title: Attractor states and infrared scaling in de Sitter space

abstract:
  The renormalized expectation value of the energy-momentum tensor for a scalar
field with any mass m and curvature coupling xi is studied for an arbitrary
homogeneous and isotropic physical initial state in de Sitter spacetime. We
prove quite generally that <T_{ab}> has a fixed point attractor behavior at
late times, which depends only on m and xi, for any fourth order adiabatic
state that is infrared finite. Specifically, when m^2 + xi R > 0, <T_{ab}>
approaches the Bunch-Davies de Sitter invariant value at late times,
independently of the initial state. When m = xi = 0, it approaches instead the
de Sitter invariant Allen-Folacci value. When m = 0 and xi \ge 0 we show that
this state independent asymptotic value of the energy-momentum tensor is
proportional to the conserved geometrical tensor (3)H_{ab}, which is related to
the behavior of the quantum effective action of the scalar field under global
Weyl rescaling. This relationship serves to generalize the definition of the
trace anomaly in the infrared for massless, non-conformal fields. In the case
m^2 + xi R = 0, but m and xi separately different from zero, <T_{ab}> grows
linearly with cosmic time at late times. For most values of m and xi in the
tachyonic cases, m^2 + xi R < 0, <T_{ab}> grows exponentially at late cosmic
times for all physically admissable initial states.


title: p-Adic and Adelic Generalization of Quantum Cosmology

abstract:
  p-Adic and adelic generalization of ordinary quantum cosmology is considered.
In [1], we have calculated p-adic wave functions for some minisuperspace
cosmological models according to the "no-boundary" Hartle-Hawking proposal. In
this article, applying p-adic and adelic quantum mechanics, we show existence
of the corresponding vacuum eigenstates. Adelic wave function contains some
information on discrete structure of space-time at the Planck scale.


title: Quintessential Inflation with Dissipative fluid

abstract:
  We have investigated cosmological models with a self-interacting scalar field
and a dissipative matter fluid as the sources of matter. Different variables
are expressed in terms of a {\it generating function}. Exact solutions are
obtained for one particular choice of the {\it generating function} The
potential corresponding to this generating function is a standard tree-level
potential arising in the perturbative regime in quantum field theory. With
suitable choice of parameters, the scale factor in our model exhibits both
inflationary behaviour in the early universe as well as an accelerating phase
at late times with a decelerating period in between. It also satisfies the
constraints for primeval nucleosynthesis and structure formation and seems to
solve the cosmic coincidence problem. The solution exhibits a attractor nature
towards a asymptotic de-sitter universe.


title:
Statistical Entropy of a Stationary Dilaton Black Hole from Cardy
  Formula

abstract:
  With Carlip's boundary conditions, a standard Virasoro subalgebra with
corresponding central charge for stationary dilaton black hole obtained in the
low-energy effective field theory describing string is constructed at a Killing
horizon. The statistical entropy of stationary dilaton black hole yielded by
standard Cardy formula agree with its Bekenstein-Hawking entropy only if we
take period $ T$ of function $v$ as the periodicity of the Euclidean black
hole. On the other hand, if we consider first-order quantum correction then the
entropy contains a logarithmic term with a factor $-{1/2}$, which is different
from Kaul and Majumdar's one, $-{3/2}$. We also show that the discrepancy is
not just for the dilaton black hole, but for any one whose corresponding
central change takes the form $\frac{c}{12}= \frac{A_H}{8\pi
G}\frac{2\pi}{\kappa T}$.


title: Optical geometry for gravitational collapse and Hawking radiation

abstract:
  The notion of optical geometry, introduced more than twenty years ago as a
formal tool in quantum field theory on a static background, has recently found
several applications to the study of physical processes around compact objects.
In this paper we define optical geometry for spherically symmetric
gravitational collapse, with the purpose of extending the current formalism to
physically interesting spacetimes which are not conformally static. The
treatment is fully general but, as an example, we also discuss the special case
of the Oppenheimer-Snyder model. The analysis of the late time behaviour shows
a close correspondence between the structure of optical spacetime for
gravitational collapse and that of flat spacetime with an accelerating
boundary. Thus, optical geometry provides a natural physical interpretation for
derivations of the Hawking effect based on the ``moving mirror analogy.''
Finally, we briefly discuss the issue of back-reaction in black hole
evaporation and the information paradox from the perspective of optical
geometry.


title:
Possibility of Control of the Gravitational Mass by means of Extra-Low
  Frequencies Radiation

abstract:
  According to the weak form of Einstein's general relativity equivalence
principle, the gravitational and inertial masses are equivalent. However recent
calculations (gr-qc/9910036) have revealed that they are correlated by an
adimensional factor, which is equal to one in absence of radiation only. We
have built an experimental system to check this unexpected theoretical result.
It verifies the effects of the extra-low frequency (ELF) radiation on the
gravitational mass of a body. We show that there is a direct correlation
between the radiation absorbed by the body and its gravitational mass,
independently of the inertial mass. This has fundamental consequences to
Unified Field Theory and Quantum Cosmology.


title: Divergence of a quantum thermal state on Kerr space-time

abstract:
  We present a simple proof, using the conservation equations, that any quantum
stress tensor on Kerr space-time which is isotropic in a frame which rotates
rigidly with the angular velocity of the event horizon must be divergent at the
velocity of light surface. We comment on our result in the light of the absence
of a `true Hartle-Hawking' vacuum for Kerr.


title:
Rotating Bianchi type V dust models generalizing the k = -1 Friedmann
  model

abstract:
  The Einstein equations for one of the hypersurface-homogeneous rotating dust
models are investigated. It is a Bianchi type V model in which one of the
Killing fields is spanned on velocity and rotation (case 1.2.2.2 in the
classification scheme of the earlier papers). A first integral of the field
equations is found, and with a special value of this integral coordinate
transformations are used to eliminate two components of the metric. The k = -1
Friedmann model is shown to be contained among the solutions in the limit of
zero rotation. The field equations for the simplified metric are reduced to 3
second-order ordinary differential equations that determine 3 metric components
plus a first integral that algebraically determines the fourth component. First
derivatives of the metric components are subject to a constraint (a
second-degree polynomial with coefficients depending on the functions). It is
shown that the set does not follow from a Lagrangian of the Hilbert type. The
group of Lie point-symmetries of the set is found, it is two-dimensional
noncommutative. Finally, a method of searching for first integrals (for sets of
differential equations) that are polynomials of degree 1 or 2 in the first
derivatives is applied. No such first integrals exist. The method is used to
find a constraint (of degree 1 in first derivatives) that could be imposed on
the metric, but it leads to a vacuum solution, and so is of no interest for
cosmology.


title: Asymptotic freedom of general relativity and its possible consequences

abstract:
  The formation of singularities in certain situations, such as the collapse of
massive stars, is one of the unresolved issues in classical general relativity.
Although no complete theory of quantum gravity exists it is often suggested
that quantum gravity effects may prevent the formation of these singularities.
In this article we will present arguments that a quantized theory of gravity
might exhibit asymptotic freedom. Considering the similarites between
non-Abelian gauge theories and general relativity it is conjectured that a
quantized theory of gravity may have a coupling strength which decreases with
increasing energy scale. Such a scale dependent coupling strength, could
provide a concrete mechanism for preventing the formation of singularities.


title: Huge Violations of Bekenstein's Entropy Bound

abstract:
  Bekenstein's conjectured entropy bound for a system of linear size R and
energy E, S < 2 pi E R, can be violated by an arbitrarily large factor, among
other ways, by a scalar field having a symmetric potential allowing domain
walls, and by the electromagnetic field modes between an arbitrarily large
number of conducting plates.


title: Quantum-Mechanical Detection of Non-Newtonian Gravity

abstract:
  In this work the possibility of detecting the presence of a Yukawa term, as
an additional contribution to the usual Newtonian gravitational potential, is
introduced. The central idea is to analyze the effects at quantum level
employing interference patterns (at this respect the present proposal resembles
the Colella, Overhauser and Werner experiment), and deduce from it the possible
effects that this Yukawa term could have. We will prove that the corresponding
interference pattern depends on the phenomenological parameters that define
this kind of terms. Afterwards, using the so called restricted path integral
formalism, the case of a particle whose position is being continuously
monitored, is analyzed, and the effects that this Yukawa potential could have
on the measurement outputs are obtained. This allows us to obtain another
scheme that could lead to the detection of these terms. This last part also
renders new theoretical predictions that could enable us to confront the
restricted path integral formalism against some future experiments.


title: Constant Crunch Coordinates for Black Hole Simulations

abstract:
  We reinvestigate the utility of time-independent constant mean curvature
foliations for the numerical simulation of a single spherically-symmetric black
hole. Each spacelike hypersurface of such a foliation is endowed with the same
constant value of the trace of the extrinsic curvature tensor, $K$. Of the
three families of $K$-constant surfaces possible (classified according to their
asymptotic behaviors), we single out a sub-family of singularity-avoiding
surfaces that may be particularly useful, and provide an analytic expression
for the closest approach such surfaces make to the singularity. We then utilize
a non-zero shift to yield families of $K$-constant surfaces which (1) avoid the
black hole singularity, and thus the need to excise the singularity, (2) are
asymptotically null, aiding in gravity wave extraction, (3) cover the
physically relevant part of the spacetime, (4) are well behaved (regular)
across the horizon, and (5) are static under evolution, and therefore have no
``grid stretching/sucking'' pathologies. Preliminary numerical runs demonstrate
that we can stably evolve a single spherically-symmetric static black hole
using this foliation. We wish to emphasize that this coordinatization produces
$K$-constant surfaces for a single black hole spacetime that are regular,
static and stable throughout their evolution.


