SR2, (c and lambda_P). We
introduce canonically-conjugate variables (chi^0, chi) to (epsilon, pi) of
Judes-Visser. Together, they bring in a formal element of linearity and
locality in an otherwise non-linear and non-local theory. Special relativities
with two invariant scales provide all corrections, say, to the standard model
of the high energy physics, in terms of one fundamental constant, lambda_P. It
is emphasized that spacetime of special relativities with two invariant scales
carries an intrinsic quantum-gravitational character. In an addenda, we also
comment on the physical importance of a phase factor that the whole literature
on the subject has missed and present a brief critique of SR2. In addition, we
remark that the most natural and physically viable SR2 shall require
momentum-space and spacetime to be non-commutative with the non-commutativity
determined by the spin content and C, P, and T properties of the examined
representation space. Therefore, in a physically successful SR2, the notion of
spacetime is expected to be deeply intertwined with specific properties of the
test particle.


abstract:
  It is introduced a hypothesis that the gravitational potential in the
universe changes linearly with the time. This enables to explain the Hubble red
shift and the anomalous acceleration of Pioneer 10 and 11.


title: Quantizing Gravitational Collapse

abstract:
  I summarize some results obtained from a canonical quantization of
gravitational collapse. The quantization is carried out in Kuchar variables on
the LeMaitre-Tolman-Bondi family of spacetimes. I show how mass quantization,
the black hole entropy and Hawking radiation may be understood in these models.
Hawking radiation is obtained in the WKB approximation but the first order
quantum gravity correction makes the near-horizon spectrum non-thermal,
suggesting that unitarity is preserved. The quantization may be used to study
quantum gravity effects in collapse leading to the formation of both covered
and naked singularities.


title: Testing non-standard cosmological models with supernovae

abstract:
  In this work we study the magnitude-redshift relation of a non-standard
cosmological model. The model under consideration was firstly investigated
within a special case of metric-affine gravity (MAG) and was recently recovered
via different approaches by two other groups. Apart from the usual cosmological
parameters for pressure-less matter $\Omega_{\rm m}$, cosmological
constant/dark energy $\Omega_{\lambda}$, and radiation $\Omega_{\rm r}$ a new
density parameter $\Omega_\psi$ emerges. The field equations of the model
reduce to a system which is effectively given by the usual Friedmann equations
of general relativity, supplied by a correction to the energy density and
pressure in form of $\Omega_\psi$, which is related to the non-Riemannian
structure of the underlying spacetime. We search for the best-fit parameters by
using recent SN Ia data sets and constrain the possible contribution of a new
dark-energy like component at low redshifts, thereby we put an upper limit on
the presence of non-Riemannian quantities in the late stages of the universe.
In addition the impact of placing the data in redshift bins of variable size is
studied. The numerical results of this work also apply to several anisotropic
cosmological models which, on the level of the field equations, exhibit a
similar scaling behavior of the density parameters like our non-Riemannian
model.


title: Controlling the Growth of Constraints in Hyperbolic Evolution Systems

abstract:
  Motivated by the need to control the exponential growth of constraint
violations in numerical solutions of the Einstein evolution equations, two
methods are studied here for controlling this growth in general hyperbolic
evolution systems. The first method adjusts the evolution equations
dynamically, by adding multiples of the constraints, in a way designed to
minimize this growth. The second method imposes special constraint preserving
boundary conditions on the incoming components of the dynamical fields. The
efficacy of these methods is tested by using them to control the growth of
constraints in fully dynamical 3D numerical solutions of a particular
representation of the Maxwell equations that is subject to constraint
violations. The constraint preserving boundary conditions are found to be much
more effective than active constraint control in the case of this Maxwell
system.


