title: Cauchy-Characteristic Matching In General Relativity

abstract:
  From Einstein's theory we know that besides the electromagnetic spectrum,
objects like quasars, active galactic nuclei, pulsars and black holes also
generate a physical signal of purely gravitational nature. The actual form of
the signal is impossible to determine analytically, which lead to use of
numerical methods.
  Two major approaches emerged. The first one formulates the gravitational
radiation problem as a standard Cauchy initial value problem, while the other
approach uses a Characteristic Initial value formulation. In the strong field
region, where caustics in the wavefronts are likely to form, the Cauchy
formulation is more advantageous. On the other side, the Characteristic
formulation is uniquely suited to study radiation problems because it describes
space-time in terms of radiation wavefronts.
  The fact that the advantages and disadvantages of these two systems are
complementary suggests that one may want to use the two of them together. In a
full nonlinear problem it would be advantageous to evolve the inner (strong
field) region using Cauchy evolution and the outer (radiation) region with the
Characteristic approach. Cauchy Characteristic Matching enables one to evolve
the whole space-time matching the boundaries of Cauchy and Characteristic
evolution. The methodology of Cauchy Characteristic Matching has been
successful in numerical evolution of the spherically symmetric
Klein-Gordon-Einstein field equations as well as for 3-D non-linear wave
equations. In this thesis the same methodology is studied in the context of the
Einstein equations.


title: Null limits of generalised Bonnor-Swaminarayan solutions

abstract:
  The Bonnor-Swaminarayan solutions are boost-rotation symmetric space-times
which describe the motion of pairs of accelerating particles which are possibly
connected to strings (struts). In an explicit and unified form we present a
generalised class of such solutions with a few new observations. We then
investigate the possible limits in which the accelerations become unbounded.
The resulting space-times represent spherical impulsive gravitational waves
with snapping or expanding cosmic strings. We also obtain an exact solution for
a snapping string of finite length.


title: Null limits of the C-metric

abstract:
  The C-metric is usually understood as describing two black holes which
accelerate in opposite directions under the action of some conical singularity.
Here, we examine all the solutions of this type which represent accelerating
sources and investigate the null limit in which the accelerations become
unbounded. We show that the resulting space-times represent spherical impulsive
gravitational waves generated by snapping or expanding cosmic strings.


title: Wave packets and initial conditions in quantum cosmology

abstract:
  We discuss the construction of wave packets resulting from the solutions of a
class of Wheeler-DeWitt equations in Robertson-Walker type cosmologies. We
present an ansatz for the initial conditions which leads to a unique
determination of the expansion coefficients in the construction of the wave
packets with probability distributions which, in an interesting contrast to
some of the earlier works, agree well with all possible classical paths. The
possible relationship between these initial conditions and signature transition
in the context of classical cosmology is also discussed.


title:
Marzke-Wheeler coordinates for accelerated observers in special
  relativity

abstract:
  In special relativity, the definition of coordinate systems adapted to
generic accelerated observers is a long-standing problem, which has found
unequivocal solutions only for the simplest motions. We show that the
Marzke-Wheeler construction, an extension of the Einstein synchronization
convention, produces accelerated systems of coordinates with desirable
properties: (a) they reduce to Lorentz coordinates in a neighborhood of the
observers' world-lines; (b) they index continuously and completely the causal
envelope of the world-line (that is, the intersection of its causal past and
its causal future: for well-behaved world-lines, the entire space-time). In
particular, Marzke-Wheeler coordinates provide a smooth and consistent
foliation of the causal envelope of any accelerated observer into space-like
surfaces.
  We compare the Marzke-Wheeler procedure with other definitions of accelerated
coordinates; we examine it in the special case of stationary motions, and we
provide explicit coordinate transformations for uniformly accelerated and
uniformly rotating observers. Finally, we employ the notion of Marzke-Wheeler
simultaneity to clarify the relativistic paradox of the twins, by pinpointing
the local origin of differential aging.


title: Green Functions for Topology Change

abstract:
  We explicitly calculate the Green functions describing quantum changes of
topology in Friedman-Lemaitre-Robertson-Walker Universes whose spacelike
sections are compact but endowed with distinct topologies. The calculations are
performed using the long wavelength approximation at second order in the
gradient expansion. We argue that complex metrics are necessary in order to
obtain a non-vanishing Green functions and interpret this fact as demonstrating
that a quantum topology change can be viewed as a quantum tunneling effect. We
demonstrate that quantum topological transitions between curved hypersurfaces
are allowed whereas no transition to or from a flat section is possible,
establishing thus a selection rule. We also show that the quantum topology
changes in the direction of negatively curved hypersurfaces are strongly
enhanced as time goes on, while transitions in the opposite direction are
suppressed.


title: Does a Kalb-Ramond field make spacetime optically active

abstract:
  A spacetime with torsion produced by a Kalb-Ramond field coupled
gravitationally to the Maxwell field, in accordance with a recent proposal by
two of us (PM and SS), is argued to lead to an optical activity in synchrotron
radiation from cosmologically distant radio sources. We suggest that this could
qualitatively explain observational data from a large number of radio sources
displaying such polarization asymmetry (after eliminating effects of Faraday
rotation due to magnetized galactic plasma). Possible implications for
heterotic string theory are also outlined.


title: Cosmological Constant and the Speed of Light

abstract:
  By exploring the relationship between the propagation of electromagnetic
waves in a gravitational field and the light propagation in a refractive
medium, it is shown that, in the presence of a positive cosmological constant,
the velocity of light will be smaller than its special relativity value. Then,
restricting again to the domain of validity of geometrical optics, the same
result is obtained in the context of wave optics. It is argued that this
phenomenon and the anisotropy in the velocity of light in a gravitational field
are produced by the same mechanism.


title: Electrostatic self-energy in static black holes with spherical symmetry

abstract:
  We determine the expression of the electrostatic self-energy for a point
charge in the static black holes with spherical symmetry having suitable
properties


title:
Lorentzian regularization and the problem of point-like particles in
  general relativity

abstract:
  The two purposes of the paper are (1) to present a regularization of the
self-field of point-like particles, based on Hadamard's concept of ``partie
finie'', that permits in principle to maintain the Lorentz covariance of a
relativistic field theory, (2) to use this regularization for defining a model
of stress-energy tensor that describes point-particles in post-Newtonian
expansions (e.g. 3PN) of general relativity. We consider specifically the case
of a system of two point-particles. We first perform a Lorentz transformation
of the system's variables which carries one of the particles to its rest frame,
next implement the Hadamard regularization within that frame, and finally come
back to the original variables with the help of the inverse Lorentz
transformation. The Lorentzian regularization is defined in this way up to any
order in the relativistic parameter 1/c^2. Following a previous work of ours,
we then construct the delta-pseudo-functions associated with this
regularization. Using an action principle, we derive the stress-energy tensor,
made of delta-pseudo-functions, of point-like particles. The equations of
motion take the same form as the geodesic equations of test particles on a
fixed background, but the role of the background is now played by the
regularized metric.


title: Gravitational Collapse: The Story so far

abstract:
  An outstanding problem in gravitation theory and relativistic astrophysics
today is to understand the final outcome of an endless gravitational collapse.
Such a continual collapse would take place when stars more massive than few
times the mass of the sun collapse under their own gravity on exhausting their
nuclear fuel. According to the general theory of relativity, this results
either in a black hole, or a naked singularity- which can communicate with
faraway observers in the universe. While black holes are (almost) being
detected and are increasingly used to model high energy astrophysical
phenomena, naked singularities have turned into a topic of active discussion,
aimed at understanding their structure and implications. Recent developments
here are reviewed, indicating future directions.


title: What can we learn about GW Physics with an elastic spherical antenna?

abstract:
  A general formalism is set up to analyse the response of an arbitrary solid
elastic body to an arbitrary metric Gravitational Wave perturbation, which
fully displays the details of the interaction antenna-wave. The formalism is
applied to the spherical detector, whose sensitivity parameters are thereby
scrutinised. A multimode transfer function is defined to study the amplitude
sensitivity, and absorption cross sections are calculated for a general metric
theory of GW physics. Their scaling properties are shown to be independent of
the underlying theory, with interesting consequences for future detector
design. The GW incidence direction deconvolution problem is also discussed,
always within the context of a general metric theory of the gravitational
field.


title: A first analysis regarding matter-dynamical diffeomorphism coupling

abstract:
  A first attempt at adding matter degrees of freedom to the two-dimensional
``vacuum'' gravity model presented in gr-qc/9907071 is analyzed in this paper.
Just as in the previous pure gravity case, quantum diffeomorphism operators
(constructed from a Virasoro algebra) possess a dynamical content; their gauge
nature is recovered only after the classical limit. Emphasis is placed on the
new physical modes modelled on a SU(1,1)-Kac-Moody algebra. The non-trivial
coupling to ``gravity'' is a consequence of the natural semi-direct structure
of the entire extended algebra. A representation associated with the discrete
series of the rigid SU(1,1) is revisited in the light of previously neglected
crucial global features which imply the appearance of an SU(1,1)-Kac-Moody
fusion rule, determining the rather entangled quantum structure of the physical
system. In the classical limit, an action which explicitly couples gravity and
matter modes governs the dynamics.


title:
Grounds for Quantum Geometrodynamics in an extended phase space and its
  cosmological consequences

abstract:
  Quantum geometrodynamics (QGD) in extended phase space essentially
distinguished from the Wheeler - DeWitt QGD is proposed. The grounds for
constructing a new version of quantum geometrodynamics are briefly discussed.
The main part in the proposed version of QGD is given to the Schrodinger
equation for a wave function of the Universe. The Schrodinger equation carries
information about a chosen gauge condition which fixes a reference system. The
reference system is represented by a continual medium that can be called ``the
gravitational vacuum condencate". A solution to the Schrodinger equation
contains information about the integrated system ``a physical object +
observation means (the gravitational vacuum condensate)". It may be
demonstrated that the gravitational vacuum condensate appears to be a
cosmological evolution factor.


