title:
TDIR: Time-Delay Interferometric Ranging for Space-Borne
  Gravitational-Wave Detectors

abstract:
  Space-borne interferometric gravitational-wave detectors, sensitive in the
low-frequency (mHz) band, will fly in the next decade. In these detectors, the
spacecraft-to-spacecraft light-travel times will necessarily be unequal and
time-varying, and (because of aberration) will have different values on up- and
down-links. In such unequal-armlength interferometers, laser phase noise will
be canceled by taking linear combinations of the laser-phase observables
measured between pairs of spacecraft, appropriately time-shifted by the light
propagation times along the corresponding arms. This procedure, known as
time-delay interferometry (TDI), requires an accurate knowledge of the
light-time delays as functions of time. Here we propose a high-accuracy
technique to estimate these time delays and study its use in the context of the
Laser Interferometer Space Antenna (LISA) mission. We refer to this ranging
technique, which relies on the TDI combinations themselves, as Time-Delay
Interferometric Ranging (TDIR). For every TDI combination, we show that, by
minimizing the rms power in that combination (averaged over integration times
$\sim 10^4$ s) with respect to the time-delay parameters, we obtain estimates
of the time delays accurate enough to cancel laser noise to a level well below
the secondary noises. Thus TDIR allows the implementation of TDI without the
use of dedicated inter-spacecraft ranging systems, with a potential
simplification of the LISA design. In this paper we define the TDIR procedure
formally, and we characterize its expected performance via simulations with the
\textit{Synthetic LISA} software package.


title:
Automorphisms and a Cartography of the Solution Space for Vacuum Bianchi
  Cosmologies: The Type III Case

abstract:
  The theory of symmetries of systems of coupled, ordinary differential
equations (ODE's) is used to develop a concise algorithm for cartographing the
space of solutions to vacuum Bianchi Einstein's Field Equations (EFE). The
symmetries used are the well known automorphisms of the Lie algebra for the
corresponding isometry group of each Bianchi Type, as well as the scaling and
the time eparameterization symmetry. Application of the method to Type III
results in: a) the recovery of all known solutions without prior assumption of
any extra symmetry, b) the enclosure of the entire unknown part of the solution
space into a single, second order ODE in terms of one dependent variable and c)
a partial solution to this ODE. It is also worth-mentioning the fact that the
solution space is seen to be naturally partitioned into three distinct,
disconnected pieces: one consisting of the known Siklos (pp-wave) solution,
another occupied by the Type III member of the known Ellis-MacCallum family and
the third described by the aforementioned ODE in which an one parameter
subfamily of the known Kinnersley geometries resides. Lastly, preliminary
results reported show that the unknown part of the solution space for other
Bianchi Types is described by a strikingly similar ODE, pointing to a natural
operational unification as far as the problem of solving the cosmological EFE's
is concerned.


title: Geodesic behavior of sudden future singularities

abstract:
  In this paper we analyze the effect of recently proposed classes of sudden
future singularities on causal geodesics of FLRW spacetimes. Geodesics are
shown to be extendible and just the equations for geodesic deviation are
singular, although tidal forces are not strong enough to produce a Big Rip. For
the sake of completeness, we compare with the typical sudden future
singularities of phantom cosmologies.


title: Quantum resolution of black hole singularities

abstract:
  We study the classical and quantum theory of spherically symmetric spacetimes
with scalar field coupling in general relativity. We utilise the canonical
formalism of geometrodynamics adapted to the Painleve-Gullstrand coordinates,
and present a new quantisation of the resulting field theory. We give an
explicit construction of operators that capture curvature properties of the
spacetime and use these to show that the black hole curvature singularity is
avoided in the quantum theory.


title: The Dynamics of Inhomogeneous Cosmologies

abstract:
  In this thesis we investigate cosmological models more general than the
isotropic and homogeneous Friedmann-Lemaitre models. We focus on cosmologies
with one spatial degree of freedom, whose matter content consists of a perfect
fluid and the cosmological constant. We formulate the Einstein field equations
as a system of quasilinear first order partial differential equations, using
scale-invariant variables.
  The primary goal is to study the dynamics in the two asymptotic regimes, i.e.
near the initial singularity and at late times. We highlight the role of
spatially homogeneous dynamics as the background dynamics, and analyze the
inhomogeneous aspect of the dynamics. We perform a variety of numerical
simulations to support our analysis and to explore new phenomena.


title: The gravitational self-force

abstract:
  The self-force describes the effect of a particle's own gravitational field
on its motion. While the motion is geodesic in the test-mass limit, it is
accelerated to first order in the particle's mass. In this contribution I
review the foundations of the self-force, and show how the motion of a small
black hole can be determined by matched asymptotic expansions of a perturbed
metric. I next consider the case of a point mass, and show that while the
retarded field is singular on the world line, it can be unambiguously
decomposed into a singular piece that exerts no force, and a smooth remainder
that is responsible for the acceleration. I also describe the recent efforts,
by a number of workers, to compute the self-force in the case of a small body
moving in the field of a much more massive black hole. The motivation for this
work is provided in part by the Laser Interferometer Space Antenna, which will
be sensitive to low-frequency gravitational waves. Among the sources for this
detector is the motion of small compact objects around massive (galactic) black
holes. To calculate the waves emitted by such systems requires a detailed
understanding of the motion, beyond the test-mass approximation.


title: Braneworld black hole gravitational lens: Strong field limit analysis

abstract:
  In this paper, a braneworld black hole is studied as a gravitational lens,
using the strong field limit to obtain the positions and magnifications of the
relativistic images. Standard lensing and retrolensing situations are analyzed
in a unified setting, and the results are compared with those corresponding to
the Schwarschild black hole lens. The possibility of observing the strong field
images is discussed.


title: Gravitation and cosmology in brane-worlds

abstract:
  In brane-worlds, our universe is assumed to be a submanifold, or brane,
embedded in a higher-dimensional bulk spacetime. Focusing on scenarios with a
curved five-dimensional bulk spacetime, I discuss their gravitational and
cosmological properties.


title: Phenomenology of brane-world cosmological models

abstract:
  We present a brief review of brane-world models - models in which our
observable Universe with its standard matter fields is assumed as localized on
a domain wall (three-brane) in a higher dimensional surrounding (bulk)
spacetime. Models of this type arise naturally in M-theory and have been
intensively studied during the last years. We pay particular attention to the
covariant projection approach, the Cardassian scenario, to induced gravity
models, self-tuning models and the Ekpyrotic scenario. A brief discussion is
given of their basic properties and their connection with conventional FRW
cosmology.


title: Minisuperspace Models in Histories Theory

abstract:
  We study the Robertson-Walker minisuperspace model in histories theory,
motivated by the results that emerged from the histories approach to general
relativity. We examine, in particular, the issue of time-reparameterisation in
such systems. The model is quantised using an adaptation of reduced-state-space
quantisation. We finally discuss the classical limit, the implementation of
initial cosmological conditions and estimation of probabilities in the
histories context.


title: Invariants and nonlinear fields in Spinor Gravity

abstract:
  Spinor gravity is a functional integral formulation of gravity based only on
fundamental spinor fields. The vielbein and metric arise as composite objects.
Due to the lack of local Lorentz-symmetry new invariants in the effective
gravitational action lead to a modification of Einstein's equations. We discuss
different geometrical viewpoints of spinor gravity with particular emphasis on
nonlinear fields. The effective gravitational field equations arise as
solutions to the lowest order Schwinger-Dyson equation for spinor gravity.


title: Scattering of High Speed Particles in the Kerr Gravitational Field

abstract:
  We calculate the angles of deflection of high speed particles projected in an
arbitrary direction into the Kerr gravitational field. This is done by first
calculating the light-like boost of the Kerr gravitational field in an
arbitrary direction and then using this boosted gravitational field as an
approximation to the gravitational field experienced by a high speed particle.
In the rest frame of the Kerr source the angles of deflection experienced by
the high speed test particle can then easily be evaluated.


title: The Feynman propagator for spin foam quantum gravity

abstract:
  We link the notion causality with the orientation of the 2-complex on which
spin foam models are based. We show that all current spin foam models are
orientation-independent, pointing out the mathematical structure behind this
independence. Using the technology of evolution kernels for quantum
fields/particles on Lie groups/homogeneous spaces, we construct a generalised
version of spin foam models, introducing an extra proper time variable and
prove that different ranges of integration for this variable lead to different
classes of spin foam models: the usual ones, interpreted as the quantum gravity
analogue of the Hadamard function of QFT or as a covariant definition of the
inner product between quantum gravity states; and a new class of causal models,
corresponding to the quantum gravity analogue of the Feynman propagator in QFT,
non-trivial function of the orientation data, and implying a notion of
''timeless ordering''.


title: On the mass of a Kerr-anti-de Sitter spacetime in D dimensions

abstract:
  We show how to compute the mass of a Kerr-anti-de Sitter spacetime with
respect to the anti-de Sitter background in any dimension, using a
superpotential which has been derived from standard Noether identities. The
calculation takes no account of the source of the curvature and confirms
results obtained for black holes via the first law of thermodynamics.


title: Addendum: Symmetries of the energy-momentum tensor

abstract:
  In recent papers [1-3], we have discussed matter symmetries of non-static
spherically symmetric spacetimes, static plane symmetric spacetimes and
cylindrically symmetric static spacetimes. These have been classified for both
cases when the energy-momentum tensor is non-degenerate and also when it is
degenerate. Here we add up some consequences and the missing references about
the Ricci tensor.


title: An expanding universe of spinning spheres

abstract:
  A novel but elementary geometric construction produces on the
seven-dimensional manifold of rotated spheres in Euclidean three-space a
finslerian geometry whose geodesics are interpreted as the paths of free,
spinning, spherical particles moving through de Sitter's expanding universe. A
particle of nonzero inertial rest mass typically follows a helical track and
exhibits behavior remindful of the phenomenon of ``Zitterbewegung'' of spinning
electrons first deduced by Schroedinger from Dirac's relativistic wave
equation. Its velocity vector and its spin vector precess about the axial
direction of the helix, with their projections onto that direction at all times
parallel or at all times antiparallel. Particles of zero rest mass follow
straight tracks at the speed of light with their spin vectors parallel or
antiparallel to their velocity vectors, thereby replicating behavior of
spinning photons predicted by the quantum theory of light.


