title: Dilatonic Quantum-Induced Two-Brane Worlds

abstract:
  The 5d dilatonic gravity action with surface counterterms, motivated by the
AdS/CFT correspondence and with contributions of brane quantum CFTs is
considered with an AdS-like bulk. The role of quantum brane CFT consists in
inducing complicated brane dilatonic gravity. For exponential bulk potentials,
a number of AdS-like bulk spaces is found in an analytical form. The
corresponding flat or curved (de Sitter or hyperbolic) dilatonic two-branes are
created.


title:
Gauge Problem in the Gravitational Self-Force I. Harmonic Gauge Approach
  in the Schwarzschild Background

abstract:
  The metric perturbation induced by a particle in the Schwarzschild background
is usually calculated in the Regge-Wheeler (RW) gauge, whereas the
gravitational self-force is known to be given by the tail part of the metric
perturbation in the harmonic gauge. Thus, to identify the gravitational
self-force correctly in a specified gauge, it is necessary to find out a gauge
transformation that connects these two gauges. This is called the gauge
problem. As a direct approach to solve the gauge problem, we formulate a method
to calculate the metric perturbation in the harmonic gauge on the Schwarzshild
backgound. We apply the Fourier-harmonic expansion to the metric perturbation
and reduce the problem to the gauge transformation of the Fourier-harmonic
coefficients (radial functions) from the RW gauge to the harmonic gauge. We
derive a set of decoupled radial equations for the gauge transformation. These
equations are found to have a simple second-order form for the odd parity part
and the forms of spin $s=0$ and 1 Teukolsky equations for the even parity part.
As a by-product, we correct typos in Zerilli's paper and present a set of
corrected equations in Appendix.


title:
Required Conditions for Late Time Acceleration and Early Time
  Deceleration in Generalized Scalar-Tensor Theories

abstract:
  We consider a generalized scalar-tensor theory, where we let the coupling
function $\omega(\phi)$ and the effective cosmological constants
$\Lambda(\phi)$ undetermined. We obtain general expressions for $\omega(\phi)$
and $\Lambda(\phi)$ in terms of the scalar field and the scale factor, and show
that $\omega(\phi)$ depends on the scalar field and the scale factor in a
complicated way. In order to study the conditions for an accelerated expansion
at the present time and a decelerated expansion in the past, we assume a power
law evolution for the scalar field and the scale factor. We analyse the
required conditions that allow our model to satisfy the weak field limits on
$\omega(\phi)$, and at the same time, to obtain the correct values of
cosmological parameters, as the energy density $ \Omega_{m0}$ and cosmological
constant $\Lambda(t_0)$. We also study the conditions for a decelerated
expansion at an early time dominated by radiation. We find values for
$\omega(\phi)$ and $\Lambda(\phi)$ consistent with the expectations of a theory
where the cosmological constant decreases with the time and the coupling
function increases until the values accepted today.


title: Quantum Mechanics and Gravitation

abstract:
  In summer 1999 an experiment at ILL, Grenoble was conducted. So-called
ultra-cold neutrons (UCN) were trapped in the vertical direction between the
Fermi-potential of a smooth mirror below and the gravitational potential of the
earth above [Ne00, Ru00]. If quantum mechanics turns out to be a sufficiently
correct description of the phenomena in the regime of classical, weak
gravitation, one should observe the forming of quantized bound states in the
vertical direction above a mirror. Already in a simplified view, the data of
the experiment provides strong evidence for the existence of such
gravitationally bound quantized states. A successful quantum-mechanical
description would then provide a convincing argument, that the socalled first
quantization can be used for gravitation as an interaction potential, as this
is widely expected. Furthermore, looking at the characteristic length scales of
about 10 mikron of such bound states formed by UCN, one sees, that a complete
quantum mechanical description of this experiment additionally would enable one
to check for possible modifications of Newtonian gravitation on distance scales
being one order of magnitude below currently available tests [Ad00]. The work
presented here deals mainly with the development of a quantum mechanical
description of the experiment.


title:
A scalar invariant and the local geometry of a class of static
  spacetimes

abstract:
  The scalar invariant, I, constructed from the "square" of the first covariant
derivative of the curvature tensor is used to probe the local geometry of
static spacetimes which are also Einstein spaces. We obtain an explicit form of
this invariant, exploiting the local warp-product structure of a 4-dimensional
static spacetime, $~^{(3)}\Sigma \times_{f} \reals$, where $^{(3)}\Sigma $ is
the Riemannian hypersurface orthogonal to a timelike Killing vector field with
norm given by a positive function, $f$ on $^{(3)}\Sigma $. For a static
spacetime which is an Einstein space, it is shown that the locally measurable
scalar, I, contains a term which vanishes if and only if $^{(3)}\Sigma$ is
conformally flat; also, the vanishing of this term implies (a) $~^{(3)}\Sigma$
is locally foliated by level surfaces of $f$, $^{(2)}S$, which are totally
umbilic spaces of constant curvature, and (b) $^{(3)}\Sigma$ is locally a
warp-product space. Futhermore, if $^{(3)}\Sigma$ is conformally flat it
follows that every non-trivial static solution of the vacuum Einstein equation
with a cosmological constant, is either Nariai-type or Kottler-type - the
classes of spacetimes relevant to quantum aspects of gravity.


title: A curious electrovac spacetime as $G = 0$ limit of the NUT space

abstract:
  We take the $G = 0$ limit of the NUT space which yields a non flat space and
show that source of its curvature is electromagnetic field generated by the NUT
parameter defining the NUT symmetry. This is a very curious electrovac NUT
space. Further it is also possible to superpose on it a global monopole.


title: Dynamics of a Generalized Cosmological Scalar-Tensor Theory

abstract:
  A generalized scalar-tensor theory is investigated whose cosmological term
depends on both a scalar field and its time derivative. A correspondence with
solutions of five-dimensional Space-Time-Matter theory is noted. Analytic
solutions are found for the scale factor, scalar field and cosmological term.
Models with free parameters of order unity are consistent with recent
observational data and could be relevant to both the dark-matter and
cosmological-"constant" problems.


title: Quantum inequalities in two dimensional curved spacetimes

abstract:
  We generalize a result of Vollick constraining the possible behaviors of the
renormalized expected stress-energy tensor of a free massless scalar field in
two dimensional spacetimes that are globally conformal to Minkowski spacetime.
Vollick derived a lower bound for the energy density measured by a static
observer in a static spacetime, averaged with respect to the observers proper
time by integrating against a smearing function. Here we extend the result to
arbitrary curves in non-static spacetimes. The proof, like Vollick's proof, is
based on conformal transformations and the use of our earlier optimal bound in
flat Minkowski spacetime. The existence of such a quantum inequality was
previously established by Fewster.


title: Noether-Charge Realization of Diffeomorphism Algebra

abstract:
  It is shown in the covariant phase space formalism that the Noether charges
with respect to the diffeomorphism generated by vector fields and their
horizontal variations in general relativity form a diffeomorphism algebra. It
is also shown with the help of the null tetrad which is well defined everywhere
that the central term of the reduced diffeomorphism algebra on the Killing
horizon for a large class of vector fields vanishes.


title: Time varying velocity of light

abstract:
  Recently there has been a lot of intersest in the superluminal phenomena, and
time varying velocity of light cosmological models. More than two decades ago
at Einstein centenary symposium, Nagpur I had put forward space-time
interaction hypothesis. One of its predictions was that velocity of light
decreased with the age of Universe. In view of the profoundness of the
hypothesis the original paper is reproduced here. We also mention that in a
paper "Quasars, Tachyons and the early universe" proc. Einstein found. Intnl.
2(3), 1985 pp 69-75, it was suggested that, "The boundary region of the
universe being the source of radiation, the slowing down of the speed of
radiation from $4.4 \times 10^{10}$ cm/sec at $t_A = 10^{10}$ yrs. to the
present value of $3 \times 10^{10}$ cm/sec should show up as a large red
shifts. The successive boundary region radiations at various epoch will give
rise to a wide range of red shifts. Therefore, defining quasars as the objects
having two properties: large red shifts and powerful emission of radiations, we
would like to identify these objects as the boundary regions of the universe".


title: Wormholes supported by the kink-like configuration of a scalar field

abstract:
  We study the problem of existence of static spherically symmetric wormholes
supported by the kink-like configuration of a scalar field. With this aim we
consider a self-consistent, real, nonlinear, nonminimally coupled scalar field
$\phi$ in general relativity with the symmetry-breaking potential $V(\phi)$
possessing two minima. We classify all possible field configurations ruling out
those of them for which wormhole solutions are impossible. Field configurations
admitting wormholes are investigated numerically. Such the configurations
represent a spherical domain wall localized near the wormhole throat.


title:
Quintessential Cosmological Scenarios in the Relativistic Theory of
  Gravitation

abstract:
  It is shown that the accelerated expansion of the universe in the framework
of the relativistic theory of gravitation can be achieved by the introduction
of the quintessential term in the energy-momentum tensor. The value of the
minimum scaling factor and the modern observational data for the density and
state parameters of the matter give the rough estimations for the maximum
graviton mass and the maximum scaling factor. The former can be very low in the
case of the primordial inflation and the latter can be extremely large for the
scalar field model of the quintessence. In any case, the massive graviton stops
the second inflation and provide the closed cosmological scenario in the
agreement with the causality principle inherent to the theory.


title: Spin polarised particles in Goedel world

abstract:
  The motion of classical test spinning particles in Godel universe in the
realm of Einstein's General Relativity (GR) is investigated by making use of
Killing conserved currents. We consider three distinct cases of motion of
spinning particles polarized along the three distinct axes of the anisotropic
metric. It is shown that in the case the spin is polarised along the
y-direction the minimum energy of the motion is attained for only for spinless
particles while the other two directions the minimum energy is obtained for
spinning particles. The continuos energy spectrum is also computed.


title: Spinning particles in gravitational wave spacetime

abstract:
  The dynamics of pseudo-classical spinning particles in spacetime of
gravitational plane waves of general polarization and harmonic profile is
studied. The resulting equations of motion are solved exactly and the results
are compared with those of the other approaches. The relative accelerations of
nearby particles is also calculated.