title: From computation to black holes and space-time foam

abstract:
  We show that quantum mechanics and general relativity limit the speed
$\tilde{\nu}$ of a simple computer (such as a black hole) and its memory space
$I$ to $\tilde{\nu}^2 I^{-1} \lsim t_P^{-2}$, where $t_P$ is the Planck time.
We also show that the life-time of a simple clock and its precision are
similarly limited. These bounds and the holographic bound originate from the
same physics that governs the quantum fluctuations of space-time. We further
show that these physical bounds are realized for black holes, yielding the
correct Hawking black hole lifetime, and that space-time undergoes much larger
quantum fluctuations than conventional wisdom claims -- almost within range of
detection with modern gravitational-wave interferometers.


title: Detection of gravitational waves with quantum encryption technology

abstract:
  We propose a new technique for detecting gravitational waves using Quantum
Entangled STate (QUEST) technology. Gravitational waves reduce the non-locality
of correlated quanta controlled by Bell's inequalities, distorting quantum
encryption key statistics away from a pure white noise. Gravitational waves
therefore act as shadow eavesdroppers. The resulting colour distortions can, at
least in principle, be separated from noise and can differentiate both
deterministic and stochastic sources.


title: A spin foam model without bubble divergences

abstract:
  We present a spin foam model in which the fundamental ``bubble amplitudes''
(the analog of the one-loop corrections in quantum field theory) are finite as
the cutoff is removed. The model is a natural variant of the field theoretical
formulation of the Barrett-Crane model. As the last, the model is a quantum BF
theory plus an implementation of the constraint that reduces BF theory to
general relativity. We prove that the fundamental bubble amplitudes are finite
by constructing an upper bound, using certain inequalities satisfied by the
Wigner (3n)j-symbols, which we derive in the paper. Finally, we present
arguments in support of the conjecture that the bubble diagrams of the model
are finite at all orders.


title: Assisted inflation in Friedmann-Robertson-Walker and Bianchi spacetimes

abstract:
  We use exact general solutions for the spatially flat FRW and the anisotropic
Bianchi I cosmologies to show that generically uncoupled scalar fields
cooperate to make inflation more probable, while the presence of several
interacting fields hinders the occurrence of the phenomenon, in accordance with
previous results based on particular power-law solutions. Similar conclusions
are reached in the case of Bianchi VI$_0$ spacetimes, for power-law solutions
which are proved to be attractors.


title:
The mathematical theory of resonant transducers in a spherical gravity
  wave antenna

abstract:
  The rigoruos mathematical theory of the coupling and response of a spherical
gravitational wave detector endowed with a set of resonant transducers is
presented and developed. A perturbative series in ascending powers of the
square root of the ratio of the resonator to the sphere mass is seen to be the
key to the solution of the problem. General layouts of arbitrary numbers of
transducers can be assessed, and a specific proposal (PHC), alternative to the
highly symmetric TIGA of Merkowitz and Johnson, is described in detail.
Frequency spectra of the coupled system are seen to be theoretically recovered
in full agreement with experimental determinations.


title:
A Plane-Symmetric Gravitational Field as a Generalized Nonlinear Sigma
  Model

abstract:
  The Einstein equations for a plane-symmetric gravitational field coupled to
an arbitrary nonlinear sigma model (NSM) are shown to be represented in the
form of dynamical equations of a {\it generalized effective NSM}. The
gravitational equations are studied in this case by the methods of analyzing
NSM equations. In the case of a two-component diagonal NSM exact solutions are
found by the functional parameter method.


title: Global monopoles in the Brans-Dicke theory

abstract:
  A gravitating global monopole produces a repulsive grativational field
outside the core in addition to a solid angular deficit in the Brans-Dicke
theory. As a new feature, the angular deficit is dependent on the values of
\phi_{\infty} and \omega, where \phi_{\infty} is asymptotic value of scalar
field in space-like infinity and \omega is the Brans-Dicke parameter.


title: On the propagation of jump discontinuities in relativistic cosmology

abstract:
  A recent dynamical formulation at derivative level $\ptl^{3}g$ for fluid
spacetime geometries $({\cal M}, {\bf g}, {\bf u})$, that employs the concept
of evolution systems in first-order symmetric hyperbolic format, implies the
existence in the Weyl curvature branch of a set of timelike characteristic
3-surfaces associated with propagation speed $|v| = \sfrac{1}{2}$ relative to
fluid-comoving observers. We show it is the physical role of the constraint
equations to prevent realisation of jump discontinuities in the derivatives of
the related initial data so that Weyl curvature modes propagating along these
3-surfaces cannot be activated. In addition we introduce a new, illustrative
first-order symmetric hyperbolic evolution system at derivative level
$\ptl^{2}g$ for baryotropic perfect fluid cosmological models that are
invariant under the transformations of an Abelian $G_{2}$ isometry group.


title: Collapsing Perfect Fluid in Higher Dimensional Spherical Spacetimes

abstract:
  The general metric for N-dimensional spherically symmetric and conformally
flat spacetimes is given, and all the homogeneous and isotropic solutions for a
perfect fluid with the equation of state $p = \alpha \rho$ are found. These
solutions are then used to model the gravitational collapse of a compact ball.
It is found that when the collapse has continuous self-similarity, the
formation of black holes always starts with zero mass, and when the collapse
has no such a symmetry, the formation of black holes always starts with a mass
gap.


title: Path Integral Quantisation of Finite Noncommutative Geometries

abstract:
  We present a path integral formalism for quantising gravity in the form of
the spectral action. Our basic principle is to sum over all Dirac operators.
The approach is demonstrated on two simple finite noncommutative geometries:
the two-point space, and the matrix geometry M_2(C). On the first, the graviton
is described by a Higgs field, and on the second, it is described by a gauge
field. We start with the partition function and calculate the propagator and
Greens functions for the gravitons. The expectation values of distances are
evaluated, and we discover that distances shrink with increasing graviton
excitations. We find that adding fermions reduces the effects of the
gravitational field. A comparison is also made with Rovelli's canonical
quantisation approach, and with his idea of spectral path integrals. We include
a brief discussion on the quantisation of a Riemannian manifold.


title: Emergent Consciousness: From the Early Universe to Our Mind

abstract:
  In a previous paper (gr-qc/9907063) we described the early inflationary
universe in terms of quantum information. In this paper, we analize those
results in more detail, and we stress the fact that, during inflation, the
universe can be described as a superposed state of quantum registers. The
self-reduction of the superposed quantum state is consistent with the Penrose's
Objective Reduction (OR) model. The quantum gravity threshold is reached at the
end of inflation, and corresponds to a superposed state of 10^9 quantum
registers. This is also the number of superposed tubulins-qubits in our brain,
which undergo the Penrose-Hameroff's Orchestrated Objective Reduction, (Orch
OR), leading to a conscious event. Then, an analogy naturally arises between
the very early quantum computing universe,and our mind.


title:
Numerical Data-Processing Simulations of Microarcsecond Classical and
  Relativistic Effects in Space Astrometry

abstract:
  The accuracy of astrometric observations conducted via a space-borne optical
interferometer orbiting the Earth is expected to approach a few
microarcseconds. Data processing of such extremely high-precision measurements
requires access to a rigorous relativistic model of light ray propagation
developed in the framework of General Relativity. The data-processing of the
space interferometric observations must rely upon the theory of
general-relativistic transformations between the spacecraft, geocentric, and
solar barycentric reference systems allowing unique and unambiguous
interpretation of the stellar aberration and parallax effects. On the other
hand, the algorithm must also include physically adequate treatment of the
relativistic effect of light deflection caused by the spherically-symmetric
(monopole-dependent) part of the gravitational field of the Sun and planets as
well as the quadrupole- and spin-dependent counterparts of it. In some
particular cases the gravitomagnetic field induced by the translational motion
of the Sun and planets should be also taken into account for unambigious
prediction of the light-ray deflection angle. In the present paper we describe
the corresponding software program for taking into account all classical
(proper motion, parallax, etc.) and relativistic (aberration, deflection of
light) effects up to the microarcsecond threshold and demonstrate, using
numerical simulations, how observations of stars and/or quasars conducted on
board a space optical interferometer orbiting the Earth can be processed and
disentangled.


title: Gravitational collapse in 2+1 dimensional AdS spacetime

abstract:
  We present results of numerical simulations of the formation of black holes
from the gravitational collapse of a massless, minimally-coupled scalar field
in 2+1 dimensional, axially-symmetric, anti de-Sitter (AdS) spacetime. The
geometry exterior to the event horizon approaches the BTZ solution, showing no
evidence of scalar `hair'. To study the interior structure we implement a
variant of black-hole excision, which we call singularity excision. We find
that interior to the event horizon a strong, spacelike curvature singularity
develops. We study the critical behavior at the threshold of black hole
formation, and find a continuously self-similar solution and corresponding
mass-scaling exponent of approximately 1.2. The critical solution is universal
to within a phase that is related to the angle deficit of the spacetime.


title:
On Killing vectors in initial value problems for asymptotically flat
  space-times

abstract:
  The existence of symmetries in asymptotically flat space-times are studied
from the point of view of initial value problems. General necessary and
sufficient (implicit) conditions are given for the existence of Killing vector
fields in the asymptotic characteristic and in the hyperboloidal initial value
problem (both of them are formulated on the conformally compactified space-time
manifold).


title: Dynamical Systems Approach to Magnetised Cosmological Perturbations

abstract:
  Assuming a large-scale homogeneous magnetic field, we follow the covariant
and gauge-invariant approach used by Tsagas and Barrow to describe the
evolution of density and magnetic field inhomogeneities and curvature
perturbations in a matter-radiation universe. We use a two parameter
approximation scheme to linearize their exact non-linear general-relativistic
equations for magneto-hydrodynamic evolution. Using a two-fluid approach we set
up the governing equations as a fourth order autonomous dynamical system.
Analysis of the equilibrium points for the radiation dominated era lead to
solutions similar to the super-horizon modes found analytically by Tsagas and
Maartens. We find that a study of the dynamical system in the dust-dominated
era leads naturally to a magnetic critical length scale closely related to the
Jeans Length. Depending on the size of wavelengths relative to this scale,
these solutions show three distinct behaviours: large-scale stable growing
modes, intermediate decaying modes, and small-scale damped oscillatory
solutions.


title: Resolving the black hole information paradox

abstract:
  The recent progress in string theory strongly suggests that formation and
evaporation of black holes is a unitary process. This fact makes it imperative
that we find a flaw in the semiclassical reasoning that implies a loss of
information. We propose a new criterion that limits the domain of classical
gravity: the hypersurfaces of a foliation cannot be stretched too much. This
conjectured criterion may have important consequences for the early Universe.


