title: Solution generating with perfect fluids

abstract:
  We apply a technique, due to Stephani, for generating solutions of the
Einstein-perfect fluid equations. This technique is similar to the vacuum
solution generating techniques of Ehlers, Harrison, Geroch and others. We start
with a ``seed'' solution of the Einstein-perfect fluid equations with a Killing
vector. The seed solution must either have (i) a spacelike Killing vector and
equation of state P=rho or (ii) a timelike Killing vector and equation of state
rho+3P=0. The new solution generated by this technique then has the same
Killing vector and the same equation of state. We choose several simple seed
solutions with these equations of state and where the Killing vector has no
twist. The new solutions are twisting versions of the seed solutions.


title: Conformal Couplings in Induced Gravity

abstract:
  It is found that the induced gravity with conformal couplings requires the
conformal invariance in both classical and quantum levels for consistency. This
is also true for the induced gravity with an extended conformal coupling
interacting with torsion.


title: New Symmetries in Two-Dimensional Dilaton Gravity

abstract:
  We present three types of non-conformal symmetries for a wide class of 2D
dilaton-gravity models. For the particular CGHS, or string-inspired model, a
linear combination of these symmetries is conformal and turns out to be the
well-known symmetry which allows to construct the exactly solvable
semiclassical RST and BPP models. We show that one of these non-conformal
symmetries can be converted into a conformal one by means of a suitable field
redefinition involving the metric and the derivatives of the dilaton. As a
consequence of this, and by defining a Polyakov-type term in terms of an
invariant metric under the symmetry, we are able to provide, for a generic 2D
dilaton gravity model, associated semiclassical models which are symmetry
invariant.


title:
Mode decomposition and unitarity in quantum cosmology, Talk given at the
  Second Meeting on Constrained Dynamics and Quantum gravity, Santa Margherita
  Ligure, September 17-21, 1996

abstract:
  Contrary to common belief, there are perspectives for generalizing the notion
of positive and negative frequency in minisuperspace quantum cosmology, even
when the wave equation does not admit symmetries. We outline a strategy in
doing so when the potential is positive. Also, an underlying unitarity
structure shows up. Starting in the framework of the Klein-Gordon type
quantization, I am led to a result that relies on global features on the model,
and that is possibly related to structures encountered in the refined algebraic
quantization scheme.


title: Telling Tails In The Presence Of A Cosmological Constant

abstract:
  We study the evolution of massless scalar waves propagating on spherically
symmetric spacetimes with a non-zero cosmological constant. Considering test
fields on both Schwarzschild-de Sitter and Reissner-Nordstrom-de Sitter
backgrounds, we demonstrate the existence of exponentially decaying tails at
late times. Interestingly the l=0 mode asymptotes to a non-zero value,
contrasting the asymptotically flat situation. We also compare these results,
for l=0, with a numerical integration of the Einstein-Scalar field equations,
finding good agreement between the two. Finally, the significance of these
results to the study of the Cauchy horizon stability in black hole-de Sitter
spacetimes is discussed.


title:
Multidimensional Quantum Cosmology: Quantum Wormholes, Third
  Quantization, Inflation from "Nothing", etc

abstract:
  A multidimensional cosmological model with space-time consisting of n (n>1)
Einstein spaces M_i is investigated in the presence of a cosmological constant
Lambda and m homogeneous minimally coupled scalar fields as a matter source.
Classes of the models integrable at classical as well as quantum levels are
found. These classes are equivalent to each other. Quantum wormhole solutions
are obtained for them and the procedure of the third quantization is performed.
An inflationary universe arising from classically forbidden Euclidean region is
investigated for a model with a cosmological constant.


title: A Comment on the Geometric Entropy and Conical Space

abstract:
  It has been recently pointed out that a definition of the geometric entropy
using the partition function in a conical space does not in general lead to a
positive definite quantity. For a scalar field model with a non-minimal
coupling we clarify the origin of the anomalous behavior from the viewpoint of
the canonical formulation.


title: Relic dilatons in string cosmology

abstract:
  The allowed mass windows for a cosmic background of relic dilatons are
estimated in the context of the pre-big bang scenario. The dilatons are
produced from the quantum fluctuations of the vacuum, and the extension of the
windows is controlled by the string mass scale. The possible relaxation of
phenomenological bounds due to an intermediate stage of reheating is discussed.
Even without such a relaxation, the allowed range of masses includes a light
sector in which the dilatons are not yet decayed, and could provide the
dominant contribution to the present large scale density.


title: Magnetic Monopoles and Massive Photons in a Weyl-Type Electrodynamics

abstract:
  In a previous work the Weyl-Dirac framework was generalized in order to
obtain a geometrically based general relativistic theory, possessing intrinsic
electric and magnetic currents and admitting massive photons. Some physical
phenomena in that framework are considered. So it is shown that massive photons
may exist only in presence of an intrinsic magnetic field. The role of massive
photons is essential in order to get an interaction between magnetic currents.
A static spherically symmetric solution is obtained. It may lead either to the
Reissner-Nordstr{\o}m metric, or to the metric created by a magnetic monopole.


title: Poisson Realization and Quantization of the Geroch Group

abstract:
  The conserved nonlocal charges generating the Geroch group with respect to
the canonical Poisson structure of the Ernst equation are found. They are shown
to build a quadratic Poisson algebra, which suggests to identify the quantum
Geroch algebra with Yangian structures.


title: Semiclassical Collapse of a Sphere of Dust and Hawking Radiation

abstract:
  The independent dynamical variables of a collapsing homogeneous sphere of
dust are canonically quantised and coupled equations describing matter (dust)
and gravitation are obtained. The conditions for the validity of the adiabatic
(Born-Oppenheimer) and semiclassical approximations are derived. On neglecting
back-reaction effects, it is also shown that in the vicinity of the horizon and
inside the dust the Wightman function for a conformal scalar field coupled to a
monopole emitter is thermal at the characteristic Hawking temperature.


title: Inflation and the Fine-Tuning Problem

abstract:
  I describe a recently derived stochastic approach to inflaton dynamics which
can address some serious problems associated with conventional inflationary
theory. Using this theory I derive an exact solution to the stochastic dynamics
for the case of a $\lambda\phi^4$ potential and use it to study the generated
primordial density fluctuations. It is found that on both sub and super-horizon
scales the theory predicts gaussian fluctuations to a very high accuracy along
with a near scale-invariant spectrum. Of most interest is that the amplitude
constraint is found to be satisfied for $\lambda\sim 10^{-5}$ rather than
$\lambda\sim 10^{-14}$ of the conventional theory. This represents a dramatic
easing of the fine-tuning constraints, a feature likely to generalize to a wide
range of potentials.


title:
A Revised Proof of the Existence of Negative Energy Density in Quantum
  Field Theory

abstract:
  Negative energy density is unavoidable in the quantum theory of field. We
give a revised proof of the existence of negative energy density unambiguously
for a massless scalar field.


title: Cosmology in Brans-Dicke theory with a scalar potential

abstract:
  We consider the general behaviour of cosmologies in Brans-Dicke theory where
the dilaton is self-interacting via a potential $V(\Phi)$. We show that the
general radiation universe is a two-dimensional dynamical system whereas the
dust or false vacuum universe is three-dimensional. This is in contrast to the
non-interacting dilaton which has uniformly a two-dimensional phase space. We
find the phase spaces in each case and the general behaviour of the
cosmologies.


title:
Electrostatic Equilibrium of Two Spherical Charged Masses in General
  Relativity

abstract:
  Approximate solutions representing the gravitational-electrostatic balance of
two arbitrary point sources in general relativity have led to contradictory
arguments in the literature with respect to the condition of balance. Up to the
present time, the only known exact solutions which can be interpreted as the
non-linear superposition of two spherically symmetric (Reissner-Nordstrom)
bodies without an intervening strut has been for critically charged masses,
$M^2_i = Q^2_i$. In the present paper, an exact electrostatic solution of the
Einstein-Maxwell equations representing the exterior field of two arbitrary
charged Reissner-Nordstrom bodies in equilibrium is studied. The invariant
physical charge for each source is found by direct integration of Maxwell's
equations. The physical mass for each source is invariantly defined in a manner
similar to which the charge was found. It is shown through numerical methods
that balance without tension or strut can occur for non-critically charged
bodies. It is demonstrated that other authors have not identified the correct
physical parameters for the mass and charge of the sources. Further properties
of the solution, including the multipole structure and comparison with other
parameterizations, are examined.


title: Universality of Einstein Equations for the Ricci Squared Lagrangians

abstract:
  It has been recently shown that, in the first order (Palatini) formalism,
there is universality of Einstein equations and Komar energy-momentum complex,
in the sense that for a generic nonlinear Lagrangian depending only on the
scalar curvature of a metric and a torsionless connection one always gets
Einstein equations and Komar's expression for the energy-momentum complex. In
this paper a similar analysis (also in the framework of the first order
formalism) is performed for all nonlinear Lagrangians depending on the
(symmetrized) Ricci square invariant. The main result is that the universality
of Einstein equations and Komar energy-momentum complex also extends to this
case (modulo a conformal transformation of the metric).


title: Energy-Momentum in Gauge Gravitation Theory

abstract:
  Building on the first variational formula of the calculus of variations, one
can derive the energy-momentum conservation laws from the condition of the Lie
derivative of gravitation Lagrangians along vector fields corresponding to
generators of general covariant transformations to be equal to zero. The goal
is to construct these vector fields. In gauge gravitation theory, the
difficulty arises because of fermion fields. General covariant transformations
fail to preserve the Dirac spin structure $S_h$ on a world manifold $X$ which
is associated with a certain tetrad field $h$. We introduce the universal Dirac
spin structure $S\to\Sigma\to X$ such that, given a tetrad field $h:X\to
\Sigma$, the restriction of $S$ to $h(X)$ is isomorphic to $S_h$. The canonical
lift of vector fields on $X$ onto $S$ is constructed. We discover the
corresponding stress-energy-momentum conservation law. The gravitational model
in the presence of a background spin structure also is examined.


title:
No-Hair Theorem for Spontaneously Broken Abelian Models in Static Black
  Holes

abstract:
  The vanishing of the electromagnetic field, for purely electric
configurations of spontaneously broken Abelian models, is established in the
domain of outer communications of a static asymptotically flat black hole. The
proof is gauge invariant, and is accomplished without any dependence on the
model. In the particular case of the Abelian Higgs model, it is shown that the
only solutions admitted for the scalar field become the vacuum expectation
values of the self-interaction.