title: Acoustic analogs of two-dimensional black holes

abstract:
  We present a general method for constructing acoustic analogs of the black
hole solutions of two-dimensional (2D) dilaton gravity. Because by dimensional
reduction every spherically symmetric, four-dimensional (4D) black hole admits
a 2D description, the method can be also used to construct analogue models of
4D black holes. We also show that after fixing the gauge degrees of freedom the
2D gravitational dynamics is equivalent to an one-dimensional fluid dynamics.
  This enables us to find a natural definition of mass $M$, temperature $T$ and
entropy $S$ of the acoustic black hole. In particular the first principle of
thermodynamics $dM=TdS$ becomes a consequence of the fluid dynamics equations.
We also discuss the general solutions of the fluid dynamics and two particular
cases, the 2D Anti-de sitter black hole and the 4D Schwarzschild black hole.


title:
Is the equivalence for the response of static scalar sources in the
  Schwarzschild and Rindler spacetimes valid only in four dimensions?

abstract:
  It was shown recently that in four dimensions scalar sources with fixed
proper acceleration minimally coupled to a massless Klein-Gordon field lead to
the same responses when they are (i) uniformly accelerated in Minkowski
spacetime (in the inertial vacuum) and (ii) static in the Schwarzschild
spacetime (in the Unruh vacuum). Here we show that this equivalence is broken
if the spacetime dimension is more than four.


title: Gravitational waves from neutron stars described by modern EOS

abstract:
  The frequencies and damping times of neutron star (and quark star)
oscillations have been computed using the most recent equations of state
available in the literature. We find that some of the empirical relations that
connect the frequencies and damping times of the modes to the mass and radius
of the star, and that were previously derived in the literature need to be
modified.


title: Ponzano-Regge model revisited II: Equivalence with Chern-Simons

abstract:
  We provide a mathematical definition of the gauge fixed Ponzano-Regge model
showing that it gives a measure on the space of flat connections whose volume
is well defined. We then show that the Ponzano-Regge model can be equivalently
expressed as Reshetikhin-Turaev evaluation of a colored chain mail link based
on D(SU(2)): a non compact quantum group being the Drinfeld double of SU(2) and
a deformation of the Poincare algebra. This proves the equivalence between spin
foam quantization and Chern-Simons quantization of three dimensional gravity
without cosmological constant. We extend this correspondence to the computation
of expectation value of physical observables and insertion of particles.


title: Singularity-free Bianchi spaces with nonlinear electrodynamics

abstract:
  In this paper we present an analysis to determine the existence of
singularities in spatially homogeneous anisotropic universes filled with
nonlinear electromagnetic radiation. These spaces are conformal to Bianchi
spaces admitting a three parameter group of motions G$_3$. For these models we
study geodesic completeness. It is shown that with nonlinear electromagnetic
field some of the Bianchi spaces are geodesically complete, like G$_3$IX and
G$_3$VIII; however, completeness depends on the curvature of the space. When
certain topology is assumed, Bianchi G$_3$IX presents geodesics that are
imprisoned. It is surprising that in the linear limit (Maxwell field) the
spacetimes are singularity-free even if the curvature parameter is zero.


title:
de Sitter inflationary expansion from a noncompact KK theory: a
  nonperturbative quantum (scalar) field formalism

abstract:
  We develop a nonperturbative quantum scalar field formalism from a noncompact
Kaluza-Klein (KK) theory using the induced-matter theory of gravity during
inflation. We study the particular case of a de Sitter expansion for the
universe.


title: Naked Singularity formation in scalar field collapse

abstract:
  We construct here a class of collapsing scalar field models with a non-zero
potential, which result in a naked singularity as collapse end state. The weak
energy condition is satisfied by the collapsing configuration. It is shown that
physically it is the rate of collapse that governs either the black hole or
naked singularity formation as the final state for the dynamical evolution. It
is seen that the cosmic censorship is violated in dynamical scalar field
collapse.


title: Space Time Defects as a Source of Curvature and Torsion

abstract:
  Space time is described as a continuum four-dimensional medium similar to
ordinary elastic continua. Exploiting the analogy internal stress states are
considered. The internal ''stress'' is originated by the presence of defects.
The defects are described according to the typical Volterra process. The case
of a point defect in an otherwise isotropic four-dimensional medium is
discussed showing that the resulting metric tensor corresponds to an expanding
(or contracting) universe filled up with a non-zero energy-momentum density.


title: Quasi-local rotating black holes in higher dimension: geometry

abstract:
  With a help of a generalized Raychaudhuri equation non-expanding null
surfaces are studied in arbitrarily dimensional case. The definition and basic
properties of non-expanding and isolated horizons known in the literature in
the 4 and 3 dimensional cases are generalized. A local description of horizon's
geometry is provided. The Zeroth Law of black hole thermodynamics is derived.
The constraints have a similar structure to that of the 4 dimensional spacetime
case. The geometry of a vacuum isolated horizon is determined by the induced
metric and the rotation 1-form potential, local generalizations of the area and
the angular momentum typically used in the stationary black hole solutions
case.


title: Spherically Symmetric Quantum Horizons

abstract:
  Isolated horizon conditions specialized to spherical symmetry can be imposed
directly at the quantum level. This answers several questions concerning
horizon degrees of freedom, which are seen to be related to orientation, and
its fluctuations at the kinematical as well as dynamical level. In particular,
in the absence of scalar or fermionic matter the horizon area is an approximate
quantum observable. Including different kinds of matter fields allows to probe
several aspects of the Hamiltonian constraint of quantum geometry that are
important in inhomogeneous situations.


title: Gravity tests in the solar system and the Pioneer anomaly

abstract:
  We build up a new phenomenological framework associated with a minimal
generalization of Einsteinian gravitation theory. When linearity, stationarity
and isotropy are assumed, tests in the solar system are characterized by two
potentials which generalize respectively the Newton potential and the parameter
$\gamma $ of parametrized post-Newtonian formalism. The new framework seems to
have the capability to account for the Pioneer anomaly besides other gravity
tests.


title:
A note on the non-existence of $\sigma$-model solitons in the 2+1
  dimensional AdS gravity

abstract:
  We show that the gravitating static soliton in the 2+1 dimensional O(3)
$\sigma$ model does not exist in the presence of a negative cosmological
constant.


title: Gauge fixing for the simulation of black hole spacetimes

abstract:
  I consider the initial-boundary-value-problem of nonlinear general
relativistic vacuum spacetimes, which today cannot yet be evolved numerically
in a satisfactory manner. Specifically, I look at gauge conditions, classifying
them into gauge evolution conditions and gauge fixing conditions. In this
terminology, a gauge fixing condition is a condition that removes all gauge
degrees of freedom from a system, whereas a gauge evolution condition
determines only the time evolution of the gauge condition, while the gauge
condition itself remains unspecified. I find that most of today's gauge
conditions are only gauge evolution conditions.
  I present a system of evolution equations containing a gauge fixing
condition, and describe an efficient numerical implementation using constrained
evolution. I examine the numerical behaviour of this system for several test
problems, such as linear gravitational waves or nonlinear gauge waves. I find
that the system is robustly stable and second-order convergent. I then apply it
to more realistic configurations, such as Brill waves or single black holes,
where the system is also stable and accurate.


title: Stress Tensor Correlators in the Schwinger-Keldysh Formalism

abstract:
  We express stress tensor correlators using the Schwinger-Keldysh formalism.
The absence of off-diagonal counterterms in this formalism ensures that the +-
and -+ correlators are free of primitive divergences. We use dimensional
regularization in position space to explicitly check this at one loop order for
a massless scalar on a flat space background. We use the same procedure to show
that the ++ correlator contains the divergences first computed by `t Hooft and
Veltman for the scalar contribution to the graviton self-energy.


title: Space-time Averages of Classical Physical Fields

abstract:
  A review on the main results concerning the algebraic and differential
properties of the averaging and coordination operators and the properties of
the space-time averages of macroscopic gravity is given. The algebraic and
differential properties of the covariant space-time averaging procedure by
means of using the parallel transportation averaging bivector operator are
analyzed. The structure of the pseudo-Riemannian space-time manifolds of
general relativity averaged by means of this procedure is discussed. A
comparison of both procedures is given and the directions of further
development of space-time averaging procedures of the physical classical fields
are outlined.


title: Perfect Fluid LRS Bianchi I with Time Varying Constants

abstract:
  It is investigated the behaviour of the ``constants'' $G,$ $c$ and $\Lambda $
in the framework of a perfect fluid LRS Bianchi I cosmological model. It has
been taken into account the effects of a $c-$variable into the curvature
tensor. Two exact cosmological solutions are investigated, arriving to the
conclusion that if $q<0$ (deceleration parameter) then $G,$ $c$ are growing
functions on time $t$ while $\Lambda $ is a negative decreasing function on
time.


title: Transonic Black Hole Accretion as Analogue System

abstract:
  Classical black hole analogues (alternatively, the analogue systems) are
fluid dynamical analogue of general relativistic black holes. Such analogue
effects may be observed when acoustic perturbations (sound waves) propagate
through a classical dissipation-less tran-sonic fluid. The acoustic horizon,
which resembles the actual black hole event horizon in many ways, may be
generated at the transonic point in the fluid flow. Acoustic horizon emits
quasi thermal phonon spectra, which is analogous to the actual Hawking
radiation, and possesses the temperature referred as the analogue Hawking
temperature, or simply, the analogue temperature.
  Transonic accretion onto astrophysical black holes is a very interesting
example of classical analogue system found naturally in the Universe. An
accreting black holes system as a classical analogue is unique in the sense
that only for such a system, both kind of horizons, the electromagnetic and the
acoustic (generated due to transonicity of accreting fluid) are simultaneously
present in the same system. Hence an accreting astrophysical black hole is the
ideal-most candidate to theoretically study and to compare the properties of
these two different kind of horizons. Also such system is unique in the aspect
that general relativistic spherical accretion onto the Schwarzschild black hole
represents the only classical analogue system found in the nature so far, where
the analogue Hawking temperature may be higher than the actual Hawking
temperature.