title: Geometric quantization of relativistic Hamiltonian mechanics

abstract:
  A relativistic Hamiltonian mechanical system is seen as a conservative Dirac
constraint system on the cotangent bundle of a pseudo-Riemannian manifold. We
provide geometric quantization of this cotangent bundle where the quantum
constraint serves as a relativistic quantum equation.


title:
The Newtonian limit of spacetimes describing uniformly accelerated
  particles

abstract:
  We discuss the Newtonian limit of boost-rotation symmetric spacetimes by
means of the Ehler's frame theory. Conditions for the existence of such a limit
are given and, in particular, we show that asymptotic flatness is an essential
requirement for the existence of such a limit. Consequently, generalized
boost-rotation symmetric spacetimes describing particles moving in uniform
fields will not possess a Newtonian limit. In the cases where the
boost-rotation symmetric spacetime is asymptotically flat and its Newtonian
limit exists, then it is non-zero only for the instant of time symmetry and its
value is given by a Poisson integral. The relation of this result with the
(Newtonian) gravitational potential suggested by the weak field approximation
is discussed. We illustrate our analysis through some examples: the two
monopoles solution, the Curzon-Chazy particle solution, the generalized
Bonnor-Swaminarayan solution, and the C metric.


title: Gravitational lensing in the strong field limit

abstract:
  We provide an analytic method to discriminate among different types of black
holes on the ground of their strong field gravitational lensing properties. We
expand the deflection angle of the photon in the neighbourhood of complete
capture, defining a strong field limit, in opposition to the standard weak
field limit. This expansion is worked out for a completely generic spherically
symmetric spacetime, without any reference to the field equations and just
assuming that the light ray follows the geodesics equation. We prove that the
deflection angle always diverges logarithmically when the minimum impact
parameter is reached. We apply this general formalism to Schwarzschild,
Reissner-Nordstrom and Janis-Newman-Winicour black holes. We then compare the
coefficients characterizing these metrics and find that different collapsed
objects are characterized by different strong field limits. The strong field
limit coefficients are directly connected to the observables, such as the
position and the magnification of the relativistic images. As a concrete
example, we consider the black hole at the centre of our galaxy and estimate
the optical resolution needed to investigate its strong field behaviour through
its relativistic images.


title:
Time asymmetries in quantum cosmology and the searching for boundary
  conditions to the Wheeler-DeWitt equation

abstract:
  The paper addresses the quantization of minisuperspace cosmological models by
studying a possible solution to the problem of time and time asymmetries in
quantum cosmology. Since General Relativity does not have a privileged time
variable of the newtonian type, it is necessary, in order to have a dynamical
evolution, to select a physical clock. This choice yields, in the proposed
approach, to the breaking of the so called clock-reversal invariance of the
theory which is clearly distinguished from the well known motion-reversal
invariance of both classical and quantum mechanics. In the light of this new
perspective, the problem of imposing proper boundary conditions on the space of
solutions of the Wheeler-DeWitt equation is reformulated. The symmetry-breaking
formalism of previous papers is analyzed and a clarification of it is proposed
in order to satisfy the requirements of the new interpretation.


title: Time asymmetry as a consequence of the global properties of the universe

abstract:
  A global definition of time-asymmetry is presented. Schulman's two arrows of
time model is criticized.


title: Numerical evidence for `multi-scalar stars'

abstract:
  We present a class of general relativistic soliton-like solutions composed of
multiple minimally coupled, massive, real scalar fields which interact only
through the gravitational field. We describe a two-parameter family of
solutions we call ``phase-shifted boson stars'' (parameterized by central
density rho_0 and phase delta), which are obtained by solving the ordinary
differential equations associated with boson stars and then altering the phase
between the real and imaginary parts of the field. These solutions are similar
to boson stars as well as the oscillating soliton stars found by Seidel and
Suen [E. Seidel and W.M. Suen, Phys. Rev. Lett. 66, 1659 (1991)]; in
particular, long-time numerical evolutions suggest that phase-shifted boson
stars are stable. Our results indicate that scalar soliton-like solutions are
perhaps more generic than has been previously thought.


title: Cheeger-Gromov Theory and Applications to General Relativity

abstract:
  This paper surveys aspects of the convergence and degeneration of Riemannian
metrics on a given manifold M - the Cheeger-Gromov theory - and extensions
thereof to Ricci curvature in place of full curvature. This theory is then
applied to study a collection of different issues in mathematical aapects of
General Relativity.


title: Potential flows in a core-dipole-shell system: numerical results

abstract:
  Numerical solutions for: the integral curves of the velocity field
(streamlines), the density contours, and the accretion rate of a steady-state
flow of an ideal fluid with p=K n^(gamma) equation of state orbiting in a
core-dipole-shell system are presented. For 1 < gamma < 2, we found that the
non-linear contribution appearing in the partial differential equation for the
velocity potential has little effect in the form of the streamlines and density
contour lines, but can be noticed in the density values. The study of several
cases indicates that this appears to be the general situation. The accretion
rate was found to increase when the constant gamma decreases.


title: Fine-structure constant variability, equivalence principle and cosmology

abstract:
  It has been widely believed that variability of the fine-structure constant
alpha would imply detectable violations of the weak equivalence principle. This
belief is not justified in general. It is put to rest here in the context of
the general framework for alpha variability [J. D. Bekenstein, Phys. Rev. D 25,
1527 (1982)] in which the exponent of a scalar field plays the role of the
permittivity and inverse permeability of the vacuum. The coupling of particles
to the scalar field is necessarily such that the anomalous force acting on a
charged particle by virtue of its mass's dependence on the scalar field is
cancelled by terms modifying the usual Coulomb force. As a consequence a
particle's acceleration in external fields depends only on its charge to mass
ratio, in accordance with the principle. And the center of mass acceleration of
a composite object can be proved to be independent of the object's internal
constitution, as the weak equivalence principle requires. Likewise the widely
employed assumption that the Coulomb energy of matter is the principal source
of the scalar field proves wrong; Coulomb energy effectively cancels out in the
continuum description of the scalar field's dynamics. This cancellation
resolves a cosmological conundrum: with Coulomb energy as source of the scalar
field, the framework would predict a decrease of alpha with cosmological
expansion, whereas an increase is claimed to be observed. Because of the said
cancellation, magnetic energy of cosmological baryonic matter is the main
source of the scalar field. Consequently the expansion is accompanied by an
increase in alpha; for reasonable values of the framework's sole parameter,
this occurs at a rate consistent with the observers' claims.


title: The Einstein-Vlasov system

abstract:
  Rigorous results on solutions of the Einstein-Vlasov system are surveyed.
After an introduction to this system of equations and the reasons for studying
it, a general discussion of various classes of solutions is given. The emphasis
is on presenting important conceptual ideas, while avoiding entering into
technical details. Topics covered include spatially homogenous models, static
solutions, spherically symmetric collapse and isotropic singularities.


title: Quantum general relativity and Hawking radiation

abstract:
  In a previous paper we have set up the Wheeler-DeWitt equation which
describes the quantum general relativistic collapse of a spherical dust cloud.
In the present paper we specialize this equation to the case of matter
perturbations around a black hole, and show that in the WKB approximation, the
wave-functional describes an eternal black hole in equilibrium with a thermal
bath at Hawking temperature.


title:
Einsteinian Strengths and Dynamical Degrees of Freedom for Alternative
  Gravity Theories

abstract:
  In this paper we present the results of our calculations of the Einsteinian
strengths S_E(d) and numbers dynamical degrees of freedom N_{DF}(d) for
alternative gravity theories in d >= 4 dimensions. In the first part we
consider the numbers S_E(d) and N_{DF}(d) for metric-compatible and quadratic
in curvature (or quadratic in curvature and in torsion) gravity. We show that
in the entire set of the metric-compatible quadratic gravity in d >= 4
dimensions the 2-nd order Einstein-Gauss-Bonnet theory has the smallest numbers
S_E(d) and N_{DF}(d), i.e., this quadratic theory of gravity has the strongest
field equations. From the physical point of view this theory is the best one
quadratic and metric-compatible theory of gravity in d >= 4 dimensions.


title: Gravity cannot be quantized

abstract:
  This work shows that the gravitational field is rather an unusual field and
cannot be quantized due to the absence of a fermion charge carrier. When its
existence is assumed quite strange results are obtained for its mass. And this
means that the graviton does not exist either since bosons act between fermion
states.


title:
Global phase time and wave function for the Kantowski-Sachs anisotropic
  universe

abstract:
  A consisten quantization with a clear notion of time and evolution is given
for the anisotropic Kantowski-SDachs cosmological model. It is shown that a
suitable coordinate choice allows to obtain a solution of the Wheeler-DeWitt
equation in the form of definite energy states, and that the results can be
associated to two disjoint equivalent theories, one for each sheet of the
constraint surface.


title: A 3+1 covariant suite of Numerical Relativity Evolution Systems

abstract:
  A suite of three evolution systems is presented in the framework of the 3+1
formalism. The first one is of second order in space derivatives and has the
same causal structure of the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) system
for a suitable choice of parameters. The second one is the standard first order
version of the first one and has the same causal structure of the Bona-Masso
system for a given parameter choice. The third one is obtained from the second
one by reducing the space of variables in such a way that the only modes that
propagate with zero characteristic speed are the trivial ones. This last system
has the same structure of the ones recently presented by Kidder, Scheel and
Teukolski: the correspondence between both sets of parameters is explicitly
given. The fact that the suite started with a system in which all the dynamical
variables behave as tensors (contrary to what happens with BSSN system) allows
one to keep the same parametrization when passing from one system to the next
in the suite. The direct relationship between each parameter and a particular
characteristic speed, which is quite evident in the second and the third
systems, is a direct consequence of the manifest 3+1 covariance of the
approach.


title: Space-time dynamics from algebra representations

abstract:
  We present a model for introducing dynamics into a space-time geometry. This
space-time structure is constructed from a C*-algebra defined in terms of the
generators of an irreducible unitary representation of a finite-dimensional Lie
algebra G. This algebra is included as a subalgebra in a bigger algebra F, the
generators of which mix the representations of G in a way that relates
different space-times and creates the dynamics. This construction can be
considered eventually as a model for 2-D quantum gravity.