title: Power, energy, and spectrum of a naked singularity explosion

abstract:
  Naked singularity occurs in the gravitational collapse of an inhomogeneous
dust ball from an initial density profile which is physically reasonable. We
show that explosive radiation is emitted during the formation process of the
naked singularity. The energy flux is proportional to $(t_{\rm CH}-t)^{-3/2}$
for a minimally coupled massless scalar field, while is proportional to
$(t_{\rm CH}-t)^{-1}$ for a conformally coupled massless scalar field, where
$t_{\rm CH}-t$ is the `remained time' until the distant observer could observe
the singularity if the naked singularity was formed. As a consequence, the
radiated energy grows unboundedly for both scalar fields. The amount of the
power and the energy depends on parameters which characterize the initial
density profile but do not depend on the gravitational mass of the cloud. In
particular, there is characteristic frequency $\nu_{s}$ of singularity above
which the divergent energy is radiated. The energy flux is dominated by
particles of which the wave length is about $t_{\rm CH}-t$ at each moment. The
observed total spectrum is nonthermal, i.e., $\nu dN/d\nu \sim
(\nu/\nu_{s})^{-1}$ for $\nu>\nu_{s}$. If the naked singularity formation could
continue until a considerable fraction of the total energy of the dust cloud is
radiated, the radiated energy would reach about $10^{54}(M/M_{\odot})$ erg. The
calculations are based on the geometrical optics approximation which turns out
to be consistent as a rough order estimate. The analysis does not depend on
whether or not the naked singularity occurs in its exact meaning. This
phenomenon may provide a new candidate for a source of ultra high energy cosmic
rays or a central engine of gamma ray bursts.


title: Hawking Radiation from AdS Black Holes

abstract:
  We investigate Hawking radiation from black holes in (d+1)-dimensional
anti-de Sitter space. We focus on s-waves, make use of the geometrical optics
approximation, and follow three approaches to analyze the radiation. First, we
compute a Bogoliubov transformation between Kruskal and asymptotic coordinates
and compare the different vacua. Second, following a method due to Kraus,
Parikh, and Wilczek, we view Hawking radiation as a tunneling process across
the horizon and compute the tunneling probablility. This approach uses an
anti-de Sitter version of a metric originally introduced by Painleve for
Schwarzschild black holes. From the tunneling probability one also finds a
leading correction to the semi-classical emission rate arising from the
backreaction to the background geometry. Finally, we consider a spherically
symmetric collapse geometry and the Bogoliubov transformation between the
initial vacuum state and the vacuum of an asymptotic observer.


title:
Dynamics of spatially homogeneous locally rotationally symmetric
  solutions of the Einstein-Vlasov equations

abstract:
  The dynamics of the Einstein-Vlasov equations for a class of cosmological
models with four Killing vectors is discussed in the case of massive particles.
It is shown that in all models analysed the solutions with massive particles
are asymptotic to solutions with massless particles at early times. It is also
shown that in Bianchi types I and II the solutions with massive particles are
asymptotic to dust solutions at late times. That Bianchi type III models are
also asymptotic to dust solutions at late times is consistent with our results
but is not established by them.


title: $\hat{Q}$ operator for canonical quantum gravity

abstract:
  We study the properties of $\hat{Q}[\omega]$ operator on the kinematical
Hilbert space ${\cal H}$ for canonical quantum gravity. Its complete spectrum
with respect to the spin network basis is obtained. It turns out that
$\hat{Q}[\omega]$ is diagonalized in this basis, and it is a well defined
self-adjoint operator on ${\cal H}$. The same conclusions are also tenable on
the SU(2) gauge invariant Hilbert space with the gauge invariant spin network
basis.


title: Cyclical Behaviour in Early Universe Cosmologies

abstract:
  We study early universe cosmologies derived from a scalar-tensor action
containing cosmological constant terms and massless fields. The governing
equations can be written as a dynamical system which contains no past or future
asymptotic equilibrium states (i.e. no sources nor sinks). This leads to
dynamics with very interesting mathematical behaviour such as the existence of
heteroclinic cycles. The corresponding cosmologies have novel characteristics,
including cyclical and bouncing behaviour possibly indicating chaos. We discuss
the connection between these early universe cosmologies and those derived from
the low-energy string effective action.


title: Modified Black Hole with Polar Jet and Vortex

abstract:
  There are many models relating an accretion disk of Black Hole to jet
outflow. The herein heuristic model describes the continuation of an external
accretion disk to an internal accretion disk for less than Black Hole horizon,
and subsequent polar jet outflow along polar axis out of polar vortex wherein
the event horizon is no longer descriptive.


title: Null surfaces formulation in 3D

abstract:
  The Null Surface Formulation of General Relativity is developed for 2+1
dimensional gravity. The geometrical meaning of the metricity condition is
analyzed and two approaches to the derivation of the field equations are
presented. One method makes explicit use of the conformal factor while the
other only uses conformal information. The resulting set of equations contain
the same geometrical meaning as the 4-D formulation without the technical
complexities of the higher dimensional analog. A canonical family of null
surfaces in this formulation, the light cone cuts of null infinity, are
constructed on asymptotically flat space times and some of their kinematical
aspects discussed. A particular example, which nevertheless contains most of
the generic features is explicitly constructed and analyzed, revealing the
behavior predicted in the full theory.


title: Non-time-orthogonal Reference Frames in the Theory of Relativity

abstract:
  A simple, though rarely considered, thought experiment on relativistic
rotation is described in which internal inconsistencies in the theory of
relativity seem to arise. These apparent inconsistencies are resolved by
appropriate insight into the nature, and unique properties, of the
non-time-orthogonal rotating frame. The analysis also explains a heretofore
inexplicable experimental result.


title:
On the Influence of Einstein-Podolsky-Rosen (EPR) Effect on the
  Probability of Domain-Wall Formation during a Cosmological Phase Transition

abstract:
  Evading formation of the domain walls in cosmological phase transitions is
one of the key problems to be solved for getting agreement with the observed
large-scale homogeneity of the Universe. The previous attempts to get around
this obstacle led to imposing severe observational constraints on the
parameters of the fields involved. Our aim is to show that yet another way to
overcome the above problem is accounting for EPR effect. Namely, if the scalar
(Higgs) field was presented by a single quantum state at the initial instant of
time, then its reduction during a phase transition at some later instant should
be correlated even at distances exceeding the local cosmological horizon. By
considering a simplest 1D model with Z_2 Higgs field, we demonstrate that EPR
effect really can substantially reduce the probability of spontaneous creation
of the domain walls.


title: Non-differentiable Degrees of Freedom : Fluctuating Metric Signature

abstract:
  In this article we investigate the metric signature as a non-differentiable
({\it i.e.} discrete as opposed to continuous) degree of freedom. The specific
model is a vacuum 7D Universe on the principal bundle with an SU(2) structural
group. An analytical solution is found which to a 4D observer appears as a flat
Universe with a fluctuating metric signature, and frozen extra dimensions with
an SU(2) instanton gauge field. A piece of this solution with linear size of
the Planck length ($\approx l_{Pl}$) can be considered as seeding the quantum
birth of a regular Universe. A boundary of this piece can initiate the
formation of a Lorentzian Universe filled with the gauge fields and in which
the extra dimensions have been ``frozen''.


title: Maximal Acceleration Effects in Reissner-Nordstrom Space

abstract:
  The dynamics of a relativistic particle in a Reissner-Nordstrom background is
studied using Caianiello model with maximal acceleration. The behaviour of the
particle, embedded in a new effective geometry, changes with respect to the
classical scenario because of the formation of repulsive potential barriers
near the horizon. Black hole formation by accretion of massive particles is not
therefore a viable process in the model. At the same time, the naked
singularity remains largely unaffected by maximal acceleration corrections.


title: Quasi-normal modes of charged, dilaton black holes

abstract:
  In this paper we study the perturbations of the charged, dilaton black hole,
described by the solution of the low energy limit of the superstring action
found by Garfinkle, Horowitz and Strominger. We compute the complex frequencies
of the quasi-normal modes of this black hole, and compare the results with
those obtained for a Reissner-Nordstr\"{o}m and a Schwarzschild black hole. The
most remarkable feature which emerges from this study is that the presence of
the dilaton breaks the \emph{isospectrality} of axial and polar perturbations,
which characterizes both Schwarzschild and Reissner-Nordstr\"{o}m black holes.


title: Quantum Geometry of Isolated Horizons and Black Hole Entropy

abstract:
  Using the earlier developed classical Hamiltonian framework as the point of
departure, we carry out a non-perturbative quantization of the sector of
general relativity, coupled to matter, admitting non-rotating isolated horizons
as inner boundaries. The emphasis is on the quantum geometry of the horizon.
Polymer excitations of the bulk quantum geometry pierce the horizon endowing it
with area. The intrinsic geometry of the horizon is then described by the
quantum Chern-Simons theory of a U(1) connection on a punctured 2-sphere, the
horizon. Subtle mathematical features of the quantum Chern-Simons theory turn
out to be important for the existence of a coherent quantum theory of the
horizon geometry. Heuristically, the intrinsic geometry is flat everywhere
except at the punctures. The distributional curvature of the U(1) connection at
the punctures gives rise to quantized deficit angles which account for the
overall curvature. For macroscopic black holes, the logarithm of the number of
these horizon microstates is proportional to the area, irrespective of the
values of (non-gravitational) charges. Thus, the black hole entropy can be
accounted for entirely by the quantum states of the horizon geometry. Our
analysis is applicable to all non-rotating black holes, including the
astrophysically interesting ones which are very far from extremality.
Furthermore, cosmological horizons (to which statistical mechanical
considerations are known to apply) are naturally incorporated. An effort has
been made to make the paper self-contained by including short reviews of the
background material.


title:
Currents and Superpotentials in classical gauge theories: II. Global
  aspects and the example of Affine gravity

abstract:
  The conserved charges associated to gauge symmetries are defined at a
boundary component of space-time because the corresponding Noether current can
be rewritten on-shell as the divergence of a superpotential. However, the
latter is afflicted by ambiguities. Regge and Teitelboim found a procedure to
lift the arbitrariness in the Hamiltonian framework. An alternative covariant
formula was proposed by one of us for an arbitrary variation of the
superpotential, it depends only on the equations of motion and on the gauge
symmetry under consideration. Here we emphasize that in order to compute the
charges, it is enough to stay at a boundary of spacetime, without requiring any
hypothesis about the bulk or about other boundary components, so one may speak
of holographic charges. It is well known that the asymptotic symmetries that
lead to conserved charges are really defined at infinity, but the choice of
boundary conditions and surface terms in the action and in the charges is
usually determined through integration by parts whereas each component of the
boundary should be considered separately. We treat the example of gravity (for
any space-time dimension, with or without cosmological constant), formulated as
an Affine theory which is a natural generalization of the Palatini and
Cartan-Weyl (vielbein) first order formulations. We then show that the
superpotential associated to a Dirichlet boundary condition on the metric (the
one needed to treat asymptotically flat or AdS spacetimes) is the one proposed
by Katz, Bi\u{c}{\'a}k and Lynden-Bell and not that of Komar. We finally
discuss the KBL superpotential at null infinity.