title: Notes on Riemann geometry and integrable systems. Part IV

abstract:
  The connection between multidimensional soliton equations and
three-dimensional Riemann space is discussed.


title:
Black-hole radiation, the fundamental area unit, and the spectrum of
  particle species

abstract:
  Bekenstein and Mukhanov have put forward the idea that, in a quantum theory
of gravity a black hole should have a discrete mass spectrum with a concomitant
{\it discrete} line emission. We note that a direct consequence of this
intriguing prediction is that, compared with blackbody radiation, black-hole
radiance is {\it less} entropic. We calculate the ratio of entropy emission
rate from a quantum black hole to the rate of black-hole entropy decrease, a
quantity which, according to the generalized second law (GSL) of
thermodynamics, should be larger than unity. Implications of our results for
the GSL, for the value of the fundamental area unit in quantum gravity, and for
the spectrum of massless particles in nature are discussed.


title:
Satellite gravitational orbital perturbations and the gravitomagnetic
  clock effect

abstract:
  In order to detect the gravitomagnetic clock effect by means of two
counter-orbiting satellites placed on identical equatorial and circular orbits
around the Earth with radius 7000 km their radial and azimuthal positions must
be known with an accuracy of delta r =10^{-1} mm and delta phi =10^{-2} mas per
revolution. In this work we investigate if the radial and azimuthal
perturbations induced by the dynamical and static parts of the Earth' s
gravitational field meet this requirements. While the radial direction is
affected only by harmonic perturbations with periods up to some tens of days,
the azimuthal location is perturbed by a secular drift and very long period
effects.It results that the present level of accuracy in the knowledge both of
the Earth solid and ocean tides, and of the static part of the geopotential
does not allow an easy detection of the gravitomagnetic clock effect, at least
by using short arcs only.

categories: gr-qc astro-ph physics.geo-ph physics.space-ph


title:
The impact of tidal errors on the determination of the Lense-Thirring
  effect from satellite laser ranging

abstract:
  The general relativistic Lense-Thirring effect can be detected by means of a
suitable combination of orbital residuals of the laser-ranged LAGEOS and LAGEOS
II satellites. While this observable is not affected by the orbital
perturbation induced by the zonal Earth solid and ocean tides, it is sensitive
to those generated by the tesseral and sectorial tides. The assessment of their
influence on the measurement of the parameter mu, with which the
gravitomagnetic effect is accounted for, is the goal of this paper. After
simulating the combined residual curve by calculating accurately the
mismodeling of the more effective tidal perturbations, it has been found that,
while the solid tides affect the recovery of mu at a level always well below
1%, for the ocean tides and the other long-period signals Delta mu depends
strongly on the observational period and the noise level: Delta mu(tides)
amounts to almost 2% after 7 years. The aliasing effect of K1 l=3 p=1 tide and
SRP(4241) solar radiation pressure harmonic, with periods longer than 4 years,
on the perigee of LAGEOS II yield to a maximum systematic uncertainty on
$\m_{LT}$ of less than 4% over different observational periods. The zonal
18.6-year tide does not affect the combined residuals.


title: Solution of Dirac equation around a spinning Black Hole

abstract:
  Chandrasekhar separated the Dirac equation for spinning and massive particles
in Kerr geometry in radial and angular parts. Chakrabarti solved the angular
equation and found the corresponding eigenvalues for different Kerr parameters.
The radial equations were solved asymptotically by Chandrasekhar. In the
present paper, we use the WKB approximation to solve the spatially complete
radial equation and calculate analytical expressions of radial wave functions
for a set of Kerr and wave parameters. From these solutions we obtain local
values of reflection and transmission coefficients.


title: Non-vacuum twisting type N metrics

abstract:
  A maximally reduced system of equations corresponding to the twisting type N
Einstein metrics is given. When the cosmological constant $\lambda\to 0$ they
reduce to the standard equations for the vacuum twisting type N's. All the
metrics which are conformally equivalent to the twisting type N metrics and
which admit 3-dimensional conformal group of symmetries are presented. In the
Feferman class of metrics an example is given of a twisting type N metric which
satisfies Bach's equations but is not Einstein.


title: Non-time-orthogonality, Gravitational Orbits, and Thomas Precession

abstract:
  Non-time-orthogonal analysis of rotating frames is applied to objects in
gravitational orbits and found to be internally consistent. The object's
surface speed about its axis of rotation, but not its orbital speed, is shown
to be readily detectable by any "enclosed box" experimenter on the surface of
such an object. Sagnac type effects manifest readily, but by somewhat subtle
means. The analysis is extended to objects bound in non-gravitational orbit,
where it is found to be fully in accord with the traditional analysis of Thomas
precession.


title: Radiative Falloff in Neutron Star Spacetimes

abstract:
  We systematically study late-time tails of scalar waves propagating in
neutron star spacetimes. We consider uniform density neutron stars, for which
the background spacetime is analytic and the compaction of the star can be
varied continously between the Newtonian limit 2M/R << 1 and the relativistic
Buchdahl limit 2M/R = 8/9. We study the reflection of a finite wave packet off
neutron stars of different compactions 2M/R and find that a Newtonian, an
intermediate, and a highly relativistic regime can be clearly distinguished. In
the highly relativistic regime, the reflected signal is dominated by
quasi-periodic peaks, which originate from the wave packet bouncing back and
forth between the center of the star and the maximum of the background
curvature potential at R ~ 3 M. Between these peaks, the field decays according
to a power-law. In the Buchdahl limit 2M/R -> 8/9 the light travel time between
the center and the maximum or the curvature potential grows without bound, so
that the first peak arrives only at infinitely late time. The modes of neutron
stars can therefore no longer be excited in the ultra-relativistic limit, and
it is in this sense that the late-time radiative decay from neutron stars
looses all its features and gives rise to power-law tails reminiscent of
Schwarzschild black holes.


title: Exact Inflationary Models and Consequences

abstract:
  New exact inflationary solutions are presented in the scalar field theory,
minimally coupled to gravity, with a potential term. No use is made of the slow
rollover approximation. The scale factors are completely nonsingular and the
transition to the deccelerating phase is smooth. Moreover, in one of these
models, asymptotically one has transition to the matter dominated Universe.


title: Theorems on gravitational time delay and related issues

abstract:
  Two theorems related to gravitational time delay are proven. Both theorems
apply to spacetimes satisfying the null energy condition and the null generic
condition. The first theorem states that if the spacetime is null geodesically
complete, then given any compact set $K$, there exists another compact set $K'$
such that for any $p,q \not\in K'$, if there exists a ``fastest null
geodesic'', $\gamma$, between $p$ and $q$, then $\gamma$ cannot enter $K$. As
an application of this theorem, we show that if, in addition, the spacetime is
globally hyperbolic with a compact Cauchy surface, then any observer at
sufficiently late times cannot have a particle horizon. The second theorem
states that if a timelike conformal boundary can be attached to the spacetime
such that the spacetime with boundary satisfies strong causality as well as a
compactness condition, then any ``fastest null geodesic'' connecting two points
on the boundary must lie entirely within the boundary. It follows from this
theorem that generic perturbations of anti-de Sitter spacetime always produce a
time delay relative to anti-de Sitter spacetime itself.


title: Method of complex paths and general covariance of Hawking radiation

abstract:
  We apply the technique of complex paths to obtain Hawking radiation in
different coordinate representations of the Schwarzschild space-time. The
coordinate representations we consider do not possess a singularity at the
horizon unlike the standard Schwarzschild coordinate. However, the event
horizon manifests itself as a singularity in the expression for the
semi-classical action. This singularity is regularized by using the method of
complex paths and we find that Hawking radiation is recovered in these
coordinates indicating the covariance of Hawking radiation. This also shows
that there is no correspondence between the particles detected by the model
detector and the particle spectrum obtained by the quantum field theoretic
analysis -- a result known in other contexts as well.


title:
Search for periodic gravitational radiation with the ALLEGRO
  gravitational wave detector

abstract:
  We describe the search for a continuous signal of gravitational radiation
from a rotating neutron star in the data taken by the ALLEGRO gravitational
wave detector in early 1994. Since ALLEGRO is sensitive at frequencies near 1
kHz, only neutron stars with spin periods near 2 ms are potential sources.
There are no known sources of this typ e for ALLEGRO, so we directed the search
towards both the galactic center and the globular clus ter 47 Tucanae. The
analysis puts a constraint of roughly $8 \times 10^{-24}$ at frequencies near 1
kHz on the gravitational strain emitted from pulsar spin-down in either 47
Tucanae or the galactic center.


title:
Classicity from Entangled Ensemble States of Knotted Spin Networks. A
  Conceptual Approach

abstract:
  Referring to a conception put forward by Stuart Kauffman in his
"Investigations", it is shown how the onset of classicity can be visualized in
terms of an emergent process originating in entangled ensemble states of
knotted spin networks. The latter exhibit a suitable autocatalytic behaviour
effectively producing knots by knots acting upon other knots. In particular, a
quantum computational structure can be described underlying spin networks such
that most conditions for a partial ordering are not more valid for the latter.
A concep- tual argument is given then indicating that on a fundamental level,
physics is non-local and a-temporal, and hence does not admit of the concept of
causality. Hence, modelling the emergence of classicity in terms of a
percolating web of coherence eventually decohering (in using a cellular
automata architecture) does not imply the necessity of visualizing histories of
directed percolation as causal sets. These aspects are compatible though with
the recent concept of spin foams which do not actually imply distinguished
directions of time flow on the micro-level.


title: Generalized Equivalence Principle in Extended New General Relativity

abstract:
  In extended new general relativity, which is formulated as a reduction of
$\bar{Poincar\'e} $gauge theory of gravity whose gauge group is the covering
group of the Poincar\'e group, we study the problem of whether the total
energy-momentum, total angular momentum and total charge are equal to the
corresponding quantities of the gravitational source. We examine this for
charged axi-symmetric solutions of gravitational field equations. Our main
concern is the restriction on the asymptotic form of the gravitational field
variables imposed by the requirement that physical quantities of the total
system are equivalent to the corresponding quantities of the charged rotating
source body. This requirement can be regarded as an equivalence principle in a
generalized sense.