title:
Numerically generated quasi-equilibrium orbits of black holes: Circular
  or eccentric?

abstract:
  We make a comparison between results from numerically generated,
quasi-equilibrium configurations of compact binary systems of black holes in
close orbits, and results from the post-Newtonian approximation. The
post-Newtonian results are accurate through third PN order (O(v/c)^6 beyond
Newtonian gravity), and include rotational and spin-orbit effects, but are
generalized to permit orbits of non-zero eccentricity. Both treatments ignore
gravitational radiation reaction. The energy E and angular momentum J of a
given configuration are compared between the two methods as a function of the
orbital angular frequency \Omega. For small \Omega, corresponding to orbital
separations a factor of two larger than that of the innermost stable orbit, we
find that, if the orbit is permitted to be slightly eccentric, with e ranging
from \approx 0.03 to \approx 0.05, and with the two objects initially located
at the orbital apocenter (maximum separation), our PN formulae give much better
fits to the numerically generated data than do any circular-orbit PN methods,
including various ``effective one-body'' resummation techniques. We speculate
that the approximations made in solving the initial value equations of general
relativity numerically may introduce a spurious eccentricity into the orbits.


title:
Stability properties of black holes in self-gravitating nonlinear
  electrodynamics

abstract:
  We analyze the dynamical stability of black hole solutions in
self-gravitating nonlinear electrodynamics with respect to arbitrary linear
fluctuations of the metric and the electromagnetic field. In particular, we
derive simple conditions on the electromagnetic Lagrangian which imply linear
stability in the domain of outer communication. We show that these conditions
hold for several of the regular black hole solutions found by Ayon-Beato and
Garcia.


title: Volume Expansion of Swiss-Cheese Universe

abstract:
  In order to investigate the effect of inhomogeneities on the volume expansion
of the universe, we study modified Swiss-Cheese universe model. Since this
model is an exact solution of Einstein equations, we can get an insight into
non-linear dynamics of inhomogeneous universe from it. We find that
inhomogeneities make the volume expansion slower than that of the background
Einstein-de Sitter universe when those can be regarded as small fluctuations in
the background universe. This result is consistent with the previous studies
based on the second order perturbation analysis. On the other hand, if the
inhomogeneities can not be treated as small perturbations, the volume expansion
of the universe depends on the type of fluctuations. Although the volume
expansion rate approaches to the background value asymptotically, the volume
itself can be finally arbitrarily smaller than the background one and can be
larger than that of the background but there is an upper bound on it.


title: Some global results for asymptotically simple spacetimes

abstract:
  The null splitting theorem (proved in math.DG/9909158) is discussed. As an
application, a uniqueness theorem for Minkowski space and for de Sitter space
associated with the occurrence of null lines (inextendible globally achronal
null geodesics) is presented.


title: Godel-type space-time metrics

abstract:
  A simple group theoretic derivation is given of the family of space-time
metrics with isometry group SO(2,1) X SO(2) X R first described by Godel, of
which the Godel stationary cosmological solution is the member with a
perfect-fluid stress-energy tensor. Other members of the family are shown to be
interpretable as cosmological solutions with a electrically charged perfect
fluid and a magnetic field.


title: What is the spacetime of {\em physically realizable} spherical collapse?

abstract:
  We argue that a particular spacetime, a spherically symmetric spacetime with
hyper-surface orthogonal, radial, homothetic Killing vector, is a physically
meaningful spacetime that describes the problem of spherical gravitational
collapse in its full "physical" generality.


title: Geometric Dilaton Coupling and Smooth Charged Wormholes

abstract:
  A particular type of coupling of the dilaton field to the metric is shown to
admit a simple geometric interpretation in terms of a volume element density
independent from the metric. For dimension n = 4 two families of either
magnetically or electrically charged static spherically symmetric solutions to
the Maxwell-Einstein-Dilaton field equations are derived. Whereas the metrics
of the "magnetic" spacetimes are smooth, geodesically complete and have the
topology of a wormhole, the "electric" metrics behave similarly as the singular
and geodesically incomplete classical Reissner-Nordstroem metrics. At the price
of losing the simple geometric interpretation, a closely related "alternative"
dilaton coupling can nevertheless be defined, admitting as solutions smooth
"electric" metrics.


title: Black hole formation in the grazing collision of high-energy particles

abstract:
  We numerically investigate the formation of D-dimensional black holes in
high-energy particle collision with the impact parameter and evaluate the total
cross section of the black hole production. We find that the formation of an
apparent horizon occurs when the distance between the colliding particles is
less than 1.5 times the effective gravitational radius of each particles. Our
numerical result indicates that although both the one-dimensional hoop and the
(D-3)-dimensional volume corresponding to the typical scale of the system give
a fairly good condition for the horizon formation in the higher-dimensional
gravity, the (D-3)-dimensional volume provide a better condition to judge the
existence of the horizon.


title: Decoherence and bare mass induced by nonconformal metric fluctuations

abstract:
  The effects, upon the Klein--Gordon field, of nonconformal stochastic metric
fluctuations, are analyzed. It will be shown that these fluctuations allow us
to consider an effective mass, i.e., the mass detected in a laboratory is not
the parameter appearing in the Klein--Gordon equation, but a function of this
parameter and of the fluctuations of the metric. In other words, in analogy to
the case of a nonrelativistic electron in interaction with a quantized
electromagnetic field, we may speak of a bare mass, where the observed mass
shows a dependence upon the stochastic terms included in the metric.
Afterwards, we prove, resorting to the influence functional, that the
energy--momentum tensor of the Klein--Gordon field inherites this stochastic
behavior, and that this feature provokes decoherence upon a particle immersed
in the region where this tensor is present.


title: A possible way for getting the information out of a black hole

abstract:
  We try to solve the problem about how to probe the inside of a black hole. We
show that in the framework of revised quantum dynamics, which may naturally
result from the combination of quantum mechanics and general relativity, the
information inside a black hole can be gotten out in principle when using the
conscious being as quantum measuring device.


title:
Finite-Range Gravity and Its Role in Gravitational Waves, Black Holes
  and Cosmology

abstract:
  Theoretical considerations of fundamental physics, as well as certain
cosmological observations, persistently point out to permissibility, and maybe
necessity, of macroscopic modifications of the Einstein general relativity. The
field-theoretical formulation of general relativity helped us to identify the
phenomenological seeds of such modifications. They take place in the form of
very specific mass-terms, which appear in addition to the field-theoretical
analog of the usual Hilbert-Einstein Lagrangian. We interpret the added terms
as masses of the spin-2 and spin-0 gravitons. The arising finite-range gravity
is a fully consistent theory, which smoothly approaches general relativity in
the massless limit, that is, when both masses tend to zero and the range of
gravity tends to infinity. We show that all local weak-field predictions of the
theory are in perfect agreement with the available experimental data. However,
some other conclusions of the non-linear massive theory are in a striking
contrast with those of general relativity. We show in detail how the
arbitrarily small mass-terms eliminate the black hole event horizon and replace
a permanent power-law expansion of a homogeneous isotropic universe with an
oscillatory behaviour. One variant of the theory allows the cosmological scale
factor to exhibit an `accelerated expansion'instead of slowing down to a
regular maximum of expansion. We show in detail why the traditional,
Fierz-Pauli, massive gravity is in conflict not only with the static-field
experiments but also with the available indirect gravitational-wave
observations. At the same time, we demonstrate the incorrectness of the widely
held belief that the non-Fierz-Pauli theories possess `negative energies' and
`instabilities'.


title: Quantum Radiation from Black Holes

abstract:
  The expectation value of the energy-momentum tensor and the Hawking flux of a
scalar field on a Schwarzschild spacetime is calculated using the zeta-function
regularisation of the heat kernel. In particular, massless particles are
considered in a spherically reduced dilaton model. The effective action is
thereby obtained by the covariant perturbation theory and the boundary
conditions are fixed by means of the energy-momentum conservation equation. In
contrast to previous approaches the expectation values are calculated directly
from the effective action which itself is derived in a straightforward manner.


title:
Canonical quantization of general relativity: the last 18 years in a
  nutshell

abstract:
  This is a summary of the lectures presented at the Xth Brazilian school on
cosmology and gravitation. The style of the text is that of a lightly written
descriptive summary of ideas with almost no formulas, with pointers to the
literature. We hope this style can encourage new people to take a look into
these results. We discuss the variables that Ashtekar introduced 18 years ago
that gave rise to new momentum in this field, the loop representation, spin
networks, measures in the space of connections modulo gauge transformations,
the Hamiltonian constraint, application to cosmology and the connection with
potentially observable effects in gamma-ray bursts and conclude with a
discussion of consistent discretizations of general relativity on the lattice.


title:
Data analysis of continuous gravitational wave: All sky search and study
  of templates

abstract:
  We have studied the problem of all sky search in reference to continuous
gravitational wave particularly for such sources whose wave-form are known in
advance. We have made an analysis of the number of templates required for
matched filter analysis as applicable to these sources. We have employed the
concept of {\it fitting factor} {\it (FF)}; treating the source location as the
parameters of the signal manifold and have studied the matching of the signal
with templates corresponding to different source locations. We have
investigated the variation of FF with source location and have noticed a
symmetry in template parameters, $\theta_T$ and $\phi_T$. It has been found
that the two different template values in source location, each in $\theta_T$
and $\phi_T$, have same {\it FF}. We have also computed the number of templates
required assuming the noise power spectral density $S_n(f)$ to be flat. It is
observed that higher {\it FF} requires exponentially increasing large number of
templates.