title: New Developments in the Search for the Topology of the Universe

abstract:
  Multi-connected Universe models with space idenfication scales smaller than
the size of the observable universe produce topological images in the catalogs
of cosmic sources. In this review, we present the recent developments for the
search of the topology of the universe focusing on three dimensional methods.
We present the crystallographic method, we give a new lower bound on the size
of locally Euclidean multi-connected universe model of $3000 h^{-1} \hbox{Mpc}$
based on this method and a quasar catalog, we discuss its successes and
failures, and the attemps to generalise it. We finally introduce a new
statistical method based on a collecting correlated pair (CCP) technique.


title: No Black Hole Theorem in Three-Dimensional Gravity

abstract:
  A common property of known black hole solutions in (2+1)-dimensional gravity
is that they require a negative cosmological constant. In this letter, it is
shown that a (2+1)-dimensional gravity theory which satisfies the dominant
energy condition forbids the existence of a black hole to explain the above
situation.


title:
Diffusion of the electromagnetic energy due to the backscattering off
  Schwarzschild geometry

abstract:
  Electromagnetic waves propagate in the Schwarzschild spacetime like in a
nonuniform medium with a varying refraction index. A fraction of the radiation
scatters off the curvature of the geometry. The energy of the backscattered
part of an initially outgoing pulse of electromagnetic radiation can be
estimated, in the case of dipole radiation, by a compact formula depending on
the initial energy, the Schwarzschild radius and the pulse location. The
magnitude of the backscattered energy depends on the frequency spectrum of the
initial configuration. This effect becomes negligible in the short wave limit,
but it can be significant in the long wave regime. Similar results hold for the
massless scalar fields and are expected to hold also for weak gravitational
waves.


title: Sonic black holes in dilute Bose-Einstein condensates

abstract:
  The sonic analog of a gravitational black hole in dilute-gas Bose-Einstein
condensates is investigated. It is shown that there exist both dynamically
stable and unstable configurations which, in the hydrodynamic limit, exhibit a
behavior completely analogous to that of gravitational black holes. The
dynamical instabilities involve creation of quasiparticle pairs in positive and
negative energy states. We illustrate these features in two qualitatively
different one-dimensional models, namely, a long, thin condensate with an
outcoupler laser beam providing an ``atom sink,'' and a tight ring-shaped
condensate. We have also simulated the creation of a stable sonic black hole by
solving the Gross-Pitaevskii equation numerically for a condensate subject to a
trapping potential which is adiabatically deformed. A sonic black hole could in
this way be created experimentally with state-of-the-art or planned technology.


title: Dynamics of the formation of an event horizon

abstract:
  The radial motion of matter in a centrally symmetric gravitational field in a
comoving reference frame is investigated for a realistic equation of state of
matter. The dynamics of the formation of an event horizon are investigated.


title:
Vacuum Energy Density Fluctuations in Minkowski and Casimir States via
  Smeared Quantum Fields and Point Separation

abstract:
  We present calculations of the variance of fluctuations and of the mean of
the energy momentum tensor of a massless scalar field for the Minkowski and
Casimir vacua as a function of an intrinsic scale defined by a smeared field or
by point separation. We point out that contrary to prior claims, the ratio of
variance to mean-squared being of the order unity is not necessarily a good
criterion for measuring the invalidity of semiclassical gravity. For the
Casimir topology we obtain expressions for the variance to mean-squared ratio
as a function of the intrinsic scale (defined by a smeared field) compared to
the extrinsic scale (defined by the separation of the plates, or the
periodicity of space). Our results make it possible to identify the spatial
extent where negative energy density prevails which could be useful for
studying quantum field effects in worm holes and baby universe, and for
examining the design feasibility of real-life `time-machines'.
  For the Minkowski vacuum we find that the ratio of the variance to the
mean-squared, calculated from the coincidence limit, is identical to the value
of the Casimir case at the same limit for spatial point separation while
identical to the value of a hot flat space result with a temporal
point-separation. We analyze the origin of divergences in the fluctuations of
the energy density and discuss choices in formulating a procedure for their
removal, thus raising new questions into the uniqueness and even the very
meaning of regularization of the energy momentum tensor for quantum fields in
curved or even flat spacetimes when spacetime is viewed as having an extended
structure.


title: Low Frequency Gravitational Waves from White Dwarf MACHO Binaries

abstract:
  The possibility that Galactic halo MACHOs are white dwarfs has recently
attracted much attention. Using the known properties of white dwarf binaries in
the Galactic disk as a model, we estimate the possible contribution of halo
white dwarf binaries to the low-frequency (10^{-5} Hz} < f < 10^{-1}Hz)
gravitational wave background. Assuming the fraction of white dwarfs in
binaries is the same in the halo as in the disk, we find the confusion
background from halo white dwarf binaries could be five times stronger than the
expected contribution from Galactic disk binaries, dominating the response of
the proposed space based interferometer LISA. Low-frequency gravitational wave
observations will be the key to discovering the nature of the dark MACHO binary
population.


title: External symmetry in general relativity

abstract:
  We propose a generalization of the isometry transformations to the geometric
context of the field theories with spin where the local frames are explicitly
involved. We define the external symmetry transformations as isometries
combined with suitable tetrad gauge transformations and we show that these form
a group which is locally isomorphic with the isometry one. We point out that
the symmetry transformations that leave invariant the equations of the fields
with spin have generators with specific spin terms which represent new physical
observables. The examples we present are the generators of the central symmetry
and those of the maximal symmetries of the de Sitter and anti-de Sitter
spacetimes derived in different tetrad gauge fixings.
  Pacs: 04.20.Cv, 04.62.+v, 11.30.-j


title: Time in Quantum Geometrodynamics

abstract:
  We revisit the issue of time in quantum geometrodynamics and suggest a
quantization procedure on the space of true dynamic variables. This procedure
separates the issue of quantization from enforcing the constraints caused by
the general covariance symmetries. The resulting theory, unlike the standard
approach, takes into account the states that are off shell with respect to the
constraints, and thus avoids the problems of time. In this approach, quantum
geometrodynamics, general covariance, and the interpretation of time emerge
together as parts of the solution of the total problem of geometrodynamic
evolution.


title: Rotating Relativistic Thin Disks

abstract:
  Two families of models of rotating relativistic disks based on Taub-NUT and
Kerr metrics are constructed using the well-known "displace, cut and reflect"
method. We find that for disks built from a generic stationary axially
symmetric metric the "sound velocity", $(pressure/density)^{1/2}$, is equal to
the geometric mean of the prograde and retrograde geodesic circular velocities
of test particles moving on the disk. We also found that for generic disks we
can have zones with heat flow. For the two families of models studied the
boundaries that separate the zones with and without heat flow are not stable
against radial perturbations (ring formation).


title: On Page's examples challenging the entropy bound

abstract:
  According to the entropy bound, the entropy of a complete physical system can
be universally bounded in terms of its circumscribing radius and total
gravitating energy. Page's three recent candidates for counterexamples to the
bound are here clarified and refuted by stressing that the energies of all
essential parts of the system must be included in the energy the bound speaks
about. Additionally, in response to an oft heard claim revived by Page, I give
a short argument showing why the entropy bound is obeyed at low temperatures by
a complete system. Finally, I remark that Page's renewed appeal to the
venerable ``many species'' argument against the entropy bound seems to be
inconsistent with quantum field theory.


title: Dynamical Formation of Horizons in Recoiling D Branes

abstract:
  A toy calculation of string/D-particle interactions within a world-sheet
approach indicates that quantum recoil effects - reflecting the gravitational
back-reaction on space-time foam due to the propagation of energetic particles
- induces the appearance of a microscopic event horizon, or `bubble', inside
which stable matter can exist. The scattering event causes this horizon to
expand, but we expect quantum effects to cause it to contract again, in a
`bounce' solution. Within such `bubbles', massless matter propagates with an
effective velocity that is less than the velocity of light in vacuo, which may
lead to observable violations of Lorentz symmetry that may be tested
experimentally. The conformal invariance conditions in the interior geometry of
the bubbles select preferentially three for the number of the spatial
dimensions, corresponding to a consistent formulation of the interaction of D3
branes with recoiling D particles, which are allowed to fluctuate independently
only on the D3-brane hypersurface.


title: Black Hole Critical Phenomena Without Black Holes

abstract:
  Studying the threshold of black hole formation via numerical evolution has
led to the discovery of fascinating nonlinear phenomena. Power-law mass
scaling, aspects of universality, and self-similarity have now been found for a
large variety of models. However, questions remain. Here I briefly review
critical phenomena, discuss some recent results, and describe a model which
demonstrates similar phenomena without gravity.


title: Generic Isolated Horizons and their Applications

abstract:
  Boundary conditions defining a generic isolated horizon are introduced. They
generalize the notion available in the existing literature by allowing the
horizon to have distortion and angular momentum. Space-times containing a black
hole, itself in equilibrium but possibly surrounded by radiation, satisfy these
conditions. In spite of this generality, the conditions have rich consequences.
They lead to a framework, somewhat analogous to null infinity, for extracting
physical information, but now in the \textit{strong} field regions. The
framework also generalizes the zeroth and first laws of black hole mechanics to
more realistic situations and sheds new light on the `origin' of the first law.
Finally, it provides a point of departure for black hole entropy calculations
in non-perturbative quantum gravity.


title:
A class of colliding waves in metric-affine gravity, nonmetricity and
  torsion shock waves

abstract:
  By using our recent generalization of the colliding waves concept to
metric-affine gravity theories, and also our generalization of the advanced and
retarded time coordinate representation in terms of Jacobi functions, we find a
general class of colliding wave solutions with fourth degree polynomials in
metric-affine gravity. We show that our general approach contains the standard
second degree polynomials colliding wave solutions as a particular case.