title:
Palatini formulation of the $R^{-1}$modified gravity with an
  additionally squared scalar curvature term

abstract:
  In this paper by deriving the Modified Friedmann equation in the Palatini
formulation of $R^2$ gravity, first we discuss the problem of whether in
Palatini formulation an additional $R^2$ term in Einstein's General Relativity
action can drive an inflation. We show that the Palatini formulation of $R^2$
gravity cannot lead to the gravity-driven inflation as in the metric formalism.
If considering no zero radiation and matter energy densities, we obtain that
only under rather restrictive assumption about the radiation and matter energy
densities there will be a mild power-law inflation $a(t)\sim t^2$, which is
obviously different from the original vacuum energy-like driven inflation. Then
we demonstrate that in the Palatini formulation of a more generally modified
gravity, i.e., the $1/R+R^2$ model that intends to explain both the current
cosmic acceleration and early time inflation, accelerating cosmic expansion
achieved at late Universe evolution times under the model parameters satisfying
$\alpha\ll\beta$.


title: Recent results in mathematical relativity

abstract:
  We review selected recent results concerning the global structure of
solutions of the vacuum Einstein equations. The topics covered include
quasi-local mass, strong cosmic censorship, non-linear stability, new
constructions of solutions of the constraint equations, improved understanding
of asymptotic properties of the solutions, existence of solutions with low
regularity, and construction of initial data with trapped surfaces or apparent
horizons.
  This is an expanded version of a plenary lecture, sponsored by Classical and
Quantum Gravity, held at the GR17 conference in Dublin in July 2004.


title: Reflection on event horizon for collapsing black holes

abstract:
  It was argued recently that there exists an unexpected phenomenon, the
reflection of incoming particles on the event horizon of black holes
(Kuchiev(2003)). This means that a particle approaching the black hole can
bounce back into the outside world due to those events that take part strictly
on the horizon. Previously the effect was discussed in relation to eternal
black holes. The present work shows that the effect exists for collapsing black
holes as well.


title: Results for the LISA Phase Measurement System Project

abstract:
  This article presents some of the more topical results of a study into the
LISA phase measurement system. This system is responsible for measuring the
phase of the heterodyne signal caused by the interference of the laser beams
between the local and far spacecraft. Interactions with the LISA systems that
surround the phase measurement system imply additional non-trivial requirements
on the phase measurement system.


title: Kasner generalization of Levi-Civita spacetime

abstract:
  We investigate some cylindrically symmetric nonstationary and nonstatic
solutions of Einstein field equations. We first study some physical properties
of a solution which can be considered as Kasner generalization of static
Levi-Civita vacuum solution. Then we generalize this metric to include a
solution where a space-time filled with null dust or a stiff fluid.


title: Primordial Density Perturbation in Effective Loop Quantum Cosmology

abstract:
  It is widely believed that quantum field fluctuation in an inflating
background creates the primeval seed perturbation which through subsequent
evolution leads to the observed large scale structure of the universe. The
standard inflationary scenario produces scale invariant power spectrum quite
generically but it produces, unless fine tuned, too large amplitude for the
primordial density perturbation than observed. Using similar techniques it is
shown that loop quantum cosmology induced inflationary scenario can produce
scale invariant power spectrum as well as small amplitude for the primordial
density perturbation without fine tuning. Further its power spectrum has a
qualitatively distinct feature which is in principle falsifiable by observation
and can distinguish it from the standard inflationary scenario.


title: Partial and Complete Observables for Hamiltonian Constrained Systems

abstract:
  We will pick up the concepts of partial and complete observables introduced
by Rovelli in order to construct Dirac observables in gauge systems. We will
generalize these ideas to an arbitrary number of gauge degrees of freedom.
Different methods to calculate such Dirac observables are developed. For
background independent field theories we will show that partial and complete
observables can be related to Kucha\v{r}'s Bubble Time Formalism. Moreover one
can define a non-trivial gauge action on the space of complete observables and
also state the Poisson brackets of these functions.
  Additionally we will investigate, whether it is possible to calculate Dirac
observables starting with partially invariant partial observables, for instance
functions, which are invariant under the spatial diffeomorphism group.


title: Geodesics in a Toroidal space-time

abstract:
  We take a three dimensional Euclidian metric in toroidal coordinates and
consider the corresponding Laplace equation. The simplest solution of this
equation is taken. Based on this we build a Weyl space-time. This space-time is
transformed to cylindrical coordinates. It is shown by using Mathematica that
Weyl equations in cylindrical coordinates are satisfied. Geodesic motion is
considered along the symmetric axis as well as along the radii of the
singularity, which is the cause of the space time.


title: Role of Modified Chaplygin Gas in Accelerated Universe

abstract:
  In this paper we have considered a model of modified Chaplygin gas and its
role in accelerating phase of the universe. We have assumed that the equation
of state of this modified model is valid from the radiation era to $\Lambda$CDM
model. We have used recently developed statefinder parameters in characterizing
different phase of the universe diagrammatically.


title:
Lambda-renormalized Einstein-Schrodinger theory with spin-0 and spin-1/2
  sources

abstract:
  The Einstein-Schrodinger theory is extended to include spin-0 and spin-1/2
sources, and the theory is derived from a Lagrangian density which allows other
fields to be easily added. The original theory is also modified by including a
cosmological constant caused by zero-point fluctuations. This cosmological
constant which multiplies the symmetric metric is assumed to be nearly
cancelled by Schrodinger's ``bare'' cosmological constant which multiplies the
nonsymmetric fundamental tensor, such that the total ``physical'' cosmological
matches measurement. We show that the resulting Lambda-renormalized
Einstein-Schrodinger theory closely approximates ordinary Einstein-Maxwell
theory and one-particle quantum mechanics. In particular, the field equations
match the ordinary Einstein and Maxwell equations except for additional terms
which are $<10^{-16}$ of the usual terms for worst-case field strengths and
rates-of-change accessible to measurement. We also show that the theory
predicts the exact Lorentz force equation and the exact Klein-Gordon and Dirac
equations. And the theory becomes exactly Einstein-Maxwell theory and
one-particle quantum mechanics in the limit as the cosmological constant from
zero-point fluctuations goes to infinity. Lastly, we discuss the merits of our
Lagrangian density compared to the Einstein-Maxwell Lagrangian density.


title:
Probing anisotropies of gravitational-wave backgrounds with a
  space-based interferometer: geometric properties of antenna patterns and
  their angular power

abstract:
  We discuss the sensitivity to anisotropies of stochastic gravitational-wave
backgrounds (GWBs) observed via space-based interferometer. In addition to the
unresolved galactic binaries as the most promising GWB source of the planned
Laser Interferometer Space Antenna (LISA), the extragalactic sources for GWBs
might be detected in the future space missions. The anisotropies of the GWBs
thus play a crucial role to discriminate various components of the GWBs. We
study general features of antenna pattern sensitivity to the anisotropies of
GWBs beyond the low-frequency approximation. We show that the sensitivity of
space-based interferometer to GWBs is severely restricted by the data
combinations and the symmetries of the detector configuration. The spherical
harmonic analysis of the antenna pattern functions reveals that the angular
power of the detector response increases with frequency and the detectable
multipole moments with effective sensitivity h_{eff} \sim 10^{-20} Hz^{-1/2}
may reach $\ell \sim$ 8-10 at $f \sim f_*=10$ mHz in the case of the single
LISA detector. However, the cross correlation of optimal interferometric
variables is blind to the monopole (\ell=0) intensity anisotropy, and also to
the dipole (\ell=1) in some case, irrespective of the frequency band. Besides,
all the self-correlated signals are shown to be blind to the odd multipole
moments (\ell=odd), independently of the frequency band.


title: Krein space quantization in curved and flat spacetimes

abstract:
  We reexamine in detail a canonical quantization method a la Gupta-Bleuler in
which the Fock space is built over a so-called Krein space. This method has
already been successfully applied to the massless minimally coupled scalar
field in de Sitter spacetime for which it preserves covariance. Here, it is
formulated in a more general context. An interesting feature of the theory is
that, although the field is obtained by canonical quantization, it is
independent of Bogoliubov transformations. Moreover no infinite term appears in
the computation of $T^{\mu\nu}$ mean values and the vacuum energy of the free
field vanishes: $<0|T^{00}|0>=0$. We also investigate the behaviour of the
Krein quantization in Minkowski space for a theory with interaction. We show
that one can recover the usual theory with the exception that the vacuum energy
of the free theory is zero.


title: Evolution equations for slowly rotating stars

abstract:
  We present a hyperbolic formulation of the evolution equations describing
non-radial perturbations of slowly rotating relativistic stars in the
Regge--Wheeler gauge. We demonstrate the stability preperties of the new
evolution set of equations and compute the polar w-modes for slowly rotating
stars.


title: Pioneer's Final Riddle

abstract:
  Launched more than thirty years ago and now drifting in space with no further
contact, the Pioneer 10 and 11 spacecraft are currently at the center of a
small but developing concern: are they under the influence of an anomalous
acceleration that reflects new, yet unknown physics, or merely experiencing
some unexpected technical problem ? The proposals vary from basic engineering
principles to extra spatial dimensions, but most probably an answer can only be
obtained after a dedicated mission is underway.


title: Coupling of radial and non-radial oscillations of Neutron stars

abstract:
  This is a progress report on our study of the coupling of first-order radial
and non-radial relativistic perturbations of a static spherical star. Our goal
is to investigate the effects of this coupling on the gravitational wave signal
of neutron stars. In particular, we are looking for the existence of resonances
and parametric amplifications, changes in the damping time of non-radial
oscillations, etc. To that end, we have developed a formalism that introduces
gauge invariant quantities to describe the coupling. Their equations have the
same structure as the equations for first-order non-radial perturbations plus
some source terms, which makes them very appealing for time domain studies.


title: Newman-Penrose quantities as valuable tools in astrophysical relativity

abstract:
  In this talk I will briefly outline work in progress in two different
contexts in astrophysical relativity, i.e. the study of rotating star
spacetimes and the problem of reliably extracting gravitational wave templates
in numerical relativity. In both cases the use of Weyl scalars and curvature
invariants helps to clarify important issues.


title: Self-Interaction and Gauge Invariance

abstract:
  A simple unified closed form derivation of the non-linearities of the
Einstein, Yang-Mills and spinless (e.g., chiral) meson systems is given. For
the first two, the non-linearities are required by locality and consistency; in
all cases, they are determined by the conserved currents associated with the
initial (linear) gauge invariance of the first kind. Use of first-order
formalism leads uniformly to a simple cubic self-interaction.


