title: On Hypothesis of the Two Large Extradimensions

abstract:
  Recently there was proposeda hypothesis about existence of the two large
extradimensions. This hypothesis demands, e.g., modification of Newton law at
submilimeter scale. In this brief report we show that this hypothesis cannot be
correct in presen formulation.


title: Inertial forces and photon surfaces in arbitrary spacetimes

abstract:
  Given, in an arbitrary spacetime, a 2-dimensional timelike submanifold
(worldsheet) and an observer field on this worldsheet, we assign gravitational,
centrifugal, Coriolis and Euler forces to every particle worldline in the
worldsheet with respect to the observer field. We prove that centrifugal and
Coriolis forces vanish, for all particle worldlines with respect to any
observer field, if and only if the worldsheet is a photon 2-surface, i.e.,
generated by two families of lightlike geodesics. We further demonstrate that a
photon 2-surface can be characterized in terms of gyroscope transport and we
give several mathematical criteria for the existence of photon 2-surfaces.
Finally, examples of photon 2-surfaces in conformally flat spacetimes, in
Schwarzschild and Reissner-Nordstroem spacetimes, and in Goedel spacetime are
worked out.


title: A principal positioning system for the Earth

abstract:
  The project SYPOR wishes to use the global navigation satellite system
GALILEO as an autonomous relativistic positioning system for the Earth.
Motivations and a sketch of the basic concepts underlying the project are
presented. For non geodetic (perturbed) satellites, a two-dimensional example
describes how the dynamics of the constellation of satellites and that of the
users may be deduced from the knowledge of the dynamics of only one of the
satellites during a partial interval.


title:
Hawking Radiation of an Arbitrarily Accelerating Kinnersley Black Hole:
  Spin-Acceleration Coupling Effect

abstract:
  The Hawking radiation of Weyl neutrinos in an arbitrarily accelerating
Kinnersley black hole is investigated by using a method of the generalized
tortoise coordinate transformation. Both the location and temperature of the
event horizon depend on the time and on the angles. They coincide with previous
results, but the thermal radiation spectrum of massless spinor particles
displays a kind of spin-acceleration coupling effect.


title: Exact Quantum State of Collapse and Black Hole Radiation

abstract:
  We construct an exact quantum gravitational state describing the collapse of
an inhomogeneous spherical dust cloud using a lattice regularization of the
Wheeler-DeWitt equation. In the semiclassical approximation around a black
hole, this state describes Hawking radiation. We show that the leading quantum
gravitational correction to Hawking radiation renders the spectrum non-thermal.


title:
3-Body Dynamics in a (1+1) Dimensional Relativistic Self-Gravitating
  System

abstract:
  The results of our study of the motion of a three particle, self-gravitating
system in general relativistic lineal gravity is presented for an arbitrary
ratio of the particle masses. We derive a canonical expression for the
Hamiltonian of the system and discuss the numerical solution of the resulting
equations of motion. This solution is compared to the corresponding
non-relativistic and post-Newtonian approximation solutions so that the
dynamics of the fully relativistic system can be interpretted as a correction
to the one-dimensional Newtonian self-gravitating system. We find that the
structure of the phase space of each of these systems yields a large variety of
interesting dynamics that can be divided into three distinct regions: annulus,
pretzel, and chaotic; the first two being regions of quasi-periodicity while
the latter is a region of chaos. By changing the relative masses of the three
particles we find that the relative sizes of these three phase space regions
changes and that this deformation can be interpreted physically in terms of the
gravitational interactions of the particles. Furthermore, we find that many of
the interesting characteristics found in the case where all of the particles
share the same mass also appears in our more general study. We find that there
are additional regions of chaos in the unequal mass system which are not
present in the equal mass case. We compare these results to those found in
similar systems.


title: Tests of Lorentz Invariance Using a Microwave Resonator: An Update

abstract:
  The frequencies of a cryogenic sapphire oscillator and a hydrogen maser are
compared to set new constraints on a possible violation of Lorentz invariance.
We determine the variation of the oscillator frequency as a function of its
orientation (Michelson-Morley test) and of its velocity (Kennedy-Thorndike
test) with respect to a preferred frame candidate. We constrain the
corresponding parameters of the Mansouri and Sexl test theory to $\delta -
\beta + 1/2 \leq 3.4 \times 10^{-9}$ and $\beta - \alpha - 1 \leq 4.1 \times
10^{-7}$ which is of the same order as the best previous result for the former
and represents a 50 fold improvement for the latter. These results correspond
to an improvement of our previously published limits [Wolf P. et al., Phys.
Rev. Lett. {\bf 90}, 6, 060402, (2003)] by about a factor 2. We describe the
changes of the experiment, and show the new data that lead to that improvement.


title: Novel Properties of Massive Higher Spin Fields

abstract:
  I outline a series of results obtained in collaboration with A. Waldron on
the properties of massive higher (s>1) spin fields in cosmological, constant
curvature, backgrounds and the resulting unexpected qualitative effects on
their degrees of freedom and unitarity properties. The dimensional parameter
$\L$ extends the flat space m-line to a $(m^2,\L)$ "phase" plane in which these
novel phenomena unfold. In this light, I discuss a possible partial
resurrection of deSitter supergravity. I will also exhibit the well-known
causality problems of coupling these systems to gravity and, for complex
fields, to electromagnetism, systematizing some of the occasionally
misunderstood obstacles to interactions, particularly for s = 3/2 and 2.


title:
Topological Characteristics of Random Surfaces Generated by Cubic
  Interactions

abstract:
  We consider random topologies of surfaces generated by cubic interactions.
Such surfaces arise in various contexts in 2-dimensional quantum gravity and as
world-sheets in string theory. Our results are most conveniently expressed in
terms of a parameter h = n/2 + \chi, where n is the number of interaction
vertices and \chi is the Euler characteristic of the surface. Simulations and
results for similar models suggest that Ex[h] = log (3n) + \gamma + O(1/n) and
Var[h] = log (3n) + \gamma - \pi^2/6 + O(1/n). We prove rigourously that Ex[h]
= log n + O(1) and Var[h] = O(log n). We also derive results concerning a
number of other characteristics of the topology of these random surfaces.


title: Optimising the directional sensitivity of LISA

abstract:
  It was shown in a previous work that the data combinations canceling laser
frequency noise constitute a module - the module of syzygies. The cancellation
of laser frequency noise is crucial for obtaining the requisite sensitivity for
LISA. In this work we show how the sensitivity of LISA can be optimised for a
monochromatic source - a compact binary - whose direction is known, by using
appropriate data combinations in the module. A stationary source in the
barycentric frame appears to move in the LISA frame and our strategy consists
of "coherently tracking" the source by appropriately "switching" the data
combinations so that they remain optimal at all times. Assuming that the
polarisation of the source is not known, we average the signal over the
polarisations. We find that the best statistic is the `network' statistic, in
which case LISA can be construed of as two independent detectors. We compare
our results with the Michelson combination, which has been used for obtaining
the standard sensitivity curve for LISA, and with the observable obtained by
optimally switching the three Michelson combinations. We find that for sources
lying in the ecliptic plane the improvement in SNR increases from 34% at low
frequencies to nearly 90% at around 20 mHz. Finally we present the
signal-to-noise ratios for some known binaries in our galaxy. We also show
that, if at low frequencies SNRs of both polarisations can be measured, the
inclination angle of the plane of the orbit of the binary can be estimated.


title: Recent progress in wormhole dynamics

abstract:
  Space-time wormholes were introduced in Wheeler's idea of space-time foam.
Traversible wormholes as defined by Morris & Thorne became popular as potential
short cuts across the universe and even time machines. More recently, the
author proposed a general theory of wormhole dynamics, unified with black-hole
dynamics. This article gives a brief review of the above ideas and summarizes
progress on wormhole dynamics in the last year. Firstly, a numerical study of
dynamical perturbations of the first Morris-Thorne wormhole showed it to be
unstable, either collapsing to a black hole or exploding to an inflationary
universe. This provides a mechanism for inflating a wormhole from space-time
foam to usable size. Intriguing critical behaviour was also discovered.
Secondly, a wormhole solution supported by pure radiation was discovered and
used to find analytic examples of dynamic wormhole processes which were also
recently found in a two-dimensional dilaton gravity model: the construction of
a traversible wormhole from a Schwarzschild black hole and vice versa, and the
enlargement or reduction of the wormhole.


title: The motion of point particles in curved spacetime

abstract:
  This review is concerned with the motion of a point scalar charge, a point
electric charge, and a point mass in a specified background spacetime. In each
of the three cases the particle produces a field that behaves as outgoing
radiation in the wave zone, and therefore removes energy from the particle. In
the near zone the field acts on the particle and gives rise to a self-force
that prevents the particle from moving on a geodesic of the background
spacetime. The field's action on the particle is difficult to calculate because
of its singular nature: the field diverges at the position of the particle. But
it is possible to isolate the field's singular part and show that it exerts no
force on the particle -- its only effect is to contribute to the particle's
inertia. What remains after subtraction is a smooth field that is fully
responsible for the self-force. Because this field satisfies a homogeneous wave
equation, it can be thought of as a free (radiative) field that interacts with
the particle; it is this interaction that gives rise to the self-force. The
mathematical tools required to derive the equations of motion of a point scalar
charge, a point electric charge, and a point mass in a specified background
spacetime are developed here from scratch. The review begins with a discussion
of the basic theory of bitensors (part I). It then applies the theory to the
construction of convenient coordinate systems to chart a neighbourhood of the
particle's word line (part II). It continues with a thorough discussion of
Green's functions in curved spacetime (part III). The review concludes with a
detailed derivation of each of the three equations of motion (part IV).


title: Dual recycling for GEO600

abstract:
  Dual recycling is the combination of signal recycling and power recycling;
both optical techniques improve the shot-noise-limited sensitivity of
interferometric gravitational-wave detectors. In addition, signal recycling can
reduce the loss of light power due to imperfect interference and allows, in
principle, to beat the standard quantum limit. The interferometric
gravitational-wave detector GEO600 is the first detector to use signal
recycling. We have recently equipped the detector with a signal-recycling
mirror with a transmittance of 1%. In this paper, we present details of the
detector commissioning and the first locks of the dual- recycled
interferometer.