title: Experimental Challenges for Quantum Gravity

abstract:
  The existence of a new fundamental scale may lead to modified dispersion
relations for particles at high energies. Such modifications seem to be
realized with the Planck scale in certain descriptions of quantum gravity. We
apply effective field theory to this problem and identify dimension 5 operators
that would lead to cubic modifications of dispersion relations for Standard
Model particles. We also discuss other issues related to this approach
including various experimental bounds on the strength of these interactions.
Further we sketch a scenario where mixing of these operators with dimensions 3
and 4 due to quantum effects is minimal.


title:
Induced quantum metric fluctuations and the validity of semiclassical
  gravity

abstract:
  We propose a criterion for the validity of semiclassical gravity (SCG) which
is based on the stability of the solutions of SCG with respect to quantum
metric fluctuations. We pay special attention to the two-point quantum
correlation functions for the metric perturbations, which contain both
intrinsic and induced fluctuations. These fluctuations can be described by the
Einstein-Langevin equation obtained in the framework of stochastic gravity.
Specifically, the Einstein-Langevin equation yields stochastic correlation
functions for the metric perturbations which agree, to leading order in the
large $N$ limit, with the quantum correlation functions of the theory of
gravity interacting with $N$ matter fields. The homogeneous solutions of the
Einstein-Langevin equation are equivalent to the solutions of the perturbed
semiclassical equation, which describe the evolution of the expectation value
of the quantum metric perturbations. The information on the intrinsic
fluctuations, which are connected to the initial fluctuations of the metric
perturbations, can also be retrieved entirely from the homogeneous solutions.
However, the induced metric fluctuations proportional to the noise kernel can
only be obtained from the Einstein-Langevin equation (the inhomogeneous term).
These equations exhibit runaway solutions with exponential instabilities. A
detailed discussion about different methods to deal with these instabilities is
given. We illustrate our criterion by showing explicitly that flat space is
stable and a description based on SCG is a valid approximation in that case.


title: A general thick brane supported by a scalar field

abstract:
  A thick Z_2-symmetric domain wall supported by a scalar field with an
arbitrary potential V(\phi) in 5D general relativity is considered as a
candidate brane world. We show that, under the global regularity requirement,
such a configuration (i) has always an AdS asymptotic far from the brane, (ii)
is only possible if V(\phi) has an alternating sign and (iii) V(\phi) satisfies
a certain fine-tuning type equality. The thin brane limit is well defined and
conforms to the Randall-Sundrum (RS2) brane world model if the asymptotic value
of V(\phi) (related to \Lambda, the effective cosmological constant) is kept
thickness-independent. Universality of such a transition is demonstrated using
as an example exact solutions for stepwise potentials of different shapes.
Also, due to scale invariance of the Einstein-scalar equations, any given
regular solution creates a one-parameter family of solutions with different
potentials. In such families, a thin brane limit does not exist while the ratio
\Lambda/(brane tension)^2 is thickness-independent and is in general different
from its value in the RS2 model.


title: Constraints on a new alternative model to dark energy

abstract:
  The recent type Ia supernova data suggest that the universe is accelerating
now and decelerated in recent past. This may provide the evidence that the
standard Friedmann equation needs to be modified. We analyze in detail a new
model in the context of modified Friedmann equation using the supernova data
published by the High-$z$ Supernova Search Team and the Supernova Cosmology
Project. The new model explains recent acceleration and past deceleration.
Furthermore, the new model also gives a decelerated universe in the future.


title: General framework of higher order gauge invariant perturbation theory

abstract:
  Based on the gauge invariant variables proposed in [K. Nakamura, Prog. Theor.
Phys. vol.110 (2003), 723.], general framework of the second order gauge
invariant perturbation theory on arbitrary background spacetime is considered.
We derived formulae of the perturbative Einstein tensor of each order, which
have the similar form to the definitions of gauge invariant variables for
arbitrary perturbative fields. As a result, each order Einstein equation is
necessarily given in terms of gauge invariant variables.