title:
On the reliability of the so far performed tests for measuring the
  Lense-Thirring effect with the LAGEOS satellites

abstract:
  In this paper we will show in detail that the performed attempts aimed at the
detection of the general relativistic Lense-Thirring effect in the
gravitational field of the Earth with the existing LAGEOS satellites are often
presented in an optimistic and misleading way which is inadequate for such an
important test of fundamental physics. E.g., in the latest reported measurement
of the gravitomagnetic shift with the nodes of the LAGEOS satellites and the
2nd generation GRACE-only EIGEN-GRACE02S Earth gravity model over an
observational time span of 11 years a 5-10% total accuracy is claimed at
1-3sigma, respectively. We will show that, instead, it might be 15-45%
(1-3sigma) if the impact of the secular variations of the even zonal harmonics
is considered as well.


title: Black hole quasinormal modes: hints of quantum gravity?

abstract:
  This is a short review of the quasinormal mode spectrum of Schwarzschild,
Reissner-Nordstrom and Kerr black holes. The summary includes previously
unpublished calculations of i) the eigenvalues of spin-weighted spheroidal
harmonics, and ii) quasinormal frequencies of extremal Reissner-Nordstrom black
holes.


title:
How Special Relativity Determines the Signs of the Nonrelativistic,
  Coulomb and Newtonian, Forces

abstract:
  We show that the empirical signs of the fundamental {\it static}
Coulomb/Newton forces are dictated by the seemingly unrelated requirement that
the photons/gravitons in the respective underlying Maxwell/Einstein physics be
stable. This linkage, which is imposed by special relativity, is manifested
upon decomposing the corresponding fields and sources in a gauge-invariant way,
and without appeal to static limits. The signs of these free field excitation
energies determine those of the instantaneous forces between sources; opposite
Coulomb/Newton signs are direct consequences of the Maxwell/Einstein free
excitations' odd/even spins.


title:
Observation results by the TAMA300 detector on gravitational wave bursts
  from stellar-core collapses

abstract:
  We present data-analysis schemes and results of observations with the TAMA300
gravitational-wave detector, targeting burst signals from stellar-core collapse
events. In analyses for burst gravitational waves, the detection and
fake-reduction schemes are different from well-investigated ones for a
chirp-wave analysis, because precise waveform templates are not available. We
used an excess-power filter for the extraction of gravitational-wave
candidates, and developed two methods for the reduction of fake events caused
by non-stationary noises of the detector. These analysis schemes were applied
to real data from the TAMA300 interferometric gravitational wave detector. As a
result, fake events were reduced by a factor of about 1000 in the best cases.
The resultant event candidates were interpreted from an astronomical viewpoint.
We set an upper limit of 2.2x10^3 events/sec on the burst gravitational-wave
event rate in our Galaxy with a confidence level of 90%. This work sets a
milestone and prospects on the search for burst gravitational waves, by
establishing an analysis scheme for the observation data from an
interferometric gravitational wave detector.


title:
Phenomenology for an extra-dimension from gravitational waves
  propagation on a Kaluza-Klein space-time

abstract:
  In the present work we analize the behavior of 5-dimensional gravitational
waves propagating on a Kaluza-Klein background and we face separately the two
cases in which respectively the waves are generated before and after the
process of dimensional compactification. We show that if the waves are
originated on a 5-d space-time which fulfills the principle of general
relativity, then the process of compactification can not reduce the dynamics to
the pure 4-dimensional scalar, vector and tensor degrees of freedom. In
particular, while the electromagnetic waves evolve independently, the scalar
and tensor fields couple to each other; this feature appears because, when the
gauge conditions are splitted, the presence of the scalar ripple prevents that
the 4-d gravitational waves are traceless. The phenomenological issue of this
scheme consists of an anomalous relative amplitude of the two independent
polarizations which characterize the 4-d gravitational waves. Such profile of
polarization amplitudes, if detected, would outline the extra-dimension in a
very reliable way, because a wave with non-zero trace can not arise from
ordinary matter sources. We discuss the above mentioned phenomenon either in
the case of a unit constant value of the background scalar component (when the
geodesic deviation is treated with precise outputs), and assuming such
background field as a dynamical degree (only qualitative conclusion are
provided here, because the details of the polarization amplitudes depend on the
choice of specific metric forms). Finally we perturb a real Kaluza-Klein theory
showing that in this context, while the electromagnetic waves propagate
independently, the 4-d gravitational waves preserve their ordinary structure,
while the scalar plays for them the role of source.


title: Mathematical Structure of Tetrad Equations for Vacuum Relativity

abstract:
  The tetrad partial differential equations formulated by Buchman and Bardeen
for vacuum gravity are shown to be well posed by calculation of the Cartan
characters of an associated exterior differential system. Gauge specializations
are discussed. A Cartan 4-form is found for this field theory, together with
its intrinsic version the Lagrangian density.


title:
The gravitational wave spectrum of non-axisymmetric, freely precessing
  neutron stars

abstract:
  Evidence for free precession has been observed in the radio signature of
several pulsars. Freely precessing pulsars radiate gravitationally at
frequencies near the rotation rate and twice the rotation rate, which for
rotation frequencies greater than $\sim 10$ Hz is in the LIGO band. In older
work, the gravitational wave spectrum of a precessing neutron star has been
evaluated to first order in a small precession angle. Here we calculate the
contributions to second order in the wobble angle, and we find that a new
spectral line emerges. We show that for reasonable wobble angles, the
second-order line may well be observable with the proposed advanced LIGO
detector for precessing neutron stars as far away as the galactic center.
Observation of the full second-order spectrum permits a direct measurement of
the star's wobble angle, oblateness, and deviation from axisymmetry, with the
potential to significantly increase our understanding of neutron star
structure.


title: Reduced Phase Space Quantization and Dirac Observables

abstract:
  In her recent work, Dittrich generalized Rovelli's idea of partial
observables to construct Dirac observables for constrained systems to the
general case of an arbitrary first class constraint algebra with structure
functions rather than structure constants. Here we use this framework and
propose a new way for how to implement explicitly a reduced phase space
quantization of a given system, at least in principle, without the need to
compute the gauge equivalence classes. The degree of practicality of this
programme depends on the choice of the partial observables involved. The
(multi-fingered) time evolution was shown to correspond to an automorphism on
the set of Dirac observables so generated and interesting representations of
the latter will be those for which a suitable preferred subgroup is realized
unitarily. We sketch how such a programme might look like for General
Relativity. We also observe that the ideas by Dittrich can be used in order to
generate constraints equivalent to those of the Hamiltonian constraints for
General Relativity such that they are spatially diffeomorphism invariant. This
has the important consequence that one can now quantize the new Hamiltonian
constraints on the partially reduced Hilbert space of spatially diffeomorphism
invariant states, just as for the recently proposed Master constraint
programme.


title: The Kantowski-Sachs Space-Time in Loop Quantum Gravity

abstract:
  We extend the ideas introduced in the previous work to a more general
space-time. In particular we consider the Kantowski-Sachs space time with space
section with topology $R \times S^2$. In this way we want to study a general
space time that we think to be the space time inside the horizon of a black
hole. In this case the phase space is four dimensional and we simply apply the
quantization procedure suggested by Loop Quantum Gravity and based on an
alternative to the Schroedinger representation introduced by H. Halvorson.
Through this quantization procedure we show that the inverse of the volume
density and the Schwarzschild curvature invariant are upper bounded and so the
space time is singularity free. Also in this case we can extend dynamically the
space time beyond the classical singularity.


title: Arbitrary Dimensional Schwarzschild-FRW Black Holes

abstract:
  The metric of arbitrary dimensional Schwarzschild black hole in the
background of Friedman-Robertson-Walker universe is presented in the cosmic
coordinates system. In particular, the arbitrary dimensional Schwarzschild-de
Sitter metric is rewritten in the Schwarzschild coordinates system and basing
on which the even more generalized higher dimensional Schwarzschild-de Sitter
metric with another extra dimensions is found. The generalized solution shows
that the cosmological constant may roots in the extra dimensions of space.


title: Effective refractive index tensor for weak field gravity

abstract:
  Gravitational lensing in a weak but otherwise arbitrary gravitational field
can be described in terms of a 3 x 3 tensor, the "effective refractive index".
If the sources generating the gravitational field all have small internal
fluxes, stresses, and pressures, then this tensor is automatically isotropic
and the "effective refractive index" is simply a scalar that can be determined
in terms of a classic result involving the Newtonian gravitational potential.
In contrast if anisotropic stresses are ever important then the gravitational
field acts similarly to an anisotropic crystal. We derive simple formulae for
the refractive index tensor, and indicate some situations in which this will be
important.


title:
An improved estimate of black hole entropy in the quantum geometry
  approach

abstract:
  A proper counting of states for black holes in the quantum geometry approach
shows that the dominant configuration for spins are distributions that include
spins exceeding one-half at the punctures. This raises the value of the Immirzi
parameter and the black hole entropy. However, the coefficient of the
logarithmic correction remains -1/2 as before.


title: Alignment and the classification of Lorentz-signature tensors

abstract:
  We define the notion of an aligned null direction, a Lorentz-signature
analogue of the eigenvector concept that is valid for arbitrary tensor types.
The set of aligned null directions is described by a a system of alignment
polynomials whose coefficients are derived from the components of the tensor.
The algebraic properties of the alignment polynomials can be used to classify
the corresponding tensors and to put them into normal form. The alignment
classification paradigm is illustrated with a discussion of bivectors and of
Weyl-type tensors. Note: an earlier version of this manuscript was published in
the proceedings of SPT 2004. The present version has been expanded to include a
discussion of complexified alignment. Section 4 also corrects errors contained
in the earlier manuscript.


title: Twisted Electromagnetic Modes and Sagnac Ring-Lasers

abstract:
  A new approximation scheme, designed to solve the covariant Maxwell equations
inside a rotating hollow slender conducting cavity (modelling a ring-laser), is
constructed. It is shown that for well-defined conditions there exist TE and TM
modes with respect to the longitudinal axis of the cavity. A twisted mode
spectrum is found to depend on the integrated Frenet torsion of the cavity and
this in turn may affect the Sagnac beat frequency induced by a non-zero
rotation of the cavity. The analysis is motivated by attempts to use
ring-lasers to measure terrestrial gravito-magnetism or the Lense-Thirring
effect produced by the rotation of the Earth.