title: Phase Transitions and Critical Behavior for Charged Black Holes

abstract:
  We investigate the thermodynamics of a four-dimensional charged black hole in
a finite cavity in asymptotically flat and asymptotically de Sitter space. In
each case, we find a Hawking-Page-like phase transition between a black hole
and a thermal gas very much like the known transition in asymptotically anti-de
Sitter space. For a ``supercooled'' black hole--a thermodynamically unstable
black hole below the critical temperature for the Hawking-Page phase
transition--the phase diagram has a line of first-order phase transitions that
terminates in a second order point. For the asymptotically flat case, we
calculate the critical exponents at the second order phase transition and find
that they exactly match the known results for a charged black hole in anti-de
Sitter space. We find strong evidence for similar phase transitions for the de
Sitter black hole as well. Thus many of the thermodynamic features of charged
anti-de Sitter black holes do not really depend on asymptotically anti-de
Sitter boundary conditions; the thermodynamics of charged black holes is
surprisingly universal.


title:
Quantum noise in gravitational-wave interferometers: Overview and recent
  developments

abstract:
  We present an overview of quantum noise in gravitational wave
interferometers. Gravitational wave detectors are extensively modified variants
of a Michelson interferometer and the quantum noise couplings are strongly
influenced by the interferometer configuration. We describe recent developments
in the treatment of quantum noise in the complex interferometer configurations
of present-day and future gravitational-wave detectors. In addition, we explore
prospects for the use of squeezed light in future interferometers, including
consideration of the effects of losses, and the choice of optimal readout
schemes.


title:
A Fast Apparent-Horizon Finder for 3-Dimensional Cartesian Grids in
  Numerical Relativity

abstract:
  In 3+1 numerical simulations of dynamic black hole spacetimes, it's useful to
be able to find the apparent horizon(s) (AH) in each slice of a time evolution.
A number of AH finders are available, but they often take many minutes to run,
so they're too slow to be practically usable at each time step. Here I present
a new AH finder,_AHFinderDirect_, which is very fast and accurate: at typical
resolutions it takes only a few seconds to find an AH to $\sim 10^{-5} m$
accuracy on a GHz-class processor.
  I assume that an AH to be searched for is a Strahlk\"orper (star-shaped
region) with respect to some local origin, and so parameterize the AH shape by
$r = h(angle)$ for some single-valued function $h: S^2 \to \Re^+$. The AH
equation then becomes a nonlinear elliptic PDE in $h$ on $S^2$, whose
coefficients are algebraic functions of $g_{ij}$, $K_{ij}$, and the
Cartesian-coordinate spatial derivatives of $g_{ij}$. I discretize $S^2$ using
6 angular patches (one each in the neighborhood of the $\pm x$, $\pm y$, and
$\pm z$ axes) to avoid coordinate singularities, and finite difference the AH
equation in the angular coordinates using 4th order finite differencing. I
solve the resulting system of nonlinear algebraic equations (for $h$ at the
angular grid points) by Newton's method, using a "symbolic differentiation"
technique to compute the Jacobian matrix._AHFinderDirect_ is implemented as a
thorn in the_Cactus_ computational toolkit, and is freely available by
anonymous CVS checkout.


title: Time Delay Interferometry and LISA Optimal Sensitivity

abstract:
  The sensitivity of LISA depends on the suppression of several noise sources;
dominant one is laser frequency noise. It has been shown that the six Doppler
data streams obtained from three space-crafts can be appropriately time delayed
and optimally combined to cancel this laser frequency noise. We show that the
optimal data combinations when operated in a network mode improves the
sensitivity over Michelson ranging from 40 % to 100 %. In this article, we
summarize these results. We further show that the residual laser noise in the
optimal data combination due to typical arm-length inaccuracy of 200 m is much
below the level of optical path and the proof mass noises.


title: Rotating Dilaton Black Holes with Hair

abstract:
  We consider stationary rotating black holes in SU(2) Einstein-Yang-Mills
theory, coupled to a dilaton. The black holes possess non-trivial non-Abelian
electric and magnetic fields outside their regular event horizon. While generic
solutions carry no non-Abelian magnetic charge, but non-Abelian electric
charge, the presence of the dilaton field allows also for rotating solutions
with no non-Abelian charge at all. As a consequence, these special solutions do
not exhibit the generic asymptotic non-integer power fall-off of the
non-Abelian gauge field functions. The rotating black hole solutions form
sequences, characterized by the winding number $n$ and the node number $k$ of
their gauge field functions, tending to embedded Abelian black holes. The
stationary non-Abelian black hole solutions satisfy a mass formula, similar to
the Smarr formula, where the dilaton charge enters instead of the magnetic
charge. Introducing a topological charge, we conjecture, that black hole
solutions in SU(2) Einstein-Yang-Mills-dilaton theory are uniquely
characterized by their mass, their angular momentum, their dilaton charge,
their non-Abelian electric charge, and their topological charge.


title: A simple background-independent hamiltonian quantum model

abstract:
  We study formulation and probabilistic interpretation of a simple
general-relativistic hamiltonian quantum system. The system has no unitary
evolution in background time. The quantum theory yields transition
probabilities between measurable quantities (partial observables). These
converge to the classical predictions in the $\hbar\to 0$ limit. Our main tool
is the kernel of the projector on the solutions of Wheeler-deWitt equation,
which we analyze in detail. It is a real quantity, which can be seen as a
propagator that propagates "forward" as well as "backward" in a local parameter
time. Individual quantum states, on the other hand, may contain only "forward
propagating" components. The analysis sheds some light on the interpretation of
background independent transition amplitudes in quantum gravity.


title: Introduction to Bosonic String Theory

abstract: Introductory Notes in Bosonic String Theory and its Canonical Quantization.


title: Adiabatic decaying vacuum model for the universe

abstract:
  We study a model that the entropy per particle in the universe is constant.
The sources for the entropy are the particle creation and a lambda decaying
term. We find exact solutions for the Einstein field equations and show the
compatibilty of the model with respect to the age and the acceleration of the
universe.


title: Multipole particle in relativity

abstract:
  We discuss the motion of extended objects in a spacetime by considering a
gravitational field created by these objects. We define multipole moments of
the objects as a classification by Lie group SO(3). Then, we construct an
energy-momentum tensor for the objects and derive equations of motion from it.
As a result, we reproduce the Papapetrou equations for a spinning particle.
Furthermore, we will show that we can obtain more simple equations than the
Papapetrou equations by changing the center-of-mass.


title:
Compact anisotropic stars with membrane - a new class of exact solutions
  to the Einstein field equations

abstract:
  A new class of solutions to Einstein's classical field equations of general
relativity is presented. The solutions describe a non-rotating, spherically
symmetric, compact self gravitating object, residing in a static electro-vacuum
space time.
  The solutions generally have an interior non-zero matter-distribution. A wide
class of interior solutions can be constructed for any specific set of exterior
parameters (mass, charge). The original Schwarzschild and Reissner-Nordstroem
solutions constitute special cases within the variety of interior solutions.
  An outstanding feature of the new solutions is a non-continuous boundary of
the matter-distribution, accompanied by a two dimensional membrane at the
boundary. The membrane consists of an infinitesimally thin spherical shell of
tangential pressure (surface tension/stress). The interior matter state
generally has a locally anisotropic pressure.
  A general procedure for generating the new solutions is given. A few
solutions are derived and discussed briefly. In order to identify the
physically most promising solutions, a selection principle is formulated, based
on the holographic principle. One solution of particular interest emerges. It
is characterized by the property, that the "stress-energy content" of the
membrane is equal to the gravitating mass of the object.


title:
A New Approach to Quantising Space-Time: III. State Vectors as Functions
  on Arrows

abstract:
  In two recent papers by the author, a new approach was suggested for
quantising space-time, or space. This involved developing a procedure for
quantising a system whose configuration space--or history-theory analogue--is
the set of objects, $\Ob\Q$, in a (small) category $\Q$. The quantum states in
this approach are cross-sections of a bundle $A\leadsto\K[A]$ of Hilbert spaces
over $\Ob\Q$. The Hilbert spaces $\K[A]$, $A\in\Ob\Q$, depend strongly on the
object $A$, and have to be chosen so as to get an irreducible, faithful,
representation of the basic `category quantisation monoid'. In the present
paper, we develop a different approach in which the state vectors are
complex-valued functions on the set of {\em arrows} in $\Q$. This throws a new
light on the Hilbert bundle scheme: in particular, we recover the results of
that approach in the, physically important, example when $\Q$ is a small
category of finite sets.


title: Cosmology in a Higher-Curvature Gravity

abstract:
  We investigated the cosmology in a higher-curvature gravity where the
dimensionality of spacetime gives rise to only quantitative difference,
contrary to Einstein gravity. We found exponential type solutions for flat
isotropic and homogeneous vacuum universe for the case in which the
higher-curvature term in the Lagrangian density is quadratic in the scalar
curvature, $\xi R^2$. The solutions are classified according to the sign of the
cosmological constant, $\Lambda$, and the magnitude of $\Lambda\xi$. For these
solutions 3-dimensional space has a specific feature in that the solutions are
independent of the higher curvature term. For the universe filled with perfect
fluid, numerical solutions are investigated for various values of the parameter
$\xi$. Evolutions of the universes in different dimensionality of spacetime are
compared.


title:
The holostar - a self-consistent model for a compact self-gravitating
  object

abstract:
  The holostar is an exact spherically symmetric solution to the field
equations of general relativity with anisotropic interior pressure. Its
properties are similar to a black hole. It has an internal temperature inverse
proportional to the square root of the radial coordinate value, from which the
Hawking temperature law follows. The number of particles within any concentric
region of the holostar's interior is proportional to the proper area of its
boundary. The holostar-metric is static throughout the whole space-time. There
are no trapped surfaces, no singularity and no event horizon. Information is
not lost. The weak and strong energy conditions are fulfilled everywhere,
except for a Planck-size region at the center.
  Geodesic motion of massive particles in a large holostar is similar to what
is observed in the universe today: A material observer moving geodesically
experiences an isotropic outward directed Hubble-flow of massive particles. The
total matter-density decreases over proper time by an inverse square law. The
local Hubble radius increases linearly over time. Geodesic motion of photons
preserves the Planck-distribution. The local radiation temperature decreases
over time by an inverse square law. The current radial position r of an
observer can be determined by measurements of the total local mass-density, the
local radiation temperature or the local Hubble-flow. The values of r
determined from the CBMR-temperature, the Hubble constant and the total
mass-density of the universe are equal within an error of 15 percent to the
radius of the observable universe.
  The holographic solution also admits microscopic self-gravitating objects
with a surface area of roughly the Planck-area and zero gravitating mass.