title: Nonequilibrium dynamics of quantum fields in inflationary cosmology

abstract:
  The nonequilibrium dynamics of quantum fields is studied in inflationary
cosmology, with particular emphasis on applications to the problem of
post-inflation reheating. The Schwinger-Keldysh closed-time-path (CTP)
formalism is utilized along with the two-particle-irreducible (2PI) effective
action in order to obtain coupled, nonperturbative equations for the mean field
and variance in a general curved background spacetime. For a model consisting
of a quartically self-interacting O(N) field theory (with unbroken symmetry) in
spatially flat FRW spacetime, the dynamics of the mean field is studied
numerically, at leading order in the large-N expansion. The time evolution of
the scale factor is determined self-consistently using the semiclassical
Einstein equation. It is found that cosmic expansion can dramatically affect
the efficiency of parametric resonance-induced particle production. The
production of fermions due to the oscillating inflaton mean field is studied
for the case of a scalar inflaton coupled to a fermion field via a Yukawa
coupling $f$. The dissipation and noise kernels appearing at $O(f^2)$ in the
one-loop CTP effective action are shown to satisfy a zero-temperature
fluctuation-dissipation relation (FDR). The effective stochastic equation
obeyed by the inflaton zero mode at $O(f^4)$ contains multiplicative noise. It
is shown that stochasticity becomes important to the dynamics of the inflaton
zero mode before the end of reheating. The thermalization problem is discussed,
and a strategy is presented for obtaining time-local equations for equal-time
correlation functions which goes beyond the Hartree-Fock approximation.


title: The LISA Response Function

abstract:
  The orbital motion of the Laser Interferometer Space Antenna (LISA)
introduces modulations into the observed gravitational wave signal. These
modulations can be used to determine the location and orientation of a
gravitational wave source. The complete LISA response to an arbitary
gravitational wave is derived using a coordinate free approach in the
transverse-traceless gauge. The general response function reduces to that found
by Cutler (PRD 57, 7089 1998) for low frequency, monochromatic plane waves.
Estimates of the noise in the detector are found to be complicated by the time
variation of the interferometer arm lengths.


title:
Tuning gravitational-wave detector networks to measure compact binary
  mergers

abstract:
  Gravitational waves generated by the final merger of compact binary systems
depend on the structure of the binary's members. If the binary contains neutron
stars, measuring such waves can teach us about the properties of matter at
extreme densities. Unfortunately, these waves are typically at high frequency
where the sensitivity of broad-band detectors is not good. Learning about dense
matter from these waves will require networks of broad-band detectors combined
with narrow-band detectors that have good sensitivity at high frequencies. This
paper presents an algorithm by which a network can be ``tuned'', in accordance
with the best available information, in order to most effectively measure
merger waves. The algorithm is presented in the context of a toy model that
captures the qualitative features of narrow-band detectors and of certain
binary neutron star merger wave models. By using what is learned from a
sequence of merger measurements, the network can be gradually tuned in order to
accurately measure the waves. The number of measurements needed to reach this
stage depends upon the waves' signal strength, the number of narrow-band
detectors available for the measurement, and the detailed characteristics of
the waves that carry the merger information. Future studies will go beyond this
toy model, encompassing a more realistic description of both the detectors and
the gravitational waves.


title:
Invariant definition of rest mass and dynamics of particles in 4D from
  bulk geodesics in brane-world and non-compact Kaluza-Klein theories

abstract:
  In the Randall-Sundrum brane-world scenario and other non-compact
Kaluza-Klein theories, the motion of test particles is higher-dimensional in
nature. In other words, all test particles travel on five-dimensional geodesics
but observers, who are bounded to spacetime, have access only to the 4D part of
the trajectory. Conventionally, the dynamics of test particles as observed in
4D is discussed on the basis of the splitting of the geodesic equation in 5D.
However, this procedure is {\em not} unique and therefore leads to some
problems. The most serious one is the ambiguity in the definition of rest mass
in 4D, which is crucial for the discussion of the dynamics. We propose the
Hamilton-Jacobi formalism, instead of the geodesic one, to study the dynamics
in 4D. On the basis of this formalism we provide an unambiguous expression for
the rest mass and its variation along the motion as observed in 4D. It is
independent of the coordinates and any parameterization used along the motion.
Also, we are able to show a comprehensive picture of the various physical
scenarios allowed in 4D, without having to deal with the subtle details of the
splitting formalism. Moreover we study the extra non-gravitational forces
perceived by an observer in 4D who describes the geodesic motion of a bulk test
particle in 5D. Firstly, we show that the so-called fifth force fails to
account for the variation of rest mass along the particle's worldline.
Secondly, we offer here a new definition that correctly takes into account the
change of mass observed in 4D.


title: Varying Constants, Black Holes, and Quantum Gravity

abstract:
  Tentative observations and theoretical considerations have recently led to
renewed interest in models of fundamental physics in which certain
``constants'' vary in time. Assuming fixed black hole mass and the standard
form of the Bekenstein-Hawking entropy, Davies, Davis and Lineweaver have
argued that the laws of black hole thermodynamics disfavor models in which the
fundamental electric charge $e$ changes. I show that with these assumptions,
similar considerations severely constrain ``varying speed of light'' models,
unless we are prepared to abandon cherished assumptions about quantum gravity.
Relaxation of these assumptions permits sensible theories of quantum gravity
with ``varying constants,'' but also eliminates the thermodynamic constraints,
though the black hole mass spectrum may still provide some restrictions on the
range of allowable models.


title: Compact Gravity Wave Detector

abstract:
  An incoming gravity wave being a stress wave is a surface with intrinsic
curvature. When a light beam is parallel transported on this non-Euclidian
surface it acquires an excess phase which accumulates with each curcuit. We
calculate the separate contributions to excess phase from the wave geometry as
well as the dynamic response of mirrors in a Michelson interferometer. Using
these results and a combination of analogue and digital signal processing
techniques we show how a compact interferometer can be made sensitive to
gravity waves of amplitude density $10^{-23}/\sqrt{Hz}$ within a frequency
range $10^{-4}Hz$ to $10^4Hz$. As an example we describe a 10cm Michelson
interferometer designed to measure gravity waves from sources as far as the
Virgo cluster.


title:
Update on an Electromagnetic Basis for Inertia, Gravitation, the
  Principle of Equivalence, Spin and Particle Mass Ratios

abstract:
  A possible connection between the electromagnetic quantum vacuum and inertia
was first published by Haisch, Rueda and Puthoff (1994). If correct, this would
imply that mass may be an electromagnetic phenomenon and thus in principle
subject to modification, with possible technological implications for
propulsion. A multiyear NASA-funded study at the Lockheed Martin Advanced
Technology Center further developed this concept, resulting in an independent
theoretical validation of the fundamental approach (Rueda and Haisch, 1998ab).
Distortion of the quantum vacuum in accelerated reference frames results in a
force that appears to account for inertia. We have now shown that the same
effect occurs in a region of curved spacetime, thus elucidating the origin of
the principle of equivalence (Rueda, Haisch and Tung, 2001). A further
connection with general relativity has been drawn by Nickisch and Mollere
(2002): zero-point fluctuations give rise to spacetime micro-curvature effects
yielding a complementary perspective on the origin of inertia. Numerical
simulations of this effect demonstrate the manner in which a massless
fundamental particle, e.g. an electron, acquires inertial properties; this also
shows the apparent origin of particle spin along lines originally proposed by
Schroedinger. Finally, we suggest that the heavier leptons (muon and tau) may
be explainable as spatial-harmonic resonances of the (fundamental) electron.
They would carry the same overall charge, but with the charge now having
spatially lobed structure, each lobe of which would respond to higher frequency
components of the electromagnetic quantum vacuum, thereby increasing the
inertia and thus manifesting a heavier mass.


title:
Well posed constraint-preserving boundary conditions for the linearized
  Einstein equations

abstract:
  In the Cauchy problem of general relativity one considers initial data that
satisfies certain constraints. The evolution equations guarantee that the
evolved variables will satisfy the constraints at later instants of time. This
is only true within the domain of dependence of the initial data. If one wishes
to consider situations where the evolutions are studied for longer intervals
than the size of the domain of dependence, as is usually the case in three
dimensional numerical relativity, one needs to give boundary data. The boundary
data should be specified in such a way that the constraints are satisfied
everywhere, at all times. In this paper we address this problem for the case of
general relativity linearized around Minkowski space using the generalized
Einstein-Christoffel symmetric hyperbolic system of evolution equations. We
study the evolution equations for the constraints, specify boundary conditions
for them that make them well posed and further choose these boundary conditions
in such a way that the evolution equations for the metric variables are also
well posed. We also consider the case of a manifold with a non-smooth boundary,
as is the usual case of the cubic boxes commonly used in numerical relativity.
The techniques discussed should be applicable to more general cases, as
linearizations around more complicated backgrounds, and may be used to
establish well posedness in the full non-linear case.


title: Conformal Einstein evolution

abstract:
  We discuss various properties of the conformal field equations and their
consequences for the asymptotic structure of space-times.


title: Studies in Gravitational Wave Data Analysis

abstract:
  This thesis is devoted to the investigations of gravitational wave (GW) data
analysis from a continuous source e.g. a pulsar, a binary star system. The
first Chapter is an introduction to gravitational wave and second Chapter is on
the data analysis concept for the detection of GW. In third Chapter we
developed the Fourier Transform (FT) of a continuous gravitational wave (CGW)
for ground based laser interferometric detectors for the data set of one day
observation time incorporating the effects arising due to rotational as well as
orbital motion of the earth. The transform is applicable for arbitrary location
of detector and source. In Chapter four we have generalized the FT for the data
set for (i) one year observation time and (ii) arbitrary observation time. As
an application of the transform we considered spin down and N-component signal
analysis. In fifth Chapter we have made an analysis of the number of templates
required for matched filter analysis as applicable to these sources. We have
employed the concept of {\it Fitting Factor (FF)}; treating the source location
as the parameters of the signal manifold and have studied the matching of the
signal with templates corresponding to different source locations. We have
investigated the variation of {\it FF} with source location and have noticed a
symmetry in template parameters, $\theta_T$ and $\phi_T$. It has been found
that the two different template values in source location, each in $\theta_T$
and $\phi_T$, have same {\it FF}. We have also computed the number of templates
required assuming the noise power spectral density $S_n(f)$ to be flat. It is
observed that higher {\it FF} requires exponentially increasing large number of
templates. Appendix contains the source codes developed for the computation.


title: Moment Problems and the Causal Set Approach to Quantum Gravity

abstract:
  We study a collection of discrete Markov chains related to the causal set
approach to modeling discrete theories of quantum gravity. The transition
probabilities of these chains satisfy a general covariance principle, a
causality principle, and a renormalizability condition. The corresponding
dynamics are completely determined by a sequence of nonnegative real coupling
constants. Using techniques related to the classical moment problem, we give a
complete description of any such sequence of coupling constants. We prove a
representation theorem: every discrete theory of quantum gravity arising from
causal set dynamics satisfying covariance, causality and renormalizability
corresponds to a unique probability distribution function on the nonnegative
real numbers, with the coupling constants defining the theory given by the
moments of the distribution.