title:
Gauge and Cutoff Function Dependence of the Ultraviolet Fixed Point in
  Quantum Gravity

abstract:
  The exact renormalization group equation for pure quantum gravity is derived
for an arbitrary gauge parameter in the space-time dimension $d=4$. This
equation is given by a non-linear functional differential equation for the
effective average action. An action functional of the effective average action
is approximated by the same functional space of the Einstein-Hilbert action.
  From this approximation, $\beta$-functions for the dimensionless Newton
constant and cosmological constant are derived non-perturbatively. These are
used for an analysis of the phase structure and the ultraviolet non-Gaussian
fixed point of the dimensionless Newton constant. This fixed point strongly
depends on the gauge parameter and the cutoff function. However, this fixed
point exists without these ambiguities, except for some gauges. Hence, it is
possible that pure quantum gravity in $d=4$ is an asymptotically safe theory
and non-perturbatively renormalizable.


title:
The classical regime of a quantum universe obtained through a functional
  method

abstract:
  The functional method, introduced to deal with systems endowed with a
continuous spectrum, is used to study the problem of decoherence and
correlations in a simple cosmological model.


title: Entropy gap and time asymmetry II

abstract:
  In this letter the paper [R. Aquilano, M. Castagnino, Mod. Phys. Lett A,11,
755 (1996)] is improved by considering that the main source of entropy
production are the stars photospheres.


title:
Addemdum to: ''The Mathematical Structure of Quantum Superspace as a
  Consequence of Time Asymmetry''

abstract:
  In this paper we improve the results of sec. VI of paper [M. Castagnino,
Phys. Rev. D 57, 750 (1998)] by considering that the main source of entropy
production are the photospheres of the stars.


title:
Functional Approach to Quantum Decoherence and the Classical Final
  Limit: the Mott and Cosmological problems

abstract:
  Decoherence and the approach to the classical final limit are studied in two
similar cases: the Mott and the Cosmological problems.


title: Hamiltonian analysis of General relativity with the Immirzi parameter

abstract:
  Starting from a Lagrangian we perform the full constraint analysis of the
Hamiltonian for General relativity in the tetrad-connection formulation for an
arbitrary value of the Immirzi parameter and solve the second class
constraints, presenting the theory with a Hamiltonian composed of first class
constraints which are the generators of the gauge symmetries of the action. In
the time gauge we then recover Barbero's formulation of gravity.


title:
Regular Magnetic Black Holes and Monopoles from Nonlinear
  Electrodynamics

abstract:
  It is shown that general relativity coupled to nonlinear electrodynamics
(NED) with the Lagrangian $L(F)$, $F = F_mn F^mn$ having a correct weak field
limit, leads to nontrivial static, spherically symmetric solutions with a
globally regular metric if and only if the electric charge is zero and $L(F)$
tends to a finite limit as $F \to \infty$. Properties and examples of such
solutions, which include magnetic black holes and soliton-like objects
(monopoles), are discussed. Magnetic solutions are compared with their electric
counterparts. A duality between solutions of different theories specified in
two alternative formulations of NED (called $FP$ duality) is used as a tool for
this comparison.


title: Extended Thermodynamics to Einstein-Cartan Cosmology

abstract:
  The thermodynamics is extented to spacetimes with spin-torsion
density.Impplications to Einstein-Cartan-de Sitter inflationary phases are
discussed.A relation between the spin-torsion density,entropy and temperature
is presented.A lower limit for the radius of the Universe may be obtained from
the spin-torsion density and the Planck lenght.


title: An Approximate Model of the Spacetime Foam

abstract:
  An approximate model of the spacetime foam is offered in which a quantum
handle (wormhole) is a 5D wormhole-like solution. Neglecting the linear sizes
of the wormhole throat we can introduce a spinor field for an approximate and
effective description of the foam. The definition of the spinor field can be
made by a dynamic and non-dynamic ways. In the first case some field equations
are used and the second case leads to superspace. It is shown that : the
spacetime with the foam is similar to a dielectric with dipoles and
supergravity theories with a non-minimal interaction between spinor and
electromagnetic fields can be considered as an effective model for the
spacetime foam.


title: On the convergence of Regge calculus to general relativity

abstract:
  Motivated by a recent study casting doubt on the correspondence between Regge
calculus and general relativity in the continuum limit, we explore a mechanism
by which the simplicial solutions can converge whilst the residual of the Regge
equations evaluated on the continuum solutions does not. By directly
constructing simplicial solutions for the Kasner cosmology we show that the
oscillatory behaviour of the discrepancy between the Einstein and Regge
solutions reconciles the apparent conflict between the results of Brewin and
those of previous studies. We conclude that solutions of Regge calculus are, in
general, expected to be second order accurate approximations to the
corresponding continuum solutions.


title:
The Issue of Choosing Nothing: What Determines the Low Energy Vacuum
  State of Nature?

abstract:
  Starting from an (unknown) quantum gravitational model, one can invoke a
sequence of approximations to progressively arrive at quantum field theory
(QFT) in curved spacetime, QFT in flat spacetime, nonrelativistic quantum
mechanics and newtonian mechanics. The more exact theory can put restrictions
on the range of possibilities allowed for the approximate theory which are not
derivable from the latter - an example being the symmetry restrictions on the
wave function for a pair of electrons. We argue that the choice of vacuum state
at low energies could be such a `relic' arising from combining the principles
of quantum theory and general relativity, and demonstrate this result in a
simple toy model. Our analysis suggests that the wave function of the universe,
when it describes the large volume limit of the universe, dynamically selects a
vacuum state for matter fields - which in turn defines the concept of particle
in the low energy limit. The result also has the potential for providing a
concrete quantum mechanical version of Mach's principle.


title:
Negative Norm States in de Sitter Space and QFT without Renormalization
  Procedure

abstract:
  In recent papers [1,2], it has been shown that the presence of negative norm
states or negative frequency solutions are indispensable for a fully covariant
quantization of the minimally coupled scalar field in de Sitter space. Their
presence, while leaving unchanged the physical content of the theory, offers
the advantage of eliminating any ultraviolet divergence in the vacuum energy
[2] and infrared divergence in the two point function [3]. We attempt here to
extend this method to the interacting quantum field in Minkowski space-time. As
an illustration of the procedure, we consider the $\lambda\phi^4$ theory in
Minkowski space-time. The mathematical consequences of this method is the
disappearance of the ultraviolet divergence to the one-loop approximation. This
means, the effect of these auxiliary negative norm states is to allow an
automatic renormalization of the theory in this approximation.


title: Fractal Scales in a Schwarzschild Atmosphere

abstract:
  Recently, Glass and Krisch have extended the Vaidya radiating metric to
include both a radiation fluid and a string fluid [1999 Class. Quantum Grav.
vol 16, 1175]. Mass diffusion in the extended Schwarzschild atmosphere was
studied. The continuous solutions of classical diffusive transport are believed
to describe the envelope of underlying fractal behavior. In this work we
examine the classical picture at scales on which fractal behavior might be
evident.


title: Probing Quantum Aspects of Gravity

abstract:
  We emphasize that a specific aspect of quantum gravity is the absence of a
super-selection rule that prevents a linear superposition of different
gravitational charges. As an immediate consequence, we obtain a tiny, but
observable, violation of the equivalence principle, provided, inertial and
gravitational masses are not assumed to be operationally identical objects. In
this framework, the cosmic gravitational environment affects local experiments.
A range of terrestrial experiments, from neutron interferometry to neutrino
oscillations, can serve as possible probes to study the emergent quantum
aspects of gravity.


title: Probing Quantum Violations of the Equivalence Principle

abstract:
  The joint realm of quantum mechanics and the general-relativistic description
of gravitation is becoming increasingly accessible to terrestrial experiments
and observations. In this essay we study the emerging indications of the
violation of equivalence principle (VEP). While the solar neutrino anomaly may
find its natural explanation in a VEP, the statistically significant
discrepancy observed in the gravitationally induced phases of neutron
interferometry seems to be the first indication of a VEP. However, such a view
would seem immediately challenged by the atomic interferometry results. The
latter experiments see no indications of VEP, in apparent contradiction to the
neutron interferometry results. Here we present arguments that support the view
that these, and related torsion pendulum experiments, probe different aspects
of gravity; and that current experimental techniques, when coupled to the
solar-neutrino data, may be able to explore quantum mechanically induced
violations of the equivalence principle. We predict quantum violation of the
equivalence principle (qVEP) for next generation of atomic interferometry
experiments. The prediction entails comparing free fall of two different linear
superpositions of Cesium atomic states.


title: Non-time-orthogonality and Tests of Special Relativity

abstract:
  An intriguing, and possibly significant, anomalous signal in the Brillet and
Hall experiment is contrasted with a simple first order test of special
relativity subsequently performed to discount that signal as spurious. Analysis
of the non-time-orthogonal nature of the rotating earth frame leads to the
conclusion that the latter test needed second order accuracy in order to detect
the effect sought, and hence was not sufficient to discount the potential cause
of the anomalous signal. The analysis also explains the results found in Sagnac
type experiments wherein different media were placed in the path of the light
beams.


title: Spaces with contravariant and covariant affine connections and metrics

abstract:
  The theory of spaces with different (not only by sign) contravariant and
covariant affine connections and metrics [}$(\bar{L}_n,g)$\QTR{it}{-spaces] is
worked out within the framework of the tensor analysis over differentiable
manifolds and in a volume necessary for the further considerations of the
kinematics of vector fields and the Lagrangian theory of tensor fields
over}$(\bar{L}_n,g)$\QTR{it}{-spaces. The possibility of introducing affine
connections (whose components differ not only by sign) for contravariant and
covariant tensor fields over differentiable manifolds with finite dimensions is
discussed. The action of the deviation operator, having an important role for
deviation equations in gravitational physics, is considered for the case of
contravariant and covariant vector fields over differentiable manifolds with
different affine connections A deviation identity for contravariant vector
fields is obtained. The notions covariant, contravariant, covariant projective,
and contravariant projective metrics are introduced in
(}$\bar{L}_n,g$\{)-spaces. The action of the covariant and the Lie differential
operators on the different type of metrics is found. The notions of symmetric
covariant and contravariant (Riemannian) connections are determined and
presented by means of the covariant and contravariant metrics and the
corresponding torsion tensors. The different types of relative tensor fields
(tensor densities) as well as the invariant differential operators acting on
them are considered. The invariant volume element and its properties under the
action of different differential operators are investigated.