title: Inflation for Bianchi IX model

abstract:
  The influence of Inflation on initial (i.e. at Planck's epoch) large
anisotropy of the Universe is studied, considering a more general metric than
the isotropic one: the locally rotationally symmetric (L.R.S.) Bianchi IX
metric. We find, then, a large set of initial conditions of intrinsic curvature
and shear allowing an inflationary epoch that make the anisotropy negligible.
These are not trivial because of the non-linearity of the Einstein's equations.


title: Superrelativity as a unification of quantum theory and relativity(II)

abstract:
  A underlying dynamical structure for both relativity and quantum
theory-``superrelativity'' has been proposed in order to overcome the well
known incompatibility between these theories. The relationship between
curvature of spacetime (gravity) and curvature of the projective Hilbert space
of pure quantum states is established as well.


title:
Geometry of the Dirac and reduced phase space quantization of
  constrained systems

abstract:
  Geometric properties of operators of quantum Dirac constraints and physical
observables are studied in semiclassical theory of generic constrained systems.
The invariance transformations of the classical theory -- contact canonical
transformations and arbitrary changes of constraint basis -- are promoted to
the quantum domain as unitary equivalence transformations. Geometry of the
quantum reduction of the Dirac formalism to the physical sector of the theory
is presented in the coordinate gauges and extended to unitary
momentum-dependent gauges of a general type. The operators of physical
observables are constructed satisfying one-loop quantum gauge invariance and
Hermiticity with respect to a physical inner product. Abelianization procedure
on Lagrangian constraint surfaces of phase space is discussed in the framework
of the semiclassical expansion.


title: Quantum origin of the early inflationary Universe

abstract:
  We give a detailed presentation of a recently proposed mechanism of
generating the energy scale of inflation by loop effects in quantum cosmology.
We discuss the quantum origin of the early inflationary Universe from the
no-boundary and tunneling quantum states and present a universal effective
action algorithm for the distribution function of chaotic inflationary
cosmologies in both of these states. The energy scale of inflation is
calculated by finding a sharp probability peak in this distribution function
for a tunneling model driven by the inflaton field with large negative constant
$\xi$ of non-minimal interaction. The sub-Planckian parameters of this peak
(the mean value of the corresponding Hubble constant $H\simeq 10^{-5}m_P$, its
quantum width $\Delta H/H\simeq 10^{-5}$ and the number of inflationary
e-foldings $N\geq 60$) are found to be in good correspondence with the
observational status of inflation theory, provided the coupling constants of
the theory are constrained by a condition which is likely to be enforced by the
(quasi) supersymmetric nature of the sub-Planckian particle physics model.


title: A Local Variational Theory for the Schmidt metric

abstract:
  We study local variations of causal curves in a space-time with respect to
b-length (or generalised affine parameter length). In a convex normal
neighbourhood, causal curves of maximal metric length are geodesics. Using
variational arguments, we show that causal curves of minimal b-length in
sufficiently small globally hyperbolic sets are geodesics. As an application we
obtain a generalisation of a theorem by B. G. Schmidt, showing that the cluster
curve of a partially future imprisoned, future inextendible and future
b-incomplete curve must be a null geodesic. We give examples which illustrate
that the cluster curve does not have to be closed or incomplete. The theory of
variations developed in this work provides a starting point for a Morse theory
of b-length.


title:
Exact Self-consistent Particle-like Solutions to the Equations of
  Nonlinear Scalar Electrodynamics in General Relativity

abstract:
  Exact self-consistent particle-like solutions with spherical and/or
cylindrical symmetry to the equations governing the interacting system of
scalar, electromagnetic and gravitational fields have been obtained. As a
particular case it is shown that the equations of motion admit a special kind
of solutions with sharp boundary known as droplets. For these solutions, the
physical fields vanish and the space-time is flat outside of the critical
sphere or cylinder. Therefore, the mass and the electric charge of these
configurations are zero.


title:
Ehlers-Harrison transformations and black holes in Dilaton-Axion Gravity
  with multiple vector fields

abstract:
  Dilaton-axion gravity with $p U(1)$ vector fields is studied on space-times
admitting a timelike Killing vector field. Three-dimensional sigma-model is
derived in terms of K\"ahler geometry, and holomorphic representation of the
SO(2,2+p) global symmetry is constructed. A general static black hole solution
depending on $2p+5$ parameters is obtained via SO(2,2+p) covariantization of
the Schwarzschild solution. The metric in the curvature coordinates looks as
the variable mass Reissner-Nordstr\"om one and generically possesses two
horizons. The inner horizon is pushed to the singularity if electric and
magnetic SO(p) charge vectors are parallel. For non-parallel charges the inner
horizon has a finite area except for an extremal limit when this property is
preserved only for orthogonal charges. Extremal dyon configurations with
orthogonal charges have finite horizon radii continuously varying from zero to
the ADM mass. New general solution is endowed with a NUT parameter, asymptotic
values of dilaton and axion, and a gauge parameter which can be used to ascribe
any given value to one of scalar charges.


title: Gravitational radiation from monopoles connected by strings

abstract:
  Monopole-antimonopole pairs connected by strings can be formed as topological
defects in a sequence of cosmological phase transitions. Such hybrid defects
typically decay early in the history of the universe but can still generate an
observable background of gravitational waves. We study the spectrum of
gravitational radiation from these objects both analytically and numerically,
concentrating on the simplest case of an oscillating pair connected by a
straight string.


title: Signal analysis of gravitational waves

abstract:
  In this lecture we describe the data analysis problem for insparlling
binaries. We discuss the detection statistic, how to make realiable estimation
and how to compute bias in the estimation of parameters. A combination of
geometrical ideas and numerical methods are employed to estimate computational
costs involved in searching for post-Newtonian wave forms.


title: On the quantization of the Null-Surface formulation of GR

abstract:
  We define and discuss various quantum operators that describe the geometry of
spacetime in quantum general relativity. These are obtained by combining the
Null-Surface Formulation of general relativity, recently developed, with
asymptotic quantization. One of the operators defined describes a ``fuzzy''
quantum light cone structure. Others, denoted ``spacetime-point operators'',
characterize geometrically-defined physical points. We discuss the
interpretation of these operators. This seems to suggest a picture of quantum
spacetime as made of ``fuzzy'' physical points. We derive the commutation
algebra of the quantum spacetime point operators in the linearization around
flat space.


title: Dirac symmetry operators from conformal Killing-Yano tensors

abstract:
  We show how, for all dimensions and signatures, a symmetry operator for the
massless Dirac equation can be constructed from a conformal Killing-Yano tensor
of arbitrary degree.


title: Exact Path Integral Quantization of Generic 2-D Dilaton Gravity

abstract:
  Local path integral quantization of generic 2D dilaton gravity is considered.
Locality means that we assume asymptotic fall off conditions for all fields. We
demonstrate that in the absence of `matter' fields to all orders of
perturbation theory and for all 2D dilaton theories the quantum effective
action coincides with the classical one. This resolves the apparent
contradiction between the well established results of Dirac quantization and
perturbative (path-integral) approaches which seemed to yield non-trivial
quantum corrections. For a particular case, the Jackiw--Teitelboim model, our
result is even extended to the situation when a matter field is present.


title: Towards possibility of self-maintained vacuum traversible wormhole

abstract:
  We calculate renormalised vacuum expectation values of electromagnetic
stress-energy tensor in the static spherically-symmetrical wormhole topology.
We find that for metric tensor sufficiently slow varied with distance violation
of the averaged weak energy condition takes place irrespectively of the
detailed form of metric. This is a necessary condition for the electromagnetic
vacuum to be able to support the wormhole geometry.


title:
Invariant construction of solutions to Einstein`s field equations - LRS
  perfect fluids I

abstract:
  The properties of some locally rotationally symmetric (LRS) perfect fluid
space-times are examined in order to demonstrate the usage of the description
of geometries in terms of the Riemann tensor and a finite number of its
covariant derivatives for finding solutions to Einstein's field equations. A
new method is introduced, which makes it possible to choose the coordinates at
any stage of the calculations. Three classes are examined, one with fluid
rotation, one with spatial twist in the preferred direction and the space-time
homogeneous models. It is also shown that there are no LRS space-times with
dependence on one null coordinate. Using an extension of the method, we find
the full metric in terms of curvature quantities for the first two classes.


title: Choptuik scaling and the scale invariance of Einstein's equation

abstract:
  The relationship of Choptuik scaling to the scale invariance of Einstein's
equation is explored. Ordinary dynamical systems often have limit cycles:
periodic orbits that are the asymptotic limit of generic solutions. We show how
to separate Einstein's equation into the dynamics of the overall scale and the
dynamics of the ``scale invariant'' part of the metric. Periodicity of the
scale invariant part implies periodic self-similarity of the spacetime. We also
analyze a toy model that exhibits many of the features of Choptuik scaling.


title: General Treatment of All 2d Covariant Models

abstract:
  General matterless models of gravity include dilaton gravity, arbitrary
powers in curvature, but also dynamical torsion. They are a special class of
"Poisson-sigma-models" whose solutions are known completely, together with
their general global structure. Beside the ordinary black hole, arbitrary
singularity structures can be studied. It is also possible to derive an action
"backwards", starting from a given manifold. The role of conservation laws,
Noether charge and the quantization have been investigated. Scalar and
fermionic matter fields may be included as well.


title: Toward a definition of chaos for general relativity

abstract:
  General relativity exhibits a unique feature not represented in standard
examples of chaotic systems; it is a spacetime diffeomorphism invariant theory.
Thus many characterizations of chaos do not work. It is therefore necessary to
develop a definition of chaos suitable for application to general relativity.
This presentation will present results towards this goal.


title: Numerical quantum gravity by dynamical triangulation

abstract:
  Recently an alternate technique for numerical quantum gravity, dynamical
triangulation, has been developed. In this method, the geometry is varied by
adding and subtracting equilateral simplices from the simplicial complex. This
method overcomes certain difficulties associated with the traditional approach
in Regge calculus of varying geometry by varying edge lengths. However
additional complications are introduced: three of the four moves in dynamical
triangulation can violate the simplicial nature of the complex. Simulations
indicate that the rate of these violations is significant. Thus additional
conditions must be placed on the dynamical triangulation moves to ensure that
the simplicial complex and its topology are preserved.