title: Comment on "Uncertainty in measurements of distance"

abstract:
  We have argued that quantum mechanics and general relativity give a lower
bound $\delta l \gtrsim l^{1/3} l_P^{2/3}$ on the measurement uncertainty of
any distance $l$ much greater than the Planck length $l_P$. Recently Baez and
Olson have claimed that one can go below this bound by attaching the measuring
device to a massive elastic rod. Here we refute their claim. We also reiterate
(and invite our critics to ponder on) the intimate relationship and consistency
between black hole physics (including the holographic principle) and our bound
on distance measurements.


title: Nonlinear massive spin-two field generated by higher derivative gravity

abstract:
  We present a systematic exposition of the Lagrangian field theory for the
massive spin-two field generated in higher-derivative gravity. It has been
noticed by various authors that this nonlinear field overcomes the well known
inconsistency of the theory for a linear massive spin-two field interacting
with Einstein's gravity. Starting from a Lagrangian quadratically depending on
the Ricci tensor of the metric, we explore the two possible second-order
pictures usually called "(Helmholtz-)Jordan frame" and "Einstein frame". In
spite of their mathematical equivalence, the two frames have different
structural properties: in Einstein frame, the spin-two field is minimally
coupled to gravity, while in the other frame it is necessarily coupled to the
curvature, without a separate kinetic term. We prove that the theory admits a
unique and linearly stable ground state solution, and that the equations of
motion are consistent, showing that these results can be obtained independently
in either frame. The full equations of motion and the energy-momentum tensor
for the spin--two field in Einstein frame are given, and a simple but
nontrivial exact solution to these equations is found. The comparison of the
energy-momentum tensors for the spin-two field in the two frames suggests that
the Einstein frame is physically more acceptable. We point out that the
energy-momentum tensor generated by the Lagrangian of the linearized theory is
unrelated to the corresponding tensor of the full theory. It is then argued
that the ghost-like nature of the nonlinear spin-two field, found long ago in
the linear approximation, may not be so harmful to classical stability issues,
as has been expected.


title: Asymptotics of Relativistic Spin Networks

abstract:
  The stationary phase technique is used to calculate asymptotic formulae for
SO(4) Relativistic Spin Networks. For the tetrahedral spin network this gives
the square of the Ponzano-Regge asymptotic formula for the SU(2) 6j symbol. For
the 4-simplex (10j-symbol) the asymptotic formula is compared with numerical
calculations of the Spin Network evaluation. Finally we discuss the asymptotics
of the SO(3,1) 10j-symbol.


title: All spacetimes with vanishing curvature invariants

abstract:
  All Lorentzian spacetimes with vanishing invariants constructed from the
Riemann tensor and its covariant derivatives are determined. A subclass of the
Kundt spacetimes results and we display the corresponding metrics in local
coordinates. Some potential applications of these spacetimes are discussed.


title: Relativistic Rotation in the Large Radius, Small Angular Velocity Limit

abstract:
  Relativistic rotation is considered in the limit of angular velocity
approaching zero and radial distance approaching infinity, such that
centrifugal acceleration is immeasurably small while tangent velocity remains
close to the speed of light. For this case, the predictions of the traditional
approach to relativistic rotation using local co-moving Lorentz frames are
compared and contrasted with those of the differential geometry based
non-time-orthogonal analysis approach. Different predictions by the two
approaches imply that only the non-time-orthogonal approach is valid.


title:
Three-dimensional interior solutions from Jordan-Brans-Dicke Theory of
  Gravity

abstract:
  We study spherically symmetric solutions to the Jordan-Brans-Dicke field
equations under the assumption that the space-time may possess an arbitrary
number of spatial dimensions. Assuming a perfect fluid with the equation of
state, we show that there are static interior nontrivial solutions in three
dimensional Jordan-Brans-Dicke gravity theory.


title:
LAGEOS-type Satellites in Critical Supplementary Orbit Configuration and
  the Lense-Thirring Effect Detection

abstract:
  In this paper we analyze quantitatively the concept of LAGEOS--type
satellites in critical supplementary orbit configuration (CSOC) which has
proven capable of yielding various observables for many tests of General
Relativity in the terrestrial gravitational field, with particular emphasis on
the measurement of the Lense--Thirring effect.


title: The equivalence principle and the bending of light

abstract:
  The apparent discrepancy between the bending of light predicted by the
equivalence principle and its corresponding value in general relativity is
resolved by evaluating the deflection of light with respect to a direction that
is parallel transported along the ray trajectory in 3-space. In this way the
bending predicted by the equivalence principle is fulfilled in general
relativity and other alternative metric theories of gravity.


title: On the Renormalization Group in Curved Spacetime

abstract:
  We define the renormalization group flow for a renormalizable interacting
quantum field in curved spacetime via its behavior under scaling of the
spacetime metric, $\g \to \lambda^2 \g$. We consider explicitly the case of a
scalar field, $\phi$, with a self-interaction of the form $\kappa \phi^4$,
although our results should generalize straightforwardly to other
renormalizable theories. We construct the interacting field--as well as its
Wick powers and their time-ordered-products--as formal power series in the
algebra generated by the Wick powers and time-ordered-products of the free
field, and we determine the changes in the interacting field observables
resulting from changes in the renormalization prescription. Our main result is
the proof that, for any fixed renormalization prescription, the interacting
field algebra for the spacetime $(M, \lambda^2 \g)$ with coupling parameters
$p$ is isomorphic to the interacting field algebra for the spacetime $(M, \g)$
but with different values, $p(\lambda)$, of the coupling parameters. The map $p
\to p(\lambda)$ yields the renormalization group flow. The notion of essential
and inessential coupling parameters is defined, and we define the notion of a
fixed point as a point, $p$, in the parameter space for which there is no
change in essential parameters under renormalization group flow.


title: Hydrogen atom in the gravitational fields of topological defects

abstract:
  We consider a hydrogen atom in the background spacetimes generated by an
infinitely thin cosmic string and by a point-like global monopole. In both
cases, we find the solutions of the corresponding Dirac equations and we
determine the energy levels of the atom. We investigate how the geometric and
topological features of these spacetimes leads to shifts in the energy levels
as compared with the flat Minkowski spacetime.


title: Electromagnetic Wavelets as Hertzian Pulsed Beams in Complex Spacetime

abstract:
  Electromagnetic wavelets are a family of 3x3 matrix fields W_z(x')
parameterized by complex spacetime points z=x+iy with y timelike. They are
translates of a \sl basic \rm wavelet W(z) holomorphic in the future-oriented
union T of the forward and backward tubes. Applied to a complex polarization
vector p (representing electric and magnetic dipole moments), W(z) gives an
anti-selfdual solution W(z)p of Maxwell's equations derived from a selfdual
Hertz potential Z(z)=-iS(z)p, where S is the \sl Synge function \rm acting as a
Whittaker-like scalar Hertz potential. Resolutions of unity exist giving
representations of sourceless electromagnetic fields as superpositions of
wavelets. With the choice of a branch cut, S(z) splits into a difference of
retarded and advanced \sl pulsed beams \rm whose limits as y\to 0 give the
propagators of the wave equation. This yields a similar splitting of the
wavelets and leads to their complete physical interpretation as EM pulsed beams
absorbed and emitted by a \sl disk source \rm D(y) representing the branch cut.
The choice of y determines the beam's orientation, collimation and duration,
giving beams as sharp and pulses as short as desired. The sources are computed
as spacetime distributions of electric and magnetic dipoles supported on D(y).
The wavelet representation of sourceless electromagnetic fields now splits into
representations with advanced and retarded sources. These representations are
the electromagnetic counterpart of relativistic coherent-state representations
previously derived for massive Klein-Gordon and Dirac particles.


title: The general double-dust solution

abstract:
  The gravitational field of two identical rotating and counter-moving dust
beams is found in full generality. The solution depends on an arbitrary
function and a parameter. Some of its properties are studied. Previous
particular solutions are derived as subcases.


title: Acceleration and Cyclotron Radiation, Induced by Gravitational Waves

abstract:
  The equations which determine the response of a charged particle moving in a
magnetic field to an incident gravitational wave(GW) are derived in the
linearized approximation to general relativity. We briefly discuss several
astrophysical applications of the derived formulae taking into account the
resonance between the wave and the particle's motion which occurs at
$\omega_g=2\Omega$, whenever the GW is parallel to the constant magnetic field.
In the case where the GW is perpendicular to the constant magnetic field,
magnetic resonances appear at $\omega_g=\Omega$ and $\omega_g=2\Omega$. Such
resonant mechanism may be useful to build models of GW driven cyclotron
emitters.


title: Spin-2 fields on Minkowski space near space-like and null infinity

abstract:
  We show that the spin-2 equations on Minkowski space in the gauge of the
`regular finite initial value problem at space-like infinity' imply estimates
which, together with the transport equations on the cylinder at space-like
infinity, allow us to obtain for a certain class of initial data information on
the behaviour of the solution near space-like and null infinity of any desired
precision.


title: Spherical collapse with heat flow and without horizon

abstract:
  We present a class of solutions for a heat conducting fluid sphere, which
radiates energy during collapse without the appearance of horizon at the
boundary at any stage of the collapse. A simple model shows that there is no
accumulation of energy due to collapse since it radiates out at the same rate
as it is being generated.


title: Null energy conditions in quantum field theory

abstract:
  For the quantised, massless, minimally coupled real scalar field in
four-dimensional Minkowski space, we show (by an explicit construction) that
weighted averages of the null-contracted stress-energy tensor along null
geodesics are unbounded from below on the class of Hadamard states. Thus there
are no quantum inequalities along null geodesics in four-dimensional Minkowski
spacetime. This is in contrast to the case for two-dimensional flat spacetime,
where such inequalities do exist. We discuss in detail the properties of the
quantum states used in our analysis, and also show that the renormalized
expectation value of the stress energy tensor evaluated in these states
satisfies the averaged null energy condition (as expected), despite the
nonexistence of a null-averaged quantum inequality. However, we also show that
in any globally hyperbolic spacetime the null-contracted stress energy averaged
over a timelike worldline does satisfy a quantum inequality bound (for both
massive and massless fields). We comment briefly on the implications of our
results for singularity theorems.