title:
A Note on the Integral Formulation of Einstein's Equations Induced on a
  Braneworld

abstract:
  We revisit the integral formulation (or Green's function approach) of
Einstein's equations in the context of braneworlds. The integral formulation
has been proposed independently by several authors in the past, based on the
assumption that it is possible to give a reinterpretation of the local metric
field in curved spacetimes as an integral expression involving sources and
boundary conditions. This allows one to separate source-generated and
source-free contributions to the metric field. As a consequence, an exact
meaning to Mach's Principle can be achieved in the sense that only
source-generated (matter fields) contributions to the metric are allowed for;
universes which do not obey this condition would be non-Machian. In this paper,
we revisit this idea concentrating on a Randall-Sundrum-type model with a
non-trivial cosmology on the brane. We argue that the role of the surface term
(the source-free contribution) in the braneworld scenario may be quite subtler
than in the 4D formulation. This may pose, for instance, an interesting issue
to the cosmological constant problem.


title: On the Physical Hilbert Space of Loop Quantum Cosmology

abstract:
  In this paper we present a model of Riemannian loop quantum cosmology with a
self-adjoint quantum scalar constraint. The physical Hilbert space is
constructed using refined algebraic quantization. When matter is included in
the form of a cosmological constant, the model is exactly solvable and we show
explicitly that the physical Hilbert space is separable consisting of a single
physical state. We extend the model to the Lorentzian sector and discuss
important implications for standard loop quantum cosmology.


title: Higher Dimensional Reissner-Nordstr\"om-FRW metric

abstract:
  By inspecting some known solutions to Einstein equations, we present the
metric of higher dimensional Reissner-Nordstr$\ddot{o}$m black hole in the
background of Friedman-Robertson-Walker universe. Then we verify the solution
with a perfect fluid. The discussion of the event horizon of the black hole
reveals that the scale of the black hole would increase with the expansion of
the universe and decrease with the contraction of the universe.


title: Quasinormal Ringing for Acoustic Black Holes at Low Temperature

abstract:
  We investigate a condensed matter ``black hole'' analogue, taking the
Gross-Pitaevskii (GP) equation as a starting point. The linearized GP equation
corresponds to a wave equation on a black hole background, giving quasinormal
modes under some appropriate conditions. We suggest that we can know the
detailed characters and corresponding geometrical information about the
acoustic black hole by observing quasinormal ringdown waves in the low
temperature condensed matters.


title: Gravitational Tunnelling of Relativistic Shells

abstract:
  Thin shells in general relativity have been used in the past as keystones to
obtain realistic models of cosmological and astrophysical situations. A crucial
role for these developments was played by the compact description of their
dynamics in terms of Israel's junction conditions. Starting from this
geometrical formulation we present a problem related to the WKB regime of shell
dynamics and suggest a possible solution.


title: Vacuum decay by p-branes production

abstract:
  We present a generalization to the N-dimensional case for the nucleation
coefficient of a spherical p-brane, separating two (anti-)de Sitter spacetimes.
We use a semiclassical approximation based on the analytical continuation to
the Euclidean sector of a suitable effective action describing a p-brane in
General Relativity.


title:
Frame-independence of the Inhomogeneous Mixmaster Chaos via
  Misner-Chitre'-like variables

abstract:
  We outline the covariant nature,with respect to the choice of a reference
frame, of the chaos characterizing the generic cosmological solution near the
initial singularity, i.e. the so-called inhomogeneous Mixmaster model. Our
analysis is based on a "gauge" independent ADM-reduction of the dynamics to the
physical degrees of freedom. The out coming picture shows how the inhomogeneous
Mixmaster model is isomorphic point by point in space to a billiard on a
Lobachevsky plane. Indeed, the existence of an asymptotic (energy-like)
constant of the motion allows to construct the Jacobi metric associated to the
geodesic flow and to calculate a non-zero Lyapunov exponent in each space
point. The chaos covariance emerges from the independence of our scheme with
respect to the form of the lapse function and the shift vector; the origin of
this result relies on the dynamical decoupling of the space-points which takes
place near the singularity, due to the asymptotic approach of the potential
term to infinite walls. At the ground of the obtained dynamical scheme is the
choice of Misner-Chitre' like variables which allows to fix the billiard
potential walls.


title: New Isotropic and Anisotropic Sudden Singularities

abstract:
  We show the existence of an infinite family of finite-time singularities in
isotropically expanding universes which obey the weak, strong, and dominant
energy conditions. We show what new type of energy condition is needed to
exclude them ab initio. We also determine the conditions under which
finite-time future singularities can arise in a wide class of anisotropic
cosmological models. New types of finite-time singularity are possible which
are characterised by divergences in the time-rate of change of the
anisotropic-pressure tensor. We investigate the conditions for the formation of
finite-time singularities in a Bianchi type $VII_{0}$ universe with anisotropic
pressures and construct specific examples of anisotropic sudden singularities
in these universes.


title: Vacuum polarization around stars: nonlocal approximation

abstract:
  We compute the vacuum polarization associated with quantum massless fields
around stars with spherical symmetry. The nonlocal contribution to the vacuum
polarization is dominant in the weak field limit, and induces quantum
corrections to the exterior metric that depend on the inner structure of the
star. It also violates the null energy conditions. We argue that similar
results also hold in the low energy limit of quantum gravity. Previous
calculations of the vacuum polarization in spherically symmetric spacetimes,
based on local approximations, are not adequate for newtonian stars.


title: A classical cosmological model for triviality

abstract:
  The aim of this paper is to study the triviality of $\lambda\phi^{4}$ theory
in a classical gravitational model. Starting from a conformal invariant scalar
tensor theory with a self-interaction term $\lambda\phi^{4}$, we investigate
the effect of a conformal symmetry breaking emerging from the gravitational
coupling of the large-scale distribution of matter in the universe. Taking in
this cosmological symmetry breaking phase the infinite limit of the maximal
length (the size of the universe) and the zero limit of the minimal length (the
Planck length) implies triviality, i.e. a vanishing coupling constant
$\lambda$. It suggests that the activity of the self-interaction term
$\lambda\phi^{4}$ in the cosmological context implies that the universe is
finite and a minimal fundamental length exists.


title: A note on the resonant frequencies of rapidly rotating black holes

abstract:
  I discuss the range of validity of Detweiler's formula for the resonant
frequencies of rapidly rotating Kerr black holes. While his formula is correct
for extremal black holes, it has also been commonly accepted that it describes
very well the resonant frequencies of near extremal black holes, and that
therefore there is a large number of modes clustering on the real axis as the
black hole becomes extremal. I will show that this last statement is not only
incorrect, but that it also does not follow from Detweiler's formula, provided
it is handled with due care. It turns out that only the first n <<
-log{(r_+-r_-)/r_+} modes are well described by that formula, which translates,
for any astrophysical black hole, into one or two modes only. All existing
numerical data gives further support to this claim. I also discuss some
implications of this result for recent investigations on the late-time dynamics
of rapidly rotating black holes.


title:
Improved Torsion Pendulum for Ground Testing of LISA Displacement
  Sensors

abstract:
  We discuss a new torsion pendulum design for ground testing of prototype LISA
(Laser Interferometer Space Antenna) displacement sensors. This new design is
directly sensitive to net forces and therefore provides a more representative
test of the noisy forces and parasitic stiffnesses acting on the test mass as
compared to previous ground-based experiments. We also discuss a specific
application to the measurement of thermal gradient effects.


title:
Quasinormal mode expansion and the exact solution of the Cauchy problem
  for wave equations

abstract:
  Solutions for a class of wave equations with effective potentials are
obtained by a method of a Laplace-transform. Quasinormal modes appear naturally
in the solutions only in a spatially truncated form; their coefficients are
uniquely determined by the initial data and are constant only in some region of
spacetime -- in contrast to normal modes. This solves the problem of divergence
of the usual expansion into spatially unbounded quasinormal modes and a
contradiction with the causal propagation of signals. It also partially answers
the question about the region of validity of the expansion. Results of
numerical simulations are presented. They fully support the theoretical
predictions.


title: Stationary spacetimes and the Simon tensor

abstract:
  For stationary vacuum spacetimes the Bianchi identities of the second kind
equate the Simon tensor to the Simon-Mars tensor, the latter having a clear
geometrical interpretation. The equivalence of these two tensors is broken in
the nonvacuum case by additional source energy-momentum terms, but absorbing
these source terms into a redefinition of the Simon tensor restores the
equality. Explicit examples are discussed for electrovacuum and rigidly
rotating matter fields.


title: Quantization of the Classical Maxwell-Nordstrom Fields

abstract:
  The classical electromagnetic and gravitomagnetic fields in the vacuum, in
(3+2) dimensions, described by the Maxwell-Nordstrom equations, are quantized.
These equations are rederived from the field tensor which follows from a
five-dimensional form of the Dirac equation. The electromagnetic field depends
on the customary time t, and the hypothetical gravitomagnetic field depends on
the second time variable u. The total field energy is identified with the
component T44 of the five-dimensional energy-stress tensor of the
electromagnetic and gravitomagnetic fields. In the ground state, the
electromagnetic field and the gravitomagnetic field energies cancel out. The
quanta of the gravitomagnetic field have spin 1.


title: Geometry, pregeometry and beyond

abstract:
  This article explores the overall geometric manner in which human beings make
sense of the world around them by means of their physical theories; in
particular, in what are nowadays called pregeometric pictures of Nature. In
these, the pseudo-Riemannian manifold of general relativity is considered a
flawed description of spacetime and it is attempted to replace it by
theoretical constructs of a different character, ontologically prior to it.
However, despite its claims to the contrary, pregeometry is found to
surreptitiously and unavoidably fall prey to the very mode of description it
endeavours to evade, as evidenced in its all-pervading geometric understanding
of the world. The question remains as to the deeper reasons for this human,
geometric predilection--present, as a matter of fact, in all of physics--and as
to whether it might need to be superseded in order to achieve the goals that
frontier theoretical physics sets itself at the dawn of a new century: a
sounder comprehension of the physical meaning of empty spacetime.