title:
Asymptotic expansions of the Cotton-York tensor on slices of stationary
  spacetimes

abstract:
  We discuss expansions for the Cotton-York tensor near infinity for arbitrary
slices of stationary spacetimes. From these expansions it follows directly that
a necessary condition for the existence of conformally flat slices in
stationary solutions is the vanishing of a certain quantity of quadrupolar
nature (obstruction). The obstruction is nonzero for the Kerr solution. Thus,
the Kerr metric admits no conformally flat slices. An analysis of higher orders
in the expansions of the Cotton-York tensor for solutions such that the
obstruction vanishes suggests that the only stationary solution admitting
conformally flat slices are the Schwarzschild family of solutions.


title:
Thermoelastic dissipation in inhomogeneous media: loss measurements and
  displacement noise in coated test masses for interferometric gravitational
  wave detectors

abstract:
  The displacement noise in the test mass mirrors of interferometric
gravitational wave detectors is proportional to their elastic dissipation at
the observation frequencies. In this paper, we analyze one fundamental source
of dissipation in thin coatings, thermoelastic damping associated with the
dissimilar thermal and elastic properties of the film and the substrate. We
obtain expressions for the thermoelastic dissipation factor necessary to
interpret resonant loss measurements, and for the spectral density of
displacement noise imposed on a Gaussian beam reflected from the face of a
coated mass. The predicted size of these effects is large enough to affect the
interpretation of loss measurements, and to influence design choices in
advanced gravitational wave detectors.


title: Eigenmodes of Dodecahedral space

abstract:
  Cosmological models where spatial sections are the Poincar\'e dodecahedral
space D have been recently invoked to give an account of the lower modes of the
angular anisotropies of the cosmic microwave background. Further explorations
of this possibility require the knowledge of the eigenmodes of the Laplacian of
D. Only the first modes have been calculated numerically. Here we give an
explicit form for these modes up to arbitrary order, in term of eigenvectors of
a small rank matrix, very easy to calculate numerically. As an illustration we
give the first modes, up to the eigenvalue $-k (k+2)$ for $k=62$. These results
are obtained by application of a more general method (presented in a previous
work) which allows to express the properties of any eigenfunction of the
Laplacian of the three sphere under an arbitrary rotation of SO(4).


title: Symmetries and observables in topological gravity

abstract:
  After a brief review of topological gravity, we present a superspace approach
to this theory. This formulation allows us to recover in a natural manner
various known results and to gain some insight into the precise relationship
between different approaches to topological gravity. Though the main focus of
our work is on the vielbein formalism, we also discuss the metric approach and
its relationship with the former formalism.


title: Instability of Massive Scalar Fields in Kerr-Newman Spacetime

abstract:
  We investigate the instability of charged massive scalar fields in
Kerr-Newman spacetime. Due to the super-radiant effect of the background
geometry, the bound state of the scalar field is unstable, and its amplitude
grows in time. By solving the Klein-Gordon equation of the scalar field as an
eigenvalue problem, we numerically obtain the growth rate of the amplitude of
the scalar field. Although the dependence of the scalar field mass and the
scalar field charge on this growth rate agrees with the result of the analytic
approximation, the maximum value of the growth rate is three times larger than
that of the analytic approximation. We also discuss the effect of the electric
charge on the instability of the scalar field.


title:
A Metropolis-Hastings algorithm for extracting periodic gravitational
  wave signals from laser interferometric detector data

abstract:
  The Markov chain Monte Carlo methods offer practical procedures for detecting
signals characterized by a large number of parameters and under conditions of
low signal-to-noise ratio. We present a Metropolis-Hastings algorithm capable
of inferring the spin and orientation parameters of a neutron star from its
periodic gravitational wave signature seen by laser interferometric detectors


title: Isotropic cosmologies in Weyl geometry

abstract:
  We study homogeneous and isotropic cosmologies in a Weyl spacetime. We show
that for homogeneous and isotropic spacetimes, the field equations can be
reduced to the Einstein equations with a two-fluid source. We write the
equations as a two-dimensional dynamical system and analyze the qualitative,
asymptotic behavior of the models. We examine the possibility that in certain
theories the Weyl 1-form may give rise to a late accelerated expansion of the
Universe and conclude that such behaviour is not met as a generic feature of
the simplest cosmologies.