title:
"Particle-like" singular solutions in Einstein-Maxwell theory and in
  algebraic dynamics

abstract:
  Foundations of algebrodynamics based on earlier proposed equations of
biquaternionic holomorphy are briefly expounded. Free Maxwell and Yang-Mills
Eqs. are satisfied identically on the solutions of primary system which is also
related to the Eqs. of shear-free null congruences (SFC), and through them - to
the Einstein-Maxwell electrovacuum system. Kerr theorem for SFC reduces the
basic system to one algebraic equation, so that with each solution of the
latter some (singular) solution of vacuum Eqs. may be associated. We present
some exact solutions of basic algebraic and of related field Eqs. with compact
structure of singularities of electromagnetic field, in particular having the
form of figure "8" curve. Fundamental solution to primary system is analogous
to the metric and fields of the Kerr-Newman solution. In addition, in the
framework of algebraic dynamics the value of electric charge for this solution
is strictly fixed in magnitude and may be set equal to the elementary charge.


title: Biquaternion Electrodynamics and Weyl-Cartan Geometry of Space-Time

abstract:
  The generalized Cauchy-Riemann equations (GCRE) in biquaternion algebra
appear to be Lorentz-invariant. The Laplace equation is in this case replaced
by a nonlinear (complexified) eikonal equation. GCRE contain the 2-spinor and
the gauge structures, and their integrability conditions take the form of
free-source Maxwell and Yang-Mills equations. For the value of electric charge
from GCRE only the quantization rule follows, as well as the treatment of
Coulomb law as a stereographic map. The equivalent geometrodynamics in a
Weyl-Cartan affine space and the conjecture of a complex-quaternion structure
of space-time are discussed.


title:
Quasiequilibrium sequences of synchronized and irrotational binary
  neutron stars in general relativity. I. Method and tests

abstract:
  We present a numerical method to compute quasiequilibrium configurations of
close binary neutron stars in the pre-coalescing stage. A hydrodynamical
treatment is performed under the assumption that the flow is either rigidly
rotating or irrotational. The latter state is technically more complicated to
treat than the former one (synchronized binary), but is expected to represent
fairly well the late evolutionary stages of a binary neutron star system. As
regards the gravitational field, an approximation of general relativity is
used, which amounts to solving five of the ten Einstein equations (conformally
flat spatial metric). The obtained system of partial differential equations is
solved by means of a multi-domain spectral method. Two spherical coordinate
systems are introduced, one centered on each star; this results in a precise
description of the stellar interiors. Thanks to the multi-domain approach, this
high precision is extended to the strong field regions. The computational
domain covers the whole space so that exact boundary conditions are set to
infinity. Extensive tests of the numerical code are performed, including
comparisons with recent analytical solutions. Finally a constant baryon number
sequence (evolutionary sequence) is presented in details for a polytropic
equation of state with gamma=2.


title: Thin shell quantization in Weyl spacetime

abstract:
  We study the problem of quantization of thin shells in a Weyl-Dirac theory by
deriving a Wheeler-DeWitt equation from the dynamics. Solutions are found which
have interpretations in both cosmology and particle physics.


title: Regular quantum interiors for black holes

abstract:
  A family of spacetimes suitable for describing the interior of a
non-rotational black hole is constructed. The stress-energy tensor is that of a
spherically symmetric vacuum, as commonly assumed nowadays. The problem of
matching the exterior with the interior region is solved exactly, without using
any massive shell nor having to restrict oneself to only asymptotically
well-behaved solutions, whatsoever. The main physical and geometrical
properties of the resulting black hole solutions are described. As models for
the interior the general solution found includes, in particular, two known
previous atttempts at solving the problem. Finally, effective macroscopic
properties of the solution are linked with quantization issues of the
corresponding spacetime.


title: Gravity with a dynamical preferred frame

abstract:
  We study a generally covariant model in which local Lorentz invariance is
broken "spontaneously" by a dynamical unit timelike vector field $u^a$---the
"aether". Such a model makes it possible to study the gravitational and
cosmological consequences of preferred frame effects, such as ``variable speed
of light" or high frequency dispersion, while preserving a generally covariant
metric theory of gravity. In this paper we restrict attention to an action for
an effective theory of the aether which involves only the antisymmetrized
derivative $\nabla_{[a}u_{b]}$. Without matter this theory is equivalent to a
sector of the Einstein-Maxwell-charged dust system. The aether has two massless
transverse excitations, and the solutions of the model include all vacuum
solutions of general relativity (as well as other solutions). However, the
aether generally develops gradient singularities which signal a breakdown of
this effective theory. Including the symmetrized derivative in the action for
the aether field may cure this problem.


title:
Spin-1/2 Particles in Non-Inertial Reference Frames: Low- and
  High-Energy Approximations

abstract:
  Spin-1/2 particles can be used to study inertial and gravitational effects by
means of interferometers, particle accelerators, and ultimately quantum
systems. These studies require, in general, knowledge of the Hamiltonian and of
the inertial and gravitational quantum phases. The procedure followed gives
both in the low- and high-energy approximations. The latter affords a more
consistent treatment of mass at high energies. The procedure is based on
general relativity and on a solution of the Dirac equation that is exact to
first-order in the metric deviation. Several previously known acceleration and
rotation induced effects are re-derived in a comprehensive, unified way.
Several new effects involve spin, electromagnetic and inertial/gravitational
fields in different combinations.


title: Radiation-reaction force on a particle plunging into a black hole

abstract:
  We calculate the self force acting on a scalar particle which is falling
radially into a Schwarzschild black hole. We treat the particle's self-field as
a linear perturbation over the fixed Schwarzschild background. The force is
calculated by numerically solving the appropriate wave equation for each mode
of the field in the time domain, calculating its contribution to the self
force, and summing over all modes using Ori's mode-sum regularization
prescription. The radial component of the force is attractive at large
distances, and becomes repulsive as the particle approaches the event horizon.


title:
Hyperbolic formulations and numerical relativity II: Asymptotically
  constrained systems of the Einstein equations

abstract:
  We study asymptotically constrained systems for numerical integration of the
Einstein equations, which are intended to be robust against perturbative errors
for the free evolution of the initial data. First, we examine the previously
proposed "$\lambda$-system", which introduces artificial flows to constraint
surfaces based on the symmetric hyperbolic formulation. We show that this
system works as expected for the wave propagation problem in the Maxwell system
and in general relativity using Ashtekar's connection formulation. Second, we
propose a new mechanism to control the stability, which we call the ``adjusted
system". This is simply obtained by adding constraint terms in the dynamical
equations and adjusting its multipliers. We explain why a particular choice of
multiplier reduces the numerical errors from non-positive or pure-imaginary
eigenvalues of the adjusted constraint propagation equations. This ``adjusted
system" is also tested in the Maxwell system and in the Ashtekar's system. This
mechanism affects more than the system's symmetric hyperbolicity.


title:
Cosmological Electromagnetic Fields due to Gravitational Wave
  Perturbations

abstract:
  We consider the dynamics of electromagnetic fields in an
almost-Friedmann-Robertson-Walker universe using the covariant and
gauge-invariant approach of Ellis and Bruni. Focusing on the situation where
deviations from the background model are generated by tensor perturbations
only, we demonstrate that the coupling between gravitational waves and a weak
magnetic test field can generate electromagnetic waves. We show that this
coupling leads to an initial pulse of electromagnetic waves whose width and
amplitude is determined by the wavelengths of the magnetic field and
gravitational waves. A number of implications for cosmology are discussed, in
particular we calculate an upper bound of the magnitude of this effect using
limits on the quadrapole anisotropy of the Cosmic Microwave Background.


title: Covariant and locally Lorentz-invariant varying speed of light theories

abstract:
  We propose definitions for covariance and local Lorentz invariance applicable
when the speed of light $c$ is allowed to vary. They have the merit of
retaining only those aspects of the usual definitions which are invariant under
unit transformations, and which can therefore legitimately represent the
outcome of an experiment. We then discuss some possibilities for invariant
actions governing the dynamics of such theories. We consider first the
classical action for matter fields and the effects of a changing $c$ upon
quantization. We discover a peculiar form of quantum particle creation due to a
varying $c$. We then study actions governing the dynamics of gravitation and
the speed of light. We find the free, empty-space, no-gravity solution, to be
interpreted as the counterpart of Minkowksi space-time, and highlight its
similarities with Fock-Lorentz space-time. We also find flat-space string-type
solutions, in which near the string core $c$ is much higher. We label them
fast-tracks and compare them with gravitational wormholes. We finally discuss
general features of cosmological and black hole solutions, and digress on the
meaning of singularities in these theories.


title: Quantum creation and inflationary universes: a critical appraisal

abstract:
  We contrast the possibility of inflation starting a) from the universe's
inception or b) from an earlier non-inflationary state. Neither case is ideal
since a) assumes quantum mechanical reasoning is straightforwardly applicable
to the early universe; while case b) requires that a singularity still be
present. Further, in agreement with Vachaspati and Trodden [1] case b) can only
solve the horizon problem if the non-inflationary phase has equation of state
$\gamma<4/3$.


title:
Cosmological scaling solutions of minimally coupled scalar fields in
  three dimensions

abstract:
  We examine Friedmann-Robertson-Walker models in three spacetime dimensions.
The matter content of the models is composed of a perfect fluid, with a
$\gamma$-law equation of state, and a homogeneous scalar field minimally
coupled to gravity with a self-interacting potential whose energy density
red-shifts as $a^{-2 \nu}$, where a denotes the scale factor. Cosmological
solutions are presented for different range of values of $\gamma$ and $\nu$.
The potential required to agree with the above red-shift for the scalar field
energy density is also calculated.


title: Boson stars driven to the brink of black hole formation

abstract:
  We present a study of black hole threshold phenomena for a self-gravitating,
massive complex scalar field in spherical symmetry. We construct Type I
critical solutions dynamically by tuning a one-parameter family of initial data
composed of a boson star and a massless real scalar field. The real field is
used to perturb the boson star via a gravitational interaction which results in
a {\em significant} transfer of energy. The resulting critical solutions, which
show great similarity with unstable boson stars, persist for a finite time
before dispersing or forming a black hole. We extend the stability analysis of
Gleiser and Watkins [Nucl. Phys. B319, 733 (1989)], providing a method for
calculating the radial dependence of boson star modes of nonzero frequency. We
find good agreement between our critical solutions and boson star modes. For
critical solutions less than 90% of the maximum boson star mass $M_{\rm max}
\simeq 0.633 M_{Pl}^2/m$, a small halo of matter appears in the tail of the
solution. This halo appears to be an artifact of the collision between the
original boson star and the real field, and does not belong to the true
critical solution. It seems that unstable boson stars are unstable to dispersal
in addition to black hole formation. Given the similarity in macroscopic
stability between boson and neutron stars, we suggest that neutron stars at or
beyond the point of instability may also be unstable to explosion.