title: A Coherent Strategy for Qauntum Gravity

abstract:
  Affine quantum gravity, which differs notably from either string theory or
loop quantum gravity, is briefly reviewed. Emphasis in this article is placed
on the use of affine coherent states in this program.


title: Attractions of Affine Quantum Gravity

abstract:
  All attempts to quantize gravity face several difficult problems. Among these
problems are: (i) metric positivity (positivity of the spatial distance between
distinct points), (ii) the presence of anomalies (partial second-class nature
of the quantum constraints), and (iii) perturbative nonrenormalizability (the
need for infinitely many distinct counterterms). In this report, a relatively
nontechnical discussion is presented about how the program of affine quantum
gravity proposes to deal with these problems.


title: On the Tensor/Scalar Ratio in Inflation with UV Cutoff

abstract:
  Anisotropy of the cosmic microwave background radiation (CMB) originates from
both tensor and scalar perturbations. To study the characteristics of each of
these two kinds of perturbations, one has to determine the contribution of each
to the anisotropy of CMB. For example, the ratio of the power spectra of
tensor/scalar perturbations can be used to tighten bounds on the scalar
spectral index. We investigate here the implications for the tensor/scalar
ratio of the recent discovery (noted in astro-ph/0410139) that the introduction
of a minimal length cutoff in the structure of spacetime does not leave
boundary terms invariant. Such a cutoff introduces an ambiguity in the choice
of action for tensor and scalar perturbations, which in turn can affect this
ratio. We numerically solve for both tensor and scalar mode equations in a
near-de-sitter background and explicitly find the cutoff dependence of the
tensor/scalar ratio during inflation.


title:
Third post-Newtonian constrained canonical dynamics for binary point
  masses in harmonic coordinates

abstract:
  The conservative dynamics of two point masses given in harmonic coordinates
up to the third post-Newtonian (3pN) order is treated within the framework of
constrained canonical dynamics. A representation of the approximate Poincar\'e
algebra is constructed with the aid of Dirac brackets. Uniqueness of the
generators of the Poincar\'e group resp. the integrals of motion is achieved by
imposing their action on the point mass coordinates to be identical with that
of the usual infinitesimal Poincar\'e transformations. The second
post-Coulombian approximation to the dynamics of two point charges as predicted
by Feynman-Wheeler electrodynamics in Lorentz gauge is treated similarly.


title: New Issues in the Inflationary Scenario

abstract:
  We briefly review the arising of an inflationary phase in the Universe
evolution in order to discuss an inhomogeneous cosmological solution in
presence of a real self interacting scalar field minimally coupled to gravity
in the region of a slow rolling potential plateau. During the inhomogeneous de
Sitter phase the scalar field dominant term is a function of the spatial
coordinates only. We apply this generic solution to the Coleman-Weinberg
potential and to the Lemaitre-Tolman metric. This framework specialized nearby
the FLRW model allows a classical origin for the inhomogeneous perturbations
spectrum.


title: Decay of massive scalar field in a Schwarzschild background

abstract:
  The decay of massive scalar field in the Schwarzschild black hole background
is investigated here by consideration its quasinormal spectrum. It has been
proved that the so-called $quasi-resonant$ modes, which are arbitrary long
living (purely real) modes, can exist only if the effective potential is not
zero at least at one of the boundaries of the $R$-region. We have observed that
the quasinormal spectrum exists for all field masses and proved both
analytically and numerically that when $n \to \infty$ the real part of the
frequencies approaches the same asymptotical value ($\ln3/(8\pi M)$) as in the
case of the massless field.


title: The river model of black holes

abstract:
  This paper presents an under-appreciated way to conceptualize stationary
black holes, which we call the river model. The river model is mathematically
sound, yet simple enough that the basic picture can be understood by
non-experts. %that can by understood by non-experts. In the river model, space
itself flows like a river through a flat background, while objects move through
the river according to the rules of special relativity. In a spherical black
hole, the river of space falls into the black hole at the Newtonian escape
velocity, hitting the speed of light at the horizon. Inside the horizon, the
river flows inward faster than light, carrying everything with it. We show that
the river model works also for rotating (Kerr-Newman) black holes, though with
a surprising twist. As in the spherical case, the river of space can be
regarded as moving through a flat background. However, the river does not
spiral inward, as one might have anticipated, but rather falls inward with no
azimuthal swirl at all. Instead, the river has at each point not only a
velocity but also a rotation, or twist. That is, the river has a Lorentz
structure, characterized by six numbers (velocity and rotation), not just three
(velocity). As an object moves through the river, it changes its velocity and
rotation in response to tidal changes in the velocity and twist of the river
along its path. An explicit expression is given for the river field, a
six-component bivector field that encodes the velocity and twist of the river
at each point, and that encapsulates all the properties of a stationary
rotating black hole.


title: Inside charged black holes I. Baryons

abstract:
  An extensive investigation is made of the interior structure of self-similar
accreting charged black holes. In this, the first of two papers, the black hole
is assumed to accrete a charged, electrically conducting, relativistic baryonic
fluid. The mass and charge of the black hole are generated self-consistently by
the accreted material. The accreted baryonic fluid undergoes one of two
possible fates: either it plunges directly to the spacelike singularity at zero
radius, or else it drops through the Cauchy horizon. The baryons fall directly
to the singularity if the conductivity either exceeds a certain continuum
threshold kappa_oo, or else equals one of an infinite spectrum kappa_n of
discrete values. Between the discrete values kappa_n, the solution is
characterized by the number of times that the baryonic fluid cycles between
ingoing and outgoing. If the conductivity is at the continuum threshold
kappa_oo, then the solution cycles repeatedly between ingoing and outgoing,
displaying a discrete self-similarity reminiscent of that observed in critical
collapse. Below the continuum threshold kappa_oo, and except at the discrete
values kappa_n, the baryonic fluid drops through the Cauchy horizon, and in
this case undergoes a shock, downstream of which the solution terminates at an
irregular sonic point where the proper acceleration diverges, and there is no
consistent self-similar continuation to zero radius. As far as the solution can
be followed inside the Cauchy horizon, the radial direction is timelike. If the
radial direction remains timelike to zero radius (which cannot be confirmed
because the self-similar solutions terminate), then there is presumably a
spacelike singularity at zero radius inside the Cauchy horizon, which is
distinctly different from the vacuum solution for a charged black hole.


title: Inside charged black holes II. Baryons plus dark matter

abstract:
  (Abridged) This is the second of two companion papers on the interior
structure of self-similar accreting charged black holes. In the first paper,
the black hole was allowed to accrete only a single fluid of charged baryons.
In this second paper, the black hole is allowed to accrete in addition a
neutral fluid of almost non-interacting dark matter. Relativistic streaming
between outgoing baryons and ingoing dark matter leads to mass inflation near
the inner horizon. When enough dark matter has been accreted that the center of
mass frame near the inner horizon is ingoing, then mass inflation ceases and
the fluid collapses to a central singularity. A null singularity does not form
on the Cauchy horizon. Although the simultaneous presence of ingoing and
outgoing fluids near the inner horizon is essential to mass inflation, reducing
one or other of the ingoing dark matter or outgoing baryonic streams to a trace
relative to the other stream makes mass inflation more extreme, not the other
way round as one might naively have expected. Consequently, if the dark matter
has a finite cross-section for being absorbed into the baryonic fluid, then the
reduction of the amount of ingoing dark matter merely makes inflation more
extreme, the interior mass exponentiating more rapidly and to a larger value
before mass inflation ceases. However, if the dark matter absorption
cross-section is effectively infinite at high collision energy, so that the
ingoing dark matter stream disappears completely, then the outgoing baryonic
fluid can drop through the Cauchy horizon. In all cases, the solutions do not
depend on what happens in the infinite past or future. We discuss in some
detail the physical mechanism that drives mass inflation.


title:
Conformal continuations and wormhole instability in scalar-tensor
  gravity

abstract:
  We study the stability of static, spherically symmetric, traversable
wormholes existing due to conformal continuations in a class of scalar-tensor
theories with zero scalar field potential (so that Fisher's well-known
scalar-vacuum solution holds in the Einstein conformal frame). Specific
examples of such wormholes are those with nonminimally (e.g., conformally)
coupled scalar fields. All boundary conditions for scalar and metric
perturbations are taken into account. All such wormholes are shown to be
unstable under spherically symmetric perturbations. The instability is proved
analytically with the aid of the theory of self-adjoint operators in Hilbert
space and is confirmed by a numerical computation.


title:
Symmetry relating Gravity with Antigravity: A possible resolution of the
  Cosmological Constant Problem?

abstract:
  I discuss possible implications a symmetry relating gravity with antigravity
might have for smoothing out of the cosmological constant puzzle. For this
purpose, a very simple model with spontaneous symmetry breaking is explored,
that is based on Einstein-Hilbert gravity with two self-interacting scalar
fields. The second (exotic) scalar particle with negative energy density, could
be interpreted, alternatively, as an antigravitating particle with positive
energy.


title:
A follow-up to 'Does Nature abhor a logarithm?' (and apparently she
  doesn't)

abstract:
  This letter contains a brief discussion on the leading-order canonical
correction to the Bekenstein-Hawking (black hole) entropy. In particular, we
address some recent criticism directed at an earlier commentary.


title: 5-dimensional Brans-Dicke Theory and Cosmic Acceleration

abstract:
  We consider a 5-dimensional scalar-tensor theory which is a direct
generalization of the original 4-dimensional Brans-Dicke theory to
5-dimensions. By assuming that there is a hypersurface-orthogonal spacelike
Killing vector field in the underlying 5-dimensional spacetime, the theory is
reduced to a 4-dimensional theory where the 4-metric is coupled with two scalar
fields. The cosmological implication of this reduced theory is then studied in
the Robertson-Walker model. It turns out that the two scalar fields may account
naturally for the present accelerated expansion of our universe. The
observational restriction of the reduced cosmological model is also analyzed.