title: Invariant quantization in warped spacetimes

abstract:
  We argue that quantum theory in curved spacetime should be invariant under
the continuous spacetime symmetries thaat are connected with the identity. For
typical warped-product spacetimes, we prove that such invariance can be
actually implemented, at least at the level of first quantization. Our approach
rests on a mode decomposition which is special to the context of warped
spacetimes.


title: Radially homothetic spacetime is of Petrov-type D

abstract:
  It is well-known \cite{mtbh} that {\em all} black hole solutions of General
Relativity are of Petrov-type D. It may thus be expected that the spacetime of
{\em physically realizable} spherical gravitational collapse is also of
Petrov-type D. We show that a radially homothetic spacetime, {\em ie}, a
spherically symmetric spacetime with hyper-surface orthogonal, radial,
homothetic Killing vector, is of Petrov-type D. As has been argued in
\cite{prl1}, it is a spacetime of {\em physically realizable} spherical
collapse.


title: The LISA Optimal Sensitivity

abstract:
  The multiple Doppler readouts available on the Laser Interferometer Space
Antenna (LISA) permit simultaneous formation of several interferometric
observables. All these observables are independent of laser frequency
fluctuations and have different couplings to gravitational waves and to the
various LISA instrumental noises. Within the functional space of
interferometric combinations LISA will be able to synthesize, we have
identified a triplet of interferometric combinations that show optimally
combined sensitivity. As an application of the method, we computed the
sensitivity improvement for sinusoidal sources in the nominal, equal-arm LISA
configuration. In the part of the Fourier band where the period of the wave is
longer than the typical light travel-time across LISA, the sensitivity gain
over a single Michelson interferometer is equal to $\sqrt{2}$. In the mid-band
region, where the LISA Michelson combination has its best sensitivity, the
improvement over the Michelson sensitivity is slightly better than $\sqrt{2}$,
and the frequency band of best sensitivity is broadened. For frequencies
greater than the reciprocal of the light travel-time, the sensitivity
improvement is oscillatory and $\sim \sqrt{3}$, but can be greater than
$\sqrt{3}$ near frequencies that are integer multiples of the inverse of the
one-way light travel-time in the LISA arm.


title: Gravitational effects in terms of paths in Minkowski space

abstract:
  An approach is developed which enables one to analyze gravitational effects
without usage of any concrete model of geometry (or a class of models of
geometry) of space-time and even without any coordinate system. Instead, the
formalism of the group of paths is used. An element of this group (a class of
curves in Minkowski space) is associated with each curve in the curved
space-time and called its `flat model'. The analysis of observational data in
terms of flat models of closed curves is interpreted as a formalization of the
analysis which a `naive observer' (knowing nothing about the space-time being
curved) applies to his observations.


title: Colliding beams of light

abstract:
  The stationary gravitational field of two identical counter-moving beams of
pure radiation is found in full generality. The solution depends on an
arbitrary function and a parameter which sets the scale of the energy density.
Some of its properties are studied. Previous particular solutions are derived
as subcases.


title:
Automorphisms of Real 4 Dimensional Lie Algebras and the Invariant
  Characterization of Homogeneous 4-Spaces

abstract:
  The automorphisms of all 4-dimensional, real Lie Algebras are presented in a
comprehensive way. Their action on the space of $4\times 4$, real, symmetric
and positive definite, matrices, defines equivalence classes which are used for
the invariant characterization of the 4-dimensional homogeneous spaces which
possess an invariant basis.


title: Topological Structure of The Upper End of Future Null Infinity

abstract:
  We propose a method to determine the topological structure of an event
horizon far in the future of a spacetime from the geometrical information of
its future null infinity. In the present article, we mainly consider spacetimes
with two black holes. Although, in most of cases, the black holes coalesce and
their event horizon is topologically a single sphere far in the future, there
are several possibilities that the black holes do not coalesce eternally and
such exact solutions. In our formulation, the geometrical structure of future
null infinity is related to the topological structure of the upper end of the
future null infinity through the Poincare\'-Hopf's theorem. Since the upper end
of the future null infinity determines the event horizon far in the future
under the conformal embedding, the topology of event horizon far in the future
will be affected by the geometrical structure of the future null infinity. Our
method is not only for the case of black hole coalescence. Also we can consider
more than two black holes or a black hole with non-trivial topology.


title: On The Symplectic Two-Form of Gravity in Terms of Dirac Eigenvalues

abstract:
  The Dirac eigenvalues form a subset of observables of the Euclidean gravity.
The symplectic two-form in the covariant phase space could be expressed, in
principle, in terms of the Dirac eigenvalues. We discuss the existence of the
formal solution of the equations defining the components of the symplectic form
in this framework.


title: Multidimensional cosmology and asymptotical AdS

abstract:
  A non-linear gravitational model with a multidimensional geometry and
quadratic scalar curvature is considered. For certain parameter ranges, the
extra dimensions are stabilized if the internal spaces have negative curvature.
As a consequence, the 4-dimensional effective cosmological constant as well as
the bulk cosmological constant become negative. The homogeneous and isotropic
external space is asymptotically AdS. The connection between the D-dimensional
and the 4-dimensional fundamental mass scales sets an additional restriction on
the parameters of the considered non-linear models.


title: The State of the Universe

abstract:
  What is the quantum state of the universe? That is the central question of
quantum cosmology. This essay describes the place of that quantum state in a
final theory governing the regularities exhibited universally by all physical
systems in the universe. It is possible that this final theory consists of two
parts: (1) a dynamical theory such as superstring theory, and (2) a state of
the universe such as Hawking's no-boundary wave function. Both are necessary
because prediction in quantum mechanics requires both a Hamiltonian and a
state. Complete ignorance of the state leads to predictions inconsistent with
observation. The simplicity observed in the early universe gives hope that
there is a simple, discoverable quantum state of the universe. It may be that,
like the dynamical theory, the predictions of the quantum state for late time,
low energy observations can be summarized by an effective cosmological theory.
That should not obscure the need to provide a fundamental basis for such an
effective theory which gives a a unified explanation of its features and is
applicable without restrictive assumptions. It could be that there is one
principle that determines both the dynamical theory and the quantum state. That
would be a truly unified final theory. (talk given The Future of Theoretical
Physics and Cosmology: Stephen Hawking 60th Birthday Symposium)


title: Theories of Everything and Hawking's Wave Function of the Universe

abstract:
  If a cat, a cannonball, and an economics textbook are all dropped from the
same height, they fall to the ground with exactly the same acceleration under
the influence of gravity. This equality of gravitational accelerations of
different things is one of the most accurately tested laws of physics. That
law, however, tells us little about cats, cannonballs, or economics. This
lecture expands on this theme to address the question of what features of our
world are predicted by a fundamental ``theory of everything'' governing the
regularities exhibited universally by all physical systems. This may consist of
two parts: a dynamical law governing regularities in time (e.g superstring
theory) and a law of cosmological initial condition governing mostly
regularities in space (e.g. Hawking's no-boundary initial condition). The
lecture concludes that: (1) ``A theory of everything'' is not a theory of
everything in a quantum mechanical universe. (2) If the laws are short enough
to be discoverable then they are probably too short to predict everything. (3)
The regularities of human history, economics, biology, geology, etc are
consistent with the fundamental laws of physics but do not follow from them.
(Public lecture given at The Future of Theoretical Physics and Cosmology:
Stephen Hawking 60th Birthday Symposium.)


title: Finitary, Causal and Quantal Vacuum Einstein Gravity

abstract:
  We continue recent work and formulate the gravitational vacuum Einstein
equations over a locally finite spacetime by using the basic axiomatics,
techniques, ideas and working philosophy of Abstract Differential Geometry. The
whole construction is `fully covariant', `inherently quantum' (both expressions
are analytically explained in the paper) and genuinely smooth background
spacetime independent.


title: Dispelling the Anthropic Principle from the Dimensionality Arguments

abstract:
  It is shown that in d=11 supergravity, under a very reasonable ansatz, the
nearly flat spacetime in which we are living must be 4-dimensional without
appealing to the Anthropic Principle. Can we dispel the Anthropic Principle
completely from cosmology?


title: Absolute Parallelism Geometry: Developments, Applications and Problems

abstract:
  Absolute parallelism geometry is frequently used for physical applications.
It has two main defects, from the point of view of applications. The first is
the identical vanishing of its curvature tensor. The second is that its
autoparallel paths do not represent physical trajectories. The present work
shows how these defects were treated in the course of development of the
geometry. The new version of this geometry contains simultaneous non-vanishing
torsion and curvatures. Also, the new paths discovered in this geometry do
represent physical trajectories. Advantages and disadvantages of this geometry
are given for each stage of its development. Physical applications are just
mentioned without giving any details.


title: Covariant Perturbations of Schwarzschild Black Holes

abstract:
  We present a new covariant and gauge-invariant perturbation formalism for
dealing with spacetimes having spherical symmetry (or some preferred spatial
direction) in the background, and apply it to the case of gravitational wave
propagation in a Schwarzschild black hole spacetime. The 1+3 covariant approach
is extended to a `1+1+2 covariant sheet' formalism by introducing a radial unit
vector in addition to the timelike congruence, and decomposing all covariant
quantities with respect to this. The background Schwarzschild solution is
discussed and a covariant characterisation is given. We give the full
first-order system of linearised 1+1+2 covariant equations, and we show how, by
introducing (time and spherical) harmonic functions, these may be reduced to a
system of first-order ordinary differential equations and algebraic constraints
for the 1+1+2 variables which may be solved straightforwardly. We show how both
the odd and even parity perturbations may be unified by the discovery of a
covariant, frame- and gauge-invariant, transverse-traceless tensor describing
gravitational waves, which satisfies a covariant wave equation equivalent to
the Regge-Wheeler equation for both even and odd parity perturbations. We show
how the Zerilli equation may be derived from this tensor, and derive a similar
transverse traceless tensor equivalent to this equation. The so-called
`special' quasinormal modes with purely imaginary frequency emerge naturally.
The significance of the degrees of freedom in the choice of the two frame
vectors is discussed, and we demonstrate that, for a certain frame choice, the
underlying dynamics is governed purely by the Regge-Wheeler tensor. The two
transverse-traceless Weyl tensors which carry the curvature of gravitational
waves are discussed.


