title: A fully (3+1)-D Regge calculus model of the Kasner cosmology

abstract:
  We describe the first discrete-time 4-dimensional numerical application of
Regge calculus. The spacetime is represented as a complex of 4-dimensional
simplices, and the geometry interior to each 4-simplex is flat Minkowski
spacetime. This simplicial spacetime is constructed so as to be foliated with a
one parameter family of spacelike hypersurfaces built of tetrahedra. We
implement a novel two-surface initial-data prescription for Regge calculus, and
provide the first fully 4-dimensional application of an implicit decoupled
evolution scheme (the ``Sorkin evolution scheme''). We benchmark this code on
the Kasner cosmology --- a cosmology which embodies generic features of the
collapse of many cosmological models. We (1) reproduce the continuum solution
with a fractional error in the 3-volume of 10^{-5} after 10000 evolution steps,
(2) demonstrate stable evolution, (3) preserve the standard deviation of
spatial homogeneity to less than 10^{-10} and (4) explicitly display the
existence of diffeomorphism freedom in Regge calculus. We also present the
second-order convergence properties of the solution to the continuum.


title: Symmetries in two-dimensional dilaton gravity with matter

abstract:
  The symmetries of generic 2D dilaton models of gravity with (and without)
matter are studied in some detail. It is shown that $\delta_2$, one of the
symmetries of the matterless models, can be generalized to the case where
matter fields of any kind are present. The general (classical) solution for
some of these models, in particular those coupled to chiral matter, which
generalizes the Vaidya solution of Einstein Gravity, is also given.


title: Disks in Expanding FRW Universes

abstract:
  We construct exact solutions to Einstein equations which represent
relativistic disks immersed into an expanding FRW Universe. It is shown that
the expansion influences dynamical characteristics of the disks such as
rotational curves, surface mass density, etc. The effects of the expansion is
exemplified with non-static generalizations of Kuzmin-Curzon and generalized
Schwarzschild disks.


title: Birth of the Universe in string cosmology

abstract:
  The decay of the string perturbative vacuum into our present cosmological
state is associated to the transition from a phase of growing curvature and
growing dilaton, to a phase of decreasing curvature and frozen dilaton. The
possible approaches to a classical and quantum description of such a transition
are introduced and briefly discussed.


title: Simplifying the spectral analysis of the volume operator

abstract:
  The volume operator plays a central role in both the kinematics and dynamics
of canonical approaches to quantum gravity which are based on algebras of
generalized Wilson loops. We introduce a method for simplifying its spectral
analysis, for quantum states that can be realized on a cubic three-dimensional
lattice. This involves a decomposition of Hilbert space into sectors
transforming according to the irreducible representations of a subgroup of the
cubic group. As an application, we determine the complete spectrum for a class
of states with six-valent intersections.


title:
Investigation of the Interior of Colored Black Holes and the
  Extendability of Solutions of the Einstein-Yang/Mills Equations

abstract:
  We prove that any asymptotically flat solution to the spherically symmetric
SU(2) Einstein-Yang/Mills equations is globally defined. This result applies in
particular to the interior of colored black holes.


title: Dynamics of Cosmic Strings in Schwarzschild Spacetime

abstract:
  Cosmic strings are topological defects thought to have formed early in the
life of the universe. If such objects exist, a study of their interaction with
black holes is of interest. The equations of motion of a cosmic string have the
form of highly non-linear wave equations. General analytic solutions, except
for motion in certain backgrounds such as flat and shockwave spacetimes, remain
unknown; consequently, much of the work must be carried out numerically. To do
this, an implicit finite difference scheme was developed that involves solving
large block tridiagonal systems. This paper discusses the numerical method, its
validation against analytic and semi-analytic solutions, and preliminary
results on the interaction of a cosmic string with Schwarzschild black holes.


title: On a certain formulation of the Einstein equations

abstract:
  We define a certain differential system on an open set of $R^6$. The system
locally defines a Lorentzian 4-manifold satisfying the Einstein equations. The
converse statement is indicated and its details are postponed to the
furthcoming paper.


title: Elliptic fibrations associated with the Einstein spacetimes

abstract:
  Given a conformally nonflat Einstein spacetime we define a fibration $P$ over
it. The fibres of this fibration are elliptic curves (2-dimensional tori) or
their degenerate counterparts. Their topology depends on the algebraic type of
the Weyl tensor of the Einstein metric. The fibration $P$ is a double branched
cover of the bundle of null direction over the spacetime and is equipped with
six linearly independent 1-forms which satisfy certain relatively simple system
of equations.


title: A new class of inhomogeneous cosmological models with Yang-Mills fields

abstract:
  Exact solutions corresponding to spherically symmetric inhomogeneous
nonstationary Tolman metrics are obtained for the self-consistent


title: Thermodynamics of Black Holes in Brans-Dicke Gravity

abstract:
  It has recently been argued that non-trivial Brans-Dicke black hole solutions
different from the usual Schwarzschild solution could exist. We attemt here to
``censor'' these non-trivial Brans-Dicke black hole solutions by examining
their thermodynamic properties. Quantities like Hawking temperature and entropy
of the black holes are computed. Analysis of the behaviors of these
thermodynamic quantities appears to show that even in Brans-Dicke gravity, the
usual Schwarzschild spacetime turns out to be the only physically relevant
uncharged static black hole solution.


title:
General-relativistic coupling between orbital motion and internal
  degrees of freedom for inspiraling binary neutron stars

abstract:
  We analyze the coupling between the internal degrees of freedom of neutron
stars in a close binary, and the stars' orbital motion. Our analysis is based
on the method of matched asymptotic expansions and is valid to all orders in
the strength of internal gravity in each star, but is perturbative in the
``tidal expansion parameter'' (stellar radius)/(orbital separation). At first
order in the tidal expansion parameter, we show that the internal structure of
each star is unaffected by its companion, in agreement with post-1-Newtonian
results of Wiseman (gr-qc/9704018). We also show that relativistic interactions
that scale as higher powers of the tidal expansion parameter produce
qualitatively similar effects to their Newtonian counterparts: there are
corrections to the Newtonian tidal distortion of each star, both of which occur
at third order in the tidal expansion parameter, and there are corrections to
the Newtonian decrease in central density of each star (Newtonian ``tidal
stabilization''), both of which are sixth order in the tidal expansion
parameter. There are additional interactions with no Newtonian analogs, but
these do not change the central density of each star up to sixth order in the
tidal expansion parameter. These results, in combination with previous analyses
of Newtonian tidal interactions, indicate that (i) there are no large
general-relativistic crushing forces that could cause the stars to collapse to
black holes prior to the dynamical orbital instability, and (ii) the
conventional wisdom with respect to coalescing binary neutron stars as sources
of gravitational-wave bursts is correct: namely, the finite-stellar-size
corrections to the gravitational waveform will be unimportant for the purpose
of detecting the coalescences.


title:
Late time behaviour of the maximal slicing of the Schwarzschild black
  hole

abstract:
  A time-symmetric Cauchy slice of the extended Schwarzschild spacetime can be
evolved into a foliation of the $r>3m/2$-region of the spacetime by maximal
surfaces with the requirement that time runs equally fast at both spatial ends
of the manifold. This paper studies the behaviour of these slices in the limit
as proper time-at-infinity becomes arbitrarily large and gives an analytic
expression for the collapse of the lapse.


title: Fuzzy Surfaces of Genus Zero

abstract:
  A fuzzy version of the ordinary round 2-sphere has been constructed with an
invariant curvature. We here consider linear connections on arbitrary fuzzy
surfaces of genus zero. We shall find as before that they are more or less
rigidly dependent on the differential calculus used but that a large number of
the latter can be constructed which are not covariant under the action of the
rotation group. For technical reasons we have been forced to limit our
considerations to fuzzy surfaces which are small perturbations of the fuzzy
sphere.


title:
Non-Newtonian Dynamic Gravitational Field from The Longitudinally
  Asymmetric Rotating Objects

abstract:
  The dynamic shift of the center of mass for a rotating hemisphere prompts us
the question of what might be its physical consequences. Despite the fact that
accelerating object is known to create gravitational field, there is no known
external dynamic gravitational force from a rotating sphere where the
individual mass components are in constant acceleration. However, Thirring's
`induced centrifugal force' and the component of the force along the
longitudinal axis inside a rotating spherical shell indicate that they are
non-radiative dynamic forces which depend on $\omega^2$. In this report,
Thirring's force is derived by considering the component-wise acceleration of
the rotating hemisphere in the weak field approximation. This new analytic
solution provides the gravitational explanation of the jet phenomena observed
from the fast rotating cosmological bodies, which demands a major revision in
our understanding of the universe since it suggests there exists a strong, long
ranged, non-Newtonian dynamic gravitational force in our universe. This also
raises an interesting question of how the strength of the dipole moment can be
maximized for a given mass by configuring the specific geometrical shape of the
rotating source.


title: On Gravitational Repulsion

abstract:
  The concepts of negative gravitational mass and gravitational repulsion are
alien to general relativity. Still, we show here that small negative
fluctuations - small dimples in the primordial density field - that act as if
they have an effective negative gravitational mass, play a dominant role in
shaping our Universe. These initially tiny perturbations repel matter
surrounding them, expand and grow to become voids in the galaxy distribution.
These voids - regions with a diameter of $40 \h$ Mpc which are almost devoid of
galaxies - are the largest object in the Universe.


title: Gravitational excitons from extra dimensions

abstract:
  Inhomogeneous multidimensional cosmological models with a higher dimensional
space-time manifold are investigated under dimensional reduction. In the
Einstein conformal frame, small excitations of the scale factors of the
internal spaces near minima of an effective potential have a form of massive
scalar fields in the external space-time. Parameters of models which ensure
minima of the effective potentials are obtained for particular cases and masses
of gravitational excitons are estimated.


title:
Reduced phase space formalism for spherically symmetric geometry with a
  massive dust shell

abstract:
  We perform a Hamiltonian reduction of spherically symmetric Einstein gravity
with a thin dust shell of positive rest mass. Three spatial topologies are
considered: Euclidean (R^3), Kruskal (S^2 x R), and the spatial topology of a
diametrically identified Kruskal (RP^3 - {a point at infinity}). For the
Kruskal and RP^3 topologies the reduced phase space is four-dimensional, with
one canonical pair associated with the shell and the other with the geometry;
the latter pair disappears if one prescribes the value of the Schwarzschild
mass at an asymptopia or at a throat. For the Euclidean topology the reduced
phase space is necessarily two-dimensional, with only the canonical pair
associated with the shell surviving. A time-reparametrization on a
two-dimensional phase space is introduced and used to bring the shell
Hamiltonians to a simpler (and known) form associated with the proper time of
the shell. An alternative reparametrization yields a square-root Hamiltonian
that generalizes the Hamiltonian of a test shell in Minkowski space with
respect to Minkowski time. Quantization is briefly discussed. The discrete mass
spectrum that characterizes natural minisuperspace quantizations of vacuum
wormholes and RP^3-geons appears to persist as the geometrical part of the mass
spectrum when the additional matter degree of freedom is added.