title: Dark Energy in the Universe, the Irreversibility of Time and Neutrinos

abstract:
  In this review, I discuss briefly how the presence of a cosmological constant
in the Universe may imply a decoherent evolution of quantum matter in it, and
as a consequence a fundamental irreversibility of time unrelated in principle
to CP properties (Cosmological CPT Violation).In this context, I also discuss
recently suggested novel possible contributions of massive neutrinos to the
cosmological constant, which are not due to the standard loop expansion in
quantum field theory, but rather due to unconventional properties of (some
version of) the quantum theory underlying flavour mixing. It is also argued
that quantum space time foam may be responsible for the neutrino mass
differences, observed today, and through the above considerations, for the
(majority of the) dark energy of the Universe in the present era. In the above
context, I also present a fit of all the currently available neutrino
oscillation data, including the LSND ``anomalous'' experimental results, based
on such a CPT Violating decoherent neutrino model. The key feature is to use
different decoherent parameters between neutrinos and antineutrinos, due to the
above mentioned CPT violation. This points to the necessity of future
experiments, concentrating on the antineutrino sector, in order to falsify the
model.


title:
Discrete quantum gravity: the Lorentz invariant weight for the
  Barrett-Crane model

abstract:
  In a recent paper [1] we have constructed the spin and tensor representations
of SO(4) from which the invariant weight can be derived for the Barrett-Crane
model in quantum gravity. By analogy with the SO(4) group, we present the
complexified Clebsch-Gordan coefficients in order to construct the
Biedenharn-Dolginov function for the SO(3,1) group and the spherical function
as the Lorentz invariant weight of the model.


title: From Einstein's 1905 Postulates to the Geometry of Flat Space-Time

abstract:
  Minkowski diagrams in 1+1 dimensional flat space-time are given a strictly
geometric derivation, directly from two gedanken experiments incorporating the
principle of the constancy of the velocity of light and the principle of
(special) relativity. Rectangles of photon trajectories play a central role in
determining the simultaneity convention and in establishing the invariance of
the interval.


title: Structure and stability of the Lukash plane-wave spacetime

abstract:
  We study the vacuum, plane-wave Bianchi $VII{}_{h}$ spacetimes described by
the Lukash metric. Combining covariant with orthonormal frame techniques, we
describe these models in terms of their irreducible kinematical and geometrical
quantities. This covariant description is used to study analytically the
response of the Lukash spacetime to linear perturbations. We find that the
stability of the vacuum solution depends crucially on the background shear
anisotropy. The stronger the deviation from the Hubble expansion, the more
likely the overall linear instability of the model. Our analysis addresses
rotational, shear and Weyl curvature perturbations and identifies conditions
sufficient for the linear growth of these distortions.


title: Mission design for LISA Pathfinder

abstract:
  Here we describe the mission design for SMART-2/LISA Pathfinder. The best
trade-off between the requirements of a low-disturbance environment and
communications distance is found to be a free-insertion Lissajous orbit around
the first co-linear Lagrange point of the Sun-Earth system L1, 1.5x 10^6 km
from Earth. In order to transfer SMART-2/LISA Pathfinder from a low Earth
orbit, where it will be placed by a small launcher, the spacecraft carries out
a number of apogee-raise manoeuvres, which ultimatively place it to a parabolic
escape trajectory towards L1. The challenges of the design of a small mission
are met, fulfilling the very demanding technology demonstration requirements
without creating excessive requirements on the launch system or the ground
segment.


title: Nonlinear evolution of r-modes: the role of differential rotation

abstract:
  Recent work has shown that differential rotation, producing large scale
drifts of fluid elements along stellar latitudes, is an unavoidable feature of
r-modes in the nonlinear theory. We investigate the role of this differential
rotation in the evolution of the l=2 r-mode instability of a newly born, hot,
rapidly rotating neutron star. It is shown that the amplitude of the r-mode
saturates a few hundred seconds after the mode instability sets in. The
saturation amplitude depends on the amount of differential rotation at the time
the instability becomes active and can take values much smaller than unity. It
is also shown that, independently of the saturation amplitude of the mode, the
star spins down to rotation rates that are comparable to the inferred initial
rotation rates of the fastest pulsars associated with supernova remnants.
Finally, it is shown that, when the drift of fluid elements at the time the
instability sets in is significant, most of the initial angular momentum of the
star is transferred to the r-mode and, consequently, almost none is carried
away by gravitational radiation.


title: On General Relativity extension

abstract:
  The careful analysis of the duality properties of Riemann's curvature tensor
points to possibility of extension of Einstein's General Relativity to the
nonabelian Yang-Mills theory. The motion equations of the theory are
Yang-Mills' equations for the curvature tensor. Einstein's equations (with
cosmological term to appear as an integration constant) are contained in the
theory proposed. New is that now gravitational field is not exceptionally
determined by matter energy-momentum but can possess its own non-Einsteinian
dynamics(vacuum fluctuations, self-interaction)which is generally an attribute
of nonabelian gauge field. The gravitational equations proper due to either
matter energy-momentum or vacuum fluctuations are side conditions imposed on
the Riemann tensor, like self-duality conditions.


title:
A scalar field governed cosmological model from noncompact Kaluza-Klein
  theory

abstract:
  This paper is a review of a recently introduced cosmological model from a
noncompact Kaluza-Klein theory for a single scalar field minimally coupled to
gravity. We obtain that the 4D scalar potential has a geometrical origin and
assume different representations in different frames. It should be responsible
for the expansion of the universe. In this framework we explain the (neutral
scalar field governed) evolution of the universe from an initially inflationary
expansion that has a change of phase towards a decelerated expansion and
thereinafter evolves towards the present day observed accelerated
(quintessential) expansion. Finally, using the Hamilton-Jacobi formalism, we
study extra force and extra mass from this 5D cosmological model.


title:
An extension principle for the Einstein-Vlasov system in spherical
  symmetry

abstract:
  We prove that "first singularities" in the non-trapped region of the maximal
development of spherically symmetric asymptotically flat data for the
Einstein-Vlasov system must necessarily emanate from the center. The notion of
"first" depends only on the causal structure and can be described in the
language of terminal indecomposable pasts (TIPs). This result suggests a local
approach to proving weak cosmic censorship for this system. It can also be used
to give the first proof of the formation of black holes by the collapse of
collisionless matter from regular initial configurations.


title: Classical limit of quantum gravity in an accelerating universe

abstract:
  A one-parameter deformation of Einstein?Hilbert gravity with an inverse
Riemann curvature term is derived as the classical limit of quantum gravity
compatible with an accelerating universe. This result is based on the
investigation of semi-classical theories with sectional curvature bounds which
are shown not to admit static spherically symmetric black holes if otherwise of
phenomenological interest. We discuss the impact on the canonical quantization
of gravity, and observe that worldsheet string theory is not affected.


title: The Pioneer Anomaly: The Data, its Meaning, and a Future Test

abstract:
  The radio-metric Doppler tracking data from the Pioneer 10/11 spacecraft,
from between 20-70 AU, yields an unambiguous and independently confirmed
anomalous blue shift drift of a_t = (2.92 \pm 0.44)\times 10^{-18} s/s^2. It
can be interpreted as being due to a constant acceleration of a_P = (8.74 \pm
1.33) \times 10^{-8} cm/s^2 directed towards the Sun. No systematic effect has
been able to explain the anomaly, even though such an origin is an obvious
candidate. We discuss what has been learned (and what might still be learned)
from the data about the anomaly, its origin, and the mission design
characteristics that would be needed to test it. Future mission options are
proposed.


title: News from Critical Collapse: Bondi Mass, Tails and Quasinormal Modes

abstract:
  We discuss critical gravitational collapse on the threshold of apparent
horizon formation as a model both for the discussion of global aspects of
critical collapse and for numerical studies in a compactified context. For our
matter model we choose a self-gravitating massless scalar field in spherical
symmetry, which has been studied extensively in the critical collapse
literature. Our evolution system is based on Bondi coordinates, the mass
function is used as an evolution variable to ensure regularity at null
infinity. We compute radiation quantities like the Bondi mass and news function
and find that they reflect the DSS behavior. Surprisingly, the period of
radiation at null infinity is related to the formal result for the leading
quasi-normal mode of a black hole with rapidly decreasing mass. Furthermore,
our investigations shed some light on global versus local issues in critical
collapse, and the validity and usefulness of the concept of null infinity when
predicting detector signals.


title: Riemannian geometry of gravity waves turbulent black hole analogs

abstract:
  The gravity water wave black (GWBH) hole analog discovered by Schutzhold and
Unruh (SU) is extended to allow for the presence of turbulent shear flow. The
Riemannian geometry of turbulent black holes (BH) analogs in water waves is
computed in the case of laminar tirbulent shear flow. The Riemann curvature is
constant and the geodesic deviation equation shows that the curvature acts
locally as a diverging lens and the stream lines on opposite sides of the
analog black hole flow apart from each other. In this case it is shown that the
curvature quantities can be expressed in terms of the Newtonian gravitational
constant in the ergoregion. The dispersion relation is obtained for the case of
constant flow injection.


title:
Anisotropic cosmological models with a perfect fluid and a $\Lambda$
  term

abstract:
  We consider a self-consistent system of Bianchi type-I (BI) gravitational
field and a binary mixture of perfect fluid and dark energy given by a
cosmological constant. The perfect fluid is chosen to be the one obeying either
the usual equation of state, i.e., $p = \zeta \ve$, with $\zeta \in [0, 1]$ or
a van der Waals equation of state. Role of the $\Lambda$ term in the evolution
of the BI Universe has been studied.


title: Elliptic systems

abstract:
  In this article I will review some basic results on elliptic boundary value
problems with applications to General Relativity.


title: Laser Ranging to the Moon, Mars and Beyond

abstract:
  Current and future optical technologies will aid exploration of the Moon and
Mars while advancing fundamental physics research in the solar system.
Technologies and possible improvements in the laser-enabled tests of various
physical phenomena are considered along with a space architecture that could be
the cornerstone for robotic and human exploration of the solar system. In
particular, accurate ranging to the Moon and Mars would not only lead to
construction of a new space communication infrastructure enabling an improved
navigational accuracy, but will also provide a significant improvement in
several tests of gravitational theory: the equivalence principle, geodetic
precession, PPN parameters $\beta$ and $\gamma$, and possible variation of the
gravitational constant $G$. Other tests would become possible with an optical
architecture that would allow proceeding from meter to centimeter to millimeter
range accuracies on interplanetary distances. This paper discusses the current
state and the future improvements in the tests of relativistic gravity with
Lunar Laser Ranging (LLR). We also consider precision gravitational tests with
the future laser ranging to Mars and discuss optical design of the proposed
Laser Astrometric Test of Relativity (LATOR) mission. We emphasize that already
existing capabilities can offer significant improvements not only in the tests
of fundamental physics, but may also establish the infrastructure for space
exploration in the near future. Looking to future exploration, what
characteristics are desired for the next generation of ranging devices, what is
the optimal architecture that would benefit both space exploration and
fundamental physics, and what fundamental questions can be investigated? We try
to answer these questions.