title: Holostar thermodynamics

abstract:
  The holostar is an exact solution of the Einstein field equations with a
singularity free interior matter-density rho = 1 / (8 pi r^2) and a boundary
membrane consisting out of tangential pressure. Although the interior matter
has on overall string equation of state, part of the matter can be interpreted
in terms of particles. A simple thermodynamic model is presented, treating the
matter as an ideal gas of (ultrarelativistic) fermions and bosons.
  The number of ultra-relativistic particles within a holostar is proportional
its surface-area, indicating that the holographic principle is valid in
classical GR for self gravitating objects of any size. Using the grand
canonical formalism we show, that the interior temperature is given by T
\propto / \sqrt{r}. With a surface redshift z \propto \sqrt{r} the holostar's
temperature at infinity is equal to the Hawking result, up to a constant
factor. The factor depends on the number of particle degrees of freedom at the
Planck energy, which is estimated as f ~ 7000. The holostar's total
thermodynamic entropy is proportional to the area of its boundary membrane.
  The ultra-relativistic fermions in the interior space-time must acquire a
non-zero chemical potential, which acts as a natural source for a profound
matter-antimatter asymmetry at high temperatures.
  The local values of the interior temperature and matter-density are related
to the holostar's temperature at infinity, enabling a "measurement" of the
Hawking temperature from the interior space-time. Using the experimental values
for the CMBR-temperature and the total matter-density of the universe
determined by WMAP the Hawking result is verified to an accuracy of 1%.ior
particles. Some properties expected from a rotating holostar are discussed
briefly.


title: Charged holostars

abstract:
  A charged holostar is an exact solution of the Einstein field equations. Its
interior matter distribution rho = 1 / (8 pi r^2) is singularity free with an
overall string equation of state. It has a boundary membrane of tangential
pressure (but no mass-energy) situated roughly a Planck coordinate distance
outside of the outer horizon of the RN-solution with the same mass and charge.
  The geometric mass Mg = M + r0/2 of a charged holostar is always larger than
its charge. r0 is a Planck size correction to the gravitational mass M with r0
2 r_Pl. For a large holostar this condition is practically identical to the
classical condition M >= Q. Whereas RN solutions with M < Q are possible, a
charged holostar with Mg > Q doesn't exist.
  The total charge Q is derived by the proper integral over the interior charge
density, which is attributed to the charged massive particles. The interior
energy density splits into an electromagnetic and a "matter" contribution. Both
contributions are proportional to 1/r^2. The ratio of electro-magnetic to total
energy density rho_em / rho = 4 pi Q^2/A is constant throughout the whole
interior. It is related to the dimensionless ratio of the exterior conserved
quantities Q^2/A (or alternatively Q/M_g). An extremely charged holostar has a
surface area A = 4 pi Q^2, so that its interior energy density consists
entirely out of electromagnetic energy.
  A large holostar can be regarded as the classical analogue of a loop quantum
gravity (LQG) spin-network state. The Immirzi parameter is determined: g = s
/(pi \sqrt{3}), where s is the mean entropy per particle. g is larger by a
factor of ~4.8 than the LQG-result. An explanation for the discrepancy is
given.


title: Axisymmetric metrics in arbitrary dimensions

abstract:
  We consider axially symmetric static metrics in arbitrary dimension, both
with and without a cosmological constant. The most obvious such solutions have
an SO(n) group of Killing vectors representing the axial symmetry, although one
can also consider abelian groups which represent a flat `internal space'. We
relate such metrics to lower dimensional dilatonic cosmological metrics with a
Liouville potential. We also develop a duality relation between vacuum
solutions with internal curvature and those with zero internal curvature but a
cosmological constant. This duality relation gives a solution generating
technique permitting the mapping of different spacetimes. We give a large class
of solutions to the vacuum or cosmological constant spacetimes. We comment on
the extension of the C-metric to higher dimensions and provide a novel solution
for a braneworld black hole.


title: Asymptotic dynamics in 3D gravity with torsion

abstract:
  We study the nature of boundary dynamics in the teleparallel 3D gravity. The
asymptotic field equations with anti-de Sitter boundary conditions yield only
two non-trivial boundary modes, related to a conformal field theory with
classical central charge. After showing that the teleparallel gravity can be
formulated as a Chern-Simons theory, we identify dynamical structure at the
boundary as the Liouville theory.


title:
SyZyGy: A Straight Interferometric Spacecraft System for Gravity Wave
  Observations

abstract:
  We apply TDI, unfolding the general triangular configuration, to the special
case of a linear array of three spacecraft. We show that such an array
("SyZyGy") has, compared with an equilateral triangle GW detector of the same
scale, degraded (but non-zero) sensitivity at low-frequencies (f<<c/(arrany
size)) but similar peak and high-frequency sensitivities to GWs. Sensitivity
curves are presented for SyZyGys having various arm-lengths. A number of
technical simplifications result from the linear configuration. These include
only one faceted (e.g., cubical) proof mass per spacecraft, intra-spacecraft
laser metrology needed only at the central spacecraft, placement in a single
appropriate orbit can reduce Doppler drifts so that no laser beam modulation is
required for ultra-stable oscillator noise calibration, and little or no
time-dependent articulation of the telescopes to maintain pointing. Because
SyZyGy's sensitivity falls off more sharply at low frequency than that of an
equilateral triangular array, it may be more useful for GW observations in the
band between those of ground-based interferometers (10-2000 Hz) and LISA (.1
mHz-.1 Hz). A SyZyGy with ~1 light- second scale could, for the same
instrumental assumptions as LISA, make obseervations in this intermediate
frequency GW band with 5 sigma sensitivity to sinusoidal waves of ~2.5 x 10^-23
in a year's integration.


title:
On the thin-shell limit of branes in the presence of Gauss-Bonnet
  interactions

abstract:
  In this paper we study thick-shell braneworld models in the presence of a
Gauss-Bonnet term. We discuss the peculiarities of the attainment of the
thin-shell limit in this case and compare them with the same situation in
Einstein gravity. We describe the two simplest families of thick-brane models
(parametrized by the shell thickness) one can think of. In the thin-shell
limit, one family is characterized by the constancy of its internal density
profile (a simple structure for the matter sector) and the other by the
constancy of its internal curvature scalar (a simple structure for the
geometric sector). We find that these two families are actually equivalent in
Einstein gravity and that the presence of the Gauss-Bonnet term breaks this
equivalence. In the second case, a shell will always keep some non-trivial
internal structure, either on the matter or on the geometric sectors, even in
the thin-shell limit.


title: An explicit global covering of the Schwarzschild-Tangherlini black holes

abstract:
  Explicit regular coordinates that cover all of the Tangherlini solutions
(Schwarzschild black holes of dimension $D>4$) are given. The coordinates
reduce to Israel coordinates for D=4.


title: Conformal isometry of the Reissner-Nordstrom-de Sitter black hole

abstract:
  It was pointed out by Couch and Torrence that the extreme Reissner-Nordstrom
solution possesses a discrete conformal isometry. Using results of Romans, it
is shown that such a symmetry also exists when a non-zero cosmological constant
is allowed.


title: Relativistic Models for Binary Neutron Stars with Arbitrary Spins

abstract:
  We introduce a new numerical scheme for solving the initial value problem for
quasiequilibrium binary neutron stars allowing for arbitrary spins. The coupled
Einstein field equations and equations of relativistic hydrodynamics are solved
in the Wilson-Mathews conformal thin sandwich formalism. We construct sequences
of circular-orbit binaries of varying separation, keeping the rest mass and
circulation constant along each sequence. Solutions are presented for
configurations obeying an n=1 polytropic equation of state and spinning
parallel and antiparallel to the orbital angular momentum. We treat stars with
moderate compaction ((m/R) = 0.14) and high compaction ((m/R) = 0.19). For all
but the highest circulation sequences, the spins of the neutron stars increase
as the binary separation decreases. Our zero-circulation cases approximate
irrotational sequences, for which the spin angular frequencies of the stars
increases by 13% (11%) of the orbital frequency for (m/R) = 0.14 ((m/R) = 0.19)
by the time the innermost circular orbit is reached. In addition to leaving an
imprint on the inspiral gravitational waveform, this spin effect is measurable
in the electromagnetic signal if one of the stars is a pulsar visible from
Earth.


title: Relativity of GPS Measurement

abstract:
  The relativity of Global Positioning System (GPS) pseudorange measurements is
explored within the geometrical optics approximation in the curved space-time
near Earth. A space-time grid for navigation is created by the discontinuities
introduced in the electromagnetic field amplitude by the P-code broadcast by
the GPS satellites. We compute the world function of space-time near Earth, and
we use it to define a scalar phase function that describes the space-time grid.
We use this scalar phase function to define the measured pseudorange, which
turns out to be a two-point space-time scalar under generalized coordinate
transformations. Though the measured pseudorange is an invariant, it depends on
the world lines of the receiver and satellite. While two colocated receivers
measure two different pseudoranges to the same satellite, they obtain correct
position and time, independent of their velocity. We relate the measured
pseudorange to the geometry of space-time and find corrections to the
conventional model of pseudorange that are on the order of the gravitational
radius of the Earth.


title:
Study of an electro-optic modulator capable of generating simultaneous
  amplitude and phase modulations

abstract:
  We report on the analysis and prototype-characterization of a dual-electrode
electro-optic modulator that can generate both amplitude and phase modulations
with a selectable relative phase, termed a universally tunable modulator (UTM).
All modulation states can be reached by tuning only the electrical inputs,
facilitating real-time tuning, and the device is shown to have good suppression
and stability properties. A mathematical analysis is presented, including the
development of a geometric phase representation for modulation. The
experimental characterization of the device shows that relative suppressions of
38 dB, 39 dB and 30 dB for phase, single-sideband and carrier-suppressed
modulations, respectively, can be obtained, as well as showing the device is
well-behaved when scanning continuously through the parameter space of
modulations. Uses for the device are discussed, including the tuning of lock
points in optical locking schemes, single sideband applications, modulation
fast-switching applications, and applications requiring combined modulations.