title:
The Schwarzschild Solution in the 4-Dimensional Kaluza-Klein Description
  of The Einstein's Equations

abstract:
  The Kaluza-Klein formalism of the Einstein's theory, based on the
(2,2)-fibration of a generic 4-dimensional spacetime, describes general
relativity as a Yang-Mills gauge theory on the 2-dimensional base manifold,
where the local gauge symmetry is the group of the diffeomorphisms of the
2-dimensional fibre manifold. As a way of illustrating how to use this
formalism in finding exact solutions, we apply this formalism to the
spherically symmetric case, and obtain the Schwarzschild solution by solving
the field equations.


title: The fine tuning problem in pre-big-bang inflation

abstract:
  We examine the effect of spatial curvature in the pre-big-bang inflationary
model suggested by string theory. We study $O(\alpha ')$ corrections and we
show that, independently of the initial curvature, they lead to a phase of
exponential inflation. The amount of inflation in this phase is long enough to
solve the horizon and flatness problems if the evolution starts deeply into the
weak coupling regime. There is a region of the parameter space of the model
where such a long inflationary phase at the string scale is consistent with
COBE anisotropies, millisecond pulsar timing and nucleosynthesis constraints.
We discuss implications for the spectrum of relic gravitational waves at the
frequencies of LIGO and Virgo.


title: Quantum correction to thermodynamical entropy of black hole

abstract:
  The entropy of a black hole can differ from a quarter of the area of the
horizon because of quantum corrections. The correction is related to the
contribution to the Euclidean functional integral from quantum fluctuations but
is not simply equal to the correction to the effective action. A (2+1)
dimensional rotating black hole is explicitly considered.


title: Generalization Of Lorentz-Poincare Ether Theory To Quantum Gravity

abstract:
  We present a quantum theory of gravity which is in agreement with observation
in the relativistic domain. The theory is not relativistic, but a Galilean
invariant generalization of Lorentz-Poincare ether theory to quantum gravity.
  If we apply the methodological rule that the best available theory has to be
preferred, we have to reject the relativistic paradigm and return to Galilean
invariant ether theory.


title: Inertia as the ``Threshold of Elasticity'' of Quantum States

abstract:
  A quantum mechanism of the inertia generation has been proposed. The
threshold of the parametric instability of ``goemetric'' Goldstone modes is
treated as a rest mass.


title:
Tidal Stabilization of Rigidly Rotating, Fully Relativistic Neutron
  Stars

abstract:
  It is shown analytically that an external tidal gravitational field increases
the secular stability of a fully general relativistic, rigidly rotating neutron
star that is near marginal stability, protecting it against gravitational
collapse. This stabilization is shown to result from the simple fact that the
energy $\delta M(Q,R)$ required to raise a tide on such a star, divided by the
square of the tide's quadrupole moment $Q$, is a decreasing function of the
star's radius $R$, $(d/dR)[\delta M(Q,R)/Q^2]<0$ (where, as $R$ changes, the
star's structure is changed in accord with the star's fundamental mode of
radial oscillation). If $(d/dR)[\delta M(Q,R)/Q^2]$ were positive, the tidal
coupling would destabilize the star. As an application, a rigidly rotating,
marginally secularly stable neutron star in an inspiraling binary system will
be protected against secular collapse, and against dynamical collapse, by tidal
interaction with its companion. The ``local-asymptotic-rest-frame'' tools used
in the analysis are somewhat unusual and may be powerful in other studies of
neutron stars and black holes interacting with an external environment. As a
byproduct of the analysis, in an appendix the influence of tidal interactions
on mass-energy conservation is elucidated.


title: The self-screening Hawking atmosphere

abstract:
  A model is proposed in which the Hawking particles emitted by a black hole
are treated as an envelope of matter that obeys an equation of state, and acts
as a source in Einstein's equations. This is a crude but interesting way to
accommodate for the back reaction. For large black holes, the solution can be
given analytically, if the equation of state is $p=\kappa\rho$, with
$0<\kappa<1$. The solution exhibits a singularity at the origin. If we assume
$N$ free particle types, we can use a Hartree-Fock procedure to compute the
contribution of one such field to the entropy, and the result scales as
expected as $1/N$. A slight mismatch is found that could be attributed to
quantum corrections to Einstein's equations, but can also be made to disappear
when $\k$ is set equal to one. The case $\kappa=1$ is further analysed.


title: Foundation of The Two dimensional Quantum Theory of Gravity

abstract:
  The two dimensional substructure of general relativity and gravity, and the
two dimensional geometry of quantum effect by black hole are disclosed. Then
the canonical quantization of the two dimensional theory of gravity is
performed. It is shown that the resulting uncertainty relations can explain
black hole quantum effects. A quantum gravitational length is also derived
which can clarify the origin of Planck length.


title: The random walks of a Schwarzschild black hole

abstract:
  We show that spinless and neutral black holes in thermal equilibrium with
radiation undergo fluctuations of charge and angular momentum. The
corresponding spreads for a black hole in contact with charged scalar particles
is calculated. The angular momentum spread turns out to grow with the size of
the cavity. Charge spread does not depend either on the size of the cavity nor
on the elementary charge of the field. Then, either the scale of the elementary
chage is fixed by black hole physics $\alpha \sim 1/4\pi$ or the underlying
physics of these fluctuations is not the random absorption and emission of
charged particles from the bath, it remains unknown and must be clarified.


title: Adiabatic Invariants and Scalar Fields in a de Sitter Space-Time

abstract:
  The method of adiabatic invariants for time dependent Hamiltonians is applied
to a massive scalar field in a de Sitter space-time. The scalar field ground
state, its Fock space and coherent states are constructed and related to the
particle states. Diverse quantities of physical interest are illustrated, such
as particle creation and the way a classical probability distribution emerges
for the system at late times.


title:
The TIGA technique for detecting gravitational waves with a spherical
  antenna

abstract:
  We report the results of a theoretical and experimental study of a spherical
gravitational wave antenna. We show that it is possible to understand the data
from a spherical antenna with 6 radial resonant transducers attached to the
surface in the truncated icosahedral arrangement. We find that the errors
associated with small deviations from the ideal case are small compared to
other sources of error, such as a finite signal-to-noise ratio. An in situ
measurement technique is developed along with a general algorithm that
describes a procedure for determining the direction of an external force acting
on the antenna, including the force from a gravitational wave, using a
combination of the transducer responses. The practicality of these techniques
was verified on a room-temperature prototype antenna.


title: Singularities inside non-Abelian black holes

abstract:
  Singularities inside static spherically symmetric black holes in the SU(2)
Einstein-Yang-Mills and Einstein-Yang-Mills-dilaton theories are investigated.
Analytical formulas are presented describing oscillatory and power law metric
behavior near spacelike singularities in generic solutions.


title:
Stationary perturbations and infinitesimal rotations of static
  Einstein-Yang-Mills configurations with bosonic matter

abstract:
  Using the Kaluza-Klein structure of stationary spacetimes, a framework for
analyzing stationary perturbations of static Einstein-Yang-Mills configurations
with bosonic matter fields is presented. It is shown that the perturbations
giving rise to non-vanishing ADM angular momentum are governed by a
self-adjoint system of equations for a set of gauge invariant scalar
amplitudes. The method is illustrated for SU(2) gauge fields, coupled to a
Higgs doublet or a Higgs triplet. It is argued that slowly rotating black holes
arise generically in self-gravitating non-Abelian gauge theories with bosonic
matter, whereas, in general, soliton solutions do not have rotating
counterparts.


title: Chaos in the Einstein-Yang-Mills Equations

abstract:
  Yang-Mills color fields evolve chaotically in an anisotropically expanding
universe. The chaotic behaviour differs from that found in anisotropic
Mixmaster universes. The universe isotropizes at late times, approaching the
mean expansion rate of a radiation-dominated universe. However, small chaotic
oscillations of the shear and color stresses continue indefinitely. An
invariant, coordinate-independent characterisation of the chaos is provided by
means of fractal basin boundaries.


title:
Singular Regions in Black Hole Solutions in Higher Order Curvature
  Gravity

abstract:
  Four-dimensional black hole solutions generated by the low energy string
effective action are investigated outside and inside the event horizon. A
restriction for a minimal black hole size is obtained in the frame of the model
discussed. Intersections, turning points and other singular points of the
solution are investigated. It is shown that the position and the behavior of
these particular points are definded by various kinds of zeros of the main
system determinant. Some new aspects of the $r_s$ singularity are discussed.


title: Power-law mass inflation in Einstein-Yang-Mills-Higgs black holes

abstract:
  Analytical formulas are presented describing a generic singularity inside the
static spherically symmetric black holes in the SU(2) Einstein-Yang-Mills-Higgs
theories with triplet or doublet Higgs field. The singularity is spacelike and
exhibits a `power-low mass inflation'. Alternatively this asymptotic may be
interpreted as a pointlike singularity with a non-vanishing shear in the
Kantowski-Sachs anisotropic cosmology.


title: Post-Riemannian Spacetimes Admit a Causal Structure

abstract:
  Paper withdrawn due to conceptual mistakes. A corrected version will soon be
available at the gr-qc archive.


title: Geometrical Formulation of Quantum Mechanics

abstract:
  States of a quantum mechanical system are represented by rays in a complex
Hilbert space. The space of rays has, naturally, the structure of a K\"ahler
manifold. This leads to a geometrical formulation of the postulates of quantum
mechanics which, although equivalent to the standard algebraic formulation, has
a very different appearance. In particular, states are now represented by
points of a symplectic manifold (which happens to have, in addition, a
compatible Riemannian metric), observables are represented by certain
real-valued functions on this space and the Schr\"odinger evolution is captured
by the symplectic flow generated by a Hamiltonian function. There is thus a
remarkable similarity with the standard symplectic formulation of classical
mechanics. Features---such as uncertainties and state vector reductions---which
are specific to quantum mechanics can also be formulated geometrically but now
refer to the Riemannian metric---a structure which is absent in classical
mechanics. The geometrical formulation sheds considerable light on a number of
issues such as the second quantization procedure, the role of coherent states
in semi-classical considerations and the WKB approximation. More importantly,
it suggests generalizations of quantum mechanics. The simplest among these are
equivalent to the dynamical generalizations that have appeared in the
literature. The geometrical reformulation provides a unified framework to
discuss these and to correct a misconception. Finally, it also suggests
directions in which more radical generalizations may be found.