title:
Stability and Instability of the Reissner-Nordstrom Cauchy Horizon and
  the Problem of Uniqueness in General Relativity

abstract:
  This talk describes some recent results [16] regarding the problem of
uniqueness in the large (also known as strong cosmic censorship) for the
initial value problem in general relativity. In order to isolate the essential
analytic features of the problem from the complicated setting of gravitational
collapse in which it arises, some familiarity with conformal properties of
certain celebrated special solutions of the theory of relativity will have to
be developed. This talk is an attempt to present precisely these features to an
audience of non-specialists, in a way which will hopefully fully motivate a
certain characteristic initial value problem for the spherically-symmetric
Einstein-Maxwell-Scalar Field system. The considerations outlined here leading
to this particular initial value problem are well known in the physics
relativity community, where the problem of uniqueness has been studied
heuristically [1, 22] and numerically [2, 3]. In [16], the global behavior of
solutions to this IVP, in particular, the issue of uniqueness, is
mathematically completely understood. A statement of the relevant Theorems is
included in Section 9. Only a sketch of the ideas of the proof is provided
here, but the readers may refer to [16] for details.


title:
Analysis of static and spherically-symmetric solutions in NDL theory of
  gravitation

abstract:
  We investigate a static solution with spherical symmetry of a recently
proposed field theory of gravitation. In this so-called NDL theory, matter
interacts with gravity in accordance with the Weak Equivalence Principle, while
gravitons have a nonlinear self-interaction. It is shown that the predictions
of NDL agree with those of General Relativity in the three classic tests.
However, there are potential differences in the strong-field limit, which we
illustrate by proving that this theory does not allow the existence of static
and spherically symmetric black holes.


title:
Quasi-Isotropization of the Inhomogeneous Mixmaster Universe Induced by
  an Inflationary Process

abstract:
  We derive a ``generic'' inhomogeneous ``bridge'' solution for a cosmological
model in the presence of a real self-interacting scalar field. This solution
connects a Kasner-like regime to an inflationary stage of evolution and
therefore provides a dynamical mechanism for the quasi-isotropization of the
universe. In the framework of a standard Arnowitt-Deser-Misner Hamiltonian
formulation of the dynamics and by adopting Misner-Chitr\`e-like variables, we
integrate the Einstein-Hamilton-Jacobi equation corresponding to a ``generic''
inhomogeneous cosmological model whose evolution is influenced by the coupling
with a bosonic field, expected to be responsible for a spontaneous symmetry
breaking configuration. The dependence of the detailed evolution of the
universe on the initial conditions is then appropriately characterized.


title:
Noise Kernel and Stress Energy Bi-Tensor of Quantum Fields in
  Conformally-Optical Metrics: Schwarzschild Black Holes

abstract:
  In Paper II [N. G. Phillips and B. L. Hu, previous abstract] we presented the
details for the regularization of the noise kernel of a quantum scalar field in
optical spacetimes by the modified point separation scheme, and a Gaussian
approximation for the Green function. We worked out the regularized noise
kernel for two examples: hot flat space and optical Schwarzschild metric. In
this paper we consider noise kernels for a scalar field in the Schwarzschild
black hole. Much of the work in the point separation approach is to determine
how the divergent piece conformally transforms. For the Schwarzschild metric we
find that the fluctuations of the stress tensor of the Hawking flux in the far
field region checks with the analytic results given by Campos and Hu earlier
[A. Campos and B. L. Hu, Phys. Rev. D {\bf 58} (1998) 125021; Int. J. Theor.
Phys. {\bf 38} (1999) 1253]. We also verify Page's result [D. N. Page, Phys.
Rev. {\bf D25}, 1499 (1982)] for the stress tensor, which, though used often,
still lacks a rigorous proof, as in his original work the direct use of the
conformal transformation was circumvented. However, as in the optical case, we
show that the Gaussian approximation applied to the Green function produces
significant error in the noise kernel on the Schwarzschild horizon. As before
we identify the failure as occurring at the fourth covariant derivative order.


title:
Noise Kernel and Stress Energy Bi-Tensor of Quantum Fields in Hot Flat
  Space and Gaussian Approximation in the Optical Schwarzschild Metric

abstract:
  Continuing our investigation of the regularization of the noise kernel in
curved spacetimes [N. G. Phillips and B. L. Hu, Phys. Rev. D {\bf 63}, 104001
(2001)] we adopt the modified point separation scheme for the class of optical
spacetimes using the Gaussian approximation for the Green functions a la
Bekenstein-Parker-Page. In the first example we derive the regularized noise
kernel for a thermal field in flat space. It is useful for black hole
nucleation considerations. In the second example of an optical Schwarzschild
spacetime we obtain a finite expression for the noise kernel at the horizon and
recover the hot flat space result at infinity. Knowledge of the noise kernel is
essential for studying issues related to black hole horizon fluctuations and
Hawking radiation backreaction. We show that the Gaussian approximated Green
function which works surprisingly well for the stress tensor at the
Schwarzschild horizon produces significant error in the noise kernel there. We
identify the failure as occurring at the fourth covariant derivative order.


title: Uniformly Accelerated Mirrors. Part 2: Quantum Correlations

abstract:
  We study the correlations between the particles emitted by a moving mirror.
To this end, we first analyze $< T_{\mu\nu}(x) T_{\alpha\beta}(x') >$, the
two-point function of the stress tensor of the radiation field. In this we
generalize the work undertaken by Carlitz and Willey. To further analyze how
the vacuum correlations on $I^-$ are scattered by the mirror and redistributed
among the produced pairs of particles, we use a more powerful approach based on
the value of $T_{\mu\nu}$ which is conditional to the detection of a given
particle on $I^+$. We apply both methods to the fluxes emitted by a uniformly
accelerated mirror. This case is particularly interesting because of its strong
interferences which lead to a vanishing flux, and because of its divergences
which are due to the infinite blue shift effects associated with the horizons.
Using the conditional value of $T_{\mu\nu}$, we reveal the existence of
correlations between created particles and their partners in a domain where the
mean fluxes and the two-point function vanish. This demonstrates that the
scattering by an accelerated mirror leads to a steady conversion of vacuum
fluctuations into pairs of quanta. Finally, we study the scattering by two
uniformly accelerated mirrors which follow symmetrical trajectories (i.e. which
possess the same horizons). When using the Davies-Fulling model, the Bogoliubov
coefficients encoding pair creation vanish because of perfectly destructive
interferences. When using regularized amplitudes, these interferences are
inevitably lost thereby giving rise to pair creation.


title: (2+1) dimensional black holes in warped product scheme

abstract:
  Exploiting a multiply warped product manifold scheme, we study the interior
solutions of the Banados-Teitelboim-Zanelli black holes and the exterior
solutions of the de Sitter black holes in the (2+1) dimensions.


title: Kerr-Schild and generalized metric motions

abstract:
  In this work we study in detail new kinds of motions of the metric tensor.
The work is divided into two main parts. In the first part we study the general
existence of Kerr-Schild motions --a recently introduced metric motion. We show
that generically, Kerr-Schild motions give rise to finite dimensional Lie
algebras and are isometrizable, i.e., they are in a one-to-one correspondence
with a subset of isometries of a (usually different) spacetime. This is similar
to conformal motions. There are however some exceptions that yield infinite
dimensional algebras in any dimension of the manifold. We also show that
Kerr-Schild motions may be interpreted as some kind of metric symmetries in the
sense of having associated some geometrical invariants. In the second part, we
suggest a scheme able to cope with other new candidates of metric motions from
a geometrical viewpoint. We solve a set of new candidates which may be
interpreted as the seeds of further developments and relate them with known
methods of finding new solutions to Einstein's field equations. The results are
similar to those of Kerr-Schild motions, yet a richer algebraical structure
appears. In conclusion, even though several points still remain open, the
wealth of results shows that the proposed concept of generalized metric motions
is meaningful and likely to have a spin-off in gravitational physics.We end by
listing and analyzing some of those open points.


title: A physical application of Kerr-Schild groups

abstract:
  The present work deals with the search of useful physical applications of
some generalized groups of metric transformations. We put forward different
proposals and focus our attention on the implementation of one of them.
Particularly, the results show how one can control very efficiently the kind of
spacetimes related by a Generalized Kerr-Schild (GKS) Ansatz through
Kerr-Schild groups. Finally a preliminar study regarding other generalized
groups of metric transformations is undertaken which is aimed at giving some
hints in new Ans\"atze to finding useful solutions to Einstein's equations.


title: Computers with closed timelike curves can solve hard problems

abstract:
  A computer which has access to a closed timelike curve, and can thereby send
the results of calculations into its own past, can exploit this to solve
difficult computational problems efficiently. I give a specific demonstration
of this for the problem of factoring large numbers, and argue that a similar
approach can solve NP-complete and PSPACE-complete problems. I discuss the
potential impact of quantum effects on this result.


title:
Optical activity induced by curvature in a gravitational pp-wave
  background

abstract:
  We study optical activity induced by curvature. The optical activity model we
present has two phenomenological gyration parameters, within which we analyze
three model cases, namely, an exactly integrable model, the Landau-Lifshitz
model and the Fedorov model, these latter two are solved in the short
wavelength approximation. The model background is a gravitational pp-wave. The
solutions show that the optical activity induced by curvature leads to Faraday
rotation.


title: Non conducting spherically symmetric fluids

abstract:
  A class of spherically symmetric spacetimes invariantly defined by a zero
flux condition is examined first from a purely geometrical point of view and
then physically by way of Einstein's equations for a general fluid
decomposition of the energy-momentum tensor. The approach, which allows a
formal inversion of Einstein's equations, explains, for example, why
spherically symmetric perfect fluids with spatially homogeneous energy density
must be shearfree.