title: Distinguishing Marks of Simply-connected Universes

abstract:
  A statistical quantity suitable for distinguishing simply-connected
Robertson-Walker (RW) universes is introduced, and its explicit expressions for
the three possible classes of simply-connected RW universes with an uniform
distribution of matter are determined. Graphs of the distinguishing mark for
each class of RW universes are presented and analyzed.There sprout from our
results an improvement on the procedure to extract the topological signature of
multiply-connected RW universes, and a refined understanding of that
topological signature of these universes studied in previous works.


title: Schwarzschild metrics and quasi-universes

abstract:
  The exterior and interior Schwarzschild solutions are rewritten replacing the
usual radial variable with an angular one. This allows to obtain some results
otherwise less apparent or even hidden in other coordinate systems.


title:
Properties of general relativistic, irrotational binary neutron stars in
  close quasiequilibrium orbits : Polytropic equations of state

abstract:
  We investigate close binary neutron stars in quasiequilibrium states in a
general relativistic framework. We assume conformal flatness for the spatial
metric and irrotational velocity field for the neutron stars. We adopt the
polytropic equation of state. The computation is performed for the polytropic
index n(=0.5, 0.66667, 0.8, 1, 1.25), and compactness of neutron stars
M/R(=0.03 - 0.3). Results of this paper are as follows. (i) The sequences of
the irrotational binary are always terminated at an innermost orbit where a
cusp (inner Lagrange point)appears at the inner edges of the stellar surface.
The binaries with cusps are found to be dynamically unstable for n=0.5 and
stable for n > 0.8 irrespective of M/R < 0.2. For n=0.66667, the stability
changes depending on M/R. (ii) The gravitational wave frequency at the
innermost orbit turns out to be between 800 and 1500 Hz for realistic
compactness 0.14 < M/R < 0.2. (iii) The ISCO for n=0.5 appears to be determined
by a hydrodynamic instability for M/R < 0.2. We derive fitting formulae for the
relation between the orbital angular velocity at the ISCO and the compactness
to clarify it. (iv) The maximum density of neutron stars in binary systems
slightly decreases with decreasing the orbital separation and hence they are
stable against individual radial collapse during the inspiral. (v) q =
J_tot/M_ADM^2 at the innermost orbits is always less than unity for M/R > 0.13
irrespective of n, which indicates that the realistic binary neutron stars
satisfy a necessary condition (q<1) for formation of a black hole before the
merger. (vi) The specific angular momentum of any mass element in irrotational
binary neutron stars at the innermost orbit appears to be too small to form a
disk around black holes formed after the merger.


title: Notes on Riemann geometry and integrable systems. Part V

abstract: Some aspects of multidimensional soliton geometry are considered.


title:
How Large are Dissipative Effects in Non-Critical Liouville String
  Theory?

abstract:
  In the context of non-critical Liouville strings, we clarify why we expect
non-quantum-mechanical dissipative effects to be of order E^2/M_P, where E is a
typical energy scale of the probe, and M_P is the Planck scale. In Liouville
strings, energy is conserved {\it at best} only as a statistical average, as
distinct from Lindblad systems, where it is {\it strictly} conserved at an
operator level, and the magnitude of dissipative effects could only be much
smaller. We also emphasize the importance of nonlinear terms in the evolution
equation for the density matrix, which are important for any analysis of
complete positivity.


title:
Three-dimensional adaptive evolution of gravitational waves in numerical
  relativity

abstract:
  Adaptive techniques are crucial for successful numerical modeling of
gravitational waves from astrophysical sources such as coalescing compact
binaries, since the radiation typically has wavelengths much larger than the
scale of the sources. We have carried out an important step toward this goal,
the evolution of weak gravitational waves using adaptive mesh refinement in the
Einstein equations. The 2-level adaptive simulation is compared with unigrid
runs at coarse and fine resolution, and is shown to track closely the features
of the fine grid run.


title:
Tunneling of the Closed Friedmann Universe with Generation of Scalar
  Waves

abstract:
  The evolution of the closed Friedmann Universe with a packet of short scalar
waves is considered with the help of the Wheeler--DeWitt equation. The packet
ensures conservation of homogeneity and isotropy of the metric on average. It
is shown that during tunneling the amplitudes of short waves of a scalar field
can increase catastrophically promptly if their influence to the metric do not
take into account. This effect is similar to the Rubakov-effect of catastrophic
particle creation calculated already in 1984.
  In our approach to the problem it is possible to consider self-consistent
dynamics of the expansion of the Universe and amplification of short waves.
  It results in a decrease of the barrier and interruption of amplification of
waves, and we get an exit of the wave function from the quantum to the
classically available region.


title:
Solar System Tests of the Equivalence Principle and Constraints on
  Higher-Dimensional Gravity

abstract:
  In most studies of equivalence principle violation by solar system bodies, it
is assumed that the ratio of gravitational to inertial mass for a given body
deviates from unity by a parameter Delta which is proportional to its
gravitational self-energy. Here we inquire what experimental constraints can be
set on Delta for various solar system objects when this assumption is relaxed.
Extending an analysis originally due to Nordtvedt, we obtain upper limits on
linearly independent combinations of Delta for two or more bodies from Kepler's
third law, the position of Lagrange libration points, and the phenomenon of
orbital polarization. Combining our results, we extract numerical upper bounds
on Delta for the Sun, Moon, Earth and Jupiter, using observational data on
their orbits as well as those of the Trojan asteroids. These are applied as a
test case to the theory of higher-dimensional (Kaluza-Klein) gravity. The
results are three to six orders of magnitude stronger than previous constraints
on the theory, confirming earlier suggestions that extra dimensions play a
negligible role in solar systemdynamics and reinforcing the value of
equivalence principle tests as a probe of nonstandard gravitational theories.


title: On the propagation speed of wavy metric tensors

abstract:
  The undulating metric tensors of general relativity do not possess a special
and common velocity of propagation. Indeed, their velocity can even coincide
with the speed of thought.


title:
Axisymmetric Simulations of Rotating Stellar Collapse in Full General
  Relativity --- Criteria for Prompt Collapse to Black Holes

abstract:
  Motivated by a recent paper by the Potsdam numerical relativity group, we
have constructed a new numerical code for hydrodynamic simulation of
axisymmetric systems in full general relativity. In this code, we solve the
Einstein field equation using Cartesian coordinates with appropriate boundary
conditions. On the other hand, the hydrodynamic equations are solved in
cylindrical coordinates. Using this code, we perform simulations to study
axisymmetric collapse of rotating stars, which thereby become black holes or
new compact stars, in full general relativity. To investigate the effects of
rotation on the criterion for prompt collapse to black holes, we first adopt a
polytropic equation of state, $P=K\rho^{\Gamma}$, where $P$, $\rho$, and $K$
are the pressure, rest mass density, and polytropic constant, with $\Gamma=2$.
In this case, the collapse is adiabatic (i.e., no change in entropy), and we
can focus on the bare effect of rotation. As the initial conditions, we prepare
rigidly and differentially rotating stars in equilibrium and then decrease the
pressure to induce collapse. In this paper, we consider cases in which $q
\equiv J/M_g^2 < 1$, where $J$ and $M_g$ are the angular momentum and the
gravitational mass. It is found that the criterion of black hole formation is
strongly dependent on the angular momentum parameter $q$. For $q < 0.5$, the
criterion is not strongly sensitive to $q$; more precisely, if the rest mass is
slightly larger than the maximum allowed value of spherical stars, a black hole
is formed. However, for $q \alt 1$, it changes significantly: For $q \simeq
0.9$, the maximum allowed rest mass becomes $\sim 70$ - 80% larger than that
for spherical stars.


title: Tumbleweeds and airborne gravitational noise sources for LIGO

abstract:
  Gravitational-wave detectors are sensitive not only to astrophysical
gravitational waves, but also to the fluctuating Newtonian gravitational forces
of moving masses in the ground and air around the detector. This paper studies
the gravitational effects of density perturbations in the atmosphere, and from
massive airborne objects near the detector. These effects were previously
considered by Saulson; in this paper I revisit these phenomena, considering
transient atmospheric shocks, and the effects of sound waves or objects
colliding with the ground or buildings around the test masses. I also consider
temperature perturbations advected past the detector as a source of
gravitational noise. I find that the gravitational noise background is below
the expected noise floor even of advanced interferometric detectors, although
only by an order of magnitude for temperature perturbations carried along
turbulent streamlines. I also find that transient shockwaves in the atmosphere
could potentially produce large spurious signals, with signal-to-noise ratios
in the hundreds in an advanced interferometric detector. These signals could be
vetoed by means of acoustic sensors outside of the buildings. Massive
wind-borne objects such as tumbleweeds could also produce gravitational signals
with signal-to-noise ratios in the hundreds if they collide with the
interferometer buildings, so it may be necessary to build fences preventing
such objects from approaching within about 30m of the test masses.


title:
General relativistic dynamics of compact binaries at the third
  post-Newtonian order

abstract:
  The general relativistic corrections in the equations of motion and
associated energy of a binary system of point-like masses are derived at the
third post-Newtonian (3PN) order. The derivation is based on a post-Newtonian
expansion of the metric in harmonic coordinates at the 3PN approximation. The
metric is parametrized by appropriate non-linear potentials, which are
evaluated in the case of two point-particles using a Lorentzian version of an
Hadamard regularization which has been defined in previous works.
Distributional forms and distributional derivatives constructed from this
regularization are employed systematically. The equations of motion of the
particles are geodesic-like with respect to the regularized metric. Crucial
contributions to the acceleration are associated with the non-distributivity of
the Hadamard regularization and the violation of the Leibniz rule by the
distributional derivative. The final equations of motion at the 3PN order are
invariant under global Lorentz transformations, and admit a conserved energy
(neglecting the radiation reaction force at the 2.5PN order). However, they are
not fully determined, as they depend on one arbitrary constant, which reflects
probably a physical incompleteness of the point-mass regularization. The
results of this paper should be useful when comparing theory to the
observations of gravitational waves from binary systems in future detectors
VIRGO and LIGO.