title:
Riemannian and Teleparallel Descriptions of the Scalar Field
  Gravitational Interaction

abstract:
  A comparative study between the metric and the teleparallel descriptions of
gravitation is made for the case of a scalar field. In contrast to the current
belief that only spin matter could detect the teleparallel geometry, scalar
matter being able to feel the metric geometry only, we show that a scalar field
is able not only to feel anyone of these geometries, but also to produce
torsion. Furthermore, both descriptions are found to be completely equivalent,
which means that in fact, besides coupling to curvature, a scalar field couples
also to torsion.


title: On the sources of static plane symmetric vacuum space-times

abstract:
  The static vacuum plane spacetimes are considered, which have two non-trivial
solutions: The Taub solution and the Rindler solution. Imposed reflection
symmetry, we find that the source for the Taub solution does not satisfy any
energy conditions, which is consistent with previous studies, while the source
for the Rindler solution satisfies the weak and strong energy conditions (but
not the dominant one). It is argued that the counterpart of the Einstein theory
to the gravitational field of a massive Newtonian plane should be described by
the Rindler solution, which represents also a uniform gravitational field.


title:
Instability of cosmological event horizons of non-static global cosmic
  strings

abstract:
  The stability of the cosmological event horizons found recently by Gregory
[Phys. Rev. D54, 4955 (1996)] for a class of non-static global cosmic strings
is studied. It is shown that they are not stable to both test particles and
physical perturbations. In particular, the back reaction of the perturbations
of null dust fluids will turn them into spacetime singularities. The resulted
singularities are strong in the sense that the distortion of test particles
diverges logarithmically when these singular hypersurfaces are approaching.


title: Axial instability of rotating relativistic stars

abstract:
  Perturbations of rotating relativistic stars can be classified by their
behavior under parity. For axial perturbations (r-modes), initial data with
negative canonical energy is found with angular dependence $e^{im\phi}$ for all
values of $m\geq 2$ and for arbitrarily slow rotation. This implies instability
(or marginal stability) of such perturbations for rotating perfect fluids. This
low $m$-instability is strikingly different from the instability to polar
perturbations, which sets in first for large values of $m$. The timescale for
the axial instability appears, for small angular velocity $\Omega$, to be
proportional to a high power of $\Omega$. As in the case of polar modes,
viscosity will again presumably enforce stability except for hot, rapidly
rotating neutron stars. This work complements Andersson's numerical
investigation of axial modes in slowly rotating stars.


title: Adiabatic Invariant Treatment of a Collapsing Sphere of Quantized Dust

abstract:
  The semiclassical collapse of a sphere of quantized dust is studied. A
Born-Oppenheimer decomposition is performed for the wave function of the system
and the semiclassical limit is considered for the gravitational part. The
method of adiabatic invariants for time dependent Hamiltonians is then employed
to find (approximate) solutions to the quantum dust equations of motions. This
allows us to obtain corrections to the adiabatic approximation of the dust
states associated with the time evolution of the metric. The diverse
non-adiabatic corrections are generally associated with particle (dust)
creation and related fluctuations. The back-reaction due to the dominant
contribution to particle creation is estimated and seen to slow-down the
collapse.


title: A new class of unstable modes of rotating relativistic stars

abstract:
  The first numerical study of axial (toroidal) pulsation modes of a slowly
rotating relativistic star is presented. The calculation includes terms of
first order in $\epsilon \equiv \Omega \sqrt{R^3/M}<<1$ ($R$ is the radius, $M$
is the mass and $\Omega$ is the rotation frequency of the star), and accounts
for effects due to the coriolis force. Effects due to the centrifugal
flattening of the star enter at order $\epsilon^2$ and are not included in the
analysis. It is shown that increased rotation tends to decrease the damping
times for prograde modes, while retrograde become longer lived. Specifically,
we show that rotation affects the axial gravitational-wave $w$-modes in this
way. We also present the first relativistic calculation of the so-called
$r$-modes (analogous to Rossby waves in the Earth's oceans). These have
frequencies of the same order of magnitude as the rotation frequency of the
star. The presented results indicate that the $r$-modes are unstable due to the
emission of gravitational radiation for \underline{all} rotating perfect fluid
stars. This is interesting since the previously considered gravitational-wave
instability associated with (for example) the $f$-mode of the star sets in at a
critical rotation rate. Because they are unstable also for the slowest rotating
stars the $r$-modes may well be of considerable astrophysical importance.


title: Solutions of Quantum Gravity Coupled to the Scalar Field

abstract:
  We consider the Wheeler-De Witt equation for canonical quantum gravity
coupled to massless scalar field. After regularizing and renormalizing this
equation, we find a one-parameter class of its solutions.


title: Notes On The Born-Oppenheimer Approach In A Closed Dynamical System

abstract:
  The various recent studies on the applications of the Born-Oppenheimer
approach in a closed gravity matter system is examined. It is pointed out that
the Born-Oppenheimer approach in the absence of an a priori time is likely to
yield potentially new results.


title: On a global conformal invariant of initial data sets

abstract:
  In the present paper a global conformal invariant $Y$ of a closed initial
data set is constructed. A spacelike hypersurface $\Sigma$ in a Lorentzian
spacetime naturally inherits from the spacetime metric a differentiation ${\cal
D}_e$, the so-called real Sen connection, which turns out to be determined
completely by the initial data $h_{ab}$ and $\chi_{ab}$ induced on $\Sigma$,
and coincides, in the case of vanishing second fundamental form $\chi_{ab}$,
with the Levi-Civita covariant derivation $D_e$ of the induced metric $h_{ab}$.
$Y$ is built from the real Sen connection ${\cal D}_e$ in the similar way as
the standard Chern-Simons invariant is built from $D_e$. The number $Y$ is
invariant with respect to changes of $h_{ab}$ and $\chi_{ab}$ corresponding to
conformal rescalings of the spacetime metric. In contrast the quantity $Y$
built from the complex Ashtekar connection is not invariant in this sense. The
critical points of our $Y$ are precisely the initial data sets which are
locally imbeddable into conformal Minkowski space.


title: Probing Black Holes and Relativistic Stars with Gravitational Waves

abstract:
  In the coming decade, gravitational waves will convert the study of general
relativistic aspects of black holes and stars from a largely theoretical
enterprise to a highly interactive, observational/theoretical one. For example,
gravitational-wave observations should enable us to observationally map the
spacetime geometries around quiescient black holes, study quantitatively the
highly nonlinear vibrations of curved spacetime in black-hole collisions, probe
the structures of neutron stars and their equation of state, search for exotic
types of general relativistic objects such as boson stars, soliton stars, and
naked singularities, and probe aspects of general relativity that have never
yet been seen such as the gravitational fields of gravitons and the influence
of gravitational-wave tails on radiation reaction.


title: Supersymmetric quantum cosmology for Bianchi class A models

abstract:
  The canonical theory of (N=1) supergravity, with a matrix representation for
the gravitino covector-spinor, is applied to the Bianchi class A spatially
homogeneous cosmologies. The full Lorentz constraint and its implications for
the wave function of the universe are analyzed in detail. We found that in this
model no physical states other than the trivial "rest frame" type occur.


title: Classical and Quantum Shell Dynamics, and Vacuum Decay

abstract:
  Following a minisuperspace approach to the dynamics of a spherically
symmetric shell, a reduced Lagrangian for the radial degree of freedom is
derived directly from the Einstein-Hilbert action. The key feature of this new
Lagrangian is its invariance under time reparametrization. Indeed, all
classical and quantum dynamics is encoded in the Hamiltonian constraint that
follows from that invariance. Thus, at the classical level, we show that the
Hamiltonian constraint reproduces, in a simple gauge, Israel's matching
condition which governs the evolution of the shell. In the quantum case, the
vanishing of the Hamiltonian (in a weak sense), is interpreted as the
Wheeler-DeWitt equation for the physical states, in analogy to the
corresponding case in quantum cosmology. Using this equation, quantum tunneling
through the classical barrier is then investigated in the WKB approximation,
and the connection to vacuum decay is elucidated.


title:
Propagation Speed of Longitudinally Oscillating Gravitational and
  Electrical Fields

abstract:
  The near-field Lienard-Wiechert potential solution of a longitudinally
oscillating electrical field produced by an oscillating charge is presented,
and the results are compared to the R. P. Feynman multipole far-field solution.
The results indicate that the phase speed of a longitudinally oscillating
electrical field is much faster than the speed of light in the near field. A
similar analysis is presented for a longitudinally oscillating gravitational
field produced by a vibrating mass. The result also indicates that the phase
speed of a longitudinally oscillating gravitational field is also much faster
than the speed of light in the near-field. The possibility of measuring the
group speed of a longitudinally oscillating electrical field and a
longitudinally oscillating gravitational field, which is commonly thought to be
equal to the speed of light, is now being considered. The basic idea is to
amplitude-modulate the longitudinal vibration of a charge or a mass and to
measure the resultant longitudinal vibration of a nearby charge or a mass due
to electrical or gravitational interaction. The modulation signal can then be
extracted using a diode detector and the group speed can then be determined
from the oscillation frequency, the separation distance between the masses, and
the measurement of the phase shift of the modulation signal. If the group speed
is equal to the speed of light, then phase shifts on the order of 1 microdegree
could be generated with a typical experimental set-up. An analysis using the
classical definition of group velocity for a longitudinally oscillating
electrical field is presented, and the results indicate that the group speed is
also much faster that the speed of light in the near field, which should not be
possible due to causality violation.


title: Physically valid black-hole interior models

abstract:
  New, simple models of ``black hole interiors'', namely spherically symmetric
solutions of the Einstein field equations in matter matching the Schwarzschild
vacuum at spacelike hypersurfaces ``R<2M'' are constructed. The models satisfy
the weak energy condition and their matter content is specified by an equation
of state of the elastic type.