title: Gravitational wave experiments and Baksan project "OGRAN"

abstract:
  A brief sketch of the present status of gravitational wave experiments is
given. Attention is concentrated to recent observations with the gravitational
detector network. The project OGRAN for a combined optic-interferometrical and
acoustical gravitation wave antenna planned for installation into underground
facilities of the Baksan Neutrino Observatory is presented. We describe general
principles of the apparatus, expected sensitivity and current characteristics
of the antenna prototype; some ways for sensitivity improvement are also
discussed.


title:
Some comments on the recent results about the measurement of the
  Lense-Thirring effect in the gravitational field of the Earth with the LAGEOS
  and LAGEOS II satellites

abstract:
  With quantitative numerical simulations we show that the secular variations
of the even zonal harmonics of the geopotential do affect the measurement of
the Lense-Thirring effect with the nodes of LAGEOS and LAGEOS II at a \sim 14%
level. Thus, the 1-sigma total error in the performed test with the 2nd
generation CHAMP-only EIGEN2 Earth gravity model amounts to 51%, contrary to
18% claimed by Ciufolini.


title:
Evolution of Cosmological Perturbations in the Universe dominated by
  Resonant Scalar Fields

abstract:
  Recently a Hamiltonian formulation for the evolution of the universe
dominated by multiple oscillatory scalar fields was developed by the present
author and was applied to the investigation of the evolution of cosmological
perturbations on superhorizon scales in the case that the scalar fields have
incommensurable masses. In the present paper, the analysis is extended to the
case that the masses of the scalar fields satisfy resonance relations
approximately. In this case, the action-angle variables for the system can be
classified into fast changing variables and slowly changing variables. We show
that after an appropriate canonical transformation, the part of the Hamiltonian
that depends on fast changing angle variables can be made negligibley small, so
that the dynamics of the system can be effectively determined by a truncated
Hamiltonian that describes a closed dynamics of the slowly changing varables.
Utilizing this formulation, we show that the system is unstable if this
truncated Hamiltonian system has hyperbolic fixed point and as a consequence,
the Bardeen parameter for a perturbation of the system grows.


title:
(Anti-)de Sitter Black Hole Thermodynamics and the Generalized
  Uncertainty Principle

abstract:
  We extend the derivation of the Hawking temperature of a Schwarzschild black
hole via the Heisenberg uncertainty principle to the de Sitter and anti-de
Sitter spacetimes. The thermodynamics of the Schwarzschild-(anti-)de Sitter
black holes is obtained from the generalized uncertainty principle of string
theory and non-commutative geometry. This may explain why the thermodynamics of
(anti-)de Sitter-like black holes admits a holographic description in terms of
a dual quantum conformal field theory, whereas the thermodynamics of
Schwarzschild-like black holes does not.


abstract:
  Integral equations for the spin-weighted spheroidal wave functions is given.
For the prolate spheroidal wave function with m=0, there exists the integral
equation whose kernel is(sin x)/x, and the sinc function kernel (sin x)/x is of
great mathematical significance. In the paper, we also extend the similar sinc
function kernel (sin x)/x to the case m and s both are not zero, which
interestingly turn out as some kind of Hankel transformation.


title: Tachyon driven solution to Cosmic Coincidence Problrm

abstract:
  Here, non-minimally coupled tachyon to gravity is considered as a source of
"dark energy". It is demonstrated that with expansion of the universe, tachyon
dark energy decays to "dark matter" providing a solution to "cosmic coincidence
problem".Moreover, it is found that universe undergoes accelerated expansion
simultaneously.


title: Quantum Time Uncertainty in a Gravity's Rainbow Formalism

abstract:
  The existence of a minimum time uncertainty is usually argued to be a
consequence of the combination of quantum mechanics and general relativity.
Most of the studies that point to this result are nonetheless based on
perturbative quantization approaches, in which the effect of matter on the
geometry is regarded as a correction to a classical background. In this paper,
we consider rainbow spacetimes constructed from doubly special relativity by
using a modification of the proposals of Magueijo and Smolin. In these models,
gravitational effects are incorporated (at least to a certain extent) in the
definition of the energy-momentum of particles without adhering to a
perturbative treatment of the back reaction. In this context, we derive and
compare the expressions of the time uncertainty in quantizations that use as
evolution parameter either the background or the rainbow time coordinates.
These two possibilities can be regarded as corresponding to perturbative and
non-perturbative quantization schemes, respectively. We show that, while a
non-vanishing time uncertainty is generically unavoidable in a perturbative
framework, an infinite time resolution can in fact be achieved in a
non-perturbative quantization for the whole family of doubly special relativity
theories with unbounded physical energy.


title:
WKB Analysis of the Scattering of Massive Dirac Fields in Schwarzschild
  Black Hole Spacetimes

abstract:
  We analysis the radial equations for massive Dirac fields in Schwarzschild
black hole spacetimes. Different approximation formulae under the WKB scheme
are developed for the transmission probability ${\cal T}$ of the radial
wavefunction with $E^{2}\gg V_{m}$, $E^{2}\approx V_{m}$, and $E^{2}\ll V_{m}$,
where $E$ is the energy of the field and $V_{m}$ is the maximum value of the
effective potential. Explicit results of ${\cal T}$ in these approximations are
given for various values of $E$, the mass $m$, and the angular momentum
parameter $\kappa$ of the fields. We also discuss the dependence of ${\cal T}$
on these parameters.


title:
The Aschenbach effect: unexpected topology changes in motion of
  particles and fluids orbiting rapidly rotating Kerr black holes

abstract:
  Newton's theory predicts that the velocity $V$ of free test particles on
circular orbits around a spherical gravity center is a decreasing function of
the orbital radius $r$, $dV/dr < 0$. Only very recently, Aschenbach (A&A 425,
p. 1075 (2004)) has shown that, unexpectedly, the same is not true for
particles orbiting black holes: for Kerr black holes with the spin parameter
$a>0.9953$, the velocity has a positive radial gradient for geodesic, stable,
circular orbits in a small radial range close to the black hole horizon. We
show here that the {\em Aschenbach effect} occurs also for non-geodesic
circular orbits with constant specific angular momentum $\ell = \ell_0 =
const$. In Newton's theory it is $V = \ell_0/R$, with $R$ being the cylindrical
radius. The equivelocity surfaces coincide with the $R = const$ surfaces which,
of course, are just co-axial cylinders. It was previously known that in the
black hole case this simple topology changes because one of the ``cylinders''
self-crosses. We show here that the Aschenbach effect is connected to a second
topology change that for the $\ell = const$ tori occurs only for very highly
spinning black holes, $a>0.99979$.


title: Concepts of Hyperbolicity and Relativistic Continuum Mechanics

abstract:
  After a short introduction to the characteristic geometry underlying weakly
hyperbolic systems of partial differential equations we review the notion of
symmetric hyperbolicity of first-order systems and that of regular
hyperbolicity of second-order systems. Numerous examples are provided, mainly
taken from nonrelativistic and relativistic continuum mechanics.


title: Categorizing Different Approaches to the Cosmological Constant Problem

abstract:
  We have found that proposals addressing the old cosmological constant problem
come in various categories. The aim of this paper is to identify as many
different, credible mechanisms as possible and to provide them with a code for
future reference. We find that they all can be classified into five different
schemes of which we indicate the advantages and drawbacks.
  Besides, we add a new approach based on a symmetry principle mapping real to
imaginary spacetime.


title: Constraint and gauge shocks in one-dimensional numerical relativity

abstract:
  We study how different types of blow-ups can occur in systems of hyperbolic
evolution equations of the type found in general relativity. In particular, we
discuss two independent criteria that can be used to determine when such
blow-ups can be expected. One criteria is related with the so-called geometric
blow-up leading to gradient catastrophes, while the other is based upon the
ODE-mechanism leading to blow-ups within finite time. We show how both
mechanisms work in the case of a simple one-dimensional wave equation with a
dynamic wave speed and sources, and later explore how those blow-ups can appear
in one-dimensional numerical relativity. In the latter case we recover the well
known ``gauge shocks'' associated with Bona-Masso type slicing conditions.
However, a crucial result of this study has been the identification of a second
family of blow-ups associated with the way in which the constraints have been
used to construct a hyperbolic formulation. We call these blow-ups ``constraint
shocks'' and show that they are formulation specific, and that choices can be
made to eliminate them or at least make them less severe.


title: Lunar Laser Ranging Science

abstract:
  Analysis of Lunar Laser Ranging (LLR) data provides science results:
gravitational physics and ephemeris information from the orbit, lunar science
from rotation and solid-body tides, and Earth science. Sensitive tests of
gravitational physics include the Equivalence Principle, limits on the time
variation of the gravitational constant G, and geodetic precession. The
equivalence principle test is used for an accurate determination of the
parametrized post-Newtonian (PPN) parameter \beta. Lunar ephemerides are a
product of the LLR analysis used by current and future spacecraft missions. The
analysis is sensitive to astronomical parameters such as orbit, masses and
obliquity. The dissipation-caused semimajor axis rate is 37.9 mm/yr and the
associated acceleration in orbital longitude is -25.7 ''/cent^2, dominated by
tides on Earth with a 1% lunar contribution. Lunar rotational variation has
sensitivity to interior structure, physical properties, and energy dissipation.
The second-degree lunar Love numbers are detected; k_2 has an accuracy of 11%.
Lunar tidal dissipation is strong and its Q has a weak dependence on tidal
frequency. A fluid core of about 20% the Moon's radius is indicated by the
dissipation data. Evidence for the oblateness of the lunar
fluid-core/solid-mantle boundary is getting stronger. This would be independent
evidence for a fluid lunar core. Moon-centered coordinates of four
retroreflectors are determined. Station positions and motion, Earth rotation
variations, nutation, and precession are determined from analyses. Extending
the data span and improving range accuracy will yield improved and new
scientific results. Adding either new retroreflectors or precise active
transponders on the Moon would improve the accuracy of the science results.