title: Global embeddings of scalar-tensor theories in (2+1)-dimensions

abstract:
  We obtain (3+3)- or (3+2)-dimensional global flat embeddings of four
uncharged and charged scalar-tensor theories with the parameters B or L in the
(2+1)-dimensions, which are the non-trivially modified versions of the
Banados-Teitelboim-Zanelli (BTZ) black holes. The limiting cases B=0 or L=0
exactly are reduced to the Global Embedding Minkowski Space (GEMS) solution of
the BTZ black holes.


title:
Demonstration of detuned dual recycling at the Garching 30m laser
  interferometer

abstract:
  Dual recycling is an advanced optical technique to enhance the
signal-to-noise ratio of laser interferometric gravitational wave detectors in
a limited bandwidth. To optimise the center of this band with respect to
Fourier frequencies of expected gravitational wave signals detuned dual
recycling has to be implemented. We demonstrated detuned dual recycling on a
fully suspended 30m prototype interferometer. A control scheme that allows to
tune the detector to different frequencies will be outlined. Good agreement
between the experimental results and numerical simulations has been achieved.


title: Quantization of the Taub cosmological model with extrinsic time

abstract:
  The paper addresses the quantization of minisuperspace cosmological models,
with application to the Taub Model. By desparametrizing the model with an
extrinsic time, a formalism is developed in order to define a conserved
Schr\"{o}dinger inner product in the space of solutions of the Wheeler-De Witt
equation. A quantum version of classical canonical transformations is
introduced for connecting the solutions of the Wheeler-De Witt equation with
the wave functions of the desparametrized system. Once this correspondence is
established, boundary conditions on the space of solutions of the Wheeler-De
Witt equation are found to select the physical subspace. The question of
defining boundary conditions on the space of solutions of the Wheeler-De Witt
equation without having reduced the system is examined.


title: Entropy generation in cosmological particle creation

abstract:
  A very simplified model of the Universe is considered in order to propose an
alternative approach to the irreversible evolution of the Universe at very
early times. The entropy generation at the quantum stage can be thought as a
consequence of an instability of the system. Then particle creation arises from
this instability.


title: General Relativity and Spatial Flows: I. Absolute Relativistic Dynamics

abstract:
  Two complementary and equally important approaches to relativistic physics
are explained. One is the standard approach, and the other is based on a study
of the flows of an underlying physical substratum. Previous results concerning
the substratum flow approach are reviewed, expanded, and more closely related
to the formalism of General Relativity. An absolute relativistic dynamics is
derived in which energy and momentum take on absolute significance with respect
to the substratum. Possible new effects on satellites are described.


title: Non-linear gravitational wave interactions with plasmas

abstract:
  We consider the interactions of a strong gravitational wave with
electromagnetic fields using the 1+3 orthonormal tetrad formalism. A general
system of equations are derived, describing the influence of a plane fronted
parallel (pp) gravitational wave on a cold relativistic multi-component plasma.
We focus our attention on phenomena that are induced by terms that are higher
order in the gravitational wave amplitude. In particular, it is shown that
parametric excitations of plasma oscillations takes place, due to higher order
gravitational non-linearities. The implications of the results are discussed.


title: Renormalization Group Approach to Cosmological Back Reaction Problems

abstract:
  We investigated the back reaction of cosmological perturbations on the
evolution of the universe using the second order perturbation of the Einstein's
equation. To incorporate the back reaction effect due to the inhomogeneity into
the framework of the cosmological perturbation, we used the renormalization
group method. The second order zero mode solution which appears by the
non-linearities of the Einstein's equation is regarded as a secular term of the
perturbative expansion, we renormalized a constant of integration contained in
the background solution and absorbed the secular term to this constant. For a
dust dominated universe, using the second order gauge invariant quantity, we
derived the renormalization group equation which determines the effective
dynamics of the Friedman-Robertson-Walker universe with the back reaction
effect in a gauge invariant manner. We obtained the solution of the
renormalization group equation and found that perturbations of the scalar mode
and the long wavelength tensor mode works as positive spatial curvature, and
the short wavelength tensor mode as radiation fluid.


title: Metric-affine gravity and the Nester-Witten 2-form

abstract:
  In this paper we redefine the well-known metric-affine Hilbert Lagrangian in
terms of a spin-connection and a spin-tetrad. On applying the Poincar\'e-Cartan
method and using the geometry of gauge-natural bundles, a global gravitational
superpotential is derived. On specializing to the case of the Kosmann lift, we
recover the result originally found by Kijowski (1978) for the metric (natural)
Hilbert Lagrangian. On choosing a different, suitable lift, we can also recover
the Nester-Witten 2-form, which plays an important role in the energy
positivity proof and in many quasi-local definitions of mass.


title: On the concept of mass point in general relativity

abstract:
  The correct characterization of the concept of mass point in general
relativity is a straightforward consequence of the original form of solution
given by Schwarzschild to the problem of the Einstein field of a material
point.


title: Self-similar spherically symmetric wave maps coupled to gravity

abstract:
  We investigate spherically symmetric continuously self-similar (CSS)
solutions in the SU(2) sigma model coupled to gravity. Using mixed numerical
and analytical methods, we provide evidence for the existence (for small
coupling) of a countable family of regular CSS solutions. This fact is argued
to have important implications for the ongoing studies of black hole formation
in the model.


title: The Bianchi IX attractor

abstract:
  We consider the asymptotic behaviour of spatially homogeneous spacetimes of
Bianchi type IX close to the singularity (we also consider some of the other
Bianchi types, e. g. Bianchi VIII in the stiff fluid case). The matter content
is assumed to be an orthogonal perfect fluid with linear equation of state and
zero cosmological constant. In terms of the variables of Wainwright and Hsu, we
have the following results. In the stiff fluid case, the solution converges to
a point for all the Bianchi class A types. For the other matter models we
consider, the Bianchi IX solutions generically converge to an attractor
consisting of the closure of the vacuum type II orbits. Furthermore, we observe
that for all the Bianchi class A spacetimes, except those of vacuum Taub type,
a curvature invariant is unbounded in the incomplete directions of inextendible
causal geodesics.


title: Nonthermal nature of extremal Kerr black holes

abstract:
  Liberati, Rothman and Sonego have recently showed that objects collapsing
into extremal Reissner-Nordstrom black holes do not behave as thermal objects
at any time in their history. In particular, a temperature, and hence
thermodynamic entropy, are undefined for them. I demonstrate that the analysis
goes through essentially unchanged for Kerr black holes.


title:
Equivalence principle and radiation by a uniformly accelerated charged
  particle

abstract:
  We address the old question of whether or not a uniformly accelerated charged
particle radiates, and consequently, if weak equivalence principle is violated
by electrodynamics. We show that radiation has different meanings; some
absolute, some relative. Detecting photons or electromagnetic waves is NOT
absolute, it depends both on the electromagnetic field and on the state of
motion of the antenna. An antenna used by a Rindler observer does not detect
any radiation from a uniformly accelerated co-moving charged particle.
Therefore, a Rindler observer cannot decide whether or not he is in an
accelerated lab or in a gravitational field. We also discuss the general case.


title: Horizon Instability in the Cross Polarized Bell-Szekeres Spacetime

abstract:
  The quasiregular singularities (horizons) that form in the collision of cross
polarized electromagnetic waves are, as in the linear polarized case unstable.
The validity of the Helliwell-Konkowski stability conjecture is tested for a
number of exact back-reaction cases. In the test electromagnetic case the
conjecture fails to predict the correct nature of the singularity while in the
scalar field and in the null dust cases the aggrement is justified.


title: The Quantum States and the Statistical Entropy of the Charged Black Hole

abstract:
  We quantize the Reissner-Nordstr\"om black hole using an adaptation of
Kucha\v{r}'s canonical decomposition of the Kruskal extension of the
Schwarzschild black hole. The Wheeler-DeWitt equation turns into a functional
Schroedinger equation in Gaussian time by coupling the gravitational field to a
reference fluid or dust. The physical phase space of the theory is spanned by
the mass, $M$, the charge, $Q$, the physical radius, $R$, the dust proper time,
$\tau$, and their canonical momenta. The exact solutions of the functional
Schroedinger equation imply that the difference in the areas of the outer and
inner horizons is quantized in integer units. This agrees in spirit, but not
precisely, with Bekenstein's proposal on the discrete horizon area spectrum of
black holes. We also compute the entropy in the microcanonical ensemble and
show that the entropy of the Reissner-Nordstr\"om black hole is proportional to
this quantized difference in horizon areas.


title:
Black Holes in Non-flat Backgrounds: the Schwarzschild Black Hole in the
  Einstein Universe

abstract:
  As an example of a black hole in a non-flat background a composite static
spacetime is constructed. It comprises a vacuum Schwarzschild spacetime for the
interior of the black hole across whose horizon it is matched on to the
spacetime of Vaidya representing a black hole in the background of the Einstein
universe. The scale length of the exterior sets a maximum to the black hole
mass. To obtain a non-singular exterior, the Vaidya metric is matched to an
Einstein universe. The behaviour of scalar waves is studied in this composite
model.


title: On the stress-energy tensor of a rotating wormhole

abstract:
  We analyze the stress-energy tensor necessary to generate a general
stationary and axisymmetric spacetime. The constraints on the geometry arising
from considering a perfect fluid as a source are derived. For a fluid with a
nonzero stress tensor, we obtain two necessary conditions on the metric. As an
example, we show that the rotating wormhole presented in the literature can not
be described by either a perfect fluid or by a fluid with anisotropic stresses.


title:
On long-time evolution in general relativity and geometrization of
  3-manifolds

abstract:
  We describe some relations between the long-time asymptotic behavior of the
vacuum Einstein evolution equations and the geometrization of 3-manifolds.
These relations are expressed in terms of evolution of CMC hypersurfaces in the
vacuum space-time.Some results are also obtained on the singularity avoidance
of CMC foliations. In addition, the paper describes a number of open problems
relating these two areas.


title:
Measurement of Newton's Constant Using a Torsion Balance with Angular
  Acceleration Feedback

abstract:
  We measured Newton's gravitational constant G using a new torsion balance
method. Our technique greatly reduces several sources of uncertainty compared
to previous measurements: (1) it is insensitive to anelastic torsion fiber
properties; (2) a flat plate pendulum minimizes the sensitivity due to the
pendulum density distribution; (3) continuous attractor rotation reduces
background noise. We obtain G = (6.674215 +- 0.000092)x10^-11 m^3kg^-1s^-2; the
Earth's mass is, therefore, M = (5.972245 +- 0.000082)x10^24 kg and the Sun's
mass is M = (1.988435 +- 0.000027)x10^30kg.