title: A Low Matter Density Decaying Vacuum Cosmology from Complex Metric

abstract:
  A low matter density decaying vacuum cosmology is proposed on the assumption
that the universe's radius is a complex quantity \hat{R} if it is regarded as
having a zero energy-momentum tensor. But we find that when the radius is real,
it contains matter. Using the Einstein-Hilbert action principle, the physical
scale factor R(t) =|\hat{R}| is obtained as equal to (R_0^{2} + t^{2})^{1/2}
with R_0 representing the finite radius of the universe at t=0. The resulting
physical picture is roughly a theoretical justification of the old Ozer-Taha
model. The new model is devoid of all cosmological problems. In particular, it
confirms the bounds on H_p, the present value of the Hubble parameter: 0.85 <
H_p t_p < 1.91 and faces no age problem. We argue that the total energy density
consists of parts corresponding to relativistic/non-relativistic matter, a
positive vacuum energy and a form of matter with equation of state p_K = -(1/3)
rho_K (textures or generally K-matter), and the following predictions are made
for the present nonrelativistic era: Omega_{M,n.rel.} \approx 2/3,
Omega_{V,n.rel.} \approx 1/3, Omega_ <<1, Omega_K \approx 1, where a parameter
corresponding to K-matter is taken to be unity. It is shown that the spacetime
with complex metric has signature changing properties. Using quantum
cosmological considerations, it is shown that the wave function is peaked about
the classical contour of evolution and the minimum radius R_0 of the
nonsingular model is predicted as comparable with the Planck length.
  PACS No(s); 98.80 Hw, 04.20, 04.60


title: Studies on a New Cosmological Model Based on Complex Metric

abstract:
  In this thesis, the implications of a new cosmological model are studied,
which has features similar to that of decaying vacuum cosmologies. Decaying
vacuum (or cosmological constant \Lambda) models are the results of attempts to
resolve the problems that plague the standard hot big bang model - the problems
which elude a satisfactory solution even after the two decades of of
inflationary models, the first and much publicised cure to them. We arrive at
the present model by a radically new route, which extends the idea of a
signature change in the metric, a widely discussed speculation in the current
literature. An alternative approach uses some dimensional considerations in
line with quantum cosmology and gives an almost identical model. Both
derivations involve some fundamental issues in general theory of relativity.
The model has a coasting evolution (i.e., a \propto t). It claims the absence
of all the aforementioned puzzles in the standard model and has very good
predictions. In the first two chapters of the thesis, we review the general
theory of relativity, the standard model in cosmology, its successes, the
problems in it and also the most successful of those attempts to solve them,
namely, the inflationary and decaying vacuum models. In the third chapter, we
present and discuss the new cosmological model in detail. The fourth chapter is
concerned with quantum cosmology. We briefly review the canonical quantisation
programme of solving the Wheeler-DeWitt equation, then apply the procedure to
our model and show that it satisfies many of the much sought-after ideals of
this formalism. The last chapter of the thesis compares the new model with
other ones. It also discusses the appearance of a Casimir type negative energy
density in it and the prospects and challenges ahead for the model.


title: The Earliest Phase Transition?

abstract:
  The question of a phase transition in exiting the Planck epoch of the early
universe is addressed. An order parameter is proposed to help decide the issue,
and estimates are made concerning its behavior. Our analysis is suggestive that
a phase transition occurred.


title: Study of Coincidences between Resonant Gravitational Wave Detectors

abstract:
  Coincidences are searched with the cryogenic resonant gravitational wave
detectors EXPLORER and NAUTILUS, during a period of about six months (2 June-14
December 1998) for a total measuring time of 94.5 days, with the purpose to
study new algorithms of analysis, based on the physical characteristics of the
detectors.


title: Lagrangian formalism for tensor fields

abstract:
  The Lagrangian formalism for tensor fields over differentiable manifolds with
contravariant and covariant affine connections (whose components differ not
only by sign) and metrics [$(\bar{L}_n,g)$-spaces] is considered. The
functional variation and the Lie variation of a Lagrangian density, depending
on components of tensor fields (with finite rank) and their first and second
covariant derivatives are established. A variation operator is determined and
the corollaries of its commutation relations with the covariant and the Lie
differential operators are found. The canonical (common) method of Lagrangians
with partial derivatives (MLPD) and the method of Lagrangians with covariant
derivatives (MLCD) are outlined. They differ from each other by the commutation
relations the variation operator has to obey with the covariant and the Lie
differential operator. The canonical and covariant Euler-Lagrange equations are
found as well as their corresponding $(\bar{L}_n,g)$-spaces. The
energy-momentum tensors are considered on the basis of the Lie variation and
the covariant Noether identities.


title:
Satellite non-gravitational orbital perturbations and the detection of
  the gravitomagnetic clock effect

abstract:
  The general relativistic gravitomagnetic clock effect consists in the fact
that two massive test bodies orbiting a central spinning mass in its equatorial
plane along two identical circular trajectories, but in opposite directions,
take different times in describing a full revolution with respect to an
asymptotically inertial observer. In the field of the Earth such time shift
amounts to 10^{-7} s. Detecting it by means of a space based mission with
artificial satellites is a very demanding task because there are severe
constraints on the precision with which the radial and azimuthal positions of a
satellite must be known: delta r= 10^{-2} cm and delta phi= 10^{-2}
milliarcseconds per revolution. In this paper we assess if the systematic
errors induced by various non-gravitational perturbations allow to meet such
stringent requirements. A couple of identical, passive laser-ranged satellites
of LAGEOS type with their spins aligned with the Earth's one is considered. It
turns out that all the non vanishing non-gravitational perturbations induce
systematic errors in r and phi within the required constraints for a reasonable
assumption of the mismodeling in some satellite's and Earth's parameters and/or
by using dense satellites with small area-to-mass ratio. However, the error in
the Earth's GM is by far the largest source of uncertainty in the azimuthal
location which is affected at a level of 1.2 milliarcseconds per revolution.


title: Black hole horizon and space-time foam

abstract:
  We introduce, by means of the Brans-Dicke scalar field, space-time
fluctuations at scale comparable to Planck length near the event horizon of a
black hole and examine their dramatic effects.


title:
Dynamical Properties of Euclidean Solutions in a Multidimensional
  Cosmological Model

abstract:
  In the framework of the Hartle-Hawking no-boundary proposal, we investigated
quantum creation of the multidimensional universe with a cosmological constant
($\Lambda$) but without matter fields. We have found that the classical
solutions of the Euclidean Einstein equations in this model have
``quasi-attractors'', i.e., most trajectories on the a-b plane, where a and b
are the scale factors of external and internal spaces, go around a point. It is
presumed that the wave function of the universe has a hump near this
quasi-attractor point. In the case that both the curvatures of external and
internal spaces are positive, and $\Lambda>0$, there exist Lorentzian solutions
which start near the quasi-attractor, the internal space remains microscopic,
and the external space evolves into our macroscopic universe.


title: Numerical Analysis of the Wave Function of the Multidimensional Universe

abstract:
  In the framework of the Hartle-Hawking no-boundary proposal, we investigate
quantum creation of the multidimensional universe with the cosmological
constant $\Lambda$ but without matter fields. In this paper we solved the
Wheeler-de Witt equation numerically. We find that the universe in which both
of the spaces expand exponentially is the most probable in this model.


title: Anisotropic Homogeneous Cosmologies in the Post-Newtonian Approximation

abstract:
  In this paper we explore how far the post-Newtonian theory goes in overcoming
the difficulties associated with anisotropic homogeneous cosmologies in the
Newtonian approximation. It will be shown that, unlike in the Newtonian case,
the cosmological equations of the post-Newtonian approximation are much more in
the spirit of general relativity with regard to the nine Bianchi types and
issues of singularities. The situations of vanishing rotation and vanishing
shear are treated separately. The homogeneous Bianchi I model is considered as
an example of a rotation-free cosmology with anisotropy. It is found in the
Newtonian approximation that there are arbitrary functions that need to be
given for all time if the initial value problem is to be well-posed, while in
the post-Newtonian case there is no such need. For the general case of a
perfect fluid only the post-Newtonian theory can satisfactorily describe the
effects of pressure. This is in accordance with findings in an earlier paper
where the post-Newtonian approximation was applied to homogeneous cosmologies.
For a shear-free anisotropic homogeneous cosmology the Newtonian theory of
Heckmann and Sch\"ucking is explored. Comparisons with its relativistic and
post-Newtonian counterparts are made. In the Newtonian theory solutions exist
to which there are no analogues in general relativity. The post-Newtonian
approximation may provide a way out.


title: Holographic Bound from Second Law

abstract:
  The holographic bound that the entropy (log of number of quantum states) of a
system is bounded from above by a quarter of the area of a circumscribing
surface measured in Planck areas is widely regarded a desideratum of any
fundamental theory, but some exceptions occur. By suitable black hole gedanken
experiments I show that the bound follows from the generalized second law for
two broad classes of isolated systems: generic weakly gravitating systems
composed of many elementary particles, and quiescent, nonrotating strongly
gravitating configurations well above Planck mass. These justify an early claim
by Susskind.


title: Decoherence Caused by Topology in a Time-Machine Spacetime

abstract:
  Non-relativistic quantum theory of non-interacting particles in the spacetime
containing a region with closed time-like curves (time-machine spacetime) is
considered with the help of the path-integral technique. It is argued that, in
certain conditions, a sort of superselection may exist for evolution of a
particle in such a spacetime. All types of evolution are classified by the
number $n$ defined as the number of times the particle returns back to its
past. It corresponds also to the topological class of trajectories of the
particle. The evolutions corresponding to different values of $n$ are
non-coherent. The amplitudes corresponding to such evolutions may not be
superposed. Instead of one evolution operator, as in the conventional
(coherent) description, evolution of the particle is described by a family
$U_n$ of partial evolution operators. This is done in analogy with the
formalism of quantum theory of measurements, but with essential new features in
the dischronal region (the region with closed time-like curves) of the
time-machine spacetime. Partial evolution operators $U_n$ are equal to
integrals over the topological classes of paths if the evolution begins and
ends in the chronal regions. If the evolution begins or/and ends in the
dischronal region, the integral over the topological class should be multiplied
by a certain projector to give the partial evolution operator $U_n$. Thus
defined partial evolution operators possess the property of generalized
unitarity and multiplicativity. The part of evolution containing repeated
returning backward in time cannot be factorized: all backward passages of the
particle have to be considered as a single act, that cannot be presented as
gradually, step by step, passing through `causal loops'.