title: On the Collapse of Charged Scalar Fields

abstract:
  We explore numerically the evolution of a collapsing spherical shell of
charged, massless scalar field. We obtain an external \RN space-time, and an
inner space-time that is bounded by a singularity on the Cauchy Horizon. We
compare these results with previous analysis and discuss some of the numerical
problems encountered.


title:
The geometrization of matter proposal in the Barrett-Crane model and
  resolution of cosmological problems

abstract:
  We give an overview of the current issues in early universe cosmology and
consider the potential resolution of these issues in an as yet nascent spin
foam cosmology. The model is the Barrett-Crane Model for quantum gravity along
with a generalization of manifold complexes to complexes including conical
singularities.


title: Loop variables in the geometry of a rotating black string

abstract:
  In this paper we analyze in the Wilson loop context the parallel transport of
vectors and spinors around a closed loop in the background space-time of a
rotating black string in order to classify its global properties. We also
examine particular closed orbits in this space-time and verify the Mandelstam
relations.


title: Quantum Mechanics at Planck's scale and Density Matrix

abstract:
  In this paper Quantum Mechanics with Fundamental Length is chosen as Quantum
Mechanics at Planck's scale. This is possible due to the presence in the theory
of General Uncertainty Relations. Here Quantum Mechanics with Fundamental
Length is obtained as a deformation of Quantum Mechanics. The distinguishing
feature of the proposed approach in comparison with previous ones, lies on the
fact that here density matrix subjects to deformation whereas so far
commutators have been deformed. The density matrix obtained by deformation of
quantum-mechanical density one is named throughout this paper density
pro-matrix. Within our approach two main features of Quantum Mechanics are
conserved: the probabilistic interpretation of the theory and the well-known
measuring procedure corresponding to that interpretation. The proposed approach
allows to describe dynamics. In particular, the explicit form of deformed
Liouville's equation and the deformed Shr\"odinger's picture are given. Some
implications of obtained results are discussed. In particular, the problem of
singularity, the hypothesis of cosmic censorship, a possible improvement of the
definition of statistical entropy and the problem of information loss in black
holes are considered. It is shown that obtained results allow to deduce in a
simple and natural way the Bekenstein-Hawking's formula for black hole entropy
in semiclassical approximation.


title: An Effective Search Method for Gravitational Ringing of Black Holes

abstract:
  We develop a search method for gravitational ringing of black holes. The
gravitational ringing is due to complex frequency modes called the quasi-normal
modes that are excited when a black hole geometry is perturbed. The detection
of it will be a direct confirmation of the existence of a black hole. Assuming
that the ringdown waves are dominated by the fundamental mode with least
imaginary part, we consider matched filtering and develop an optimal method to
search for the ringdown waves that have damped sinusoidal wave forms.
  When we use the matched filtering method, the data analysis with a lot of
templates required. Here we have to ensure a proper match between the filter as
a template and the real wave. It is necessary to keep the detection efficiency
as high as possible under limited computational costs.
  First, we consider the white noise case for which the matched filtering can
be studied analytically. We construct an efficient method for tiling the
template space. Then, using a fitting curve of the TAMA300 DT6 noise spectrum,
we numerically consider the case of colored noise. We find our tiling method
developed for the white noise case is still valid even if the noise is colored.


title: A Note On The Chern-Simons And Kodama Wavefunctions

abstract:
  Yang-Mills theory in four dimensions formally admits an exact Chern-Simons
wavefunction. It is an eigenfunction of the quantum Hamiltonian with zero
energy. It is known to be unphysical for a variety of reasons, but it is still
interesting to understand what it describes. We show that in expanding around
this state, positive helicity gauge bosons have positive energy and negative
helicity ones have negative energy. Some of the negative energy states would
have negative norm. We also show that the Chern-Simons state is the
supersymmetric partner of the naive fermion vacuum in which one does not fill
the fermi sea. Finally, we give a sort of explanation of ``why'' this state
exists. Similar properties can be expected for the analogous Kodama
wavefunction of gravity.


title: Gravitational decoherence

abstract:
  We investigate the effect of quantum metric fluctuations on qubits that are
gravitationally coupled to a background spacetime. In our first example, we
study the propagation of a qubit in flat spacetime whose metric is subject to
flat quantum fluctuations with a Gaussian spectrum. We find that these
fluctuations cause two changes in the state of the qubit: they lead to a phase
drift, as well as the expected exponential suppression (decoherence) of the
off-diagonal terms in the density matrix. Secondly, we calculate the
decoherence of a qubit in a circular orbit around a Schwarzschild black hole.
The no-hair theorems suggest a quantum state for the metric in which the black
hole's mass fluctuates with a thermal spectrum at the Hawking temperature.
Again, we find that the orbiting qubit undergoes decoherence and a phase drift
that both depend on the temperature of the black hole. Thirdly, we study the
interaction of coherent and squeezed gravitational waves with a qubit in
uniform motion. Finally, we investigate the decoherence of an accelerating
qubit in Minkowski spacetime due to the Unruh effect. In this case decoherence
is not due to fluctuations in the metric, but instead is caused by coupling
(which we model with a standard Hamiltonian) between the qubit and the thermal
cloud of Unruh particles bathing it. When the accelerating qubit is entangled
with a stationary partner, the decoherence should induce a corresponding loss
in teleportation fidelity.


title:
A gravitational memory effect in "boosted" black hole perturbation
  theory

abstract:
  Black hole perturbation theory, or more generally, perturbation theory on a
Schwarzschild bockground, has been applied in several contexts, but usually
under the simplifying assumption that the ADM momentum vanishes, namely, that
the evolution is carried out and observed in the ``center of momentum frame''.
In this paper we consider some consequences of the inclusion of a non vanishing
ADM momentum in the initial data. We first provide a justification for the
validity of the transformation of the initial data to the ``center of momentum
frame'', and then analyze the effect of this transformation on the
gravitational wave amplitude. The most significant result is the possibility of
a type of gravitational memory effect that appears to have no simple relation
with the well known Christodoulou effect.


title: SN1987A: Temporal Models

abstract:
  It is well known that carriers of astrophysical information are massless
spinning particles. These carriers are photons, neutrinos and, expectedly,
gravitons. All these particles are emitted during supernova events. Information
carried by these particles characterize their sources, but such information are
affected by the trajectories of the carriers. Recently, it is shown that these
trajectories are spin dependent. Knowing these trajectories and the arrival
times of such particles to the detectors, a spin dependent model is constructed
and compared with the conventional spin independent model.


title: Linear perturbations of spatially locally homogeneous spacetimes

abstract:
  Methods and properties regarding the linear perturbations are discussed for
some spatially closed (vacuum) solutions of Einstein's equation. The main focus
is on two kinds of spatially locally homogeneous solution; one is the Bianchi
III (Thurston's H^2 x R) type, while the other is the Bianchi II (Thurston's
Nil) type. With a brief summary of previous results on the Bianchi III
perturbations, asymptotic solutions for the gauge-invariant variables for the
Bianchi III are shown, with which (in)stability of the background solution is
also examined. The issue of linear stability for a Bianchi II solution is still
an open problem. To approach it, appropriate eigenfunctions are presented for
an explicitly compactified Bianchi II manifold and based on that, some field
equations on the Bianchi II background spacetime are studied. Differences
between perturbation analyses for Bianchi class B (to which Bianchi III
belongs) and class A (to which Bianchi II belongs) are stressed for an
intention to be helpful for applications to other models.


title: Gravitational Field of Massive Point Particle in General Relativity

abstract:
  Utilizing various gauges of the radial coordinate we give a description of
static spherically symmetric space-times with point singularity at the center
and vacuum outside the singularity. We show that in general relativity (GR)
there exist a two-parameters family of such solutions to the Einstein equations
which are physically distinguishable but only some of them describe the
gravitational field of a single massive point particle with nonzero bare mass
$M_0$. In particular, we show that the widespread Hilbert's form of
Schwarzschild solution, which depends only on the Keplerian mass $M<M_0$, does
not solve the Einstein equations with a massive point particle's stress-energy
tensor as a source. Novel normal coordinates for the field and a new physical
class of gauges are proposed, in this way achieving a correct description of a
point mass source in GR. We also introduce a gravitational mass defect of a
point particle and determine the dependence of the solutions on this mass
defect. The result can be described as a change of the Newton potential
$\phi_{{}_N}=-G_{{}_N}M/r$ to a modified one: $\phi_{{}_G}=-G_{{}_N}M/
(r+G_{{}_N} M/c^2\ln{{M_0}\over M})$ and a corresponding modification of the
four-interval. In addition we give invariant characteristics of the physically
and geometrically different classes of spherically symmetric static space-times
created by one point mass. These space-times are analytic manifolds with a
definite singularity at the place of the matter particle.


title: Surface plasmon toy-models of black holes and wormholes

abstract:
  Surface plasmons at metal interfaces are collective excitations of the
conduction electrons and the electromagnetic field. They exist in "curved
three-dimensional space-times" defined by the shape of the metal surface and
the spatial distribution of the dielectric constant near the surface. Here we
show that surface plasmon toy models of many non-trivial space-time metrics,
such as wormholes and black holes, can be easily built and studied in
experiments. For example, a droplet of dielectric on the metal surface behaves
as a black hole for surface plasmons within a substantial frequency range. On
the other hand, a nanohole in a thin metal membrane may be treated as a
wormhole connecting two "flat" surface plasmon worlds located on the opposite
interfaces of the membrane.


title: A self consistent solution to the Einstein Maxwell Dirac Equations

abstract:
  A self consistent solution to Dirac equation in a Kerr Newman space-time with
$M^2 > a^2 + Q^2$ is presented for the case when the Dirac particle is the
source of the curvature and the electromagnetic field. The solution is
localised, continuous everywhere and valid only for a special choice of the
parameters appearing in the Dirac equation.


title: Local Cosmology

abstract:
  We define the concept of a Maximally symmetric osculating space-time at any
event of any given Robertson-Walker model. We use this definition in two
circumstances: i) to approximate any given cosmological model by a simpler one
sharing the same observational parameters, i.e, the speed of light, the Hubble
constant and the deceleration parameter at the time of tangency, and ii) to
shed some light on the problem of considering an eventual influence of the
overall behaviour of the Universe on localized systems at smaller scales, or
viceversa.