title: Effective dynamics of self-gravitating extended objects

abstract:
  We introduce an effective Lagrangian which describes the classical and
semiclassical dynamics of spherically symmetric, self-gravitating objects that
may populate the Universe at large and small (Planck) scale. These include
wormholes, black holes and inflationary bubbles. We speculate that such objects
represent some possible modes of fluctuation in the primordial spacetime foam
out of which our universe was born. Several results obtained by different
methods are encompassed and reinterpreted by our effective approach. As an
example, we discuss: i) the gravitational nucleation coefficient for a pair of
Minkowski bubbles, and ii) the nucleation coefficient of an inflationary vacuum
bubble in a Minkowski background


title: Combinatorial Tools for Regge Calculus

abstract:
  In this short note we briefly review some recent mathematical results
relevant to the classical Regge Calculus evolution problem.


title: Lax pair tensors and integrable spacetimes

abstract:
  The use of Lax pair tensors as a unifying framework for Killing tensors of
arbitrary rank is discussed. Some properties of the tensorial Lax pair
formulation are stated. A mechanical system with a well-known Lax
representation -- the three-particle open Toda lattice -- is geometrized by a
suitable canonical transformation. In this way the Toda lattice is realized as
the geodesic system of a certain Riemannian geometry. By using different
canonical transformations we obtain two inequivalent geometries which both
represent the original system. Adding a timelike dimension gives
four-dimensional spacetimes which admit two Killing vector fields and are
completely integrable.


title: A Derivation of Three-Dimensional Inertial Transformations

abstract:
  The derivation of the transformations between inertial frames made by
Mansouri and Sexl is generalised to three dimensions for an arbitrary direction
of the velocity. Assuming lenght contraction and time dilation to have their
relativistic values, a set of transformations kinematically equivalent to
special relativity is obtained. The ``clock hypothesis'' allows the derivation
to be extended to accelerated systems. A theory of inertial transformations
maintaining an absolute simultaneity is shown to be the only one logically
consistent with accelerated movements. Algebraic properties of these
transformations are discussed. Keywords: special relativity, synchronization,
one-way velocity of light, ether, clock hypothesis.


title: About Synchronisation of Clocks in Free Fall Around a Central Body

abstract:
  The conventional nature of synchronisation is discussed in inertial frames,
where it is found that theories using different synchronisations are
experimentally equivalent to special relativity. In contrary, in accelerated
systems only a theory maintaining an absolute simultaneity is consistent with
the natural behaviour of clocks. The principle of equivalence is discussed, and
it is found that any synchronisation can be used locally in a freely falling
frame. Whatever the choosen synchronisation, the first derivatives of the
metric tensor disapear and a geodesic is locally a straight line. But it is
shown that only a synchronisation maintaining an absolute simultaneity allows
to define time consistently on circular orbits of a Schwarzschild metric. Key
words: special and general relativity, synchronisation, one-way velocity of
light, ether, principle of equivalence.


title: Quantum Evaporating Black Holes in Higher Dimensions

abstract:
  We study an $N + 1$ dimensional generalization of the Schwarzschild black
hole from the quantum mechanical viewpoint. It is shown that the mass loss rate
of this higher dimensional black hole due to the black hole radiation is
proportional to $1 \over r^{N-1}$ where $r$ is the radial coordinate. This fact
implies that except in four dimensions the quantum formalism developed in this
letter gives a different result with respect to the mass loss rate from the
semiclassical formalism where the Stefan-Bolzmann formula for a blackbody
radiation is used. As shown previously in the study of the four dimensional
Schwarzschild metric, the wave function in this case has also quite curious
features that it is singular owing to strong quantum fluctuation of the
gravitational field at the singularity while completely regular in the other
regions of the spacetime.


title: Quantum fluctuations in the open universe

abstract:
  We solve a continuing controversy when dealing with density fluctuations in
open Friedman-Robertson-Walker universes, on the physical relevance of a class
of exponential modes. We show explicitly and rigorously that these modes enter
the expansion of quantum fields. In the maximally symmetric de Sitter case,
encountered in inflationary models, they are excited for fields with mass below
a critical value. They are seen to be responsible for the breaking of the de
Sitter symmetry for a massless field. We provide an exact calculation of the
power spectrum for any mass. Our method is free of the divergences that appear
in earlier treatments. We extend the construction to a generic open FRW
universe.


title: Gravity on parallelizable manifold

abstract:
  General relativity postulates that the gravity field is defined on a
Riemannian manifold. The field equations are $R^\mu_\nu = 0$ i.e. Ricci's
curvature tensor vanishes. The field equations have to be augmented by natural
physical requirements like orientability, time orientability and existence of a
spinorial structure. Moreover, it is impossible to define the energy of the
gravity field only by the metric tensor. We suggest to impose an additional
structure and consider parallelizable manifold i.e. manifolds for which a
smooth field of frames exists. The derivation of the field equations is by an
action principle. A Lagrangian, which is quadratic in the differentials, is
defined. The minimum of the action is achieved at a $16 \times 16$ second order
quasi linear system. It is of Laplacian type. The system admits a unique exact
solution for a centrally symmetric, static and assimptotically flat field. The
resulting metric is the celebrated Rosen metric, which is very close to the
Schwarzchild metric. The two are intrinsicly different since the scalar
curvature of the Schuarzschild metric is zero, in contrast to Rosen's which is
positive. The suggested field admits black holes which are briefly discussed.


title:
Canonical Quantum Statistics of an Isolated Schwarzschild Black Hole
  with a Spectrum E_n = sigma sqrt{n} E_P

abstract:
  Many authors - beginning with Bekenstein - have suggested that the energy
levels E_n of a quantized isolated Schwarzschild black hole have the form E_n =
sigma sqrt{n} E_P, n=1,2,..., sigma =O(1), with degeneracies g^n. In the
present paper properties of a system with such a spectrum, considered as a
quantum canonical ensemble, are discussed: Its canonical partition function
Z(g,beta=1/kT), defined as a series for g<1, obeys the 1-dimensional heat
equation. It may be extended to values g>1 by means of an integral
representation which reveals a cut of Z(g,beta) in the complex g-plane from g=1
to infinity. Approaching the cut from above yields a real and an imaginary part
of Z. Very surprisingly, it is the (explicitly known) imaginary part which
gives the expected thermodynamical properties of Schwarzschild black holes:
Identifying the internal energy U with the rest energy Mc^2 requires beta to
have the value (in natural units) beta = 2M(lng/sigma^2)[1+O(1/M^2)], (4pi
sigma^2=lng gives Hawking's beta_H), and yields the entropy S=[lng/(4pi
sigma^2)] A/4 + O(lnA), where A is the area of the horizon.


title: Quantum tetrahedra and simplicial spin networks

abstract:
  A new link between tetrahedra and the group SU(2) is pointed out: by
associating to each face of a tetrahedron an irreducible unitary SU(2)
representation and by imposing that the faces close, the concept of quantum
tetrahedron is seen to emerge. The Hilbert space of the quantum tetrahedron is
introduced and it is shown that, due to an uncertainty relation, the ``geometry
of the tetrahedron'' exists only in the sense of ``mean geometry''. A
kinematical model of quantum gauge theory is also proposed, which shares the
advantages of the Loop Representation approach in handling in a simple way
gauge- and diff-invariances at a quantum level, but is completely
combinatorial. The concept of quantum tetrahedron finds a natural application
in this model, giving a possible intepretation of SU(2) spin networks in terms
of geometrical objects.


title: Charged Black Cosmic String

abstract:
  Global U(1) strings with cylindrical symmetry are studied in anti-de Sitter
spacetime. According as the magnitude of negative cosmological constant, they
form regular global cosmic strings, extremal black cosmic strings and charged
black cosmic strings, but no curvature singularity is involved. The
relationship between the topological charge of a neutral global string and the
black hole charge is clarified by duality transformation. Physical relevance as
straight string is briefly discussed.


title: Black Holes

abstract:
  Lecture notes for a 'Part III' course 'Black Holes' given in DAMTP,
Cambridge. The course covers some of the developments in Black Hole physics of
the 1960s and 1970s.


title: Internal thermal noise in the LIGO test masses : a direct approach

abstract:
  The internal thermal noise in LIGO's test masses is analyzed by a new
technique, a direct application of the Fluctuation-Dissipation Theorem to
LIGO's readout observable, $x(t)=$(longitudinal position of test-mass face,
weighted by laser beam's Gaussian profile). Previous analyses, which relied on
a normal-mode decomposition of the test-mass motion, were valid only if the
dissipation is uniformally distributed over the test-mass interior, and they
converged reliably to a final answer only when the beam size was a
non-negligible fraction of the test-mass cross section. This paper's direct
analysis, by contrast, can handle inhomogeneous dissipation and arbitrary beam
sizes. In the domain of validity of the previous analysis, the two methods give
the same answer for $S_x(f)$, the spectral density of thermal noise, to within
expected accuracy. The new analysis predicts that thermal noise due to
dissipation concentrated in the test mass's front face (e.g. due to mirror
coating) scales as $1/r_0^2$, by contrast with homogeneous dissipation, which
scales as $1/r_0$ ($r_0$ is the beam radius); so surface dissipation could
become significant for small beam sizes.


title:
Charged particle trajectories in a toroidal magnetic and
  rotation-induced electric field around a black hole

abstract:
  Trajectories of charged particle in combined poloidal, toroidal magnetic
field and rotation-induced unipolar electric field superposed in Schwarzschild
background geometry have been investigated extensively in the context of
accreting black holes. The main purpose of the paper is to obtain a reasonably
well insight on the effect of spacetime curvature to the electromagnetic field
surrounding black holes. The coupled equations of motion have been solved
numerically and the results have been compared with that for flat spacetime. It
is found that the toroidal magnetic field dominates the induced electric field
in determining the motion of charged particles in curved spacetime. The
combined electromagnetic field repels a charged particle from the vicinity of a
compact massive object and deconfines the particle from its orbit. In the
absence of toroidal magnetic field the particle is trapped in a closed orbit.
The major role of gravitation is to reduce the radius of gyration significantly
while the electric field provides an additional force perpendicular to the
circular orbit. Although the effect of inertial frame dragging and the effect
of magnetospheric plasma have been neglected, the results provide a reasonably
well qualitative picture of the important role played by gravitation in
modifying the electromagnetic field near accreting black holes and hence the
results have potentially important implications on the dynamics of the fluid
and the radiation spectrum associated with accreting black holes.