title: Dark Matter Gravitational Interactions

abstract:
  We argue that the conjectured dark mater in the Universe may be endowed with
a new kind of gravitational charge that couples to a short range gravitational
interaction mediated by a massive vector field. A model is constructed that
assimilates this concept into ideas of current inflationary cosmology. The
model is also consistent with the observed behaviour of galactic rotation
curves according to Newtonian dynamics. The essential idea is that stars
composed of ordinary (as opposed to dark matter) experience Newtonian forces
due to the presence of an all pervading background of massive gravitationally
charged cold dark matter. The novel gravitational interactions are predicted to
have a significant influence on pre-inflationary cosmology. The precise details
depend on the nature of a gravitational Proca interaction and the description
of matter. A gravitational Proca field configuration that gives rise to
attractive forces between dark matter charges of like polarity exhibits
homogeneous isotropic eternal cosmologies that are free of cosmological
curvature singularities thus eliminating the horizon problem associated with
the standard big-bang scenario. Such solutions do however admit dense hot
pre-inflationary epochs each with a characteristic scale factor that may be
correlated with the dark matter density in the current era of expansion. The
model is based on a theory in which a modification of Einsteinian gravity at
very short distances can be expressed in terms of the gradient of the Einstein
metric and the torsion of a non-Riemannian connection on the bundle of linear
frames over spacetime. Indeed we demonstrate that the genesis of the model
resides in a remarkable simplification that occurs when one analyses the
variational equations associated with a broad class of non-Riemannian actions.


title: Differential Forms and Wave Equations for General Relativity

abstract:
  Recently, Choquet-Bruhat and York and Abrahams, Anderson, Choquet-Bruhat, and
York (AACY) have cast the 3+1 evolution equations of general relativity in
gauge-covariant and causal ``first-order symmetric hyperbolic form,'' thereby
cleanly separating physical from gauge degrees of freedom in the Cauchy problem
for general relativity. A key ingredient in their construction is a certain
wave equation which governs the light-speed propagation of the extrinsic
curvature tensor. Along a similar line, we construct a related wave equation
which, as the key equation in a system, describes vacuum general relativity.
Whereas the approach of AACY is based on tensor-index methods, the present
formulation is written solely in the language of differential forms. Our
approach starts with Sparling's tetrad-dependent differential forms, and our
wave equation governs the propagation of Sparling's 2-form, which in the
``time-gauge'' is built linearly from the ``extrinsic curvature 1-form.'' The
tensor-index version of our wave equation describes the propagation of (what is
essentially) the Arnowitt-Deser-Misner gravitational momentum.


title:
Boundary Conditions and Quasilocal Energy in the Canonical Formulation
  of All 1+1 Models of Gravity

abstract:
  Within a first-order framework, we comprehensively examine the role played by
boundary conditions in the canonical formulation of a completely general
two-dimensional gravity model. Our analysis particularly elucidates the
perennial themes of mass and energy. The gravity models for which our arguments
are valid include theories with dynamical torsion and so-called generalized
dilaton theories (GDTs). Our analysis of the canonical action principle (i)
provides a rigorous correspondence between the most general first-order
two-dimensional Einstein-Cartan model (ECM) and GDT and (ii) allows us to
extract in a virtually simultaneous manner the ``true degrees of freedom'' for
both ECMs and GDTs. For all such models, the existence of an absolutely
conserved (in vacuo) quantity C is a generic feature, with (minus) C
corresponding to the black-hole mass parameter in the important special cases
of spherically symmetric four-dimensional general relativity and standard
two-dimensional dilaton gravity. The mass C also includes (minimally coupled)
matter into a ``universal mass function.'' We place particular emphasis on the
(quite general) class of models within GDT possessing a Minkowski-like
groundstate solution (allowing comparison between $C$ and the
Arnowitt-Deser-Misner mass for such models).


title:
Possible quantum gravity effects in a charged Bose condensate under
  variable e.m. field

abstract:
  In the weak field approximation to quantum gravity, a "local" positive
cosmological term mu^2(x) corresponds to a local negative squared mass term in
the Lagrangian and may thus induce instability and local pinning of the
gravitational field. Such a term can be produced by the coupling to an external
Bose condensate. In the functional integral, the local pinning acts as a
constraint on the field configurations. We discuss this model in detail and
apply it to a phenomenological analysis of recent experimental results.


title: Initial Data and the Final Fate of Inhomogeneous Dust Collapse

abstract:
  We examine here the relevance of the initial state of a collapsing dust cloud
towards determining it's final fate in the course of a continuing gravitational
collapse. It is shown that given any arbitrary matter distribution $M(r)$ for
the cloud at the initial epoch, there is always a freedom to choose rest of the
initial data, namely the initial velocities of the collapsing spherical shells,
so that the collapse could result either in a black hole or a naked singularity
depending on this choice. Thus, given the initial density profile, to achieve
the desired end state of the gravitational collapse one has to give a suitable
initial velocity to the cloud. We also characterize here a wide new family of
black hole solutions resulting from inhomogeneous dust collapse. These
configurations obey the usual energy conditions demanding the positivity of
energy density.


title: Black Hole Thermodynamics, Casimir Effect and Induced Gravity

abstract:
  An analogy between the subtraction procedure in the Gibbons-Hawking Euclidean
path integral approach to Horizon's Thermodynamics and the Casimir effect is
shown. Then a conjecture about a possible Casimir nature of the Gibbons-Hawking
subtraction is made in the framework of Sakharov's induced gravity. In this
framework it appears that the degrees of freedom involved in the
Bekenstein-Hawking entropy are naturally identified with zero--point modes of
the matter fields. Some consequences of this view are sketched.


title: On Global Conservation Laws at Null Infinity

abstract:
  The ``standard'' expressions for total energy, linear momentum and also
angular momentum of asymptotically flat Bondi metrics at null infinity are also
obtained from differential conservation laws on asymptotically flat
backgrounds, derived from a quadratic Lagrangian density by methods currently
used in classical field theory. It is thus a matter of taste and commodity to
use or not to use a reference spacetime in defining these globally conserved
quantities. Backgrounds lead to N\oe ther conserved currents; the use of
backgrounds is in line with classical views on conservation laws. Moreover, the
conserved quantities are in principle explicitly related to the sources of
gravity through Einstein's equations, while standard definitions are not. The
relations depend, however, on a rule for mapping spacetimes on backgrounds.


title: Scalar Wave Falloff in Asymptotically Anti-de Sitter Backgrounds

abstract:
  Conformally invariant scalar waves in black hole spacetimes which are
asymptotically anti-de Sitter are investigated. We consider both the
$(2+1)$-dimensional black hole and $(3+1)$-dimensional Schwarzschild-anti-de
Sitter spacetime as backgrounds. Analytical and numerical methods show that the
waves decay exponentially in the $(2+1)$ dimensional black hole background.
However the falloff pattern of the conformal scalar waves in the
Schwarzschild-anti-de Sitter background is generally neither exponential nor an
inverse power rate, although the approximate falloff of the maximal peak is
weakly exponential. We discuss the implications of these results for mass
inflation.


title: A Topological Extension of General Relativity

abstract:
  A set of algebraic equations for the topological properties of space-time is
derived, and used to extend general relativity into the Planck domain. A unique
basis set of three-dimensional prime manifolds is constructed which consists of
$S^3$, $S^1\times S^2$, and $T^3$. The action of a loop algebra on these prime
manifolds yields topological invariants which constrain the dynamics of the
four-dimensional space-time manifold. An extended formulation of Mach's
principle and Einstein's equivalence of inertial and gravitational mass is
proposed which leads to the correct classical limit of the theory.
  It is found that the vacuum possesses four topological degrees of freedom
corresponding to a lattice of three-tori. This structure for the quantum foam
naturally leads to gauge groups O(n) and SU(n) for the fields, a boundary
condition for the universe, and an initial state characterized by local thermal
equilibrium. The current observational estimate of the cosmological constant is
reproduced without fine-tuning and found to be proportional to the number of
macroscopic black holes. The black hole entropy follows immediately from the
theory and the quantum corrections to its Schwarzschild horizon are computed.


title: Modeling the decoherence of spacetime

abstract:
  The question of whether unobserved short-wavelength modes of the
gravitational field can induce decoherence in the long-wavelength modes (``the
decoherence of spacetime'') is addressed using a simplified model of
perturbative general relativity, related to the Nordstrom-Einstein-Fokker
theory, where the metric is assumed to be conformally flat. For some
long-wavelength coarse grainings, the Feynman-Vernon influence phase is found
to be effective at suppressing the off-diagonal elements of the decoherence
functional. The requirement that the short-wavelength modes be in a
sufficiently high-temperature state places limits on the applicability of this
perturbative approach.


title: On Quantum Inequalities

abstract:
  Building on the "quantum inequalities" introduced by Ford, I argue that the
negative local energies encountered in quantum field theory can only be
observed by detectors with positive energies at least as great in magnitude.
This means that operationally the total energy density must be non-negative.
Like reasoning shows that, in a similar operational sense, the dominant energy
condition must hold: any timelike component of the four-momentum density is
positive.


title: Real and complex connections for canonical gravity

abstract:
  Both real and complex connections have been used for canonical gravity: the
complex connection has SL(2,C) as gauge group, while the real connection has
SU(2) as gauge group. We show that there is an arbitrary parameter $\beta$
which enters in the definition of the real connection, in the Poisson brackets,
and therefore in the scale of the discrete spectra one finds for areas and
volumes in the corresponding quantum theory. A value for $\beta$ could be could
be singled out in the quantum theory by the Hamiltonian constraint, or by the
rotation to the complex Ashtekar connection.


title: Testing the Equivalence Principle using Atomic Vacuum Energy Shifts

abstract:
  We consider possible tests of the Einstein Equivalence Principle for
quantum-mechanical vacuum energies by evaluating the Lamb shift transition in a
class of non-metric theories of gravity described by the \tmu formalism. We
compute to lowest order the associated red shift and time dilation parameters,
and discuss how (high-precision) measurements of these quantities could provide
new information on the validity of the equivalence principle.