title: Three-Dimensional Billiards with Time Machine

abstract:
  Self-collision of a non-relativistic classical point-like body, or particle,
in the spacetime containing closed time-like curves (time-machine spacetime) is
considered. A point-like body (particle) is an idealization of a small ideal
elastic billiard ball. The known model of a time machine is used containing a
wormhole leading to the past. If the body enters one of the mouths of the
wormhole, it emerges from another mouth in an earlier time so that both the
particle and its "incarnation" coexist during some time and may collide. Such
self-collisions are considered in the case when the size of the body is much
less than the radius of the mouth, and the latter is much less than the
distance between the mouths. Three-dimensional configurations of trajectories
with a self-collision are presented. Their dynamics is investigated in detail.
Configurations corresponding to multiple wormhole traversals are discussed. It
is shown that, for each world line describing self-collision of a particle,
dynamically equivalent configurations exist in which the particle collides not
with itself but with an identical particle having a closed trajectory (Jinnee
of Time Machine).


title: Kinks, energy conditions and closed timelike curves

abstract:
  A link between the possibility of extending a geodessically incomplete kinked
spacetime to a spacetime which is geodesically complete and the energy
conditions is discussed for the case of a cylindrically-symmetric spacetime
kink. It is concluded that neither the strong nor the weak energy condition can
be satisfied in the four-dimensional example, though the latter condition may
survive on the transversal sections of such a spacetime. It is also shown that
the matter which propagates quantum-mechanically in a kinked spacetime can
always be trapped by closed timelike curves, but signaling connections between
that matter and any possible observer can only be made of totally incoherent
radiation, so preventing observation of causality violation.


title: The Geometric Gravitational Internal Problem

abstract:
  In a geometric unified theory there is an energy momentum equation, apart
from the field equations and equations of motion. The general relativity
Einstein equation with cosmological constant follows from this energy momentum
equation for empty space. For non empty space we obtain a generalized Einstein
equation, relating the Einstein tensor to a geometric stress energy tensor. The
matching exterior solution is in agreement with the standard relativity tests.
Furthermore, there is a Newtonian limit where we obtain Poisson's equation.


title: Gravity as a Key Problem of the Millenium

abstract:
  Gravitation as a fundamental interaction that governs all phenomena at large
and very small scales, but still not well understood at a quantum level, is a
missing cardinal link to unification of all physical interactions. Problems of
the absolute G measurements and its possible time and range variations are
reflections of the unification problem. Integrable multidimensional models of
gravitation and cosmology make up one of the proper approaches to study basic
issues and strong field objects, the Early Universe and black hole physics in
particular. The choice, nature, classification and precision of determination
of fundamental physical constants are described. The problem of their temporal
variations is also discussed, temporal and range variations of G in particular.
A need for further absolute measurements of G, its possible range and time
variations is pointed out. The novel multipurpose space project SEE, aimed for
measuring G and its stability in space and time 3-4 orders better than at
present, may answer many important questions posed by gravitation, cosmology
and unified theories.


title: Some Higher Dimensional Vacuum Solutions

abstract:
  We study an even dimensional manifold with a pseudo-Riemannian metric with
arbitrary signature and arbitrary dimensions. We consider the Ricci flat
equations and present a procedure to construct solutions to some higher (even)
dimensional Ricci flat field equations from the four diemnsional Ricci flat
metrics. When the four dimensional Ricci flat geometry correponds to a
colliding gravitational vacuum spacetime our approach provides an exact
solution to the vacuum Einstein field equations for colliding graviational
plane waves in an (arbitrary) even dimensional spacetime. We give explicitly
higher dimensional Szekeres metrics and study their singularity behaviors.


title: How to Extract Energy Directly from a Gravitational Field

abstract:
  Gravity is related to gravitational mass of the bodies. According to the weak
form of Einstein's General Relativity equivalence principle, the gravitational
and inertial masses are equivalent. However recent calculations (gr-qc/9910036)
have revealed that they are correlated by an adimensional factor, which depends
on the incident radiation upon the particle. It was shown that there is a
direct correlation between the radiation absorbed by the particle and its
gravitational mass, independently of the inertial mass. This finding has
fundamental consequences to Unified Field Theory and Quantum Cosmology. It was
also shown that only in the absence of electromagnetic radiation this factor
becomes equal to one and that, in specific electromagnetic conditions, it can
be reduced, nullified or made negative. This means that there is the
possibility of control of the gravitational mass by means of the incident
radiation. This unexpected theoretical result was recently confirmed by an
experiment (gr-qc/0005107). Consequently there is a strong evidence that the
gravitational forces can be reduced, nullified and inverted by means of
electromagnetic radiation. This means that, in practice we can produce
gravitational binaries, and in this way to extract energy from a gravitational
field. Here we describe a process by which energy can be extracted directly
from any site of a gravitational field.


title: Causality of the brane universe

abstract:
  Causal structure of the brane universe with respect to null geodesics in the
bulk spacetime is studied. It is pointed out that apparent causality violation
is possible for the brane universe which contains matter energy. It is also
shown that there is no 'horizon problem' in the Friedmann-Robertson-Walker
brane universe.


title: Mechanical quality factor of a sapphire fiber at cryogenic temperatures

abstract:
  A mechanical quality factor of $1.1 \times 10^{7}$ was obtained for the 199
Hz bending vibrational mode in a monocrystalline sapphire fiber at 6 K.
Consequently, we confirm that pendulum thermal noise of cryogenic mirrors used
for gravitational wave detectors can be reduced by the sapphire fiber
suspension.


title: Gravitational Goldstone fields from affine gauge theory

abstract:
  In order to facilitate the application of standard renormalization
techniques, gravitation should be decribed, if possible, in pure connection
formalism, as a Yang-Mills theory of a certain spacetime group, say the
Poincare or the affine group. This embodies the translational as well as the
linear connection. However, the coframe is not the standard Yang-Mills type
gauge field of the translations, since it lacks the inhomogeneous gradient term
in the gauge transformations. By explicitly restoring the "hidden" piece
responsible for this behavior within the framework of nonlinear realizations,
the usual geometrical interpretation of the dynamical theory becomes possible,
and in addition one can avoid the metric or coframe degeneracy which would
otherwise interfere with the integrations within the path integral. We claim
that nonlinear realizations provide a general mathematical scheme clarifying
the foundations of gauge theories of spacetime symmetries. When applied to
construct the Yang-Mills theory of the affine group, tetrads become identified
with nonlinear translational connections; the anholonomic metric does not
constitute any more an independent gravitational potential, since its degrees
of freedom reveal to correspond to eliminable Goldstone bosons. This may be an
important advantage for quantization.


title: Exact Solutions with w - modes

abstract:
  An explicit necessary condition for the occurrence of resonance scattering of
axial gravitational waves, along with the internal trapping of null geodesics,
is proposed for static spherically symmetric perfect fluid solutions to
Einstein's equations. Some exact inhomogeneous solutions which exhibit this
trapping are given with special attention to boundary conditions and the
physical acceptability of the space times. In terms of the tenuity ($\alpha =
R/M$ at the boundary) all the examples given lie in the narrow range $2.8 <
\alpha < 2.9$. The tenuity can be raised to more interesting values by the
addition of an envelope without altering the trapping.


title:
Gravitational Waves from a Compact Star in a Circular, Inspiral Orbit,
  in the Equatorial Plane of a Massive, Spinning Black Hole, as Observed by
  LISA

abstract:
  Results are presented from high-precision computations of the orbital
evolution and emitted gravitational waves for a stellar-mass object spiraling
into a massive black hole in a slowly shrinking, circular, equatorial orbit.
The focus of these computations is inspiral near the innermost stable circular
orbit (isco)---more particularly, on orbits for which the angular velocity
Omega is 0.03 < Omega/Omega_{isco} < 1. The computations are based on the
Teukolsky-Sasaki-Nakamura formalism, and the results are tabulated in a set of
functions that are of order unity and represent relativistic corrections to
low-orbital-velocity formulas. These tables can form a foundation for future
design studies for the LISA space-based gravitational-wave mission. A first
survey of applications to LISA is presented: Signal to noise ratios S/N are
computed and graphed as functions of the time-evolving gravitational-wave
frequency for representative values of the hole's mass M and spin a and the
inspiraling object's mass \mu, with the distance to Earth chosen to be r_o = 1
Gpc. These S/N's show a very strong dependence on the black-hole spin, as well
as on M and \mu. A comparison with predicted event rates shows strong promise
for detecting these waves, but not beyond about 1Gpc if the inspiraling object
is a white dwarf or neutron star. This argues for a modest lowering of LISA's
noise floor. A brief discussion is given of the prospects for extracting
information from the observed waves


title:
(D-E)-dimensional brane worlds and de Rham distribution formalism:
  Singular split versus compactification, restrictions on scenario and revision
  of gravitational energy problem

abstract:
  The proposed so far brane-world cosmological scenarios are concerned with
(D-1)-dimensional embeddings into the D-dimensional spacetime, besides, it is
supposed D=5 as a rule. However, it would be much more realistic to consider
our four-Universe as 4-shell or 3-brane inside, e.g., 10-dimensional spacetime.
In turn it immediately means that the theory of the $(D-D_E)$-dimensional
singular embeddings, where the number of extra dimensions $D_E > 1$, is needed.
Hence, the aim of this work is to provide such a theory: we construct the
rigorous general theory of the induced gravity on singular submanifolds. At
first, we perform the decomposition of the tangent bundle into the two
subbundles which will be associated later with external and visible (with
respect to some low-dimensional observer) parts of the high-$D$ manifold. Then
we go to physics and perform the split of the manifold (in addition to the
split of the tangent bundle) to describe both the induced internal geometry and
external as-a-whole dynamics of singular embeddings, assuming matter being
confined on the singular submanifold but gravity being propagated through the
high-$D$ manifold. With the use of the de Rham axiomatic approach to
delta-distributions we demonstrate that the four-Universe can be singularly
embedded only in five- and six-dimensional space so if we want to consider its
embedding in 10D then extra dimensions must be included as a product space
only. We discuss the revealed generic features of the theory such as the
multi-normal anisotropy, restrictions on an ambient space, reformulation of the
conserved gravitational stress-energy tensor problem, etc.