title: Kerr-Schild Symmetries

abstract:
  We study continuous groups of generalized Kerr-Schild transformations and the
vector fields that generate them in any n-dimensional manifold with a
Lorentzian metric. We prove that all these vector fields can be intrinsically
characterized and that they constitute a Lie algebra if the null deformation
direction is fixed. The properties of these Lie algebras are briefly analyzed
and we show that they are generically finite-dimensional but that they may have
infinite dimension in some relevant situations. The most general vector fields
of the above type are explicitly constructed for the following cases: any
two-dimensional metric, the general spherically symmetric metric and
deformation direction, and the flat metric with parallel or cylindrical
deformation directions.


title: Differentially rotating disks of dust: Arbitrary rotation law

abstract:
  In this paper, solutions to the Ernst equation are investigated that depend
on two real analytic functions defined on the interval [0,1]. These solutions
are introduced by a suitable limiting process of Backlund transformations
applied to seed solutions of the Weyl class. It turns out that this class of
solutions contains the general relativistic gravitational field of an arbitrary
differentially rotating disk of dust, for which a continuous transition to some
Newtonian disk exists. It will be shown how for given boundary conditions (i.
e. proper surface mass density or angular velocity of the disk) the
gravitational field can be approximated in terms of the above solutions.
Furthermore, particular examples will be discussed, including disks with a
realistic profile for the angular velocity and more exotic disks possessing two
spatially separated ergoregions.


title: Static Cosmological Solutions of the Einstein-Yang-Mills-Higgs Equations

abstract:
  Numerical evidence is presented for the existence of a new family of static,
globally regular `cosmological' solutions of the spherically symmetric
Einstein-Yang-Mills-Higgs equations. These solutions are characterized by two
natural numbers ($m\geq 1$, $n\geq 0$), the number of nodes of the Yang-Mills
and Higgs field respectively. The corresponding spacetimes are static with
spatially compact sections with 3-sphere topology.


title: Intrinsic Geometry of a Null Hypersurface

abstract:
  We apply Cartan's method of equivalence to construct invariants of a given
null hypersurface in a Lorentzian space-time. This enables us to fully classify
the internal geometry of such surfaces and hence solve the local equivalence
problem for null hypersurface structures in 4-dimensional Lorentzian
space-times.


title: Fluids of Vortices And Dark Matter

abstract:
  By considering full-field string solutions of the Abelian--Higgs model, we
modify the model of a fluid of strings (which is composed of Nambu strings) to
obtain a model for a ``fluid of vortices.'' With this model, and following
closely Soleng's proposal of a fluid of strings as the source of a Milgrom-type
correction to the Newton dynamics, we determine quantitatively the modified
dynamics generated by a static, spherical fluid of vortices.


title: The Geometry of the Frame Bundle over Spacetime

abstract:
  One of the known mathematical descriptions of singularities in General
Relativity is the b-boundary, which is a way of attaching endpoints to
inextendible endless curves in a spacetime. The b-boundary of a manifold M with
connection is constructed by forming the Cauchy completion of the frame bundle
LM equipped with a certain Riemannian metric, the b-metric G. We study the
geometry of (LM,G) as a Riemannian manifold in the case when the connection is
the Levi-Civita connection of a Lorentzian metric g on M. In particular, we
give expressions for the curvature and discuss the isometries and the geodesics
of (LM,G) in relation to the geometry of (M,g).


title: On Imprisoned Curves and b-length in General Relativity

abstract:
  This paper is concerned with two themes: imprisoned curves and the b-length
functional. In an earlier paper by the author, it was claimed that an endless
incomplete curve partially imprisoned in a compact set admits an endless null
geodesic cluster curve. Unfortunately, the proof was flawed. We give an outline
of the problem and remedy the situation by providing a proof by different
methods. Next, we obtain some results concerning the structure of b-length
neighbourhoods, which gives a clue to how the geometry of a spacetime is
encoded in the pseudo-orthonormal frame bundle equipped with the b-metric. We
also show that a previous result by the author, proving total degeneracy of a
b-boundary fibre in some cases, does not apply to imprisoned curves. Finally,
we correct some results in the literature linking the b-lengths of general
curves in the frame bundle with the b-length of the corresponding horizontal
curves.


title:
Comment about the Letter entitled ``Scalar fields as dark matter in
  spiral galaxies"

abstract:
  In this comment we point out some problems with the approach used in the
paper "Scalar fields as dark matter in spiral galaxies" in the attempt to
explain the flatness of the rotation curves of galaxies.


title:
A Natural Renormalization of the One-Loop Effective Action for Scalar
  Field in Curved Space-time

abstract:
  It has been shown that the negative norm states necessarily appear in a
covariant quantization of the free minimally coupled scalar field in de Sitter
space [1,2]. In this process ultraviolet and infrared divergences have been
automatically eliminated [3]. A natural renormalization of the one-loop
interacting quantum field in Minkowski space-time ($\lambda\phi^4$ theory) has
been achieved through the consideration of the negative norm states [4].
One-loop effective action for scalar field in a general curved space-time has
been calculated by this method and a natural renormalization procedure in the
one-loop approximation has been established.


title: Suspensions Thermal Noise in the LIGO Gravitational Wave Detector

abstract:
  We present a calculation of the maximum sensitivity achievable by the LIGO
Gravitational wave detector in construction, due to limiting thermal noise of
its suspensions. We present a method to calculate thermal noise that allows the
prediction of the suspension thermal noise in all its 6 degrees of freedom,
from the energy dissipation due to the elasticity of the suspension wires. We
show how this approach encompasses and explains previous ways to approximate
the thermal noise limit in gravitational waver detectors. We show how this
approach can be extended to more complicated suspensions to be used in future
LIGO detectors.


title: Slowly rotating voids in cosmology

abstract:
  We consider a spacetime consisting of an empty void separated from an almost
Friedmann-Lema\^\i tre-Robertson-Walker (FLRW) dust universe by a spherically
symmetric, slowly rotating shell which is comoving with the cosmic dust. We
treat in a unified manner all types of the FLRW universes. The metric is
expressed in terms of a constant characterizing the angular momentum of the
shell, and parametrized by the comoving radius of the shell. Treating the
rotation as a first order perturbation, we compute the dragging of inertial
frames as well as the apparent motion of distant stars within the void.
Finally, we discuss, in terms of in principle measurable quantities, 'Machian'
features of the model.


title: Multimode gravitational wave detection: the spherical detector theory

abstract:
  A spherical gravity wave (GW) detector, unlike interferometers and bars, is a
natural multi-mode device, i.e., it is capable of independently gathering
information on all five quadrupole and one monopole amplitudes of a general
incoming GW. This is because the sphere's degenerate oscillation eigenmodes are
uniquely matched to the structure of the GWs' Riemann tensor components.
Suitable linear combinations of the system readout channels completely
deconvolve the six GW amplitudes. The present article is concerned with the
theoretical reasons for the remarkable properties of a spherical GW detector.
The analysis proceeds from first principles and is based on essentially no 'ad
hoc' hypotheses. The mathematical beauty of the theory is outstanding, and
abundant detail is given for a thorough understanding of the fundamental facts
and ideas. Experimental evidence of the accuracy of the model is also provided,
where possible.


title:
Answer to the Comment about the Letter entitled ``Scalar fields as dark
  matter in spiral galaxies''

abstract:
  In this manuscript the authors present a detailed answer to the comment in
order to avoid misunderstandings in the future.


title: Newtonian Analysis of Gravitational Waves from Naked Singularity

abstract:
  Spherical dust collapse generally forms a shell focusing naked singularity at
the symmetric center. This naked singularity is massless. Further the Newtonian
gravitational potential and speed of the dust fluid elements are everywhere
much smaller than unity until the central shell focusing naked singularity
formation if an appropriate initial condition is set up. Although such a
situation is highly relativistic, the analysis by the Newtonian approximation
scheme is available even in the vicinity of the space-time singularity. This
remarkable feature makes the analysis of such singularity formation very easy.
We investigate non-spherical even-parity matter perturbations in this scheme by
complementary using numerical and semi-analytical approaches, and estimate
linear gravitational waves generated in the neighborhood of the naked
singularity by the quadrupole formula. The result shows good agreement with the
relativistic perturbation analysis recently performed by Iguchi et al. The
energy flux of the gravitational waves is finite but the space-time curvature
carried by them diverges.


title: Black holes and a scalar field in an expanding universe

abstract:
  We consider a model of an inhomogeneous universe including a massless scalar
field, where the inhomogeneity is assumed to consist of many black holes. This
model can be constructed by following Lindquist and Wheeler, which has already
been investigated without including scalar field to show that an averaged scale
factor coincides with that of the Friedmann model. In this work we construct
the inhomogeneous universe with an massless scalar field, where we assume that
the averaged scale factor and scalar field are given by those of the Friedmann
model including a scalar field. All of our calculations are carried out in the
framework of Brans-Dicke gravity. In constructing the model of an inhomogeneous
universe, we define the mass of a black hole in the Brans-Dicke expanding
universe which is equivalent to ADM mass if the mass evolves adiabatically, and
obtain an equation relating our mass to the averaged scalar field and scale
factor. As the results we find that the mass has an adiabatic time dependence
in a sufficiently late stage of the expansion of the universe, and that the
time dependence is qualitatively diffenrent according to the sign of the
curvature of the universe: the mass increases decelerating in the closed
universe case, is constant in the flat case and decreases decelerating in the
open case. It is also noted that the mass in the Einstein frame depends on
time. Our results that the mass has a time dependence should be retained even
in the general scalar-tensor gravitiy with a scalar field potential.
Furthermore, we discuss the relation of our results to the uniqueness theorem
of black hole spacetime and gravitational memory effect.