title: Supersymmetric double Darboux method in quantum cosmology

abstract:
  We briefly present the supersymmetric double Darboux method and next apply it
to the continuum of the quantum Taub cosmological model as a toy model in order
to generate a one-parameter family of bosonic Taub potentials and the
corresponding wavefunctions


title: Edge States and Entropy of 2d Black Holes

abstract:
  In several recent publications Carlip, as well as Balachandran, Chandar and
Momen, have proposed a statistical mechanical interpretation for black hole
entropy in terms of ``would be gauge'' degrees of freedom that become dynamical
on the boundary to spacetime. After critically discussing several routes for
deriving a boundary action, we examine their hypothesis in the context of
generic 2-D dilaton gravity. We first calculate the corresponding statistical
mechanical entropy of black holes in 1+1 deSitter gravity, which has a gauge
theory formulation as a BF-theory. Then we generalize the method to dilaton
gravity theories that do not have a (standard) gauge theory formulation. This
is facilitated greatly by the Poisson-Sigma-model formulation of these
theories. It turns out that the phase space of the boundary particles coincides
precisely with a symplectic leaf of the Poisson manifold that enters as target
space of the Sigma-model. Despite this qualitatively appealing picture, the
quantitative results are discouraging: In most of the cases the symplectic
leaves are non-compact and the number of microstates yields a meaningless
infinity. In those cases where the particle phase space is compact - such as,
e.g., in the Euclidean deSitter theory - the edge state degeneracy is finite,
but generically it is far too small to account for the semiclassical
Bekenstein-Hawking entropy.


title: General Relativity in terms of Dirac Eigenvalues

abstract:
  The eigenvalues of the Dirac operator on a curved spacetime are
diffeomorphism-invariant functions of the geometry. They form an infinite set
of ``observables'' for general relativity. Recent work of Chamseddine and
Connes suggests that they can be taken as variables for an invariant
description of the gravitational field's dynamics. We compute the Poisson
brackets of these eigenvalues and find them in terms of the energy-momentum of
the eigenspinors and the propagator of the linearized Einstein equations. We
show that the eigenspinors' energy-momentum is the Jacobian matrix of the
change of coordinates from metric to eigenvalues. We also consider a minor
modification of the spectral action, which eliminates the disturbing huge
cosmological term and derive its equations of motion. These are satisfied if
the energy momentum of the trans Planckian eigenspinors scale linearly with the
eigenvalue; we argue that this requirement approximates the Einstein equations.


title: ``Sum over Surfaces'' form of Loop Quantum Gravity

abstract:
  We derive a spacetime formulation of quantum general relativity from
(hamiltonian) loop quantum gravity. In particular, we study the quantum
propagator that evolves the 3-geometry in proper time. We show that the
perturbation expansion of this operator is finite and computable order by
order. By giving a graphical representation a' la Feynman of this expansion, we
find that the theory can be expressed as a sum over topologically inequivalent
(branched, colored) 2d surfaces in 4d. The contribution of one surface to the
sum is given by the product of one factor per branching point of the surface.
Therefore branching points play the role of elementary vertices of the theory.
Their value is determined by the matrix elements of the hamiltonian constraint,
which are known. The formulation we obtain can be viewed as a continuum version
of Reisenberger's simplicial quantum gravity. Also, it has the same structure
as the Ooguri-Crane-Yetter 4d topological field theory, with a few key
differences that illuminate the relation between quantum gravity and TQFT.
Finally, we suggests that certain new terms should be added to the hamiltonian
constraint in order to implement a ``crossing'' symmetry related to 4d
diffeomorphism invariance.


title: Singularities in Inflationary Cosmology: A Review

abstract:
  We review here some recent results that show that inflationary cosmological
models must contain initial singularities. We also present a new singularity
theorem. The question of the initial singularity re-emerges in inflationary
cosmology because inflation is known to be generically future-eternal. It is
natural to ask, therefore, if inflationary models can be continued into the
infinite past in a non-singular way. The results that we discuss show that the
answer to the question is ``no.'' This means that we cannot use inflation as a
way of avoiding the question of the birth of the Universe. We also argue that
our new theorem suggests - in a sense that we explain in the paper - that the
Universe cannot be infinitely old.


title:
Gauge transformations in the Lagrangian and Hamiltonian formalisms of
  generally covariant theories

abstract:
  We study spacetime diffeomorphisms in Hamiltonian and Lagrangian formalisms
of generally covariant systems. We show that the gauge group for such a system
is characterized by having generators which are projectable under the Legendre
map. The gauge group is found to be much larger than the original group of
spacetime diffeomorphisms, since its generators must depend on the lapse
function and shift vector of the spacetime metric in a given coordinate patch.
Our results are generalizations of earlier results by Salisbury and
Sundermeyer. They arise in a natural way from using the requirement of
equivalence between Lagrangian and Hamiltonian formulations of the system, and
they are new in that the symmetries are realized on the full set of phase space
variables. The generators are displayed explicitly and are applied to the
relativistic string and to general relativity.


title:
The Tolman-Bondi Model in the Ruban-Chernin Coordinates. 1. Equations
  and Solutions

abstract:
  The Tolman-Bondi (TB) model is defined up to some transformation of a
co-moving coordinate but the transformation is not fixed. The use of an
arbitrary co-moving system of coordinates leads to the solution dependent on
three functions $f, F, {\bf F}$ which are chosen independently in applications.
  The article studies the transformation rule which is given by the definition
of an invariant mass. It is shown that the addition of the TB model by the
definition of the transformation rule leads to the separation of the couples of
functions ($f, F$) into nonintersecting classes. It is shown that every class
is characterized only by the dependence of $F$ on $f$ and connected with unique
system of co-moving coordinates. It is shown that the Ruban-Chernin system of
coordinates corresponds to identical transformation. The dependence of Bonnor's
solution on the Ruban-Chernin coordinate $M$ by means of initial density and
energy distribution is studied. It is shown that the simplest flat solution is
reduced to an explicit dependence on the coordinate $M$. Several examples of
initial conditions and transformation rules are studied.


title: Binary-pulsar tests of strong-field gravity

abstract:
  This talk is based on my work in collaboration with Thibault Damour since
1991. Unified theories, like superstrings, predict the existence of scalar
partners to the graviton. Such theories of gravity can be very close to general
relativity in weak-field conditions (solar-system experiments), but can deviate
significantly from it in the strong-field regime (near compact bodies, like
neutron stars). Binary pulsars are thus the best tools available for testing
these theories. This talk presents the four main binary-pulsar experiments, and
discusses the constraints they impose on a generic class of tensor-scalar
theories. It is shown notably that they rule out some models which are strictly
indistinguishable from general relativity in the solar system. This illustrates
the qualitative difference between binary-pulsar and solar-system tests of
relativistic gravity.


title:
Evolutionary Dynamics While Trapped in Resonance: A Keplerian Binary
  System Perturbed by Gravitational Radiation

abstract:
  The method of averaging is used to investigate the phenomenon of capture into
resonance for a model that describes a Keplerian binary system influenced by
radiation damping and external normally incident periodic gravitational
radiation. The dynamical evolution of the binary orbit while trapped in
resonance is elucidated using the second order partially averaged system. This
method provides a theoretical framework that can be used to explain the main
evolutionary dynamics of a physical system that has been trapped in resonance.


title: Trace anomaly and Hawking effect in 2D dilaton gravity theories

abstract:
  We investigate the classical and semiclassical features of generic 2D,
matter-coupled, dilaton gravity theories. In particular, we show that the mass,
the temperature and the flux of Hawking radiation associated with 2D black
holes are invariant under dilaton-dependent Weyl rescalings of the metric. The
relationship between quantum anomalies and Hawking radiation is discussed.


title: A Geometric Approach to the Quantum Mechanics of de Broglie and Vigier

abstract:
  Following de Broglie and Vigier, a fully relativistic causal interpretation
of quantum mechanics is given within the context of a geometric theory of
gravitation and electromagnetism. While the geometric model shares the
essential principles of the causal interpretation initiated by de Broglie and
advanced by Vigier, the particle and wave components of the theory are derived
from the Einstein equations rather than a nonlinear wave equation. This
geometric approach leads to several new features, including a solution to the
de Broglie variable mass problem.


title: Quantum Mechanics and Relativity --- Their Unification by Local Time ---

abstract:
  A quantum-mechanical Hamiltonian with a gravitational potential is derived in
the framework of local times. This Hamiltonian is the one used by E. H. Lieb
(Bull. Amer. Math. Soc. 22(1990), 1-49) in his explanation of stability and
instability of cold stars. Our procedure deriving the Hamiltonian is based on
an analysis of the process of the observation with the background of the notion
of quantum-mechanical local times compatible with general theory of relativity.


title: Gravitational Correction in Neutrino Oscillations

abstract:
  We investigate the quantum mechanical oscillations of neutrinos propagating
in weak gravitational field. The correction to the result in the flat
space-time is derived.


title: On the Limit Cycle of an Inflationary Universe

abstract:
  We study the dynamics of a scalar inflaton field with a symmetric
double--well potential and prove rigorously the existence of a limit cycle in
its phase space. By using analytical and numerical arguments we show that the
limit cycle is stable and give an analytical formula for its period.


title: Bound states due to an accelerated mirror

abstract:
  We discuss an effect of accelerated mirrors which remained hitherto
unnoticed, the formation of a field condensate near its surface for massive
fields. From the view point of an observer attached to the mirror, this is
effect is rather natural because a gravitational field is felt there. The
novelty here is that since the effect is not observer dependent even inertial
observers will detect the formation of this condensate. We further show that
this localization is in agreement with Bekenstein's entropy bound.


title:
Multidimensional Geometrical Model of the Electrical and SU(2) Colour
  Charge with Splitting off the Supplementary Coordinates

abstract:
  The geometrical model of an electrical charge is proposed. This model has the
''nake'' charge shunted with ``fur - coat'' consisting of virtual wormholes.
The 5D wormhole solution in the Kaluza - Klein's theory is the ''nake'' charge.
The splitting off the supplementary coordinates happens on the two spheres
(null surfaces) bounding this 5D wormhole. This allows to sew two Reissner -
Nordstr\"om's black holes to it on both sides. Virtual wormholes entrap a part
of the electrical force lines outcoming from ''nake'' charge. This effect can
essentially decrease the charge visible at infinity up to real relation $m^2 <
e^2$. The analogical construction for colour SU(2) gauge charge is made.