title:
Electromagnetic response of a Gaussian beam to high-frequency relic
  gravitational waves in quintessential inflationary models

abstract:
  Maximal signal and peak of high-frequency relic gravitational waves (GW's),
recently expected by quintessential inflationary models, may be firmly
localized in the GHz region, the energy density of the relic gravitons in
critical units (i.e., $ h_0^2 \Omega_{GW}$) is of the order $10^{-6}$, roughly
eight orders of magnitude larger than in ordinary inflationary models. This is
just right best frequency band of the electromagnetic (EM) response to the
high-frequency GW's in smaller EM detecting systems. We consider the EM
response of a Gaussian beam passing through a static magnetic field to a
high-frequency relic GW. It is found that under the synchroresonance condition,
the first-order perturbative EM power fluxes will contain "left circular wave"
and "right circular wave" around the symmetrical axis of the Gaussian beam, but
the perturbative effects produced by the states of + polarization and $\times$
polarization of the relic GW have different properties, and the perturbations
on behavior are obviously different from that of the background EM fields in
the local regions. For the high-frequency relic GW with the typical parameters
$ \nu_g = 10^{10}Hz$, $ h = 10^{- 30} $ in the quintessential inflationary
models, the corresponding perturbative photon flux passing through the region $
10^{- 2} m^{2} $ would be expected to be $ 10^{3}s^{-1} $. This is largest
perturbative photon flux we recently analyzed and estimated using the typical
laboratory parameters. In addition, we also discuss geometrical phase shift
generated by the high-frequency relic GW in the Gaussian beam and estimate
possible physical effects.


title: Three Key Tests to Gravity

abstract:
  Three presumably unrelated open questions concerning gravity and the
structure of the Universe are here discussed: 1) To which extent is Lorentz
invariance an exact symmetry ? 2) What is the equation of state of the Universe
? 3) What is the origin of the so-called Pioneer anomaly ?


title:
The Fermionic Particle Density of Flat 1+1 Dimensional Spacetime seen by
  an Arbitrarily Moving Observer

abstract:
  A coordinate system is constructed for a general accelerating observer in 1+1
dimensions, and is used to determine the particle density of the massless Dirac
vacuum for that observer. Equations are obtained for the spatial distribution
and frequency distribution of massless fermions seen by this observer, in terms
of the rapidity function of the observer's worldline. Examples that are
considered include the uniformly accelerating observer as a limiting case, but
do not always involve particle horizons. Only the low frequency limit depends
on the possible presence of particle horizons. The rest of the spectrum is
`almost thermal' whenever the observer's acceleration is `almost uniform'.


title:
Discrete quantum gravity: a mechanism for selecting the value of
  fundamental constants

abstract:
  Smolin has put forward the proposal that the universe fine tunes the values
of its physical constants through a Darwinian selection process. Every time a
black hole forms, a new universe is developed inside it that has different
values for its physical constants from the ones in its progenitor. The most
likely universe is the one which maximizes the number of black holes. Here we
present a concrete quantum gravity calculation based on a recently proposed
consistent discretization of the Einstein equations that shows that fundamental
physical constants change in a random fashion when tunneling through a
singularity.


title: The Effects of Orbital Motion on LISA Time Delay Interferometry

abstract:
  In an effort to eliminate laser phase noise in laser interferometer
spaceborne gravitational wave detectors, several combinations of signals have
been found that allow the laser noise to be canceled out while gravitational
wave signals remain. This process is called time delay interferometry (TDI). In
the papers that defined the TDI variables, their performance was evaluated in
the limit that the gravitational wave detector is fixed in space. However, the
performance depends on certain symmetries in the armlengths that are available
if the detector is fixed in space, but that will be broken in the actual
rotating and flexing configuration produced by the LISA orbits. In this paper
we investigate the performance of these TDI variables for the real LISA orbits.
First, addressing the effects of rotation, we verify Daniel Shaddock's result
that the Sagnac variables will not cancel out the laser phase noise, and we
also find the same result for the symmetric Sagnac variable. The loss of the
latter variable would be particularly unfortunate since this variable also
cancels out gravitational wave signal, allowing instrument noise in the
detector to be isolated and measured. Fortunately, we have found a set of more
complicated TDI variables, which we call Delta-Sagnac variables, one of which
accomplishes the same goal as the symmetric Sagnac variable to good accuracy.
Finally, however, as we investigate the effects of the flexing of the detector
arms due to non-circular orbital motion, we show that all variables, including
the interferometer variables, which survive the rotation-induced loss of
direction symmetry, will not completely cancel laser phase noise when the
armlengths are changing with time. This unavoidable problem will place a
stringent requirement on laser stability of 5 Hz per root Hz.


title: Notes on Choptuik Phenomena

abstract:
  We review the work going on in black-hole physics during the last ten years,
called the Choptuik Phenomenon.


title: Mode coupling in the nonlinear response of black holes

abstract:
  We study the properties of the outgoing gravitational wave produced when a
non-spinning black hole is excited by an ingoing gravitational wave.
Simulations using a numerical code for solving Einstein's equations allow the
study to be extended from the linearized approximation, where the system is
treated as a perturbed Schwarzschild black hole, to the fully nonlinear regime.
Several nonlinear features are found which bear importance to the data analysis
of gravitational waves. When compared to the results obtained in the linearized
approximation, we observe large phase shifts, a stronger than linear generation
of gravitational wave output and considerable generation of radiation in
polarization states which are not found in the linearized approximation. In
terms of a spherical harmonic decomposition, the nonlinear properties of the
harmonic amplitudes have simple scaling properties which offer an economical
way to catalog the details of the waves produced in such black hole processes.


title: On The Relation of Weyl Geometry and Bohmian Quantum Mechanics

abstract:
  It is shown that the recently geometric formulation of quantum mechanics
implies the use of Weyl geometry. It is discussed that the natural framework
for both gravity and quantum is Weyl geometry. At the end a Weyl invariant
theory is built, and it is shown that both gravity and quantum are present at
the level of equations of motion.


title: Bohmian Quantum Gravity in the Linear Field Approximation

abstract:
  In this paper we have applied Bohmian quantum theory to the linear field
approximation of gravity and present a self--consistent quantum gravity theory
in the linear field approximation. The theory is then applied to some specific
problems, the Newtonian limit, and the static spherically symmetric solution.
Some observable effects of the theory are investigated.


title: Energy Distribution of a Stringy Charged Black Hole

abstract:
  The energy distribution associated with a stringy charged black hole is
studied using M{\o}ller's energy-momentum complex. Our result is reasonable and
it differs from that known in literature using Einstein's energy-momentum
complex.


title: On the Leibniz bracket, the Schouten bracket and the Laplacian

abstract:
  The Leibniz bracket of an operator on a (graded) algebra is defined and some
of its properties are studied. A basic theorem relating the Leibniz bracket of
the commutator of two operators to the Leibniz bracket of them, is obtained.
Under some natural conditions, the Leibniz bracket gives rise to a (graded) Lie
algebra structure. In particular, those algebras generated by the Leibniz
bracket of the divergence and the Laplacian operators on the exterior algebra
are considered, and the expression of the Laplacian for the product of two
functions is generalized for arbitrary exterior forms.


title: Universal approach to gravitational thermal effects

abstract:
  A universal scheme for describing gravitational thermal effects is developed
as a generalization of Unruh effect. Quasi-Rindler (QR) coordinates are
constructed in an arbitrary curved space-time in such a way that the imaginary
QR time be periodical. The observer at rest in QR coordinates should experience
a thermal effect. Application to de Sitter space-time is considered.


title: Aspects of Information Theory in Curved Space

abstract:
  The often-asked question whether space-time is discrete or continuous may not
be the right question to ask: Mathematically, it is possible that space-time
possesses the differentiability properties of manifolds as well as the
ultraviolet finiteness properties of lattices. Namely, physical fields in
space-time could possess a finite density of degrees of freedom in the
following sense: if a field's amplitudes are given on a sufficiently dense set
of discrete points then the field's amplitudes at all other points of the
manifold are fully determined and calculable. Which lattice of sampling points
is chosen should not matter, as long as the lattices' spacings are tight
enough, for example, not exceeding the Planck distance. This type of
mathematical structure is known within information theory, as sampling theory,
and it plays a central role in all of digital signal processing.


title:
Modern Michelson-Morley experiments and gravitationally-induced
  anisotropy of c

abstract:
  The recent, precise Michelson-Morley experiment performed by Muller et al.
suggests a tiny anisotropy of the speed of light. I propose a quantitative
explanation of the observed effect based on the interpretation of gravity as a
density fluctuation of the Higgs condensate.


title:
Stability of five-dimensional rotating black holes projected on the
  brane

abstract:
  We study the stability of five-dimensional Myers-Perry black holes with a
single angular momentum under linear perturbations, and we compute the
quasinormal modes (QNM's) of the black hole metric projected on the brane,
using Leaver's continued fraction method. In our numerical search we do not
find unstable modes. The damping time of modes having l=m=2 and l=m=1 tends to
infinity as the black hole spin tends to the extremal value, showing a
behaviour reminiscent of the one observed for ordinary 4-dimensional Kerr black
holes.


title: Spacetimes foliated by Killing horizons

abstract:
  It seems to be expected, that a horizon of a quasi-local type, like a Killing
or an isolated horizon, by analogy with a globally defined event horizon,
should be unique in some open neighborhood in the spacetime, provided the
vacuum Einstein or the Einstein-Maxwell equations are satisfied. The aim of our
paper is to verify whether that intuition is correct. If one can extend a so
called Kundt metric, in such a way that its null, shear-free surfaces have
spherical spacetime sections, the resulting spacetime is foliated by so called
non-expanding horizons. The obstacle is Kundt's constraint induced at the
surfaces by the Einstein or the Einstein-Maxwell equations, and the requirement
that a solution be globally defined on the sphere. We derived a transformation
(reflection) that creates a solution to Kundt's constraint out of data defining
an extremal isolated horizon. Using that transformation, we derived a class of
exact solutions to the Einstein or Einstein-Maxwell equations of very special
properties. Each spacetime we construct is foliated by a family of the Killing
horizons. Moreover, it admits another, transversal Killing horizon. The
intrinsic and extrinsic geometry of the transversal Killing horizon coincides
with the one defined on the event horizon of the extremal Kerr-Newman solution.
However, the Killing horizon in our example admits yet another Killing vector
tangent to and null at it. The geometries of the leaves are given by the
reflection.