title: Geometry of nonextreme black holes near the extreme state

abstract:
  Nonextreme black hole in a cavity can achieve the extreme state with a zero
surface gravity at a finite temperature on a boundary, the proper distance
between the boundary and the horizon being finite. The classical geometry in
this state is found explicitly for four-dimensional spherically-symmetrical and
2+1 rotating holes. In the first case the limiting geometry depends only on one
scale factor and the whole Euclidean manifold is described by the
Bertotti-Robinson spacetime. The general structure of a metric in the limit
under consideration is also found with quantum corrections taken into account.
Its angular part represents two-sphere of a constant radius. In all cases the
Lorentzian counterparts of the metrics are free from singularities.


title:
An Isolated Gravitational Dipole Moment Placed at The Center of the Two
  Mass Pole Model Universe

abstract:
  The unexpected dynamic shift of the center of mass for a rotating hemisphere
is shown to produce the general relativistic dipole field in the macroscopic
scale. This prompts us the question of what might be its cosmological
implications. The uniformly rotating sphere has the effect of the latitude
dependent mass density distribution as reported by Bass and Pirani which is the
cause of the `induced centrifugal force' in the Thirring's geodesic equation
near the center of the rotating spherical mass shell. On the other hand, one
would expect the constant acceleration of the mass components may cause a
general relativistic gravitational field. The component-wise accumulation of
this effect has been shown to appear as the non zero gravitational dipole
moment in a rotating hemispherical mass shell. The present report discusses
this non-Newtonian force experienced by a gravitational dipole moment placed at
the center of the two mass pole model universe and its relevance to the
observed anomalous red shift from far away galaxies.


title: Regularization of the Teukolsky Equation for Rotating Black Holes

abstract:
  We show that the radial Teukolsky equation (in the frequency domain) with
sources that extend to infinity has well-behaved solutions. To prove that, we
follow Poisson approach to regularize the non-rotating hole, and extend it to
the rotating case. To do so we use the Chandrasekhar transformation among the
Teukolsky and Regge-Wheeler-like equations, and express the integrals over the
source in terms of solutions to the homogeneous Regge-Wheeler-like equation, to
finally regularize the resulting integral. We then discuss the applicability of
these results.


title: Density perturbations with relativistic thermodynamics

abstract:
  We investigate cosmological density perturbations in a covariant and
gauge-invariant formalism, incorporating relativistic causal thermodynamics to
give a self-consistent description. The gradient of density inhomogeneities
splits covariantly into a scalar part, equivalent to the usual density
perturbations, a rotational vector part that is determined by the vorticity,
and a tensor part that describes the shape. We give the evolution equations for
these parts in the general dissipative case. Causal thermodynamics gives
evolution equations for viscous stress and heat flux, which are coupled to the
density perturbation equation and to the entropy and temperature perturbation
equations. We give the full coupled system in the general dissipative case, and
simplify the system in certain cases. A companion paper uses the general
formalism to analyze damping of density perturbations before last scattering.


title: Dilaton black holes in grand canonical ensemble near the extreme state

abstract:
  Dilaton black holes with a pure electric charge are considered in a framework
of a grand canonical ensemble near the extreme state. It is shown that there
exists such a subset of boundary data that the Hawking temperature smoothly
goes to zero to an infinite value of a horizon radius but the horizon area and
entropy are finite and differ from zero. In string theory the existence of a
horizon in the extreme limit is due to the finiteness of a system only.


title:
Lagrangian and Hamiltonian formalism for discontinuous fluid and
  gravitational field

abstract:
  The barotropic ideal fluid with step and delta-function discontinuities
coupled to Einstein's gravity is studied. The discontinuities represent star
surfaces and thin shells; only non-intersecting discontinuity hypersurfaces are
considered. No symmetry (like eg. the spherical symmetry) is assumed. The
symplectic structure as well as the Lagrangian and the Hamiltonian variational
principles for the system are written down. The dynamics is described
completely by the fluid variables and the metric on the fixed background
manifold. The Lagrangian and the Hamiltonian are given in two forms: the volume
form, which is identical to that corresponding to the smooth system, but
employs distributions, and the surface form, which is a sum of volume and
surface integrals and employs only smooth variables. The surface form is
completely four- or three-covariant (unlike the volume form). The spacelike
surfaces of time foliations can have a cusp at the surface of discontinuity.
Geometrical meaning of the surface terms in the Hamiltonian is given. Some of
the constraint functions that result from the shell Hamiltonian cannot be
smeared so as to become differentiable functions on the (unconstrained) phase
space. Generalization of the formulas to more general fluid is straifgtforward.


title:
Rotating dust solutions of Einstein's equations with 3-dimensional
  symmetry groups, Part 3: All Killing fields linearly independent of
  u^{\alpha} and w^{\alpha}

abstract:
  This is the third and last part of a series of 3 papers. Using the same
method and the same coordinates as in parts 1 and 2, rotating dust solutions of
Einstein's equations are investigated that possess 3-dimensional symmetry
groups, under the assumption that each of the Killing vectors is linearly
independent of velocity $u^{\alpha}$ and rotation $w^{\alpha}$ at every point
of the spacetime region under consideration. The Killing fields are found and
the Killing equations are solved for the components of the metric tensor in
every case that arises. No progress was made with the Einstein equations in any
of the cases, and no previously known solutions were identified. A brief
overview of literature on solutions with rotating sources is given.


title: A fully covariant description of CMB anisotropies

abstract:
  Starting from the exact non-linear description of matter and radiation, a
fully covariant and gauge-invariant formula for the observed temperature
anisotropy of the cosmic microwave background (CBR) radiation, expressed in
terms of the electric ($E_{ab}$) and magnetic ($H_{ab}$) parts of the Weyl
tensor, is obtained by integrating photon geodesics from last scattering to the
point of observation today. This improves and extends earlier work by Russ et
al where a similar formula was obtained by taking first order variations of the
redshift. In the case of scalar (density) perturbations, $E_{ab}$ is related to
the harmonic components of the gravitational potential $\Phi_k$ and the usual
dominant Sachs-Wolfe contribution $\delta T_R/\bar{T}_R\sim\Phi_k$ to the
temperature anisotropy is recovered, together with contributions due to the
time variation of the potential (Rees-Sciama effect), entropy and velocity
perturbations at last scattering and a pressure suppression term important in
low density universes. We also explicitly demonstrate the validity of assuming
that the perturbations are adiabatic at decoupling and show that if the surface
of last scattering is correctly placed and the background universe model is
taken to be a flat dust dominated Friedmann-Robertson-Walker model (FRW), then
the large scale temperature anisotropy can be interpreted as being due to the
motion of the matter relative to the surface of constant temperature which
defines the surface of last scattering on those scales.


title: Group theoretical derivation of Liouville action for Regge surfaces

abstract:
  We show that the structure of the Liouville action on a two dimensional Regge
surface of the topology of the sphere and of the torus is determined by the
invariance under the transformations induced by the conformal Killing vector
fields and under modular transformations.


title: Quantum effects in the Alcubierre warp drive spacetime

abstract:
  The expectation value of the stress-energy tensor of a free conformally
invariant scalar field is computed in a two-dimensional reduction of the
Alcubierre ``warp drive'' spacetime. The stress-energy is found to diverge if
the apparent velocity of the spaceship exceeds the speed of light. If such
behavior occurs in four dimensions, then it appears implausible that ``warp
drive'' behavior in a spacetime could be engineered, even by an arbitrarily
advanced civilization.


title: Vacuum static Brans-Dicke wormhole

abstract:
  A simple Lorentzian vacuum wormhole solution of Brans-Dicke gravitation is
presented and analysed. It is shown that such solution holds for both, the
Brans-Dicke theory endowed with torsion (for a value of the coupling parameter
$\omega > 1/2$) and for the vacuum -no torsion- case (for $\omega < -2$).


title:
Constraints on Black Holes in Classical and Semiclassical Theories of
  Gravity

abstract:
  Constraints on the geometry of a static spherically symmetric black hole are
obtained by requiring the spacetime curvature to be analytic at the event
horizon. For a zero temperature black hole further constraints are obtained by
also requiring that the semiclassical trace equation be satisfied when
conformally invariant fields are present. It is found that zero temperature
black holes whose sizes lie within a certain range do not exist. The range
depends on the numbers and types of conformally invariant quantized fields that
are present.


title: Black holes with short hair

abstract:
  We present spherically symmetric black hole solutions for Einstein gravity
coupled to anisotropic matter. We show that these black holes have arbitrarily
short hair, and argue for stability by showing that they can arise from
dynamical collapse. We also show that a recent `no short hair' theorem does not
apply to these solutions.


title: Resonant transducers for a spherical Gravitational Wave antenna

abstract:
  Motion sensing in a spherical GW detector requires a multiple set of
transducers attached to its surface at suitable locations. If transducers are
of the resonant type then their motion couples to that of the sphere and the
joint dynamics of the system has to be properly understood before reliable
conclusions can be drawn from its readout. In this paper we address the problem
of the coupled motion of a sphere and a set of resonators attached to it at
arbitrary points. A remarkably elegant and powerful scheme emerges from the
general equations which shows how coupling takes place as a power series in the
small coupling constant ratio m(resonator)/M(sphere). We reasses in the new
light the response of the highly symmetric TIGA and also present a new proposal
(called PHC) which has less symmetry but which is based on 5 rather than 6
transducers per quadrupole mode sensed. We finally assess how the system
charac- teristics are affected by slight departures from ideality, and find it
to be quite robust to them. In particular we recover with full accuracy the
reportedly measured frequencies of the LSU prototype TIGA.


title: Distributional Energy-Momentum Densities of Schwarzschild Space-Time

abstract:
  For Schwarzschild space-time, distributional expressions of energy-momentum
densities and of scalar concomitants of the curvature tensors are examined for
a class of coordinate systems which includes those of the Schwarzschild and of
Kerr-Schild types as special cases. The energy-momentum density $\tilde
T_\mu^{\nu}(x)$ of the gravitational source and the gravitational
energy-momentum pseudo-tensor density $\tilde t_\mu^{\nu}$ have the expressions
$\tilde T_\mu^{\nu}(x) =-Mc^2\delta_\mu^0\delta_0^{\nu} \delta^{(3)}x)$ and
$\tilde t_\mu^{\nu}=0$, respectively. In expressions of the curvature squares
for this class of coordinate systems, there are terms like
$\delta^{(3)}(x)/r^3$ and $[\delta^{(3)}(x)}]^2$, as well as other terms, which
are singular at $x=0$. It is pointed out that the well-known expression
$R^{\rho\sigma\mu\nu}({}) R_{\rho\sigma\mu\nu}({})$ $=48G^{2}M^{2}/c^{4}r^{6}$
is not correct, if we define $1/r^6 = \lim_{\epsilon\to
0}1/(r^2+\epsilon^2)^3$.}


title: Observables of the Euclidean Supergravity

abstract:
  The set of constraints under which the eigenvalues of the Dirac operator can
play the role of the dynamical variables for Euclidean supergravity is derived.
These constraints arise when the gauge invariance of the eigenvalues of the
Dirac operator is imposed. They impose conditions which restrict the
eigenspinors of the Dirac operator.