title: Classes of Anisotropic Cosmologies of Scalar-Tensor Gravitation

abstract:
  A study of an algorithm method capable to reveal anisotropic solutions of
general scalar-tensor gravitation -including non-minimally couplings- is
presented. It is found that it is possible to classify the behavior of the
field of different scalar-tensor theories in equivalence classes, with the same
classifier function that was obtained in Friedmann-Robertson-Walker models.


title:
Classical Monopoles: Newton, NUT-space, gravomagnetic lensing and atomic
  spectra

abstract:
  Stimulated by a scholium in Newton's Principia we find some beautiful results
in classical mechanics which can be interpreted in terms of the orbits in the
field of a mass endowed with a gravomagnetic monopole. All the orbits lie on
cones! When the cones are slit open and flattened the orbits are exactly the
ellipses and hyperbolae that one would have obtained without the gravomagnetic
monopole.
  The beauty and simplicity of these results has led us to explore the similar
problems in Atomic Physics when the nuclei have an added Dirac magnetic
monopole. These problems have been explored by others and we sketch the
derivations and give details of the predicted spectrum of monopolar hydrogen.
  Finally we return to gravomagnetic monopoles in general relativity. We
explain why NUT space has a non-spherical metric although NUT space itself is
the spherical space-time of a mass with a gravomagnetic monopole. We
demonstrate that all geodesics in NUT space lie on cones and use this result to
study the gravitational lensing by bodies with gravomagnetic monopoles.
  We remark that just as electromagnetism would have to be extended beyond
Maxwell's equations to allow for magnetic monopoles and their currents so
general relativity would have to be extended to allow torsion for general
distributions of gravomagnetic monopoles and their currents. Of course if
monopoles were never discovered then it would be a triumph for both Maxwellian
Electromagnetism and General Relativity as they stand!


title:
Semiclassical Gravitational Effects in the Spacetime of a Magnetic Flux
  Cosmic String

abstract:
  It is well-known that some physical effects may arise in the spacetime of a
straigth cosmic string due to its global conic properties. Among these effects,
the vacuum polarization effect has been extensively studied in the litterature.
In papers of reference [4] a more general situation has been considered in
which the cosmic string carries a magnetic flux $\Phi$ and interacts with a
charged scalar field. In this case, the vacuum polarization arises both via
non-trivial gravitational interaction (i.e, the conical structure) and via
Aharonov-Bohm interaction. In papers [4] the non vanishing VEV of the
energy-momentum tensor of the scalar field were computed. However, this
energy-momentum tensor should, in principle, be taken into account to determine
the spacetime associated with the magnetic flux cosmic string. Using the
semiclassical approach to the Einstein eqs. we find the first-order (in
$\hbar$) metric associated to the cosmic string and we show that the
gravitational force resulting from the backreaction of the $< T^{\mu}_{\nu} >$
is attractive or repulsive depending on whether the magnetic flux is absent or
present, respectively.


title: Time evolution of observable properties of parametrized systems

abstract:
  A short review of some recent work on the problem of time and of observables
for the reparametrization invariant systems is given. A talk presented at the
Second Meeting on Constraint Dynamics and Quantum Gravity at Santa Marguerita
Ligure, September 17--21 1996.


title: Solutions to a Quantal Gravity-Matter Field Theory on a Line

abstract:
  Solutions to a scalar-tensor (dilaton) quantum gravity theory, interacting
with quantized matter, are described. Dirac quantization is frustrated by
quantal anomalies in the constraint algebra. Progress is made only after the
Wheeler--DeWitt equation is modified by quantal terms, which eliminate the
anomaly. More than one modification is possible, resulting in more than one
`physical' spectrum in the quantum theory, corresponding to the given classical
model.


title:
Some aspects of the cosmological conformal equivalence between ``Jordan
  Frame'' and ``Einstein Frame''

abstract:
  The conformal equivalence between Jordan frame and Einstein frame can be used
in order to search for exact solutions in general theories of gravity in which
scalar fields are minimally or nonminimally coupled with geometry. In the
cosmological arena a relevant role is played by the time parameter in which
dynamics is described. In this paper we discuss such issues considering also if
cosmological Noether symmetries in the ``point--like'' Lagrangian are
conformally preserved. Through this analysis and through also a careful
analysis of the cosmological parameters \Omega and \Lambda, it is possible to
contribute to the discussion on which is the physical system.


title:
Variational Approach to Gaussian Approximate Coherent States: Quantum
  Mechanics and Minisuperspace Field Theory

abstract:
  This paper has a dual purpose. One aim is to study the evolution of coherent
states in ordinary quantum mechanics. This is done by means of a Hamiltonian
approach to the evolution of the parameters that define the state. The
stability of the solutions is studied. The second aim is to apply these
techniques to the study of the stability of minisuperspace solutions in field
theory. For a $\lambda \varphi^4$ theory we show, both by means of perturbation
theory and rigorously by means of theorems of the K.A.M. type, that the
homogeneous minisuperspace sector is indeed stable for positive values of the
parameters that define the field theory.


title: Variational theory of perfect hypermomentum fluid

abstract:
  The variational theory of the perfect hypermomentum fluid is developed. The
new type of the generalized Frenkel condition is considered. The Lagrangian
density of such fluid is stated, and the equations of motion of the fluid and
the Weyssenhoff-type evolution equation of the hypermomentum tensor 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 hypermomentum
3-form) are obtained. The special case of the dilaton-spin fluid with intrinsic
spin and dilatonic charge is considered.


title: Wormholes in spacetime with torsion

abstract:
  Analytical wormhole solutions in $U_4$ theory are presented. It is discussed
whether the extremely short range repulsive forces, related to the spin angular
momentum of matter, could be the ``carrier'' of the exoticity that threads the
wormhole throat.


title: Regular Black Holes and Topology Change

abstract:
  The conditions are clarified under which regular (i.e., singularity-free)
black holes can exist. It is shown that in a large class of spacetimes that
satisfy the weak energy condition the existence of a regular black hole
requires topology change.


title: Integrable 1+1 dimensional gravity models

abstract:
  Integrable models of dilaton gravity coupled to electromagnetic and scalar
matter fields in dimensions 1+1 and 0+1 are briefly reviewed. The 1+1
dimensional integrable models are either solved in terms of explicit
quadratures or reduced to the classically integrable Liouville equation. The
0+1 dimensional integrable models emerge as sectors in generally non integrable
1+1 dimensional models and can be solved in terms of explicit quadratures. The
Hamiltonian formulation and the problem of quantizing are briefly discussed.
Applications to gravity in any space - time dimension are outlined and a
generalization of the so called `no - hair' theorem is proven using local
properties of the Lagrange equations for a rather general 1+1 dimensional
dilaton gravity coupled to matter. This report is based on the paper
hep-th/9605008 but some simplifications, corrections and new results are added.


title: All conformally flat pure radiation metrics

abstract:
  The complete class of conformally flat, pure radiation metrics is given,
generalising the metric recently given by Wils.


title: The tale of two centres

abstract:
  We study motion in the field of two fixed centres described by a family of
Einstein-dilaton-Maxwell theories. Transitions between regular and chaotic
motion are observed as the dilaton coupling is varied.


title:
Teleparallel Space-Time with Defects yields Geometrization of
  Electrodynamics with quantized Charges

abstract:
  In the present paper a geometrization of electrodynamics is proposed which
makes use of a generalization of Riemannian geometry considered already by
Einstein and Cartan in the 20ies. Cartan's differential forms description of a
teleparallel space-time with torsion is modified by introducing distortion
1-forms which correspond to the distortion tensor in dislocation theory. Under
the condition of teleparallelism, the antisymmetrized part of the distorsion
1-form approximates the electromagnetic field, whereas the antisymmetrized part
of torsion contributes to the electromagnetic current. Cartan's structure
equations, the Bianchi identities, Maxwell's equations and the continuity
equation are thus linked in a most simple way. After these purely geometric
considerations a physical interpretation, using analogies to the theory of
defects in ordered media, is given. A simple defect, which is neither a
dislocation nor disclination proper, appears as source of the electromagnetic
field. Since this defect is rotational rather than translational, there seems
to be no contradiction to Noether's theorem as in other theories relating
torsion to electromagnetism. Then,congruences of defect properties and quantum
behaviour that arise are discussed, supporting the hypothesis that elementary
particles are topological defects of space-time. In agreement with the
differential geometry results, a dimensional analysis indicates that the
physical unit (lenght)^2 rather than As is the appropriate unit of the electric
charge.


title: Scalar Deformations of Schwarzschild Holes and Their Stability

abstract:
  We construct two solutions of the minimally coupled Einstein-scalar field
equations, representing regular deformations of Schwarzschild black holes by a
self-interacting, static, scalar field. One solution features an exponentially
decaying scalar field and a triple-well interaction potential; the other one is
completely analytic and sprouts Coulomb-like scalar hair. Both evade the
no-hair theorem by having partially negative potential, in conflict with the
dominant energy condition. The linear perturbation theory around such
backgrounds is developed in general, and yields stability criteria in terms of
effective potentials for an analog Schr\"odinger problem. We can test for more
than half of the perturbation modes, and our solutions prove to be stable
against those.


title: A Phase Space Approach to the Gravitational Arrow of Time

abstract:
  We attempt to find a function that characterizes gravitational clumping and
that increases monotonically as inhomogeneity increases. We choose $S =
ln\Omega$ as the candidate ``gravitational entropy'' function, where $\Omega$
is the phase-space volume below the Hamiltonian H of the system under
consideration. We compute $\Omega$ for transverse electromagnetic waves and for
gravitational wave, radiation and density perturbations in an expanding FLRW
universe. These calculations are carried out in the linear regime under the
assumption that the phases of the oscillators comprising the system are random.
Entropy is thus attributed to the lack of knowledge of the exact field
configuration. We find that $\Omega$, and hence $ln\Omega$ behaves as required.
We also carry out calculations for Bianchi IX cosmological models and find
that, even in this homogeneous case, the function can be interpreted sensibly.
We compare our results with Penrose's C^2 hypothesis. Because S is defined to
resemble the fundamental statistical mechanics definition of entropy, we are
able to recover the entropy in a variety of familiar circumstances including,
evidently, black-hole entropy. The results point to the utility of the
relativistic ADM Hamiltonian formalism in establishing a connection between
general relativity and statistical mechanics, although fully nonlinear
calculations will need to be performed to remove any doubt.