title:
Gravitational waves from axisymmetric rotating stellar core collapse to
  a neutron star in full general relativity

abstract:
  Axisymmetric numerical simulations of rotating stellar core collapse to a
neutron star are performed in the framework of full general relativity. The
so-called Cartoon method, in which the Einstein field equations are solved in
the Cartesian coordinates and the axisymmetric condition is imposed around the
$y=0$ plane, is adopted. The hydrodynamic equations are solved in the
cylindrical coordinates (on the $y=0$ plane in the Cartesian coordinates) using
a high-resolution shock-capturing scheme with the maximum grid size
$(2500,2500)$. A parametric equation of state is adopted to model collapsing
stellar cores and neutron stars following Dimmelmeier et al. It is found that
the evolution of central density during the collapse, bounce, and formation of
protoneutron stars agree well with those in the work of Dimmelmeier et al. in
which an approximate general relativistic formulation is adopted. This
indicates that such approximation is appropriate for following axisymmetric
stellar core collapses and subsequent formation of protoneutron stars.
Gravitational waves are computed using a quadrupole formula. It is found that
the waveforms are qualitatively in good agreement with those by Dimmelmeier et
al. However, quantitatively, two waveforms do not agree well. Possible reasons
for the disagreement are discussed.


title: Covariant canonical formalism for four-dimensional BF theory

abstract:
  The covariant canonical formalism for four-dimensional BF theory is
performed. The aim of the paper is to understand in the context of the
covariant canonical formalism both the reducibility that some first class
constraints have in Dirac's canonical analysis and also the role that
topological terms play. The analysis includes also the cases when both a
cosmological constant and the second Chern character are added to the pure BF
action. In the case of the BF theory supplemented with the second Chern
character, the presymplectic 3-form is different to the one of the BF theory in
spite of the fact both theories have the same equations of motion while on the
space of solutions they both agree to each other. Moreover, the analysis of the
degenerate directions shows some differences between diffeomorphisms and
internal gauge symmetries.


title: The ACIGA Data Analysis programme

abstract:
  The Data Analysis programme of the Australian Consortium for Interferometric
Gravitational Astronomy (ACIGA) was set up in 1998 by the first author to
complement the then existing ACIGA programmes working on suspension systems,
lasers and optics, and detector configurations. The ACIGA Data Analysis
programme continues to contribute significantly in the field; we present an
overview of our activities.


title:
Graded algebraic structure in the canonical formulation of N = 3 chiral
  supergravity

abstract:
  We focus on N = 3 chiral supergravity (SUGRA) which is the lowest N theory
involving a spin-1/2 field, and derive the Ashtekar's canonical formulation of
N = 3 SUGRA starting with the chiral Lagrangian constructed by closely
following the standard SUGRA. The polynomiality of constraints in terms of
canonical variables and the graded algebraic structure of constraints are
discussed in the canonical formulation. In particular, we show the
polynomiality of the {\it rescaled} right- and left-handed SUSY constraints by
a nonpolynomial factor. And also we show the graded algebraic structure of
Osp(3/2) in the constraint algebra by calculating the Poisson brackets of
Gauss, SU(2) gauge and right-handed SUSY constraints, although the algebra
among only those three types of constraints does not closed.


title: On Gauss-Bonnet black hole entropy

abstract:
  We investigate the entropy of black holes in Gauss-Bonnet and Lovelock
gravity using the Noether charge approach, in which the entropy is given as the
integral of a suitable (n-2) form charge over the event horizon. We compare the
results to those obtained in other approaches. We also comment on the
appearance of negative entropies in some cases, and show that there is an
additive ambiguity in the definition of the entropy which can be appropriately
chosen to avoid this problem.