title: On smooth Cauchy hypersurfaces and Geroch's splitting theorem

abstract:
  Given a globally hyperbolic spacetime $M$, we show the existence of a {\em
smooth spacelike} Cauchy hypersurface $S$ and, thus, a global diffeomorphism
between $M$ and $\R \times S$.


title: Algorithmic construction of static perfect fluid spheres

abstract:
  Perfect fluid spheres, both Newtonian and relativistic, have attracted
considerable attention as the first step in developing realistic stellar models
(or models for fluid planets). Whereas there have been some early hints on how
one might find general solutions to the perfect fluid constraint in the absence
of a specific equation of state, explicit and fully general solutions of the
perfect fluid constraint have only very recently been developed. In this
article we present a version of Lake's algorithm [Phys. Rev. D 67 (2003)
104015; gr-qc/0209104] wherein: (1) we re-cast the algorithm in terms of
variables with a clear physical meaning -- the average density and the locally
measured acceleration due to gravity, (2) we present explicit and fully general
formulae for the mass profile and pressure profile, and (3) we present an
explicit closed-form expression for the central pressure. Furthermore we can
then use the formalism to easily understand the pattern of inter-relationships
among many of the previously known exact solutions, and generate several new
exact solutions.


title:
Quantum mechanics without spacetime III: a proposal for a non-linear
  Schrodinger equation

abstract:
  It is proposed that the Schrodinger equation for a free point particle has
non-linear corrections which depend on the mass of the particle. It is assumed
that the corrections become extremely small when the mass is much smaller or
much larger than a critical value (the critical value being related to but
smaller than Planck mass). The corrections become significant when the mass is
close to this critical value and could play a role in explaining wave-function
collapse. It appears that such corrections are not ruled out by present day
experimental tests of the Schrodinger equation. Corrections to the energy
levels of a harmonic oscillator are calculated.


title: Non-singular black-holes on the brane

abstract:
  We investigate the possibility of obtaining non-singular black-hole solutions
in the brane world model by solving the effective field equations for the
induced metric on the brane. The Reissner-Nordstrom solution on the brane was
obtained by Dadhich etal by imposing the null energy condition on the 3-brane
for a bulk having non zero Weyl curvature. In this work, we relax the condition
of vanishing scalar curvature $R$, however, retaining the null condition. We
have shown that it is possible to obtain class of static non-singular
spherically symmetric brane space-times admitting horizon. We obtain one such
class of solution which is a regular version of the Reissner-Nordstrom solution
in the standard general relativity.


title:
Asymptotically anti-de Sitter space-times: symmetries and conservation
  laws revisited

abstract:
  In this short note, we verify explicitly in static coordinates that the non
trivial asymptotic Killing vectors at spatial infinity for anti-de Sitter
space-times correspond one to one to the conformal Killing vectors of the
conformally flat metric induced on the boundary. The fall-off conditions for
the metric perturbations that guarantee finiteness of the associated conserved
charges are derived.


title: Comments on Challenges for Quantum Gravity

abstract:
  We examine radiative corrections arising from Lorentz violating dimension
five operators presumably associated with Planck scale physics as recently
considered by Myers and Pospelov. We find that observational data result in
bounds on the dimensionless parameters of the order $10^{-15}$. These represent
the most stringent bounds on Lorentz violation to date.


title: Shortcuts to high symmetry solutions in gravitational theories

abstract:
  We apply the Weyl method, as sanctioned by Palais' symmetric criticality
theorems, to obtain those -highly symmetric -geometries amenable to explicit
solution, in generic gravitational models and dimension. The technique consists
of judiciously violating the rules of variational principles by inserting
highly symmetric, and seemingly gauge fixed, metrics into the action, then
varying it directly to arrive at a small number of transparent, indexless,
field equations. Illustrations include spherically and axially symmetric
solutions in a wide range of models beyond D=4 Einstein theory; already at D=4,
novel results emerge such as exclusion of Schwarzschild solutions in cubic
curvature models and restrictions on ``independent'' integration parameters in
quadratic ones. Another application of Weyl's method is an easy derivation of
Birkhoff's theorem in systems with only tensor modes. Other uses are also
suggested.


title: How Black Holes Grow

abstract:
  A summary of how black holes grow in full, non-linear general relativity is
presented. Specifically, a notion of "dynamical horizons" is introduced and
expressions of fluxes of energy and angular momentum carried by gravitational
waves across these horizons are obtained. Fluxes are local and the energy flux
is positive. Change in the horizon area is related to these fluxes. The flux
formulae also give rise to balance laws analogous to the ones obtained by Bondi
and Sachs at null infinity and provide generalizations of the first and second
laws of black hole mechanics.


title: Smooth branes and junction conditions in Einstein Gauss-Bonnet gravity

abstract:
  Using "smooth brane" solutions of the field equations, we give an alternative
derivation of the junction conditions for a "brane" in a five dimensional
"bulk", when gravity is governed by the Einstein Lanczos (Gauss-Bonnet)
equations.


title: Discontinuity surface instead of singularity

abstract:
  Einstein equations are addressed with the energy-momentum tensor that appears
if the equations under discussion are required to possess conformal invariance.
It is proved that thus derived equations (equations of conformally invariant
geometrodynamics) can have not only smooth solutions, but also solutions with
discontinuities on space-like hypersurfaces. The solutions obtained are similar
to the well-known discontinuous Einstein equation solutions like shock-wave
solutions, extended-source solutions, etc.
  For the centrally symmetric stationary solution discussed in the paper, the
discontinuity surface removes the singularity. The degree of generality of this
solution regularization mechanism is discussed. The issue of the mechanism that
forces any smooth solution in the conformally invariant geometrodynamics to be
rearranged into the discontinuous one when certain conditions are met is also
discussed. The conditions can be: (1) sound speed becoming to be higher than
light speed; (2) the solution becoming intolerant to smaller and smaller-scale
perturbation modes.


title: Asymptotic isotropization in inhomogeneous cosmology

abstract:
  In this paper we investigate asymptotic isotropization. We derive the
asymptotic dynamics of spatially inhomogeneous cosmological models with a
perfect fluid matter source and a positive cosmological constant near the de
Sitter equilibrium state at late times, and near the flat FL equilibrium state
at early times. Our results show that there exists an open set of solutions
approaching the de Sitter state at late times, consistent with the cosmic
no-hair conjecture. On the other hand, solutions that approach the flat FL
state at early times are special and admit a so-called isotropic initial
singularity. For both classes of models the asymptotic expansion of the line
element contains an arbitrary spatial metric at leading order, indicating
asymptotic spatial inhomogeneity. We show, however, that in the asymptotic
regimes this spatial inhomogeneity is significant only at super-horizon scales.


title: Self-similar Bianchi models: I. Class A models

abstract:
  We present a study of Bianchi class A tilted cosmological models admitting a
proper homothetic vector field together with the restrictions, both at the
geometrical and dynamical level, imposed by the existence of the simply
transitive similarity group. The general solution of the symmetry equations and
the form of the homothetic vector field are given in terms of a set of
arbitrary integration constants. We apply the geometrical results for tilted
perfect fluids sources and give the general Bianchi II self-similar solution
and the form of the similarity vector field. In addition we show that
self-similar perfect fluid Bianchi VII$_0$ models and irrotational Bianchi
VI$_0$ models do not exist.


title: Analytic black hole perturbation approach to gravitational radiation

abstract:
  We review analytic methods to perform the post-Newtonian expansion of
gravitational waves induced by a particle orbiting a massive compact body,
based on the black hole perturbation theory. There exist two different methods
of the post-Newtonian expansion. Both are based the Teukolsky equation. In one
method, the Teukolsky equation is transformed into a Regge-Wheeler type
equation that reduces to the standard Klein-Gordon equation in the flat space
limit, while in the other method, which were introduced by Mano, Suzuki and
Takasugi relatively recently, the Teukolsky equation is directly used in its
original form. The former has an advantage that it is intuitively easy to
understand how various curved space effects come into play. However, it becomes
increasingly complicated when one goes on to higher and higher post-Newtonian
orders. In contrast, the latter has an advantage that a systematic calculation
to higher post-Newtonian orders is relatively easily implementable, but
otherwise so mathematical that it is hard to understand the interplay of higher
order terms. In this paper, we review both methods so that their pros and cons
may be clearly seen. We also review some results of calculations of
gravitational radiation emitted by a particle orbiting a black hole.


title: C-field cosmological model in higher dimensions

abstract:
  Hoyle and Narlikar's $C$-field cosmology is extended in the framework of
higher dimensional spacetime and a class of exact solutions is obtained.
Adjusting the arbitrary constants of integration one can show that our model is
amenable to the desirable property of dimensional reduction so that the
universe ends up in an effective 4D one.Further with matter creation from the
$C$-field the mass density steadies with time and the usual bigbang singularity
is avoided. An alternative mechanism is also suggested which seems to provide
matter creation in the 4D spacetime although total matter in the 5D world
remains conserved. Quintessence phenomenon and energy conditions are also
discussed and it is found that in line with the physical requirements our model
admits a solution with a decelerating phase in the early era followed by an
accelerated expansion later. Moreover, as the contribution from the $C$-field
is made negligible a class of our solutions reduces to the previously known
higher dimensional models in the framework of Einstein's theory.


title: Tips for implementing multigrid methods on domains containing holes

abstract:
  As part of our development of a computer code to perform 3D `constrained
evolution' of Einstein's equations in 3+1 form, we discuss issues regarding the
efficient solution of elliptic equations on domains containing holes (i.e.,
excised regions), via the multigrid method. We consider as a test case the
Poisson equation with a nonlinear term added, as a means of illustrating the
principles involved, and move to a "real world" 3-dimensional problem which is
the solution of the conformally flat Hamiltonian constraint with Dirichlet and
Robin boundary conditions. Using our vertex-centered multigrid code, we
demonstrate globally second-order-accurate solutions of elliptic equations over
domains containing holes, in two and three spatial dimensions. Keys to the
success of this method are the choice of the restriction operator near the
holes and definition of the location of the inner boundary. In some cases (e.g.
two holes in two dimensions), more and more smoothing may be required as the
mesh spacing decreases to zero; however for the resolutions currently of
interest to many numerical relativists, it is feasible to maintain second order
convergence by concentrating smoothing (spatially) where it is needed most.
This paper, and our publicly available source code, are intended to serve as
semi-pedagogical guides for those who may wish to implement similar schemes.