title: Time machine as four-dimensional wormhole

abstract:
  The following mechanism of action of Time machine is considered. Let
space-time $<V^4, g_{ik}>$ be a leaf of a foliation F of codimension 1 in
5-dimensional Lorentz manifold $<V^5, G_{AB}>$. If the Godbillon-Vey class
$GV(F) \neq 0$ then the foliation F has resilient leaves. Let $V^4$ be a
resilient leaf. Hence there exists an arbitrarily small neighborhood $U_a
\subset V^5$ of the event $a \in V^4$ such that $U_a \cap V^4$ consists of at
least two connected components $U_a^1$ and $U_a^2$.
  Remove the four-dimensional balls $B_a\subset U_a^1, B_b\subset U_a^2$, where
an event $b\in U_a^2$, and join the boundaries of formed two holes by means of
4-dimensional cylinder. As result we have a four-dimensional wormhole C, which
is a Time machine if b belongs to the past of event a. The past of a is lying
arbitrarily nearly. The distant Past is more accessible than the near Past. It
seems that real global space-time V^4 is a resilient one, i.e. is a resilient
leaf of some foliation F.
  It follows from the conformal Kaluza-Klein theory that the movement to the
Past through four-dimensional wormhole C along geodesic with respect to metric
G_{AB} requires for time machine of large energy and electric charge.


title: Density Spectrums from Kinetic Inflations

abstract:
  The pole-like accelerated expansion stages purely driven by the coupling
between the gravity and the dilaton field without referring to the potential
term can be realized in a class of generalized gravity theories. We consider
three such scenarios based on the scalar-tensor gravity, the induced gravity
and the string theory. Quantum fluctuations during the expansion stages
(including more general situations) can be derived in exact analytic forms.
Assuming that the pole-like acceleration stage provides a viable inflation
scenario in the early universe we derive the generated classical density
spectrums. The generated classical density field shows a generic tilted
spectrum with $n \simeq 4$ which differs from the observed spectrum supporting
$n \simeq 1$.


title: The mixmaster universe: A chaotic Farey tale

abstract:
  When gravitational fields are at their strongest, the evolution of spacetime
is thought to be highly erratic. Over the past decade debate has raged over
whether this evolution can be classified as chaotic. The debate has centered on
the homogeneous but anisotropic mixmaster universe. A definite resolution has
been lacking as the techniques used to study the mixmaster dynamics yield
observer dependent answers. Here we resolve the conflict by using observer
independent, fractal methods. We prove the mixmaster universe is chaotic by
exposing the fractal strange repellor that characterizes the dynamics. The
repellor is laid bare in both the 6-dimensional minisuperspace of the full
Einstein equations, and in a 2-dimensional discretisation of the dynamics. The
chaos is encoded in a special set of numbers that form the irrational Farey
tree. We quantify the chaos by calculating the strange repellor's Lyapunov
dimension, topological entropy and multifractal dimensions. As all of these
quantities are coordinate, or gauge independent, there is no longer any
ambiguity--the mixmaster universe is indeed chaotic.


title: Internal Structure of Einstein-Yang-Mills Black Holes

abstract:
  It is shown that a generic black hole solution of the SU(2)
Einstein-Yang-Mills equations develops a new type of an infinitely oscillating
behavior near the singularity. Only for certain discrete values of the event
horizon radius exceptional solutions exist, possessing an inner structure of
the Schwarzschild or Reissner-Nordstrom type.


title: Further results on geometric operators in quantum gravity

abstract:
  We investigate some properties of geometric operators in canonical quantum
gravity in the connection approach \`a la Ashtekar, which are associated with
volume, area and length of spatial regions. We motivate the construction of
analogous discretized lattice quantities, compute various quantum commutators
of the type [area,volume], [area,length] and [volume,length], and find they are
generally non-vanishing.
  Although our calculations are performed mostly within a lattice-regularized
approach, some are -- for special, fixed spin-network configurations --
identical with corresponding continuum computations. Comparison with the
structure of the discretized theory leads us to conclude that anomalous
commutators may be a general feature of operators constructed along similar
lines within a continuum loop representation of quantum general relativity. --
The validity of the lattice approach remains unaffected.


title:
Gravitational Waves in Brans-Dicke Theory : Analysis by Test Particles
  around a Kerr Black Hole

abstract:
  Analyzing test particles falling into a Kerr black hole, we study
gravitational waves in Brans-Dicke theory of gravity. First we consider a test
particle plunging with a constant azimuthal angle into a rotating black hole
and calculate the waveform and emitted energy of both scalar and tensor modes
of gravitational radiation. We find that the waveform as well as the energy of
the scalar gravitational waves weakly depends on the rotation parameter of
black hole $a$ and on the azimuthal angle.
  Secondly, using a model of a non-spherical dust shell of test particles
falling into a Kerr black hole, we study when the scalar modes dominate. When a
black hole is rotating, the tensor modes do not vanish even for a ``spherically
symmetric" shell, instead a slightly oblate shell minimizes their energy but
with non-zero finite value, which depends on Kerr parameter $a$. As a result,
we find that the scalar modes dominate only for highly spherical collapse, but
they never exceed the tensor modes unless the Brans-Dicke parameter
$\omega_{BD} \lsim 750 $ for $a/M=0.99$ or unless $\omega_{BD} \lsim 20,000 $
for $a/M=0.5$, where $M$ is mass of black hole.
  We conclude that the scalar gravitational waves with $\omega_{BD} \lsim$
several thousands do not dominate except for very limited situations
(observation from the face-on direction of a test particle falling into a
Schwarzschild black hole or highly spherical dust shell collapse into a Kerr
black hole). Therefore observation of polarization is also required when we
determine the theory of gravity by the observation of gravitational waves.


title:
Cosmic censorship and spherical gravitational collapse with tangential
  pressure

abstract:
  We study the spherical gravitational collapse of a compact object under the
approximation that the radial pressure is identically zero, and the tangential
pressure is related to the density by a linear equation of state. It turns out
that the Einstein equations can be reduced to the solution of an integral for
the evolution of the area radius. We show that for positive pressure there is a
finite region near the center which necessarily expands outwards, if collapse
begins from rest. This region could be surrounded by an inward moving one which
could collapse to a singularity - any such singularity will necessarily be
covered by a horizon. For negative pressure the entire object collapses
inwards, but any singularities that could arise are not naked. Thus the nature
of the evolution is very different from that of dust, even when the ratio of
pressure to density is infinitesimally small.


title: Topology of Event Horizon

abstract:
  The topologies of event horizons are investigated. Considering the existence
of the endpoint of the event horizon, it cannot be differentiable. Then there
are the new possibilities of the topology of the event horizon though they are
excluded in smooth event horizons. The relation between the topology of the
event horizon and the endpoint of it is revealed. A torus event horizon is
caused by two-dimensional endpoints. One-dimensional endpoints provide the
coalescence of spherical event horizons. Moreover, these aspects can be removed
by an appropriate timeslicing. The result will be useful to discuss the
stability and generality of the topology of the event horizon.


title: Semiclassical effects in black hole interiors

abstract:
  First-order semiclassical perturbations to the Schwarzschild black hole
geometry are studied within the black hole interior. The source of the
perturbations is taken to be the vacuum stress-energy of quantized scalar,
spinor, and vector fields, evaluated using analytic approximations developed by
Page and others (for massless fields) and the DeWitt-Schwinger approximation
(for massive fields). Viewing the interior as an anisotropic collapsing
cosmology, we find that minimally or conformally coupled scalar fields, and
spinor fields, decrease the anisotropy as the singularity is approached, while
vector fields increase the anisotropy. In addition, we find that massless
fields of all spins, and massive vector fields, strengthen the singularity,
while massive scalar and spinor fields tend to slow the growth of curvature.


title:
Dynamical Topology Change, Compactification and Waves in String
  Cosmology

abstract:
  Exact string solutions are presented, where moduli fields are varying with
time. They provide examples where a dynamical change of the topology of space
is occurring. Some other solutions give cosmological examples where some
dimensions are compactified dynamically or simulate pre-big bang type
scenarios. Some lessons are drawn concerning the region of validity of
effective theories and how they can be glued together, using stringy
information in the region where the geometry and topology are not well defined
from the low energy point of view. Other time dependent solutions are presented
where a hierarchy of scales is absent. Such solutions have dynamics which is
qualitatively different and resemble plane gravitational waves. (Talk given at
the Trieste Spring School and Workshop, 1994.)


title: Why we can not see the curvature of the quantum state space?

abstract:
  A new type of gauge quantum theory (superrelativity) has been proposed. This
differs from ordinary gauge theories in sense that the affine connection of our
theory is constructed from first derivatives of the Fubini-Study metric tensor.
That is we have not merely analogy with general relativity but this
construction should presumably provide a unification of general relativity and
quantum theory. Here we shall discuss the physical meaning of metric properties
of the projective Hilbert space and manifestation of its nontrivial physical
character.


title: Latticing quantum gravity

abstract:
  I discuss some aspects of a lattice approach to canonical quantum gravity in
a connection formulation, discuss how it differs from the continuum
construction, and compare the spectra of geometric operators - encoding
information about components of the spatial metric - for some simple lattice
quantum states.


title:
Cumulative Dragging - An Intrinsic Characteristic of Stationary
  Axisymmetric Spacetime

abstract:
  The Cumulative Drag Index defined recently by Prasanna has been generalised
to include the centrifugal acceleration. We have studied the behaviour of the
drag index for the Kerr metric and the Neugebauer-Meinel metric representing a
self-gravitating rotating disk and their Newtonian approximations. The
similarity of the behaviour of the index for a given set of parameters both in
the full and approximated forms, suggests that the index characterises an
intrinsic property of spacetime with rotation. Analysing the index for a given
set of parameters shows possible constraints on them.


title: Geodesic Deviation of Photons in Einstein and Higher Derivative Gravity

abstract:
  We derive the wave equation obeyed by electromagnetic fields in curved
spacetime. We find that there are Riemann and Ricci curvature coupling terms to
the photon polarisation which result in a polarisation dependent deviation of
the photon trajectories from null geodesics. Photons are found to have an
effective mass in an external gravitational field and their velocity in a local
inertial frame is in general less than $c$. The effective photon mass in the
Schwarzschild metric is $m_\gamma = ( 2GM/r^3 )^{1/2}$ and near the horizon it
is larger than the Hawking temperature of the blackhole. Our result implies
that Hawking radiation of photons would not take place. We also conclude that
there is no superluminal photon velocity in higher derivative gravity theories
(arising from QED radiative corrections), as has been claimed in literature. We
show that these erroneous claims are due to the neglect of the Riemann and
Ricci coupling terms which exist in Einstein's gravity.