title: The cosmic censor conjecture: Is it generically violated?

abstract:
  It has been recently argued by Hertog, Horowitz and Maeda, that generic
reasonable initial data in asymptotically anti deSitter, spherically symmetric,
space-times within an Einstein-Higgs theory, will evolve toward a naked
singularity, in clear violation of the cosmic censor conjecture. We will argue
that there is a logical and physically plausible loophole in the argument and
that the numerical evidence in a related problem suggests that this loophole is
in fact employed by physics.


title: An exact self-similar solution for an expanding ball of radiation

abstract:
  We give an exact solution of the $5D$ Einstein equations which in 4D can be
interpreted as a spherically symmetric dissipative distribution of matter, with
heat flux, whose effective density and pressure are nonstatic, nonuniform, and
satisfy the equation of state of radiation. The matter satisfies the usual
energy and thermodynamic conditions. The energy density and temperature are
related by the Stefan-Boltzmann law. The solution admits a homothetic Killing
vector in $5D$, which induces the existence of self-similar symmetry in 4D,
where the line element as well as the dimensionless matter quantities are
invariant under a simple "scaling" group.


title:
The gravitating perfect fluid-scalar field equations: quintessence and
  tachyonic

abstract:
  The system consisting of a self gravitating perfect fluid and scalar field is
considered in detail. The scalar fields considered are the quintessence and
``tachyonic'' forms which have important application in cosmology. Mathematical
properties of the general system of equations are studied including the
algebraic and differential identities as well as the eigenvalue structure. The
Cauchy problem for both quintessence and the tachyon is presented. We discuss
the initial constraint equations which must be satisfied by the initial data. A
Cauchy evolution scheme is presented in the form of a Taylor series about the
Cauchy surface. Finally, a simple numerical example is provided to illustrate
this scheme.


title: Electronic contribution to the oscillations of a gravitational antenna

abstract:
  We carefully analyse the contribution to the oscillations of a metallic
gravitational antenna due to the interaction between the electrons of the bar
and the incoming gravitational wave. To this end, we first derive the total
microscopic Hamiltonian of the wave-antenna system and then compute the
contribution to the attenuation factor due to the electron-graviton
interaction. As compared to the ordinary damping factor, which is due to the
electron viscosity, this term turns out to be totally negligible. This result
confirms that the only relevant mechanism for the interaction of a
gravitational wave with a metallic antenna is its direct coupling with the bar
normal modes.


title: The moduli space of isometry classes of globally hyperbolic spacetimes

abstract:
  This is the last article in a series of three initiated by the second author.
We elaborate on the concepts and theorems constructed in the previous articles.
In particular, we prove that the GH and the GGH uniformities previously
introduced on the moduli space of isometry classes of globally hyperbolic
spacetimes are different, but the Cauchy sequences which give rise to
well-defined limit spaces coincide. We then examine properties of the strong
metric introduced earlier on each spacetime, and answer some questions
concerning causality of limit spaces. Progress is made towards a general
definition of causality, and it is proven that the GGH limit of a Cauchy
sequence of $\mathcal{C}^{\pm}_{\alpha}$, path metric Lorentz spaces is again a
$\mathcal{C}^{\pm}_{\alpha}$, path metric Lorentz space. Finally, we give a
necessary and sufficient condition, similar to the one of Gromov for the
Riemannian case, for a class of Lorentz spaces to be precompact.


title: Tensor and spin representations of SO(4) and discrete quantum gravity

abstract:
  Starting from the defining transformations of complex matrices for the SO(4)
group, we construct the fundamental representation and the tensor and spinor
representations of the group SO(4). Given the commutation relations for the
corresponding algebra, the unitary representations of the group in terms of the
generalized Euler angles are constructed. These mathematical results help us to
a more complete description of the Barrett-Crane model in Quantum Gravity. In
particular a complete realization of the weight function for the partition
function is given and a new geometrical itnerpretation of the asymptotic limit
for the Regge action is presented.