title: Dyonic Black Holes and Related Solitons

abstract:
  There is a growing literature on dyonic black holes as they appear in string
theory. Here we examine the correspondence limit of a dyonic black hole which
is not supersymmetric. Assuming the existence of a dyon with non-supersymmetric
Kerr-Schild structure, we calculate its gravitational and electromagnetic
fields and compute its mass and angular momentum to obtain a modified B.P.S.
relation. The contributionn of the angular momentum to the mass appears in the
condition for the appearance of a horizon.


title:
Constants of motion and the conformal anti - de Sitter algebra in
  (2+1)-Dimensional Gravity

abstract:
  Constants of motion are calculated for 2+1 dimensional gravity with topology
R x T^2 and negative cosmological constant. Certain linear combinations of them
satisfy the anti - de Sitter algebra so(2,2) in either ADM or holonomy
variables. Quantisation is straightforward in terms of the holonomy parameters.
On inclusion of the Hamiltonian three new global constants are derived and the
quantum algebra extends to that of the conformal algebra so(2,3). The modular
group appears as a discrete subgroup of the conformal group. Its quantum action
is generated by these conserved quantities.


title: Exact Perturbations for inflation with smooth exit

abstract:
  Toy models for the Hubble rate or the scalar field potential have been used
to analyze the amplification of scalar perturbations through a smooth
transition from inflation to the radiation era. We use a Hubble rate that
arises consistently from a decaying vacuum cosmology, which evolves smoothly
from nearly de Sitter inflation to radiation domination. We find exact
solutions for super-horizon perturbations (scalar and tensor), and for
sub-horizon perturbations in the vacuum- and radiation-dominated eras. The
standard conserved quantity for super-horizon scalar perturbations is exactly
constant for growing modes, and zero for the decaying modes.


title: Testing string cosmology with gravity wave detectors

abstract:
  The general properties of the gravity wave backgrounds of cosmological origin
are reviewed and briefly discussed, with emphasis on the relic background
expected from an early pre-big bang phase typical of string cosmology models.


title:
Cosmological Perturbations seeded by Topological Defects: Setting the
  Initial Conditions

abstract:
  We consider a perfectly homogeneous and isotropic universe which undergoes a
sudden phase transition. If the transition produces topological defects, which
we assume, perturbations in the geometry and the cosmic fluid also suddenly
appear. We apply the standard general relativistic junction conditions to match
the pre- and post- transition eras and thus set the initial conditions for the
perturbations. We solve their evolution equations analytically in the case when
the defects act as a coherent source and their density scales like the
background density. We show that isocurvature as well as adiabatic
perturbations are created, in a ratio which is independent of the detailed
properties of the defects. We compare our result to the initial conditions
currently used in the literature and show how the cosmic fluid naturally
"compensates" for the presence of the defects.


title: Black Holes and Wormholes in 2+1 Dimensions

abstract:
  A large variety of spacetimes---including the BTZ black holes---can be
obtained by identifying points in 2+1 dimensional anti-de Sitter space by means
of a discrete group of isometries. We consider all such spacetimes that can be
obtained under a restriction to time symmetric initial data and one asymptotic
region only. The resulting spacetimes are non-eternal black holes with
collapsing wormhole topologies. Our approach is geometrical, and we discuss in
detail: The allowed topologies, the shape of the event horizons, topological
censorship and trapped curves.


title: Homothetic Wyman Spacetimes

abstract:
  The time-dependent, spherically symmetric, Wyman sector of the Unified Field
Theory is shown to be equivalent to a self-gravitating scalar field with a
positive-definite, repulsive self-interaction potential. A homothetic symmetry
is imposed on the fundamental tensor, and the resulting autonomous system is
numerically integrated. Near the critical point (between the collapsing and
non-collapsing spacetimes) the system displays an approximately periodic
alternation between collapsing and dispersive epochs.


title: Issues in Quantum-Geometric Propagation

abstract:
  A discussion of relativistic quantum-geometric mechanics on phase space and
its generalisation to the propagation of free, massive, quantum-geometric
scalar fields on curved spacetimes is given. It is shown that in an arbitrary
coordinate system and frame of reference in a flat spacetime, the resulting
propagator is necessarily the same as derived in the standard Minkowski
coordinates up to a Lorentz boost acting on the momentum content of the field,
which is therefore seen to play the role of Bogolubov transformations in this
formalism. These results are explicitly demonstrated in the context of a Milne
universe.


title:
Canonical General Relativity: the Diffeomorphism constraints and Spatial
  Frame Transformations

abstract:
  Einstein's general relativity with both metric and vielbein treated as
independent fields is considered, demonstrating the existence of a consistent
variational principle and deriving a Hamiltonian formalism that treats the
spatial metric and spatial vielbein as canonical coordinates. This results in a
Hamiltonian in standard form that consists of Hamiltonian and momentum
constraints as well as constraints that generate spatial frame
transformations---all appearing as primary, first class constraints on phase
space. The formalism encompasses the standard coordinate frame and vielbein
approaches to general relativity, and the constraint algebra derived herein
reproduces known results in either limit.


title: Global Monopoles in Brans-Dicke Theory of Gravity

abstract:
  The gravitational field of a global monopole in the context of Brans-Dicke
theory of gravity is investigated. The space-time and the scalar field
generated by the monopole are obtained by solving the field equations in the
weak field approximation. A comparison is made with the corresponding results
predicted by General Relativity.


title:
Spherical neutron star collapse toward a black hole in tensor-scalar
  theory of gravity

abstract:
  Complete tensor-scalar and hydrodynamic equations are presented and
integrated, for a self-gravitating perfect fluid. The initial conditions
describe unstable-equilibrium neutron star configuration, with a polytropic
equation of state. They are necessary in order to follow the gravitational
collapse (including full hydrodynamics) of this star toward a black hole and to
study the resulting scalar gravitational wave. The amplitude of this wave, as
well as the radiated energy dramatically increase above some critical value of
the parameter of the coupling function, due to the spontaneous scalarization,
an effect not present in Brans-Dicke theory. In most cases, the pressure of the
collapsing fluid does not have a significant impact on the resulting signal.
These kind of sources are not likely to be observed by future laser
interferometric detectors (such as VIRGO or LIGO) of gravitational waves, if
they are located at more than a few 100 kpc. However, spontaneous scalarization
could be constrained if such a gravitational collapse is detected by its
quadrupolar gravitational signal, since this latter is quite lower than the
monopolar one.


title: Non-Commutative Black Hole Algebra and String Theory from Gravity

abstract:
  We generalize the action found by 't Hooft, which describes the gravitational
interaction between ingoing and outgoing particles in the neighbourhood of a
black hole. The effect of this back-reaction is that of a shock wave, and it
provides a mechanism for recovering information about the momentum of the
incoming particles. The new action also describes particles with transverse
momenta and takes into account the transverse curvature of the hole, and has
the form of a string theory action. Apart from the Polyakov term found by 't
Hooft, we also find an antisymmetric tensor, which is here related to the
momentum of the particles. At the quantum level, the identification between
position and momentum operators leads to four non-commuting coordinates. A
certain relation to M(atrix) theory is proposed.


title:
Anisotropy of the Cosmic Background Radiation implies the Violation of
  the Strong Energy Condition in Bianchi type I Universe

abstract:
  We consider the horizon problem in a homogeneous but anisotropic universe
(Bianchi type I). We show that the problem cannot be solved if (1) the matter
obeys the strong energy condition with the positive energy density and (2) the
Einstein equations hold. The strong energy condition is violated during
cosmological inflation.


title: On the M{\o}ller's energy complex of the charged dilaton black hole

abstract:
  Using M{\o}ller's energy complex, we obtain the energy distributions of GHS
solution and dyonic dilaton black hole solution in the dilaton gravity theory.
It is confirmed that the M{\o}ller's energy complex is indeed a 3-scalar under
purely spatial transformation in these energy distributions. Some interested
properties of the energy distribution of dyonic black hole are disscussed.


title:
Static Axially Symmetric Einstein-Yang-Mills-Dilaton Solutions:
  I.Regular Solutions

abstract:
  We discuss the static axially symmetric regular solutions, obtained recently
in Einstein-Yang-Mills and Einstein-Yang-Mills-dilaton theory [1]. These
asymptotically flat solutions are characterized by the winding number $n>1$ and
the node number $k$ of the purely magnetic gauge field. The well-known
spherically symmetric solutions have winding number $n=1$. The axially
symmetric solutions satisfy the same relations between the metric and the
dilaton field as their spherically symmetric counterparts. Exhibiting a strong
peak along the $\rho$-axis, the energy density of the matter fields of the
axially symmetric solutions has a torus-like shape. For fixed winding number
$n$ with increasing node number $k$ the solutions form sequences. The sequences
of magnetically neutral non-abelian axially symmetric regular solutions with
winding number $n$ tend to magnetically charged abelian spherically symmetric
limiting solutions, corresponding to ``extremal'' Einstein-Maxwell-dilaton
solutions for finite values of $\gamma$ and to extremal Reissner-Nordstr\o m
solutions for $\gamma=0$, with $n$ units of magnetic charge.


title:
Solving the Hamilton-Jacobi equation for gravitationally interacting
  electromagnetic and scalar fields

abstract:
  The spatial gradient expansion of the generating functional was recently
developed by Parry, Salopek, and Stewart to solve the Hamiltonian constraint in
Einstein-Hamilton-Jacobi theory for gravitationally interacting dust and scalar
fields. This expansion is used here to derive an order-by-order solution of the
Hamiltonian constraint for gravitationally interacting electromagnetic and
scalar fields. A conformal transformation and functional integral are used to
derive the generating functional up to the terms fourth order in spatial
gradients. The perturbations of a flat Friedmann-Robertson-Walker cosmology
with a scalar field, up to second order in spatial gradients, are given. The
application of this formalism is demonstrated in the specific example of an
exponential potential.