title: Selfgravitating nonlinear scalar fields

abstract:
  We investigate the Cauchy problem for the Einstein - scalar field equations
in asymptotically flat spherically symmetric spacetimes, in the standard 1+3
formulation. We prove the local existence and uniqueness of solutions for
initial data given on a space-like hypersurface in the Sobolev $H_1\cap H_{1,4}
$ space. Solutions exist globally if a central (integral) singularity does not
form and/or outside an outgoing null hypersurface. An explicit example
demonstrates that there exists a local evolution with a naked initial curvature
singularity at the symmetry centre.


title: Blow-up for solutions of hyperbolic PDE and spacetime singularities

abstract:
  An important question in mathematical relativity theory is that of the nature
of spacetime singularities. The equations of general relativity, the Einstein
equations, are essentially hyperbolic in nature and the study of spacetime
singularities is naturally related to blow-up phenomena for nonlinear
hyperbolic systems. These connections are explained and recent progress in
applying the theory of hyperbolic equations in this field is presented. A
direction which has turned out to be fruitful is that of constructing large
families of solutions of the Einstein equations with singularities of a simple
type by solving singular hyperbolic systems. Heuristic considerations indicate,
however, that the generic case will be much more complicated and require
different techniques.


title: Notes for a brief history of quantum gravity

abstract:
  I sketch the main lines of development of the research in quantum gravity,
from the first explorations in the early thirties to nowadays.


title: The Life and Times of Extremal Black Holes

abstract:
  Charged extremal black holes cannot fully evaporate through the Hawking
effect and are thus long lived. Over their lifetimes, these black holes take
part in a variety of astrophysical processes, including many that lead to their
eventual destruction. This paper explores the various events that shape the
life of extremal black holes and calculates the corresponding time scales.


title: Let's call it Nonlocal Quantum Physics

abstract:
  In the following we undertake to derive quantum theory as a stochastic
low-energy and coarse-grained theory from a more primordial discrete and
basically geometric theory living on the Planck scale and which (as we argue)
possibly underlies also \tit{string theory}. We isolate the so-called
\tit{ideal elements} which represent at the same time the cornerstones of the
framework of ordinary quantum theory and show how and why they encode the
\tit{non-local} aspects, being ubiquituous in the quantum realm, in a, on the
surface, local way. We show that the quantum non-locality emerges in our
approach as a natural consequence of the underlying \tit{two-storey} nature of
space-time or the physical vacuum, that is, quantum theory turns out to be a
residual effect of the geometric depth structure of space-time on the Planck
scale. We indicate how the \tit{measurement problem} and the emergence of the
\tit{macroscopic sub-regime} can be understood in this framework.


title:
The Kerr-Schild ansatz for the Nariai spacetime and the generating
  conjecture

abstract:
  We will show that the Nariai metric, i.e. the static spherically symmetric
vacuum spacetime with a cosmological constant, admits a conformally Kerr-Schild
spacetime representation. We find the vacuum solutions of the Einstein-Maxwell
equations for the Nariai metric using the Horsky-Mitskievich generating
conjecture.


title: Self-gravitating bosons at nonzero temperature

abstract:
  A system of charged bosons at finite temperature and chemical potential is
studied in a general-relativistic framework. We assume that the boson fields
interact only gravitationally. At sufficiently low temperature the system
exists in two phases: the gas and the condensate. By studying the condensation
process numerically we determine the critical temperature $T_c$ at which the
condensate emerges. As the temperature decreases, the system eventually settles
down in the ground state of a cold boson star.


title:
Chaos in a modified Henon-Heiles system describing geodesics in
  gravitational waves

abstract:
  A Hamiltonian system with a modified Henon-Heiles potential is investigated.
This describes the motion of free test particles in vacuum gravitational
pp-wave spacetimes with both quadratic ("homogeneous") and cubic
("non-homogeneous") terms in the structural function. It is shown that, for
energies above a certain value, the motion is chaotic in the sense that the
boundaries separating the basins of possible escapes become fractal.
Similarities and differences with the standard Henon-Heiles and the monkey
saddle systems are discussed. The box-counting dimension of the basin
boundaries is also calculated.


title: A Gaussian Weave for Kinematical Loop Quantum Gravity

abstract:
  Remarkable efforts in the study of the semi-classical regime of kinematical
loop quantum gravity are currently underway. In this note, we construct a
``quasi-coherent'' weave state using Gaussian factors. In a similar fashion to
some other proposals, this state is peaked in both the connection and the spin
network basis. However, the state constructed here has the novel feature that,
in the spin network basis, the main contribution for this state is given by the
fundamental representation, independently of the value of the parameter that
regulates the Gaussian width.


title:
Localization of gravitational field energy and a procedure proposed for
  its experimental verification

abstract:
  Introduction of Vaidya metrics into the Expansive Nondecelerative Universe
model allows to localize the energy of gravitational field. On the assumption
that there is an interaction of long-range gravitational and electromagnetic
fields, the localization might be verified experimentally. In this contribution
some details on such an experiment are given.


title: Generating Conjecture and Some Einstein-Maxwell Field of High Symmetry

abstract:
  For stationary cylindrically symmetric solutions of the Einstein-Maxwell
equation we have shown that the "charged" solutions of McCrea, Chitre et
al.(CGN), Van den Bergh and Wils (VW) can be obtained from the seed metrics
using generating conjecture. The McCrea "charged" solution has as a seed vacuum
metric the Van Stockum solution with a Killing vector (0,0,1,0). The CGN
"charged" solution and the VW "charged" solution have the static seed metrics
connected by the complex substitution (t --> iz), (z --> it) and the Killing
vector which is a simple linear combination of ${\partial}_{\phi}$ and
${\partial}_{t}$ Killing vectors (VW), respectively ${\partial}_{\phi}$ and
${\partial}_{z}$ Killing vectors (CGN).


title: Microscopic Black Hole Pairs in Highly-Excited States

abstract:
  We consider the quantum mechanics of a system consisting of two identical,
Planck-size Schwarzschild black holes revolving around their common center of
mass. We find that even in a very highly-excited state such a system has very
sharp, discrete energy eigenstates, and the system performs very rapid
transitions from a one stationary state to another. For instance, when the
system is in the 100th excited state, the life times of the energy eigenstates
are of the order of $10^{-30}$ s, and the energies of gravitons released in
transitions between nearby states are of the order of $10^{22}$ eV.


title: Signature for local Mixmaster dynamics in U(1) symmetric cosmologies

abstract:
  Previous studies \cite{berger98a} have provided strong support for a local,
oscillatory approach to the singularity in U(1) symmetric, spatially
inhomogeneous vacuum cosmologies on $T^3 \times R$. The description of a vacuum
Bianchi type IX, spatially homogeneous Mixmaster cosmology (on $S^3 \times R$)
in terms of the variables used to describe the U(1) symmetric cosmologies
indicates that the oscillations in the latter are in fact those of local
Mixmaster dynamics. One of the variables of the U(1) symmetric models increases
only at the end of a Mixmaster era. Such an increase therefore yields a
qualitative signature for local Mixmaster dynamics in spatially inhomogeneous
cosmologies.


title: Relativistic Quantum Non-Locality

abstract:
  The controversy between relativistic causality and quantum non-locality can
be resolved by establishing the general relativistic background of quantum
non-locality.


title: Numerical evolution of Brill waves

abstract:
  We report a numerical evolution of axisymmetric Brill waves. The numerical
algorithm has new features, including (i) a method for keeping the metric
regular on the axis and (ii) the use of coordinates that bring spatial infinity
to the edge of the computational grid. The dependence of the evolved metric on
both the amplitude and shape of the initial data is found.


title:
Cosmology with Curvature-Saturated Gravitational Lagrangian R/\sqrt{1 +
  l^4 R^2}

abstract:
  We argue that the Lagrangian for gravity should remain bounded at large
curvature, and interpolate between the weak-field tested Einstein-Hilbert
Lagrangian L_EH = R /16 pi G and a pure cosmological constant for large R with
the curvature-saturated ansatz L_cs=L_EH/ \sqrt{1+l^4 R^2}, where l is a length
parameter expected to be a few orders of magnitude above the Planck length. The
curvature-dependent effective gravitational constant defined by dL/dR = 1/16 pi
G_eff is G_eff = G \sqrt{1+l^4 R^2}^{3}, and tends to infinity for large $R$,
in contrast to most other approaches where G_eff-> 0. The theory possesses
neither ghosts nor tachyons. In a curvature-saturated cosmology, the
coordinates with ds^2 = a^2 [da^2/B(a) - dx^2 - dy^2- dz^2] are most convenient
since the curvature scalar becomes a linear function of $B(a)$. Solutions with
a big-bang singularity have a much milder behavior of the curvature than in
Einstein's theory. In synchronized time, the metric is given by ds^2 = dt^2 -
t^{6/5(dx^2 + dy^2+ dz^2). On the technical side we show that two different
conformal transformations make L_cs asymptotically equivalent to the
Gurovich-ansatz L= | R |^{4/3} on the one hand, and to Einstein's theory with a
minimally coupled scalar field with self-interaction on the other.


title: Gravitational Effects of Rotating Bodies

abstract:
  We study two type effects of gravitational field on mechanical gyroscopes
(i.e. rotating extended bodies). The first depends on special relativity and
equivalence principle. The second is related to the coupling (i.e. a new force)
between the spins of mechanical gyroscopes, which would violate the equivalent
principle. In order to give a theoretical prediction to the second we suggest a
spin-spin coupling model for two mechanical gyroscopes. An upper limit on the
coupling strength is then determined by using the observed perihelion
precession of the planet's orbits in solar system. We also give predictions
violating the equivalence principle for free-fall gyroscopes .


title: Casimir energy and variational methods in AdS spacetime

abstract:
  Following the subtraction procedure for manifolds with boundaries, we
calculate by variational methods, the Schwarzschild-Anti-de Sitter and the
Anti-de Sitter space energy difference. By computing the one loop approximation
for TT tensors we discover the existence of an unstable mode at zero
temperature, which can be stabilized by the boundary reduction method.
Implications on a foam-like space are discussed.


title:
Singularities of wavefronts and lightcones in the context of GR via null
  foliations

abstract:
  We describe an approach to the issue of the singularities of null
hypersurfaces, due to the focusing of null geodesics, in the context of the
recently introduced formulation of GR via null foliations.