title:
Analysis of Parametric Oscillatory Instability in Power Recycled LIGO
  Interferometer

abstract:
  We present the analysis of a nonlinear effect of parametric oscillatory
instability in power recycled LIGO interferometer with the Fabry-Perot (FP)
cavities in the arms. The basis for this effect is the excitation of the
additional (Stokes) optical mode and the mirror elastic mode, when the optical
energy stored in the main FP cavity main mode exceeds the certain threshold and
the frequencies are related so that sum of frequencies of Stokes and elastic
modes are approximately equal to frequencyof main mode. The presence of
anti-Stokes modes (with frequency approximately equal to sum of frequencies of
main and elastic modes) can depress parametric instability. However, it is very
likely that the anti-Stokes modes will not compensate the parametric
instability completely.


title:
Quantum Birth of a Hot Universe II. Model Parameter Estimates from CMB
  Temperature Fluctuations

abstract:
  We consider the quantum birth of a hot FRW universe from a vacuum-dominated
quantum fluctuation with admixture of radiation and strings, which correspond
to quantum tunnelling from a discrete energy level with a non-zero temperature.
The presence of strings with the equation of state $p=-\epsilon/3$ mimics a
positive curvature term which makes it possible, in the case of a negative
deficit angle, the quantum birth of an open and flat universe. In the
pre-de-Sitter domain radiation energy levels are quantized. We calculate the
temperature spectrum and estimate the range of the model parameters restricting
temperature fluctuations by the observational constraint on the CMB anisotropy.
For the GUT scale of initial de Sitter vacuum the lower limit on the
temperature at the start of classical evolution is close to the values as
predicted by reheating theories, while the upper limit is far from the
threshold for a monopole rest mass.


title:
Improved numerical stability of stationary black hole evolution
  calculations

abstract:
  We experiment with modifications of the BSSN form of the Einstein field
equations (a reformulation of the ADM equations) and demonstrate how these
modifications affect the stability of numerical black hole evolution
calculations. We use excision to evolve both non-rotating and rotating
Kerr-Schild black holes in octant and equatorial symmetry, and without any
symmetry assumptions, and obtain accurate and stable simulations for specific
angular momenta J/M of up to about 0.9M.


title:
Gravitational Collapse of Self-Similar and Shear-free Fluid with Heat
  Flow

abstract:
  A class of solutions to Einstein field equations is studied, which represents
gravitational collapse of thick spherical shells made of self-similar and
shear-free fluid with heat flow. It is shown that such shells satisfy all the
energy conditions, and the corresponding collapse always forms naked
singularities.


title: Impulsive waves in electrovac direct product spacetimes with Lambda

abstract:
  A complete family of non-expanding impulsive waves in spacetimes which are
the direct product of two 2-spaces of constant curvature is presented. In
addition to previously investigated impulses in Minkowski, (anti-)Nariai and
Bertotti-Robinson universes, a new explicit class of impulsive waves which
propagate in the exceptional electrovac Plebanski-Hacyan spacetimes with a
cosmological constant Lambda is constructed. In particular, pure gravitational
waves generated by null particles with an arbitrary multipole structure are
described. The metrics are impulsive members of a more general family of the
Kundt spacetimes of type II. The well-known pp-waves are recovered for
Lambda=0.


title:
A Finslerian Cosmological Metric and its Riemannian Kaluza-Klein
  Extension

abstract:
  In this study a rotationally and translationally invariant metric in Finsler
space is investigated. We choose to rewrite the metric in Riemanian space by
increasing the dimension of space-time and introducing additional coordinates
such that for specific values of these coordinates, the geodesics of the four
dimensional Finslerian space-time and six dimensional Riemanian space-time are
identical. Cosmological solutions described by this metric give rise to an
equation of state corresponding to a space dominated by domain walls and an
internal space dominated by strings.


title: Thick domain walls around a black hole

abstract:
  We discuss the gravitationally interacting system of a thick domain wall and
a black hole. We numerically solve the scalar field equation in the
Schwarzschild spacetime and obtain a sequence of static axi-symmetric solutions
representing thick domain walls. We find that, for the walls near the horizon,
the Nambu--Goto approximation is no longer valid.


title: Isotropic cosmological singularities: other matter models

abstract:
  Isotropic cosmological singularities are singularities which can be removed
by rescaling the metric. In some cases already studied (gr-qc/9903008,
gr-qc/9903009, gr-qc/9903018) existence and uniqueness of cosmological models
with data at the singularity has been established. These were cosmologies with,
as source, either perfect fluids with linear equations of state or massless,
collisionless particles. In this article we consider how to extend these
results to a variety of other matter models. These are scalar fields, massive
collisionless matter, the Yang-Mills plasma of Choquet-Bruhat, or matter
satisfying the Einstein-Boltzmann equation.


title:
Regularization parameters for the self force in Schwarzschild spacetime:
  II. gravitational and electromagnetic cases

abstract:
  We obtain all ``regularization parameters'' (RP) needed for calculating the
gravitational and electromagnetic self forces for an arbitrary geodesic orbit
around a Schwarzschild black hole. These RP values are required for
implementing the previously introduced mode-sum method, which allows a
practical calculation of the self force by summing over contributions from
individual multipole modes of the particle's field. In the gravitational case,
we provide here full details of the analytic method and results briefly
reported in a recent Letter [Phys. Rev. Lett. {\bf 88}, 091101 (2002)]. In the
electromagnetic case, the RP are obtained here for the first time.


title: Regularity for Lorentz Metrics under Curvature Bounds

abstract:
  Let (M, g) be an (n+1) dimensional space-time, with bounded curvature with
respect to a bounded framing. If (M, g) is vacuum or satisfies a mild condition
on the stress-energy tensor, then we show that (M, g) locally admits coordinate
systems in which the Lorentz metric is well-controlled in the (space-time)
Sobolev space L^{2,p}, for any finite p.


title: Gravitating Isovector Solitons

abstract:
  We formulate the nonlinear isovector model in a curved background, and
calculate the spherically symmetric solutions for weak and strong coupling
regimes. The usual belief that gravity does not have appreciable effects on the
structure of solitons will be examined, in the framework of the calculated
solutions, by comparing the flat-space and curved-space solutions. It turns out
that in the strong coupling regime, gravity has essential effects on the
solutions. Masses of the self-gravitating solitons are calculated numerically
using the Tolman expression, and its behavior as a function of the coupling
constant of the model is studied.


title:
Linear Response, Validity of Semi-Classical Gravity, and the Stability
  of Flat Space

abstract:
  A quantitative test for the validity of the semi-classical approximation in
gravity is given. The criterion proposed is that solutions to the
semi-classical Einstein equations should be stable to linearized perturbations,
in the sense that no gauge invariant perturbation should become unbounded in
time. A self-consistent linear response analysis of these perturbations, based
upon an invariant effective action principle, necessarily involves metric
fluctuations about the mean semi-classical geometry, and brings in the
two-point correlation function of the quantum energy-momentum tensor in a
natural way. This linear response equation contains no state dependent
divergences and requires no new renormalization counterterms beyond those
required in the leading order semi-classical approximation. The general linear
response criterion is applied to the specific example of a scalar field with
arbitrary mass and curvature coupling in the vacuum state of Minkowski
spacetime. The spectral representation of the vacuum polarization function is
computed in n dimensional Minkowski spacetime, and used to show that the flat
space solution to the semi-classical Einstein equations for n=4 is stable to
all perturbations on distance scales much larger than the Planck length.


title: Gravitational Optics: Self-phase modulation and harmonic cascades

abstract:
  Nonlinear wave interaction of low amplitude gravitational waves in flat
space-time is considered. Analogy with optics is established. It is shown that
the flat metric space-time is equivalent to a centro-symmetric optical medium,
with no second order susceptibility. The lowest order nonlinear effects are
those due to the third order nonlinearity and include self-phase modulation and
high harmonic generation. These processes lead to an efficient energy dilution
of the gravitational wave energy over an increasingly large spectral range.

categories: gr-qc astro-ph hep-ph hep-th physics.optics


title:
Matter with dilaton charge in Weyl-Cartan spacetime and evolution of the
  Universe

abstract:
  The perfect dilaton-spin fluid (as a model of the dilaton matter, the
particles of which are endowed with intrinsic spin and dilaton charge) is
considered as the source of the gravitational field in a Weyl-Cartan spacetime.
The variational theory of such fluid is constructed and the dilaton-spin fluid
energy-momentum tensor is obtained. The variational formalism of the
gravitational field in a Weyl-Cartan spacetime ia developed in the exterior
form language. The homogeneous and isotropic Universe filled with the dilaton
matter as the dark matter is considered and one of the field equations is
represented as Einstein-like equation which leads to the modified
Friedmann-Lemaitre equation. From this equation the absence of the initial
singularity in the cosmological solution follows. Also the existence of two
points of inflection of the scale factor function is established, the first of
which corresponds to the early stage of the Universe and the second one
corresponds to the modern era when the expansion with deceleration is replaced
by the expansion with acceleration. The possible equations of state for the
self-interacting cold dark matter are found on the basis of the modern
observational data. The inflation-like solution is obtained.


title: Testing of Metric-Field Equations of Gravitation by Binary Pulsar

abstract:
  Testing of the gravitation equations, proposed by one of the authors earlier,
by a binary pulsar is considered. It has been shown that the formulas for the
gravitation radiation of the system resulting from the equations do not
contradict the available observations data.


title: Modification of the Doppler Effect due to the Helicity-Rotation Coupling

abstract:
  The helicity-rotation coupling and its current empirical basis are examined.
The modification of the Doppler effect due to the coupling of photon spin with
the rotation of the observer is considered in detail in connection with its
applications in the Doppler tracking of spacecraft. Further implications of
this coupling and the possibility of searching for it in the intensity response
of a rotating detector are briefly discussed.


title: Constants and Variations: From Alpha to Omega

abstract:
  We review some of the history and properties of theories for the variation of
the gravitation and fine structure 'constants'. We highlight some general
features of the cosmological models that exist in these theories with reference
to recent quasar data that is consistent with time-variation in alpha since a
redshift of 3.5. The behaviour of a simple class of varying-alpha cosmologies
is outlined in the light of all the observational constraints. We discuss the
key role played by non-zero vacuum energy and curvature in turning off the
variation of constants in these theories and the issue of comparing
extra-galactic and local observational data. We also show why black hole
thermodynamics does not enable us to distinguish between time variations of
different constants.