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

abstract:
  By efforts of several authors, it is recently established that the dynamical
behavior of the cosmological perturbation on superhorizon scales is well
approximated in terms of that in the long wavelength limit, and the latter can
be constructed from the evolution of corresponding exactly homogeneous
universe. Using these facts, we investigate the evolution of the cosmological
perturbation on superhorizon scales in the universe dominated by oscillating
multiple scalar fields which are generally interacting with each other, and the
ratio of whose masses is incommensurable. Since the scalar fields oscillate
rapidly around the local minimum of the potential, we use the action angle
variables. We found that this problem can be formulated as the canonical
perturbation theory in which the perturbed part appearing as the result of the
expansion of the universe and the interaction of the scalar fields is bounded
by the negative power ot time. We show that by constructing the canonical
transformations properly, the transformed hamiltonian becomes simple enough to
be solved. As the result of the invetigation using the long wavelength limit
and the canonical perturbation theory, under the sufficiently general
conditions, we prove that for the adiabatic growing mode the Bardeen parameter
stays constant and that for all the other modes the Bardeen parameter decays.
  From the viewpoint of the ergodic theory, it is discussed that as for the
Bardeen parameter, the sigularities appear probabilistically. This analysis
serves the understanding of the evolution of the cosmological perturbations on
superhorizon scales during reheating.


title:
A numerical study of spectral properties of the area operator in loop
  quantum gravity

abstract:
  The lowest 37000 eigenvalues of the area operator in loop quantum gravity is
calculated and studied numerically. We obtain an asymptotical formula for the
eigenvalues as a function of their sequential number. The multiplicity of the
lowest few hundred eigenvalues is also determined and the smoothed spectral
density is calculated. The spectral density is presented for various number of
vertices, edges and SU(2) representations. A scaling form of spectral density
is found, being a power law for one vertex, while following an exponential for
several vertices. The latter case is explained on the basis of the one vertex
spectral density.


title: Operating LISA as a Sagnac interferometer

abstract:
  A phase-locking configuration for LISA is proposed that provides a
significantly simpler mode of operation. The scheme provides one Sagnac signal
readout inherently insensitive to laser frequency noise and optical bench
motion for a non-rotating LISA array. This Sagnac output is also insensitive to
clock noise, requires no time shifting of data, nor absolute arm length
knowledge. As all measurements are made at one spacecraft, neither clock
synchronization nor exchange of phase information between spacecraft is
required. The phase-locking configuration provides these advantages for only
one Sagnac variable yet retains compatibility with the baseline approach for
obtaining the other TDI variables. The orbital motion of the LISA constellation
is shown to produce a 14 km path length difference between the
counter-propagating beams in the Sagnac interferometer. With this length
difference a laser frequency noise spectral density of 1 Hz/$\sqrt{\rm Hz}$
would consume the entire optical path noise budget of the Sagnac variables. A
significant improvement of laser frequency stability (currently at 30
Hz/$\sqrt{\rm Hz}$) would be needed for full-sensitivity LISA operation in the
Sagnac mode. Alternatively, an additional level of time-delay processing could
be applied to remove the laser frequency noise. The new time-delayed
combinations of the phase measurements are presented.


title: Spin 0 and spin 1/2 particles in a constant scalar-curvature background

abstract:
  We study the Klein-Gordon and Dirac equations in the presence of a background
metric ds^2 = -dt^2 + dx^2 + e^{-2gx}(dy^2 + dz^2) in a semi-infinite lab
(x>0). This metric has a constant scalar curvature R=6g^2 and is produced by a
perfect fluid with equation of state p=-\rho /3. The eigenfunctions of spin-0
and spin-1/2 particles are obtained exactly, and the quantized energy
eigenvalues are compared. It is shown that both of these particles must have
nonzero transverse momentum in this background. We show that there is a minimum
energy E^2_{min}=m^2c^4 + g^2c^2\hbar^2$ for bosons E_{KG} > E_{min}, while the
fermions have no specific ground state E_{Dirac}>mc^2.


title: Discrete quantum modes of the Dirac field in $AdS_{d+1}$ backgrounds

abstract:
  It is shown that the free Dirac equation in spherically symmetric static
backgrounds of any dimensions can be put in a simple form using a special
version of Cartesian gauge in Cartesian coordinates. This is manifestly
covariant under the transformations of the isometry group so that the
generalized spherical coordinates can be separated in terms of angular spinors
like in the flat case, obtaining a pair of radial equations. In this approach
the equation of the free field Dirac in $AdS_{d+1}$ backgrounds is analytically
solved obtaining the formula of the energy levels and the corresponding
normalized eigenspinors.


title:
A direct kinematical derivation of the relativistic Sagnac effect for
  light or matter beams

abstract:
  The Sagnac time delay and the corresponding Sagnac phase shift, for
relativistic matter and electromagnetic beams counter-propagating in a rotating
interferometer, are deduced on the ground of relativistic kinematics. This
purely kinematical approach allows to explain the ''universality'' of the
effect, namely the fact that the Sagnac time difference does not depend on the
physical nature of the interfering beams. The only prime requirement is that
the counter-propagating beams have the same velocity with respect to any
Einstein synchronized local co-moving inertial frame.


title: Matter collineations of Spacetime Homogeneous G\"odel-type Metrics

abstract:
  The spacetime homogeneous G\"odel-type spacetimes which have four classes of
metrics are studied according to their matter collineations. The obtained
results are compared with Killing vectors and Ricci collineations. It is found
that these spacetimes have infinite number of matter collineations in
degenerate case, i.e. det$(T_{ab}) = 0$, and do not admit proper matter
collineations in non-degenerate case, i.e. det$(T_{ab}) \ne 0$. The degenerate
case has the new constraints on the parameters $m$ and $w$ which characterize
the causality features of the G\"odel-type spacetimes.


title:
Geometrical optics analysis of the short-time stability properties of
  the Einstein evolution equations

abstract:
  Many alternative formulations of Einstein's evolution have lately been
examined, in an effort to discover one which yields slow growth of
constraint-violating errors. In this paper, rather than directly search for
well-behaved formulations, we instead develop analytic tools to discover which
formulations are particularly ill-behaved. Specifically, we examine the growth
of approximate (geometric-optics) solutions, studied only in the future domain
of dependence of the initial data slice (e.g. we study transients). By
evaluating the amplification of transients a given formulation will produce, we
may therefore eliminate from consideration the most pathological formulations
(e.g. those with numerically-unacceptable amplification). This technique has
the potential to provide surprisingly tight constraints on the set of
formulations one can safely apply. To illustrate the application of these
techniques to practical examples, we apply our technique to the 2-parameter
family of evolution equations proposed by Kidder, Scheel, and Teukolsky,
focusing in particular on flat space (in Rindler coordinates) and Schwarzchild
(in Painleve-Gullstrand coordinates).


title: Coincidence analysis to search for inspiraling compact binaries

abstract:
  We discuss a method of coincidence analysis to search for gravitational waves
from inspiraling compact binaries using the data of two laser interferometer
gravitational wave detectors. We examine the allowed difference of the wave's
parameters estimated by each detector to obtain good detection efficiency. We
also discuss a method to set an upper limit to the event rate from the results
of the coincidence analysis. For the purpose to test above methods, we
performed a coincidence analysis by applying these methods to the real data of
TAMA300 and LISM detectors taken during 2001. We show that the fake event rate
is reduced significantly by the coincidence analysis without losing real events
very much. Results of the test analysis are also given.


title:
Breakdown of supersymmetry in homogeneous cosmologies in N=1
  supergravity

abstract:
  A condition of supersymmetric cosmological solutions of simple (N=1)
supergravity is formulated in the classical case. As an application we prove
that supersymmetry is spontaneously broken in Friedmann-Robertson-Walker type
cosmologies as well as in the Kasner universe, except for the Minkowski space.


title:
Surface-Gravity Inequalities and Generic Conditions for Strong Cosmic
  Censorship

abstract:
  Transforming Penrose's intuitive picture of a strong cosmic censorship
principle, that generically forbids the appearance of locally naked space-time
singularities, into a formal mathematical proof, remains at present, one of the
most outstanding unsolved mathematical problems from the theory of
gravitational collapse. Part of the difficulty lies in the fact that we do not
possess yet a clear-cut understanding of the hypothesis needed for the
establishment of some sort of strong cosmic censorship theorem. What we have is
a selected list of solutions, which at first sight seem to go against cosmic
censorship, but at the end they fail in some way. However, the space of
solutions of Einstein's field equations is vast. In this article, we plan to
increase one's intuition by establishing a link between certain inequalities
for Cauchy-horizon stability and a set of generic conditions, such as a
reasonable equation of state--which determines whether the space-time is
asymptotically flat or not, an energy condition, and an hypothesis over the
class of metrics on which Einstein's field equations ought to be solved to
ensure strong cosmic censorship inside black-holes. With these tools in hand we
examine the Cauchy-horizon stability of the theory created by Born and
Infeld--whose action principle has been used as a prototype in superstring
theory, and the singularity-free Bardeen's black-hole model.


title: Long time black hole evaporation with bounded Hawking flux

abstract:
  The long time behavior of an evaporating Schwarzschild black hole is studied
exploiting that it can be described by an effective theory in 2D, a particular
dilaton gravity model.
  A crucial technical ingredient is Izawa's result on consistent deformations
of 2D BF theory, while the most relevant physical assumption is boundedness of
the asymptotic matter flux during the whole evaporation process.
  An attractor solution, the endpoint of the evaporation process, is found. Its
metric is flat. However, the behavior of the dilaton field is nontrivial: it is
argued that during the final flicker a first order phase transition occurs from
a linear to a constant dilaton vacuum, thereby emitting a shock wave with a
total energy of a fraction of the Planck mass. Another fraction of the Planck
mass may reside in a cold remnant. [Note: More detailed abstract in the paper]


title: Singular shell embedded into a cosmological model

abstract:
  We generalize Israel's formalism to cover singular shells embedded in a
non-vacuum Universe. That is, we deduce the relativistic equation of motion for
a thin shell embedded in a Schwarzschild/Friedmann-Lemaitre-Robertson-Walker
spacetime. Also, we review the embedding of a Schwarzschild mass into a
cosmological model using "curvature" coordinates and give solutions with
(Sch/FLRW) and without the embedded mass (FLRW).