title:
Behaviour of the Centrifugal Force and of Ellipticity for a Slowly
  Rotating Fluid Configuration with Different Equations of State

abstract:
  We have evaluated the centrifugal force acting on a fluid element and the
ellipticity of the fluid configuration, which is slowly rotating, using the
Hartle-Thorne solution for different equations of state. The centrifugal force
shows a maximum in every case, whereas the reversal in sign could be seen in
only one case, and the system becomes unstable in other cases. The ellipticity
as calculated from the usual definition shows maxima, whereas the definition
obtained from the equilibration of the inertial forces, shows a negative
behaviour, indicating that the system is prolate and not oblate. This prolate
shape of the configuration is similar to the one earlier found by Pfister and
Braun for a rotating shell of matter, using the correct centrifugal force
expression for the interior. The location of the centrifugal maxima gets
farther away from the Schwarzschild radius as the equation of state gets
softer.


title: Instability of an "Approximate Black Hole"

abstract:
  We investigate the stability of a family of spherically symmetric static
solutions in vacuum Brans-Dicke theory (with $\omega=0$) recently described by
van Putten. Using linear perturbation theory, we find one exponentially growing
mode for every member of the family of solutions, and thus conclude that the
solutions are not stable. Using a previously constructed code for spherically
symmetric Brans-Dicke, additional evidence for instability is provided by
directly evolving the static solutions with perturbations. The full non-linear
evolutions also suggest that the solutions are black-hole-threshold critical
solutions.


title: Solutions of arbitrary topology in 1+1 gravity

abstract:
  We present a classification of all global solutions for generalized 2D
dilaton gravity models (with Lorentzian signature). While for some of the
popular choices of potential-like terms in the Lagrangian, describing, e.g.,
string inspired dilaton gravity or spherically reduced gravity, the possible
topologies of the resulting spacetimes are restricted severely, we find that
for generic choices of these `potentials' there exist maximally extended
solutions to the field equations on all non-compact two-surfaces.


title: Exactly Soluble Sector of Quantum Gravity

abstract:
  Cartan's spacetime reformulation of the Newtonian theory of gravity is a
generally-covariant Galilean-relativistic limit-form of Einstein's theory of
gravity known as the Newton-Cartan theory. According to this theory, space is
flat, time is absolute with instantaneous causal influences, and the degenerate
`metric' structure of spacetime remains fixed with two mutually orthogonal
non-dynamical metrics, one spatial and the other temporal. The spacetime
according to this theory is, nevertheless, curved, duly respecting the
principle of equivalence, and the non-metric gravitational connection-field is
dynamical in the sense that it is determined by matter distributions. Here,
this generally-covariant but Galilean-relativistic theory of gravity with a
possible non-zero cosmological constant, viewed as a parameterized gauge theory
of a gravitational vector-potential minimally coupled to a complex
Schroedinger-field (bosonic or fermionic), is successfully cast -- for the
first time -- into a manifestly covariant Lagrangian form. Then, exploiting the
fact that Newton-Cartan spacetime is intrinsically globally-hyperbolic with a
fixed causal structure, the theory is recast both into a constraint-free
Hamiltonian form in 3+1-dimensions and into a manifestly covariant reduced
phase-space form with non-degenerate symplectic structure in 4-dimensions.
Next, this Newton-Cartan-Schroedinger system is non-perturbatively quantized
using the standard C*-algebraic technique combined with the geometric procedure
of manifestly covariant phase-space quantization. The ensuing unitary quantum
field theory of Newtonian gravity coupled to Galilean-relativistic matter is
not only generally-covariant, but also exactly soluble.


title: Cosmic strings in dilaton gravity

abstract:
  We examine the metric of an isolated self-gravitating abelian-Higgs vortex in
dilatonic gravity for arbitrary coupling of the vortex fields to the dilaton.
We look for solutions in both massless and massive dilaton gravity. We compare
our results to existing metrics for strings in Einstein and Jordan-Brans-Dicke
theory. We explore the generalization of Bogomolnyi arguments for our vortices
and comment on the effects on test particles.


title: Gravitational Instanton for Black Hole Radiation

abstract:
  Hawking radiation is derived from the existence of a euclidean instanton
which lives in the euclidean black hole geometry. Upon taking into account the
gravitational field of the instanton itself, its action is exactly equal to one
quarter the change in the horizon area. This result also applies to the
Schwinger process, the Unruh process, and particle creation in deSitter space.
The implications for horizon thermodynamics are discussed.


title: The Structure of Singularity in Spherical Inhomogeneous Dust Collapse

abstract:
  We study here the structure of singularity forming in gravitational collapse
of spherically symmetric inhomogeneous dust. Such a collapse is described by
the Tolman-Bondi-Lema{\^i}tre metric, which is a two-parameter family of
solutions to Einstein equations, characterized by two free functions of the
radial coordinate, namely the `mass function' F(r) and the `energy function'
f(r). The main new result here relates, in a general way, the formation of
black holes and naked shell-focusing singularities resulting as the final fate
of such a collapse to the generic form of regular initial data. Such a data is
characterized in terms of the density and velocity profiles of the matter,
specified on an initial time slice from which the collapse commences. Several
issues regarding the strength and stability of these singularities, when they
are naked, are examined with the help of the analysis developed here. In
particular, it is seen that strong curvature naked singularities can develop
from a generic form of initial data in terms of the initial density profiles
for the collapsing configuration. We also establish here that similar results
hold for black hole formation as well. We also discuss here the physical
constraints on the initial data for avoiding shell-crossing singularities; and
also the shell-focusing naked singularities, so that the collapse will
necessarily end as a black hole, preserving the cosmic censorship. These
results generalize several earlier works on inhomogeneous dust collapse as
special cases, and provide a clearer insight into the phenomena of black hole
and naked singularity formation in gravitational collapse.


title: Square-root quantization: application to quantum black holes

abstract:
  Two different ways of quantizing the relativistic Hamiltonian for radial
motion in the field of Coulomb-like potential are compared. The results depend
slightly on choice of time. In the case of Lorentzian time a Sommerfeld
spectrum is recovered. Application to quantum black holes gives a sqrt{n} mass
spectrum with about the same numerical factors.


title: Semiclassical quantum states for black holes

abstract:
  I discuss the semiclassical approximation for the Wheeler-DeWitt equation
when applied to the CGHS model and spherically symmetric gravity. Special
attention is devoted to the issues of Hawking radiation, decoherence of
semiclassical states, and black hole entropy.


title: Numerical Integration of Nonlinear Wave Equations for General Relativity

abstract:
  A second-order numerical implementation is given for recently derived
nonlinear wave equations for general relativity. The Gowdy T$^3$ cosmology is
used as a test bed for studying the accuracy and convergence of simulations of
one-dimensional nonlinear waves. The complete freedom in space-time slicing in
the present formulation is exploited to compute in the Gowdy line-element.
Second-order convergence is found by direct comparison of the results with
either analytical solutions for polarized waves, or solutions obtained from
Gowdy's reduced wave equations for the more general unpolarized waves. Some
directions for extensions are discussed.


title: Multimomentum Maps in General Relativity

abstract:
  The properties of multimomentum maps on null hypersurfaces, and their
relation with the constraint analysis of General Relativity, are described.
Unlike the case of spacelike hypersurfaces, some constraints which are second
class in the Hamiltonian formalism turn out to contribute to the multimomentum
map.


title: Janis-Newman-Winicour and Wyman solutions are the same

abstract:
  We show that the well-known most general static and spherically symmetric
exact solution to the Einstein-massless scalar equations given by Wyman is the
same as one found by Janis, Newman and Winicour several years ago. We obtain
the energy associated with this spacetime and find that the total energy for
the case of the purely scalar field is zero.


title: Quantum Cosmology: Problems for the 21st Century

abstract:
  Two fundamental laws are needed for prediction in the universe: (1) a basic
dynamical law and (2) a law for the cosmological initial condition. Quantum
cosmology is the area of basic research concerned with the search for a theory
of the initial cosmological state. The issues involved in this search are
presented in the form of eight problems. (To appear in Physics 2001, ed. by M.
Kumar and in the Proceedings of the 10th Yukawa-Nishinomiya Symposium},
November 7-8, 1996, Nishinomiya, Japan.)


title: Naked singularities and admissibility of initial conditions

abstract:
  Gravitational collapse of a spherically symmetric cloud has been extensively
studied to investigate the nature of resulting singularity. However, there has
been considerable debate about the admissibility of certain initial density
distributions. Using the Newtonian limit of the equations governing collapse of
a fluid with an equation of state $p=p(\rho)$ it is shown that the density
distribution has to be even function of r in a spherically symmetric situation
provided $dp/d\rho\ne0$. Implications of this result on formation of strong
naked singularities are examined.


title: Topology Change in Canonical Quantum Cosmology

abstract:
  We develop the canonical quantization of a midisuperspace model which
contains, as a subspace, a minisuperspace constituted of a
Friedman-Lema\^{\i}tre-Robertson-Walker Universe filled with homogeneous scalar
and dust fields, where the sign of the intrinsic curvature of the spacelike
hypersurfaces of homogeneity is not specified, allowing the study of topology
change in these hypersurfaces. We solve the Wheeler-DeWitt equation of the
midisuperspace model restricted to this minisuperspace subspace in the
semi-classical approximation. Adopting the conditional probability
interpretation, we find that some of the solutions present change of topology
of the homogeneous hypersurfaces. However, this result depends crucially on the
interpretation we adopt: using the usual probabilistic interpretation, we find
selection rules which forbid some of these topology changes.