title:
The exact cosmological solution to the dynamical equations for the
  Bianchi IX model

abstract:
  Quantum geometrodynamics in extended phase space describes phenomenologically
the integrated system ``a physical object + observation means (a gravitational
vacuum condensate)''. The central place in this version of QGD belongs to the
Schrodinger equation for a wave function of the Universe. An exact solution to
the ``conditionally-classical'' set of equations in extended phase space for
the Bianchi-IX model and the appropriate solution to the Schrodinger equation
are considered. The physical adequacy of the obtained solutions to existing
concepts about possible cosmological scenarios is demonstrated. The
gravitational vacuum condensate is shown to be a cosmological evolution factor.


title:
Gravitational Collapse of Cylindrical Shells Made of Counter-Rotating
  Dust Particles

abstract:
  The general formulas of a non-rotating dynamic thin shell that connects two
arbitrary cylindrical regions are given using Israel's method. As an
application of them, the dynamics of a thin shell made of counter-rotating dust
particles, which emits both gravitational waves and massless particles when it
is expanding or collapsing, is studied. It is found that when the models
represent a collapsing shell, in some cases the angular momentum of the dust
particles is strong enough to halt the collapse, so that a spacetime
singularity is prevented from forming, while in other cases it is not, and a
line-like spacetime singularity is finally formed on the symmetry axis.


title: Dynamics of Rotating Cylindrical Shells in General Relativity

abstract:
  Cylindrical spacetimes with rotation are studied using the Newmann-Penrose
formulas. By studying null geodesic deviations the physical meaning of each
component of the Riemann tensor is given. These spacetimes are further extended
to include rotating dynamic shells, and the general expression of the surface
energy-momentum tensor of the shells is given in terms of the discontinuation
of the first derivatives of the metric coefficients. As an application of the
developed formulas, a stationary shell that generates the Lewis solutions,
which represent the most general vacuum cylindrical solutions of the Einstein
field equations with rotation, is studied by assuming that the spacetime inside
the shell is flat. It is shown that the shell can satisfy all the energy
conditions by properly choosing the parameters appearing in the model, provided
that $ 0 \le \sigma \le 1$, where $\sigma$ is related to the mass per unit
length of the shell.


title: Self interacting Brans Dicke cosmology and Quintessence

abstract:
  Recent cosmological observations reveal that we are living in a flat
accelerated expanding universe. In this work we have investigated the nature of
the potential compatible with the power law expansion of the universe in a self
interacting Brans Dicke cosmology with a perfect fluid background and have
analyzed whether this potential supports the accelerated expansion. It is found
that positive power law potential is relevant in this scenario and can drive
accelerated expansion for negative Brans Dicke coupling parameter $\omega$. The
evolution of the density perturbation is also analyzed in this scenerio and is
seen that the model allows growing modes for negative $\omega$.


title: WKB Wave Functions with the Induced Gravity Theory

abstract:
  The Wheeler-DeWitt equation for the induced gravity theory is constructed in
the minisuperspace approximation, and then solved using the WKB method under
three types of boundary condition proposed respectively by Hartle & Hawking
(``no boundary''), Linde and Vilenkin (``tunneling from nothing''). It is found
that no matter how the gravitational and cosmological ``constants'' vary in the
classical models, they will acquire constant values when the universe comes
from quantum creation, and that, in particular, the resulting tunneling wave
function under the Linde or Vilenkin boundary condition reaches its maximum
value if the cosmological constant vanishes.


title:
Energy-momentum and angular momentum densities in gauge theories of
  gravity

abstract:
  In the $\bar{\mbox{\rm Poincar\'{e}}}$ gauge theory of gravity, which has
been formulated on the basis of a principal fiber bundle over the space-time
manifold having the covering group of the proper orthochronous Poincar\'{e}
group as the structure group, we examine the tensorial properties of the
dynamical energy-momentum density ${}^{G}{\mathbf T}_{k}{}^{\mu}$ and the ` `
spin" angular momentum density ${}^{G}{\mathbf S}_{kl}{}^{\mu}$ of the
gravitational field. They are both space-time vector densities, and transform
as tensors under {\em global} $SL(2,C)$- transformations. Under {\em local}
internal translation, ${}^{G}{\mathbf T}_{k}{}^{\mu}$ is invariant, while
${}^{G}{\mathbf S}_{kl}{}^{\mu}$ transforms inhomogeneously. The dynamical
energy-momentum density ${}^{M}{\mathbf T}_{k}{}^{\mu}$ and the ` ` spin"
angular momentum density ${}^{M}{\mathbf S}_{kl}{}^{\mu}$ of the matter field
are also examined, and they are known to be space-time vector densities and to
obey tensorial transformation rules under internal $\bar{\mbox{\rm
Poincar\'{e}}}$ gauge transformations. The corresponding discussions in
extended new general relativity which is obtained as a teleparallel limit of
$\bar{\mbox{\rm Poincar\'{e}}}$ gauge theory are also given, and
energy-momentum and ` ` spin" angular momentum densities are known to be well
behaved. Namely, they are all space-time vector densities, etc. In both
theories, integrations of these densities on a space-like surface give the
total energy-momentum and {\em total} (={\em spin}+{\em orbital}) angular
momentum for asymptotically flat space-time. The tensorial properties of
canonical energy-momentum and ` ` extended orbital angular momentum" densities
are also examined.


title: Topological Black Holes in Quantum Gravity

abstract:
  We derive the black hole solutions with horizons of non-trivial topology and
investigate their properties in the framework of an approach to quantum gravity
being an extension of Bohm's formulation of quantum mechanics. The solutions we
found tend asymptotically (for large $r$) to topological black holes. We also
analyze the thermodynamics of these space-times.


title: Warm inflation and scalar perturbations of the metric

abstract:
  A second-order expansion for the quantum fluctuations of the matter field was
considered in the framework of the warm inflation scenario. The friction and
Hubble parameters were expended by means of a semiclassical approach. The
fluctuations of the Hubble parameter generates fluctuations of the metric.
These metric fluctuations produce an effective term of curvature. The power
spectrum for the metric fluctuations can be calculated on the infrared sector.


title: Quasi-normal modes of AdS black holes : A superpotential approach

abstract:
  A novel method, based on superpotentials is proposed for obtaining the
quasi-normal modes of anti-de Sitter black holes. This is inspired by the case
of the three-dimensional BTZ black hole, where the quasi-normal modes can be
obtained exactly and are proportional to the surface gravity. Using this
approach, the quasi-normal modes of the five dimensional Schwarzschild
anti-deSitter black hole are computed numerically. The modes again seem to be
proportional to the surface gravity for very small and very large black holes.
They reflect the well-known instability of small black holes in anti-deSitter
space.


title: Initial Data for Numerical Relativity

abstract:
  Initial data are the starting point for any numerical simulation. In the case
of numerical relativity, Einstein's equations constrain our choices of these
initial data. We will examine several of the formalisms used for specifying
Cauchy initial data in the 3+1 decomposition of Einstein's equations. We will
then explore how these formalisms have been used in constructing initial data
for spacetimes containing black holes and neutron stars. In the topics
discussed, emphasis is placed on those issues that are important for obtaining
astrophysically realistic initial data for compact binary coalescence.


title: Nonlinear r-modes in Rapidly Rotating Relativistic Stars

abstract:
  The r-mode instability in rotating relativistic stars has been shown recently
to have important astrophysical implications (including the emission of
detectable gravitational radiation, the explanation of the initial spins of
young neutron stars and the spin-distribution of millisecond pulsars and the
explanation of one type of gamma-ray bursts), provided that r-modes are not
saturated at low amplitudes by nonlinear effects or by dissipative mechanisms.
Here, we present the first study of nonlinear r-modes in isentropic, rapidly
rotating relativistic stars, via 3-D general-relativistic hydrodynamical
evolutions. Our numerical simulations show that (1) on dynamical timescales,
there is no strong nonlinear coupling of r-modes to other modes at amplitudes
of order one -- unless nonlinear saturation occurs on longer timescales, the
maximum r-mode amplitude is of order unity (i.e., the velocity perturbation is
of the same order as the rotational velocity at the equator). An absolute upper
limit on the amplitude (relevant, perhaps, for the most rapidly rotating stars)
is set by causality. (2) r-modes and inertial modes in isentropic stars are
predominantly discrete modes and possible associated continuous parts were not
identified in our simulations. (3) In addition, the kinematical drift
associated with r-modes, recently found by Rezzolla, Lamb and Shapiro (2000),
appears to be present in our simulations, but an unambiguous confirmation
requires more precise initial data. We discuss the implications of our findings
for the detectability of gravitational waves from the r-mode instability.


title:
Post-Newtonian Gravitational Radiation and Equations of Motion via
  Direct Integration of the Relaxed Einstein Equations. I. Foundations

abstract:
  We present a self-contained framework called Direct Integration of the
Relaxed Einstein Equations (DIRE) for calculating equations of motion and
gravitational radiation emission for isolated gravitating systems based on the
post-Newtonian approximation. We cast the Einstein equations into their
``relaxed'' form of a flat-spacetime wave equation together with a harmonic
gauge condition, and solve the equations formally as a retarded integral over
the past null cone of the field point (chosen to be within the near zone when
calculating equations of motion, and in the far zone when calculating
gravitational radiation). The ``inner'' part of this integral(within a sphere
of radius $\cal R \sim$ one gravitational wavelength) is approximated in a
slow-motion expansion using standard techniques; the ``outer'' part, extending
over the radiation zone, is evaluated using a null integration variable. We
show generally and explicitly that all contributions to the inner integrals
that depend on $\cal R$ cancel corresponding terms from the outer integrals,
and that the outer integrals converge at infinity, subject only to reasonable
assumptions about the past behavior of the source. The method cures defects
that plagued previous ``brute-force'' slow-motion approaches to motion and
gravitational radiation for isolated systems. We detail the procedure for
iterating the solutions in a weak-field, slow-motion approximation, and derive
expressions for the near-zone field through 3.5 post-Newtonian order in terms
of Poisson-like potentials.