title:
Cosmological perturbation theory and conserved quantities in the
  large-scale limit

abstract:
  The linear cosmological perturbation theory of an almost homogeneous and
isotropic perfect fluid universe is reconsidered and formally simplified by
introducing new covariant and gauge-invariant variables with physical
interpretations on hypersurfaces of constant expansion, constant curvature or
constant energy density. The existence of conserved perturbation quantities on
scales larger than the Hubble scale is discussed. The quantity which is
conserved on large scales in a flat background universe may be expressed in
terms of the fractional, spatial gradient of the energy density on constant
expansion hypersurfaces or, alternatively, with the help of expansion or
curvature perturbation variables on hypersurfaces of constant energy density.
For nonvanishing background curvature the perturbation dynamics is most
suitably described in terms of energy density perturbations on hypersurfaces of
constant curvature.


title: The Quaternionic Geometry of 4D Conformal Field Theory

abstract:
  We show that 4--dimensional conformal field theory is most naturally
formulated on Kulkarni 4--folds, i. e. real 4--folds endowed with an integrable
quaternionic structure. This leads to a formalism that parallels very closely
that of 2--dimensional conformal field theory on Riemann surfaces. In this
framework, the notion of Fueter analyticity, the quaternionic analogue of
complex analyticity, plays an essential role. Conformal fields appear as
sections of appropriate either harmonic real or Fueter holomorphic quaternionic
line bundles. In the free case, the field equations are statements of either
harmonicity or Fueter holomorphicity of the relevant conformal fields. We
obtain compact quaternionic expressions of such basic objects as the
energy-momentum tensor and the gauge currents for some basic models in terms of
Kulkarni geometry. We also find a concise expression of the conformal anomaly
and a quaternionic 4--dimensional analogue of the Schwarzian derivative
describing the covariance of the quantum energy-momentum tensor. Finally, we
analyse the operator product expansions of free fields.


title: Gravitational waves with distinct wavefronts

abstract:
  Exact solutions of Einstein's vacuum equations are considered which describe
gravitational waves with distinct wavefronts. A family of such solutions
presented recently in which the wavefronts have various geometries and which
propagate into a number of physically significant backgrounds is here related
to an integral representation which is a generalisation of the Rosen pulse
solution for cylindrical waves. A nondiagonal solution is also constructed
which is a generalisation of the Rosen pulse, being a cylindrical pulse wave
with two states of polarization propagating into a Minkowski background. The
solution is given in a complete and explicit form. A further generalisation to
include electromagnetic waves with a distinct wavefront of the same type is
also discussed.


title: Pseudo-spectral apparent horizon finders: an efficient new algorithm

abstract:
  We review the problem of finding an apparent horizon in Cauchy data (Sigma,
g_ab, K_ab) in three space dimensions without symmetries. We describe a family
of algorithms which includes the pseudo-spectral apparent horizon finder of
Nakamura et al. and the curvature flow method proposed by Tod as special cases.
We suggest that other algorithms in the family may combine the speed of the
former with the robustness of the latter. A numerical implementation for Cauchy
data given on a grid in Cartesian coordinates is described, and tested on
Brill-Lindquist and Kerr initial data. The new algorithm appears faster and
more robust than previous ones.


title: Chaos in Robertson-Walker Cosmology

abstract:
  Chaos in Robertson-Walker cosmological models where gravity is coupled to one
or more scalar fields has been studied by a few authors, mostly using numerical
simulations. In this paper we begin a systematic study of the analytical
aspect. We consider one conformally coupled scalar field and, using the fact
that the model is integrable when the field is massless, we show in detail how
homoclinic chaos arises for nonzero masses using a perturbative method.


title: Can neutrino vacuum support the wormhole?

abstract:
  The renormalised vacuum expectation values of massless fermion
(conventionally call it neutrino) stress-energy tensor are calculated in the
static spherically-symmetrical wormhole topology. Consider the case when the
derivatives of metric tensor over radial distance are sufficiently small (in
the scale of radius) to justify studying a few first orders of quasiclassical
(WKB) expansion over derivatives. Then we find that violation of the averaged
weak energy condition takes place irrespectively of the detailed form of
metric. This is a necessary condition for the neutrino vacuum to be able to
support the wormhole geometry. In this respect, neutrino vacuum behaves like
electromagnetic one and differs from the conformal scalar vacuum which does not
seem to violate energy conditions for slowly varied metric automatically, but
requires self-consistent wormhole solution for this.


title: A Global View of Kinks in 1+1 Gravity

abstract:
  Following Finkelstein and Misner, kinks are non-trivial field configurations
of a field theory, and different kink-numbers correspond to different
disconnected components of the space of allowed field configurations for a
given topology of the base manifold. In a theory of gravity, non-vanishing
kink-numbers are associated to a twisted causal structure. In two dimensions
this means, more specifically, that the light-cone tilts around (non-trivially)
when going along a non-contractible non-selfintersecting loop on spacetime. One
purpose of this paper is to construct the maximal extensions of kink spacetimes
using Penrose diagrams. This will yield surprising insights into their geometry
but also allow us to give generalizations of some well-known examples like the
bare kink and the Misner torus. However, even for an arbitrary 2D metric with a
Killing field we can construct continuous one-parameter families of
inequivalent kinks. This result has already interesting implications in the
flat or deSitter case, but it applies e.g. also to generalized dilaton gravity
solutions. Finally, several coordinate systems for these newly obtained kinks
are discussed.


title:
Radiation fluid singular hypersurfaces with de Sitter interior as models
  of charged extended particles in general relativity

abstract:
  In present paper we construct the classical and minisuperspace quantum models
of an extended charged particle. The modelling is based on the radiation fluid
singular hypersurface filled with physical vacuum. We demonstrate that both at
classical and quantum levels such a model can have equilibrium states at the
radius equal to the classical radius of a charged particle. In the cosmological
context the model could be considered also as the primary stationary state,
having the huge internal energy being nonobservable for an external observer,
from which the Universe was born by virtue of the quantum tunnelling.


title:
Conservative Model of Black Hole and Lifting of the Information Loss
  Paradox

abstract:
  The conservative model of a black hole is advanced. The model incorporates
conservation laws such as those of baryon and lepton numbers, which lifts the
information loss paradox. A scenario of black hole evaporation is considered.
  Keywords: entropy, emission, radiation, universe, chemical potential


title: Global Vortex and Black Cosmic String

abstract:
  We study global vortices coupled to (2+1) dimensional gravity with negative
cosmological constant. We found nonsingular vortex solutions in $\phi^4$-theory
with a broken U(1) symmetry, of which the spacetimes do not involve physical
curvature singularity. When the magnitude of negative cosmological constant is
larger than a critical value at a given symmetry breaking scale, the spacetime
structure is a regular hyperbola, however it becomes a charged black hole when
the magnitude of cosmological constant is less than the critical value. We
explain through duality transformation the reason why static global vortex
which is electrically neutral forms black hole with electric charge. Under the
present experimental bound of the cosmological constant, implications on
cosmology as a straight black cosmic string is also discussed in comparison
with global U(1) cosmic string in the spacetime of the zero cosmological
constant.


title: Rotating solitons and non-rotating, non-static black holes

abstract:
  It is shown that the non-Abelian black hole solutions have stationary
generalizations which are parameterized by their angular momentum and electric
Yang-Mills charge. In particular, there exists a non-static class of stationary
black holes with vanishing angular momentum. It is also argued that the
particle-like Bartnik-McKinnon solutions admit slowly rotating, globally
regular excitations. In agreement with the non-Abelian version of the staticity
theorem, these non-static soliton excitations carry electric charge, although
their non-rotating limit is neutral.


title: States insensitive to the Unruh effect in multi-level detectors

abstract:
  We give a general treatment of the spontaneous excitation rates and the
non-relativistic Lamb shift of constantly accelerated multi-level atoms as a
model for multi-level detectors. Using a covariant formulation of the dipole
coupling between the atom and the electromagnetic field we show that new
Raman-like transitions can be induced by the acceleration. Under certain
conditions these transitions can lead to stable ground and excited states which
are not affected by the non inertial motion. The magnitude of the Unruh effect
is not altered by multi-level effects. Both the spontaneous excitation rates
and the Lamb shift are not within the range of measurability.


title: A hollow sphere as a detector of gravitational radiation

abstract:
  The most important features of the proposed spherical gravitational wave
detectors are closely linked with their symmetry. Hollow spheres share this
property with solid ones, considered in the literature so far, and constitute
an interesting alternative for the realization of an omnidirectional
gravitational wave detector. In this paper we address the problem of how a
hollow elastic sphere interacts with an incoming gravitational wave and find an
analytical solution for its normal mode spectrum and response, as well as for
its energy absorption cross sections. It appears that this shape can be
designed having relatively low resonance frequencies (about 200 Hz) yet keeping
a large cross section, so its frequency range overlaps with the projected large
interferometers. We also apply the obtained results to discuss the performance
of a hollow sphere as a detector for a variety of gravitational wave signals.


title: Exact solutions in Einstein-Yang-Mills-Dirac systems

abstract:
  We present exact solutions in Einstein-Yang-Mills-Dirac theories with gauge
groups SU(2) and SU(4) in Robertson-Walker space-time $R \times S^3 $, which
are symmetric under the action of the group SO(4) of spatial rotations. Our
approach is based on the dimensional reduction method for gauge and
gravitational fields and relates symmetric solutions in EYMD theory to certain
solutions of an effective dynamical system.
  We interpret our solutions as cosmological solutions with an oscillating
Yang-Mills field passing between topologically distinct vacua. The explicit
form of the solution for spinor field shows that its energy changes the sign
during the evolution of the Yang-Mills field from one vacuum to the other,
which can be considered as production or annihilation of fermions.
  Among the obtained solutions there is also a static sphaleron-like solution,
which is a cosmological analogue of the first Bartnik-McKinnon solution in the
presence of fermions.


title: Gravitational Properties of Quantum Bosonic Strings

abstract:
  In this thesis we are interested in the study of the gravitational properties
of quantum bosonic strings. We start by computing the quantum energy-momentum
tensor ${\hat T}^{\mu\nu}(x)$ for strings in Minkowski space-time. We perform
the calculation of its expectation value for different physical string states
both for open and closed bosonic strings. The states we consider are described
by normalizable wave-packets in the centre of mass coordinates. Amongst our
results, we find in particular that ${\hat T}^{\mu\nu}(x)$ becomes a non-local
operator at the quantum level, its position appears to be smeared out by
quantum fluctuations. We find that the expectation value acquires a non-zero
value for both massive and massless string states. After computing $<{\hat
T}^{\mu\nu}(x)>$ we proceed to calculate the gravitational field due to a
quantum massless bosonic string in the framework of a weak-field approximation
to Einstein's equations. We obtain a multipole expansion for the weak-field
metric $h^{\mu\nu}(x)$ and present its gravitational properties, including the
gravitational radiation produced by such a string. Our results are then
compared to those found for classical (cosmic) strings.