title: The constraints as evolution equations for numerical relativity

abstract:
  The Einstein equations have proven surprisingly difficult to solve
numerically. A standard diagnostic of the problems which plague the field is
the failure of computational schemes to satisfy the constraints, which are
known to be mathematically conserved by the evolution equations. We describe a
new approach to rewriting the constraints as first-order evolution equations,
thereby guaranteeing that they are satisfied to a chosen accuracy by any
discretization scheme. This introduces a set of four subsidiary constraints
which are far simpler than the standard constraint equations, and which should
be more easily conserved in computational applications. We explore the manner
in which the momentum constraints are already incorporated in several existing
formulations of the Einstein equations, and demonstrate the ease with which our
new constraint-conserving approach can be incorporated into these schemes.


title: Achieving geodetic motion for LISA test masses: ground testing result

abstract:
  The low-frequency resolution of space-based gravitational wave observatories
such as LISA (Laser Interferometry Space Antenna) hinges on the orbital purity
of a free-falling reference test mass inside a satellite shield. We present
here a torsion pendulum study of the forces that will disturb an orbiting test
mass inside a LISA capacitive position sensor. The pendulum, with a measured
torque noise floor below 10 fNm/sqrt{Hz} from 0.6 to 10 mHz, has allowed
placement of an upper limit on sensor force noise contributions, measurement of
the sensor electrostatic stiffness at the 5% level, and detection and
compensation of stray DC electrostatic biases at the mV level.


title:
General solutions of Einstein's spherically symmetric gravitational
  equations with junction conditions

abstract:
  Einstein's spherically symmetric interior gravitational equations are
investigated. Following Synge's procedure, the most general solution of the
equations is furnished in case $T^{1}_{1}$ and $T^{4}_{4}$ are prescribed. The
existence of a total mass function, $M(r,t)$, is rigorously proved. Under
suitable restrictions on the total mass function, the Schwarzschild mass
$M(r,t)=m$, implicitly defines the boundary of the spherical body as $r=B(t)$.
Both Synge's junction conditions as well as the continuity of the second
fundamental form are examined and solved in a general manner. The weak energy
conditions for an \emph{arbitrary boost} are also considered. The most general
solution of the spherically symmetric anisotropic fluid model satisfying both
junction conditions is furnished. In the final section, various exotic
solutions are explored using the developed scheme including gravitational
instantons, interior $T$-domains and $D$-dimensional generalizations.


title: Energy Distribution of a Stationary Beam of Light

abstract:
  Aguirregabiria et al showed that Einstein, Landau and Lifshitz, Papapetrou,
and Weinberg energy-momentum complexes coincide for all Kerr-Schild metric.
Bringely used their general expression of the Kerr-Schild class and found
energy and momentum densities for the Bonnor metric. We obtain these results
without using Aguirregabiria et al results and verify that Bringley's results
are correct. This also supports Aguirregabiria et al results as well as
Cooperstock hypothesis. Further, we obtain the energy distribution of the
space-time under consideration.


title: Proper co-ordinates of non-inertial observers and rotation

abstract:
  By proper co-ordinates of non-inertial observers (shortly - proper
non-inertial co-ordinates) we understand the proper co-ordinates of an
arbitrarily moving local observer. After a brief review of the theory of proper
non-inertial co-ordinates, we apply these co-ordinates to discuss the
relativistic effects seen by observers at different positions on a rotating
ring. Although there is no relative motion among observers at different
positions, they belong to different proper non-inertial frames. The
relativistic length seen by an observer depends only on his instantaneous
velocity, not on his acceleration or rotation. For any observer the velocity of
light is isotropic and equal to $c$, provided that it is measured by
propagating a light beam in a small neighbourhood of the observer.


title: Quasi-normal modes of Schwarzschild-de Sitter black holes

abstract:
  The low-laying frequencies of characteristic quasi-normal modes (QNM) of
Schwarzschild-de Sitter (SdS) black holes have been calculated for fields of
different spin using the 6th-order WKB approximation and the approximation by
the P\"{o}shl-Teller potential. The well-known asymptotic formula for large $l$
is generalized here on a case of the Schwarzchild-de Sitter black hole. In the
limit of the near extreme $\Lambda$ term the results given by both methods are
in a very good agreement, and in this limit fields of different spin decay with
the same rate.


title:
The interior of charged black holes and the problem of uniqueness in
  general relativity

abstract:
  We consider a spherically symmetric characteristic initial value problem for
the Einstein-Maxwell-scalar field equations. On the initial outgoing
characteristic, the data is assumed to satisfy the Price law decay widely
believed to hold on an event horizon arising from the collapse of an
asymptotically flat Cauchy surface. We establish that the heuristic mass
inflation scenario put forth by Israel and Poisson is mathematically correct in
the context of this initial value problem. In particular, the maximal domain of
development has a future boundary, over which the spacetime is extendible as a
continuous metric, but along which the Hawking mass blows up identically; thus,
the spacetime is inextendible as a differentiable metric. In view of recent
results of the author in collaboration with I. Rodnianski (gr-qc/0309115),
which rigorously establish the validity of Price's law as an upper bound for
the decay of scalar field hair, the continuous extendibility result applies to
the collapse of complete asymptotically flat spacelike data where the scalar
field is compactly supported on the initial hypersurface. This shows that under
Christodoulou's C^0 formulation, the strong cosmic censorship conjecture is
false for this system.


title: Quantum Mechanics and Discrete Time from "Timeless" Classical Dynamics

abstract:
  We study classical Hamiltonian systems in which the intrinsic proper time
evolution parameter is related through a probability distribution to the
physical time, which is assumed to be discrete. - This is motivated by the
``timeless'' reparametrization invariant model of a relativistic particle with
two compactified extradimensions. In this example, discrete physical time is
constructed based on quasi-local observables. - Generally, employing the
path-integral formulation of classical mechanics developed by Gozzi et al., we
show that these deterministic classical systems can be naturally described as
unitary quantum mechanical models. The emergent quantum Hamiltonian is derived
from the underlying classical one. It is closely related to the Liouville
operator. We demonstrate in several examples the necessity of regularization,
in order to arrive at quantum models with bounded spectrum and stable
groundstate.


title:
Impact of densitized lapse slicings on evolutions of a wobbling black
  hole

abstract:
  We present long-term stable and second-order convergent evolutions of an
excised wobbling black hole. Our results clearly demonstrate that the use of a
densitized lapse function extends the lifetime of simulations dramatically. We
also show the improvement in the stability of single static black holes when an
algebraic densitized lapse condition is applied. In addition, we introduce a
computationally inexpensive approach for tracking the location of the
singularity suitable for mildly distorted black holes. The method is based on
investigating the fall-off behavior and asymmetry of appropriate grid
variables. This simple tracking method allows one to adjust the location of the
excision region to follow the coordinate motion of the singularity.


title: Exact Scaling Solutions in Normal and Brans-Dicke Models of Dark Energy

abstract:
  A linear relationship between the Hubble expansion parameter and the time
derivative of the scalar field is explored in order to derive exact
cosmological, attractor-like solutions, both in Einstein's theory and in
Brans-Dicke gravity with two fluids: a background fluid of ordinary matter,
together with a self-interacting scalar field accounting for the dark energy in
the universe. A priori assumptions about the functional form of the
self-interaction potential or about the scale factor behavior are not
necessary. These are obtained as outputs of the assumed relationship between
the Hubble parameter and the time derivative of the scalar field. A parametric
class of scaling quintessence models given by a self-interaction potential of a
peculiar form: a combination of exponentials with dependence on the barotropic
index of the background fluid, arises. Both normal quintessence described by a
self-interacting scalar field minimally coupled to gravity and Brans-Dicke
quintessence given by a non-minimally coupled scalar field are then analyzed
and the relevance of these models for the description of the cosmic evolution
are discussed in some detail. The stability of these solutions is also briefly
commented on.


title: Head-on collision of ultrarelativistic charges

abstract:
  We consider the head-on collision of two opposite-charged point particles
moving at the speed of light. Starting from the field of a single charge we
derive in a first step the field generated by uniformly accelerated charge in
the limit of infinite acceleration. From this we then calculate explicitly the
burst of radiation emitted from the head-on collision of two charges and
discuss its distributional structure. The motivation for our investigation
comes from the corresponding gravitational situation where the head-on
collision of two ultrarelativistic particles (black holes) has recently aroused
renewed interest.


title: Generalized Uncertainty Relation in Thermodynamics

abstract:
  It is done by introducing of an additional term proportional to the interior
energy into the standard thermodynamic uncertainty relation that leads to
existence of the lower limit of inverse temperature


title: The gravitational energy-momentum flux

abstract:
  We present a continuity equation for the gravitational energy-momentum, which
is obtained in the framework of the teleparallel equivalent of general
relativity. From this equation it follows a general definition for the
gravitational energy-momentum flux. This definition is investigated in the
context of plane waves and of cylindrical Einstein-Rosen waves. We obtain the
well known value for the energy flux of plane gravitational waves, and conclude
that the latter exhibit features similar to plane electromagnetic waves.


title: The asymptotic quasinormal mode spectrum of non-rotating black holes

abstract:
  A conjectured connection to quantum gravity has led to a renewed interest in
highly damped black hole quasinormal modes (QNMs). In this paper we present
simple derivations (based on the WKB approximation) of conditions that
determine the asymptotic QNMs for both Schwarzschild and Reissner-Nordstrom
black holes. This confirms recent results obtained by
  Motl and Neitzke, but our analysis fills several gaps left by their
discussion. We study the Reissner-Nordstrom results in some detail, and show
that, in contrast to the asymptotic QNMs of a Schwarzschild black hole, the
Reissner-Nordstrom QNMs are typically not periodic in the imaginary part of the
frequency. This leads to the charged black hole having peculiar properties
which complicate an interpretation of the results.


title:
New Singular and Nonsingular Colliding Wave Solutions in Einstein -
  Maxwell - Scalar Theory

abstract:
  A technique is given to generate coupled scalar field solutions in colliding
Einstein - Maxwell (EM) waves. By employing the Bell - Szekeres solution as
seed and depending on the chosen scalar field it is possible to construct
nonsingular solutions. If the original EM solution is already singular addition
of scalar fields does not make the physics any better. In particular, scalar
field solution that is transformable to spherical symmetry is plagued with
singularities.