title:
Post-Newtonian SPH calculations of binary neutron star coalescence. II.
  Binary mass ratio, equation of state, and spin dependence

abstract:
  Using our new Post-Newtonian SPH (smoothed particle hydrodynamics) code, we
study the final coalescence and merging of neutron star (NS) binaries. We vary
the stiffness of the equation of state (EOS) as well as the initial binary mass
ratio and stellar spins. Results are compared to those of Newtonian
calculations, with and without the inclusion of the gravitational radiation
reaction. We find a much steeper decrease in the gravity wave peak strain and
luminosity with decreasing mass ratio than would be predicted by simple
point-mass formulae. For NS with softer EOS (which we model as simple
$\Gamma=2$ polytropes) we find a stronger gravity wave emission, with a
different morphology than for stiffer EOS (modeled as $\Gamma=3$ polytropes as
in our previous work). We also calculate the coalescence of NS binaries with an
irrotational initial condition, and find that the gravity wave signal is
relatively suppressed compared to the synchronized case, but shows a very
significant second peak of emission. Mass shedding is also greatly reduced, and
occurs via a different mechanism than in the synchronized case. We discuss the
implications of our results for gravity wave astronomy with laser
interferometers such as LIGO, and for theoretical models of gamma-ray bursts
(GRBs) based on NS mergers.


title: Response of Interferometric Detectors to Scalar Gravitational Waves

abstract:
  We rigorously analyze the frequency response functions and antenna
sensitivity patterns of three types of interferometric detectors to scalar mode
of gravitational waves which is predicted to exist in the scalar-tensor theory
of gravity. By a straightforward treatment, we show that the antenna
sensitivity pattern of the simple Michelson interferometric detector depends
strongly on the wave length $\lambda_{\rm SGW}$ of the scalar mode of
gravitational waves if $\lambda_{\rm SGW}$ is comparable to the arm length of
the interferometric detector. For the Delay-Line and Fabry-Perot
interferometric detectors with arm length much shorter than $\lambda_{\rm
SGW}$, however, the antenna sensitivity patterns depend weakly on $\lambda_{\rm
SGW}$ even though $\lambda_{\rm SGW}$ is comparable to the effective path
length of those interferometers. This agrees with the result obtained by
Maggiore and Nicolis.


title: On the influence of gravitational radiation on a gyroscope

abstract:
  We calculate the precession of a gyroscope at rest in a Bondi spacetime. It
is shown that, far from the source, the leading term in the rate of precession
of the gyroscope is simply expressed through the news function of the system,
and vanishes if and only if there is no news. Rough estimates are presented,
illustrating the order of magnitude of the expected effect for different
scenarios. It is also shown from the next order term that non-radiative (but
time dependent) spacetimes will produce a gyroscope precession of that order,
providing thereby ``observational'' evidence for the violation of the Huygens's
principle.


title: Null cone evolution of axisymmetric vacuum spacetimes

abstract:
  We present the details of an algorithm for the global evolution of
asymptotically flat, axisymmetric spacetimes, based upon a characteristic
initial value formulation using null cones as evolution hypersurfaces. We
identify a new static solution of the vacuum field equations which provides an
important test bed for characteristic evolution codes. We also show how
linearized solutions of the Bondi equations can be generated by solutions of
the scalar wave equation, thus providing a complete set of test beds in the
weak field regime. These tools are used to establish that the algorithm is
second order accurate and stable, subject to a Courant-Friedrichs-Lewy
condition. In addition, the numerical versions of the Bondi mass and news
function, calculated at scri on a compactified grid, are shown to satisfy the
Bondi mass loss equation to second order accuracy. This verifies that numerical
evolution preserves the Bianchi identities. Results of numerical evolution
confirm the theorem of Christodoulou and Klainerman that in vacuum, weak
initial data evolve to a flat spacetime. For the class of asymptotically flat,
axisymmetric vacuum spacetimes, for which no nonsingular analytic solutions are
known, the algorithm provides highly accurate solutions throughout the regime
in which neither caustics nor horizons form.


title: Ill-posedness in the Einstein equations

abstract:
  It is shown that the formulation of the Einstein equations widely in use in
numerical relativity, namely, the standard ADM form, as well as some of its
variations (including the most recent conformally-decomposed version), suffers
from a certain but standard type of ill-posedness. Specifically, the norm of
the solution is not bounded by the norm of the initial data irrespective of the
data. A long-running numerical experiment is performed as well, showing that
the type of ill-posedness observed may not be serious in specific practical
applications, as is known from many numerical simulations.


title: Symmetries of Bianchi I space-times

abstract:
  All diagonal proper Bianchi I space-times are determined which admit certain
important symmetries. It is shown that for Homotheties, Conformal motions and
Kinematic Self-Similarities the resulting space-times are defined explicitly in
terms of a set of parameters whereas Affine Collineations, Ricci Collineations
and Curvature Collineations, if they are admitted, they determine the metric
modulo certain algebraic conditions. In all cases the symmetry vectors are
explicitly computed. The physical and the geometrical consequences of the
results are discussed and a new anisitropic fluid, physically valid solution
which admits a proper conformal Killing vector, is given.


title: Quasi-circular Orbits for Spinning Binary Black Holes

abstract:
  Using an effective potential method we examine binary black holes where the
individual holes carry spin. We trace out sequences of quasi-circular orbits
and locate the innermost stable circular orbit as a function of spin. At large
separations, the sequences of quasi-circular orbits match well with
post-Newtonian expansions, although a clear signature of the simplifying
assumption of conformal flatness is seen. The position of the ISCO is found to
be strongly dependent on the magnitude of the spin on each black hole. At close
separations of the holes, the effective potential method breaks down. In all
cases where an ISCO could be determined, we found that an apparent horizon
encompassing both holes forms for separations well inside the ISCO.
Nevertheless, we argue that the formation of a common horizon is still
associated with the breakdown of the effective potential method.


title: A theory of thin shells with orbiting constituents

abstract:
  The self-gravitating, spherically symmetric thin shells built of orbiting
particles are sstudied. Two new features are found. One is the minimal possible
value for an angular momentum of particles, above which elleptic orbits become
possible. The second is the coexistence of both the wormhole solutions and the
elleptic or hyperbolic orbits for the same values of the parameters (but
different initial conditions). Possible applications of these results to
astrophysics and quantum black holes are briefly discussed.


title: Cerenkov radiation and scalar stars

abstract:
  We explore the possibility that a charged particle moving in the
gravitational field generated by a scalar star could radiate energy via a
recently proposed gravitational \v{C}erenkov mechanism. We numerically prove
that this is not possible for stable boson stars. We also show that soliton
stars could have \v{C}erenkov radiation for particular values of the boson
mass, although diluteness of the star grows and actual observational
possibility decreases for the more usually discussed boson masses. These
conclusions diminish, although do not completely rule out, the observational
possibility of actually detecting scalar stars using this mechanism, and lead
us to consider other forms, like gravitational lensing.


title: Gravitational and dilaton radiation from a relativistic membrane

abstract:
  Recent scenarios of the TeV-scale brane cosmology suggest a possibility of
existence in the early universe of two-dimensional topological defects:
relativistic membranes. Like cosmic strings, oscillating membranes could emit
gravitational radiation contributing to a stochastic background of
gravitational waves. We calculate dilaton and gravitational radiation from a
closed toroidal membrane excited along one homology cycle. The spectral-angular
distributions of dilaton and gravitational radiation are obtained in a closed
form in terms of Bessel's functions. The angular distributions are affected by
oscillating factors due to an interference of radiation from different segments
of the membrane. The dilaton radiation power is dominated by a few lower
harmonics of the basic frequency, while the spectrum of the gravitational
radiation contains also a substantial contribution from higher harmonics. The
radiative lifetime of the membrane is determined by its tension and depends
weakly on the ratio of two radii of the torus. Qualitatively it is equal to the
ratio of the membrane area at the maximal extension to the gravitational radius
of the membrane as a whole.


title:
A lattice quantum gravity model with surface-like excitations in
  4-dimensional spacetime

abstract:
  A lattice quantum gravity model in 4 dimensional Riemannian spacetime is
constructed based on the SU(2) Ashtekar formulation of general relativity. This
model can be understood as one of the family of models sometimes called ``spin
foam models.'' A version of the action of general relativity in continuum is
introduced and its lattice version is defined. A dimensionless ``(inverse)
coupling'' constant is defined so that the value of the action of the model is
finite per lattice point. The path integral of the model is expanded in the
characters and shown to be written as a sum over surface-like excitations in
spacetime. A 3 dimensional version of the model exists and can be reduced to
lattice BF theory. The expectation values of some quantities are computed in 3
dimensions and the meanings of the results are discussed. Although the model is
studied on a hyper cubic lattice for simplicity, it can be generalized to a
randomly triangulated lattice with small modifications.


title: Birth of timelike naked singularity

abstract:
  We investigate the causal structure of the Harada-Iguchi-Nakao (HIN)'s exact
solution in detail, which describes the dynamical formation of naked
singularity in the collapse of a regular spherical cluster of counterrotating
particles. There are three kinds of radial null geodesics in the HIN spacetime.
One is the regular null geodesics and the other two are the null geodesics
which terminate at the singularity. The central massless singularity is
timelike naked singularity and satisfies the strong curvature condition along
the null geodesics except for the instant of singularity formation. The cluster
dynamically asymptotes to the singular static Einstein cluster in which
centrifugal force is balanced with gravity. The HIN solution provides an
interesting example which demonstrates that collisionless particles invoke
timelike naked singularity.


title: Brans-Dicke corrections to the gravitational Sagnac effect

abstract:
  The {\it exact} formulation for the effect of the Brans-Dicke scalar field on
the gravitational corrections to the Sagnac delay in the Jordan and Einstein
frames is presented for the first time. The results completely agree with the
known PPN factors in the weak field region. The calculations also reveal how
the Brans-Dicke coupling parameter (appears in various correction terms for
different types of source/observer orbits. A first order correction of roughly
2.83 x 10^{-1} fringe shift for visible light is introduced by the
gravity-scalar field combination for Earth bound equatorial orbits. It is also
demonstrated that the final predictions in the two frames do not differ. The
effect of the scalar field on the geodetic and Lense-Thirring precession of a
spherical gyroscope in circular polar orbit around the Earth is also computed
with an eye towards the Stanford Gravity Probe-B experiment currently in
progress. The feasibility of optical and matter-wave interferometric
measurements is discussed briefly.