title: Quantum Field Theory in Curved Spacetime

abstract:
  These lectures deal with selected aspects of quantum field theory in curved
spacetime including the following topics: (1) Quantization of fields on a
curved background, particle creation by gravitational fields, particle creation
in an expanding universe; moving mirror radiation. (2) The Hawking effect -
particle creation by black holes. (3) Ultraviolet and infrared divergences,
renormalization of the expectation value of the stress tensor; global symmetry
breaking in curved spacetime. (4) Negative energy in quantum field theory, its
gravitational effects, and inequalities which limit negative energy densities
and fluxes. (5) The semiclassical theory of gravity and its limitations,
breakdown of this theory due to metric fluctuations, lightcone fluctuations.


title: Dynamics of a global string with large Higgs boson mass

abstract:
  We consider a self-gravitating string generated by a global vortex solution
in general relativity. We investigate the Einstein and field equations of a
global vortex in the region of its central line and at a distance from the
centre of the order of the inverse of its Higgs boson mass. By combining the
two we establish by a limiting process of large Higgs mass the dynamics of a
self-gravitating global string. Under our assumptions the presence of
gravitation restricts the world sheet of the global string to be totally
geodesic.


title: Black hole excision with matching

abstract:
  We present a new method for treating the inner Cauchy boundary of a black
hole spacetime by matching to a characteristic evolution. We discuss the
advantages and disadvantages of such a scheme relative to Cauchy-only
approaches. A prototype code, for the spherically symmetric collapse of a
self-gravitating scalar field, shows that matching performs at least as well as
other approaches to handling the inner boundary.


title: Estimation of parameters of gravitational waves from coalescing binaries

abstract:
  The paper deals with the estimation of parameters of gravitational waves from
coalescing binaries. It explains the discrepancy between the Monte carlo
simulations and the covariance matrix. We include the post-Newtonian as well as
the Newtonian case.


title:
Double unification, time compression, and space flatness for the
  extended particle

abstract:
  Three variational vector equations are derived for the extended
particle-field object located on the light cone. Point sources are excluded
from the pure field equations and all physical magnitudes are free from
divergences. Accepting 3D intersections of 4D cone-charges, vector
electrogravity explains all observed phenomena under common flat 3D and 1D
intervals. External cone-charges contribute to pseudo-Riemannian metrics of
proper four-spaces of charged objects, resulting in dilation-compression of
their proper time rates. Photon-type gravitational radiation is not associated
with metric modulation of flat, laboratory space. The Minkowski-Lorentz
equation for free charges corresponds to the equivalence principle for the
canonical four-space. The predicted criterion of double unification, particles
with fields - gravity with electrodynamics, is confirmed in vector
electrogravity.


title: Spacetime structure of an inflating global monopole

abstract:
  The evolution of a global monopole with an inflating core is investigated. An
analytic expression for the exterior metric at large distances from the core is
obtained. The overall spacetime structure is studied numerically, both in
vacuum and in a radiation background.


title:
The variational theory of the perfect dilaton-spin fluid in a
  Weyl-Cartan space

abstract:
  The variational theory of the perfect fluid with intrinsic spin and dilatonic
charge (dilaton-spin fluid) is developed. The spin tensor obeys the classical
Frenkel condition. The Lagrangian density of such fluid is stated, and the
equations of motion of the fluid, the Weyssenhoff-type evolution equation of
the spin tensor and the conservation law of the dilatonic charge are derived.
The expressions of the matter currents of the fluid (the canonical
energy-momentum 3-form, the metric stress-energy 4-form and the dilaton-spin
momentum 3-form) are obtained.


title: A note on post-Riemannian structures of spacetime

abstract:
  A four-dimensional differentiable manifold is given with an arbitrary linear
connection $\Gamma_\alpha^\beta=\Gamma_{i\alpha}^\beta dx^i$. Megged has
claimed that he can define a metric $G_{\alpha\beta}$ by means of a certain
integral equation such that the connection is compatible with the metric. We
point out that Megged's implicite definition of his metric $G_{\alpha\beta}$ is
equivalent to the assumption of a vanishing nonmetricity. Thus his result turns
out to be trivial.


title:
Spherically symmetric gravitating shell as a reparametrization invariant
  system

abstract:
  The subject of this paper are spherically symmetric thin shells made of
barotropic ideal fluid and moving under the influence of their own
gravitational field as well as that of a central black hole; the cosmological
constant is assumed to be zero. The general super-Hamiltonian derived in a
previous paper is rewritten for this spherically symmetric special case. The
dependence of the resulting action on the gravitational variables is
trivialized by a transformation due to Kucha\v{r}. The resulting variational
principle depends only on shell variables, is reparametrization invariant, and
includes both first- and second-class constraints. Several equivalent forms of
the constrained system are written down. Exclusion of the second-class
constraints leads to a super-Hamiltonian which appears to overlap with that by
Ansoldi et al. in a quarter of the phase space. As Kucha\v{r}' variables are
singular at the horizons of both Schwarzschild spacetimes inside and outside
the shell, the dynamics is first well-defined only inside of 16 disjoint
sectors. The 16 sectors are, however, shown to be contained in a single,
connected symplectic manifold and the constraints are extended to this manifold
by continuity. Poisson bracket between no two independent spacetime coordinates
of the shell vanish at any intersection of two horizons.


title:
Perfect fluid and test particle with spin and dilatonic charge in a
  Weyl-Cartan space

abstract:
  The equation of perfect dilaton-spin fluid motion in the form of generalized
hydrodynamic Euler-type equation in a Weyl-Cartan space is derived. The
equation of motion of a test particle with spin and dilatonic charge in the
Weyl-Cartan geometry background is obtained. The peculiarities of test particle
motion in a Weyl-Cartan space are discussed.


title:
Choosing a conformal frame in scalar-tensor theories of gravity with a
  cosmological constant

abstract:
  Cosmological solutions of the Brans-Dicke theory with an added cosmological
constant are investigated with an emphasis to select a conformal frame in order
to implement the scenario of a decaying cosmological constant, featuring an
ever growing scalar field. We focus particularly on Jordan frame, the original
frame with the nonminimal coupling, and conformally transformed Einstein frame
without it. For the asymptotoic attractor solutions as well as the "hesitation
behavior," we find that none of these conformal frames can be accepted as the
basis of analyzing primordial nucleosynthesis. As a remedy, we propose to
modify the prototype BD theory, by introducing a scale-invariant scalar-matter
coupling, thus making Einstein frame acceptable. The invariacne is broken as a
quantum anomaly effect due to the non-gravitational interactions, entailing
naturally the fifth force, characterized by a finite force-range and WEP
violation. A tentative estimate shows that the theoretical prediction is
roughly consistent with the observational upper bounds. Further efforts to
improve the experimental accuracy is strongly encouraged.


title: The Hilbert Action in Regge Calculus

abstract:
  The Hilbert action is derived for a simplicial geometry. I recover the usual
Regge calculus action by way of a decomposition of the simplicial geometry into
4-dimensional cells defined by the simplicial (Delaunay) lattice as well as its
dual (Voronoi) lattice. Within the simplicial geometry, the Riemann scalar
curvature, the proper 4-volume, and hence, the Regge action is shown to be
exact, in the sense that the definition of the action does not require one to
introduce an averaging procedure, or a sequence of continuum metrics which were
common in all previous derivations. It appears that the unity of these two dual
lattice geometries is a salient feature of Regge calculus.


title: Hamiltonian spacetime dynamics with a spherical null-dust shell

abstract:
  We consider the Hamiltonian dynamics of spherically symmetric Einstein
gravity with a thin null-dust shell, under boundary conditions that fix the
evolution of the spatial hypersurfaces at the two asymptotically flat
infinities of a Kruskal-like manifold. The constraints are eliminated via a
Kuchar-type canonical transformation and Hamiltonian reduction. The reduced
phase space $\tilde\Gamma$ consists of two disconnected copies of $R^4$, each
associated with one direction of the shell motion. The right-moving and
left-moving test shell limits can be attached to the respective components of
$\tilde\Gamma$ as smooth boundaries with topology $R^3$. Choosing the
right-hand-side and left-hand-side masses as configuration variables provides a
global canonical chart on each component of $\tilde\Gamma$, and renders the
Hamiltonian simple, but encodes the shell dynamics in the momenta in a
convoluted way. Choosing the shell curvature radius and the "interior" mass as
configuration variables renders the shell dynamics transparent in an
arbitrarily specifiable stationary gauge "exterior" to the shell, but the
resulting local canonical charts do not cover the three-dimensional subset of
$\tilde\Gamma$ that corresponds to a horizon-straddling shell. When the
evolution at the infinities is freed by introducing parametrization clocks, we
find on the unreduced phase space a global canonical chart that completely
decouples the physical degrees of freedom from the pure gauge degrees of
freedom. Replacing one infinity by a flat interior leads to analogous results,
but with the reduced phase space $R^2 \cup R^2$. The utility of the results for
quantization is discussed.


title: Bootstrap Universe from Self-Referential Noise

abstract:
  We further deconstruct Heraclitean Quantum Systems giving a model for a
universe using pregeometric notions in which the end-game problem is overcome
by means of self-referential noise. The model displays self-organisation with
the emergence of 3-space and time. The time phenomenon is richer than the
present geometric modelling.


title:
Indeterministic Quantum Gravity and Cosmology VIII. Gravilon:
  Gravitational Autolocalization

abstract:
  This paper is a sequel to the series of papers [gr-qc/9409010, gr-qc/9505034,
gr-qc/9603022, gr-qc/9609035, gr-qc/9609046, gr-qc/9704033, gr-qc/9704038].
Gravitational autolocalization of a body is considered. A self-consistent
problem is solved: A quantum state of the center of mass of the body gives rise
to a classical gravitational field, and the state, on the other hand, is an
eigenstate in the field. We call a resulting solution gravilon. Gravilons are
classified, and their properties are studied. Gravitational autolocalization is
predominantly a macroscopic effect. The motion of a gravilon as a whole is
classical.


title:
The old frequency decomposition problem in the light of new quantization
  methods

abstract:
  The question is raised whether the unique decomposition of the physical
Hilbert space, as emerging in the refined algebraic quantization of a
constrained system, may be understood in terms of the old Klein-Gordon type
quantization.