title:
Some Physical Consequences of Abrupt Changes in the Multipole Moments of
  a Gravitating Body

abstract:
  The Barrab\`es-Israel theory of light-like shells in General Relativity is
used to show explicitly that in general a light-like shell is accompanied by an
impulsive gravitational wave. The gravitational wave is identified by its
Petrov Type N contribution to a Dirac delta-function term in the Weyl conformal
curvature tensor (with the delta-function singular on the null hypersurface
history of the wave and shell). An example is described in which an
asymptotically flat static vacuum Weyl space-time experiences a sudden change
across a null hypersurface in the multipole moments of its isolated axially
symmetric source. A light-like shell and an impulsive gravitational wave are
identified, both having the null hypersurface as history. The stress-energy in
the shell is dominated (at large distance from the source) by the jump in the
monopole moment (the mass) of the source with the jump in the quadrupole moment
mainly responsible for the stress being anisotropic. The gravitational wave
owes its existence principally to the jump in the quadrupole moment of the
source confirming what would be expected.


title: Singular Hypersurfaces in Scalar-Tensor Theories of Gravity

abstract:
  We study singular hypersurfaces in tensor multi-scalar theories of gravity.
We derive in a distributional and then in an intrinsic way, the general
equations of junction valid for all types of hypersurfaces, in particular for
lightlike shells and write the general equations of evolution for these
objects. We apply this formalism to various examples in static spherically
symmetric spacetimes, and to the study of planar domain walls and plane
impulsive waves.


title: Sources of Predictability

abstract:
  Sources of predictability in the basic laws of physics are described in the
most general theoretical context -- the quantum theory of the universe as a
whole. (To appear in the Proceedings of the conference on Fundamental Sources
of Unpredictability held at the Santa Fe Institute, March 28 to 30, 1996 to be
published by Complexity.)


title: Covariant Energy-Momentum Conservation In General Relativity

abstract:
  A covariant formula for conserved currents of energy, momentum and
angular-momentum is derived from a general form of Noethers theorem applied
directly to the Einstein-Hilbert action of classical general relativity. Energy
conservation in a closed big-bang cosmology is discussed as a special case.
Special care is taken to distinguish between kinematic and dynamic expressions.


title: Is mass conformally invariant?

abstract:
  By using the Garfinkle, Horowitz and Strominger black hole solutions as
examples, we illustrate that, with respect to the reference action functional
proposed by Hawking and Horowitz, the asymptotic mass parameter is not
invariant between two conformally related static spherically symmetric metrics.


title: The graviton background at early times in string cosmology

abstract:
  We discuss some peculiar properties of the stochastic graviton background
predicted by string cosmology. At Planckian times, for the values of the
parameters of the model which are more interesting for the detection in
gravitational wave experiments, the number density of gravitons is
parametrically large compared to Planck density, and is peaked at small
energies. The large parameter is related to the duration of the string phase
and is a characteristic of string cosmology. The typical interaction time is
parametrically larger than the Planck or string time. Therefore the shape of
the graviton spectrum is not distorted by thermal effects in the Planck era and
can carry informations on the pre-big bang phase suggested by string cosmology.


title: Quantizing canonical gravity in the real domain

abstract:
  We advocate an alternative description of canonical gravity in 3+1
dimensions, obtained by using as the basic variable a real variant of the usual
Ashtekar connection variables on the spatial three-manifold. With this ansatz,
no non-trivial reality conditions have to be solved, and the Hamiltonian
constraint, though non-polynomial, can be quantized rigorously in a lattice
regularization.


title: Still on the way to quantizing gravity

abstract:
  I review and discuss some recent developments in non-perturbative approaches
to quantum gravity, with an emphasis on discrete formulations, and those coming
from a classical connection description.


title:
Binary Neutron Stars in Quasi-Equilibrium Circular Orbit: A Fully
  Relativistic Treatment

abstract:
  We present a numerical scheme that solves the initial value problem in full
general relativity for a binary neutron star in quasi-equilibrium. While
Newtonian gravity allows for a strict equilibrium, a relativistic binary system
emits gravitational radiation, causing the system to lose energy and slowly
spiral inwards. However, since inspiral occurs on a time scale much longer than
the orbital period, we can adopt a quasi-equilibrium approximation. In this
approximation, we integrate a subset of the Einstein equations coupled to the
equations of relativistic hydrodynamics to solve the initial value problem for
binaries of arbitrary separation, down to the innermost stable orbit.


title: Wave-particle duality in general relativity

abstract:
  In this paper a one to one correspondence is established between space-time
metrics of general relativity and the wave equations of quantum mechanics. This
is done by first taking the square root of the metric associated with a space
and from there, passing directly to a corresponding expression in the dual
space. It is shown that in the case of a massless particle, Maxwell's equation
for a photon follows while in the case of a particle with mass, Dirac's
equation results as a first approximation. Moreover, this one to one
correspondence suggests a natural explanation of wave-particle duality. As a
consequence, the distinction between quantum mechanics and classical
relativistic mechanics is more clearly understood and the key role of initial
conditions is emphasized. PACS NUMBERS: 03.65, 04.60


title: The two-phase approximation for black hole collisions: Is it robust?

abstract:
  Recently Abrahams and Cook devised a method of estimating the total radiated
energy resulting from collisions of distant black holes by applying Newtonian
evolution to the holes up to the point where a common apparent horizon forms
around the two black holes and subsequently applying Schwarzschild perturbation
techniques . Despite the crudeness of their method, their results for the case
of head-on collisions were surprisingly accurate. Here we take advantage of the
simple radiated energy formula devised in the close-slow approximation for
black hole collisions to test how strongly the Abrahams-Cook result depends on
the choice of moment when the method of evolution switches over from Newtonian
to general relativistic evolution. We find that their result is robust, not
depending strongly on this choice.


title: Dynamics of spin-2 fields in Kerr background geometries

abstract:
  We have developed a numerical method for evolving perturbations of rotating
black holes. Solutions are obtained by integrating the Teukolsky equation
written as a first-order in time, coupled system of equations, in a form that
explicitly exhibits the radial characteristic directions. We follow the
propagation of generic initial data through the burst, quasi-normal ringing and
power-law tail phases. Future results may help to clarify the role of black
hole angular momentum on signals produced during the final stages of black hole
coalescence.


title: Multidimensional Topological Foam

abstract:
  Multidimensional cosmological model with the topology M=RxM_1xM_2x...xM_n
where M_i (i=1,... ,n) undergo a chain splitting into arbitrary number of
compact spaces is considered. It is shown that equations of motion can be
solved exactly because they depend only on the effective curvatures and
dimensions and "forget" about inner topological structure. It is proved that
effective cosmological action for the model with n=1 in the case of infinite
splitting of the internal space coincides with the tree-level effective action
for a bosonic string.


title: Cosmological Limits on Slightly Skew Stresses

abstract:
  We present an analysis of the cosmological evolution of matter sources with
small anisotropic pressures. This includes electric and magnetic fields,
collisionless relativistic particles, gravitons, antisymmetric axion fields in
low-energy string cosmologies, spatial curvature anisotropies, and stresses
arising from simple topological defects. We calculate their evolution during
the radiation and dust eras of an almost isotropic universe. In many
interesting cases the evolution displays a special critical behaviour created
by the non-linear evolution of the pressure and expansion anisotropies. The
isotropy of the microwave background is used to place strong limits of order
$\Omega _{a0}\leq 5\times 10^{-6}\Delta (1+z_{rec})^{-\Delta }$on the possible
contribution of these matter sources to the total density of the universe,
where $1\leq \Delta \leq 3$ characterises the anisotropic stress. The present
abundance of an anisotropic stress which becomes non-relativistic at a
characteristic low-energy scale is also calculated. We explain why the limits
obtained from primordial nucleosynthesis are generally weaker than those
imposed by the microwave background isotropy. The effect of inflation on these
stresses is also calculated.


title:
Measuring gravitational waves from binary black hole coalescences: I.
  Signal to noise for inspiral, merger, and ringdown

abstract:
  We estimate the expected signal-to-noise ratios (SNRs) from the three phases
(inspiral,merger,ringdown) of coalescing binary black holes (BBHs) for initial
and advanced ground-based interferometers (LIGO/VIRGO) and for space-based
interferometers (LISA). LIGO/VIRGO can do moderate SNR (a few tens), moderate
accuracy studies of BBH coalescences in the mass range of a few to about 2000
solar masses; LISA can do high SNR (of order 10^4) high accuracy studies in the
mass range of about 10^5 to 10^8 solar masses. BBHs might well be the first
sources detected by LIGO/VIRGO: they are visible to much larger distances (up
to 500 Mpc by initial interferometers) than coalescing neutron star binaries
(heretofore regarded as the "bread and butter" workhorse source for LIGO/VIRGO,
visible to about 30 Mpc by initial interferometers). Low-mass BBHs (up to 50
solar masses for initial LIGO interferometers; 100 for advanced; 10^6 for LISA)
are best searched for via their well-understood inspiral waves; higher mass
BBHs must be searched for via their poorly understood merger waves and/or their
well-understood ringdown waves. A matched filtering search for massive BBHs
based on ringdown waves should be capable of finding BBHs in the mass range of
about 100 to 700 solar masses out to 200 Mpc (initial LIGO interferometers),
and 200 to 3000 solar masses out to about z=1 (advanced interferometers). The
required number of templates is of order 6000 or less. Searches based on merger
waves could increase the number of detected massive BBHs by a factor of order
10 or more over those found from inspiral and ringdown waves, without detailed
knowledge of the waveform shapes, using a "noise monitoring" search algorithm.
A full set of merger templates from numerical relativity could further increase
the number of detected BBHs by an additional factor of up to 4.


title: Quantum Aspects of Ergoregion Instability

abstract:
  It has been known classically that a star with an ergoregion but no event
horizon is unstable to the emission of scalar, electromagnetic and
gravitational waves. This classical ergoregion instability is characterized by
complex frequency modes. We show how to canonically quantize a neutral scalar
field in the presence of such unstable modes by considering a simple model for
a rapidly rotating star. Some of interesting results is that there exists a
physically meaningful mode decomposition including unstable normal mode
solutions whose representation turns out to be a non-Fock-like Hilbert space. A
``particle" detector model placed in the in-vacuum state also shows that stars
with ergoregions give rise to a spontaneous energy radiation to spatial
infinity until ergoregions disappear.


title: Spin Networks and Recoupling in Loop Quantum Gravity

abstract:
  I discuss the role played by the spin-network basis and recoupling theory (in
its graphical tangle-theoretic formulation) and their use for performing
explicit calculations in loop quantum gravity. In particular, I show that
recoupling theory allows the derivation of explicit expressions for the
eingenvalues of the quantum volume operator. An important side result of these
computations is the determination of a scalar product with respect to which
area and volume operators are symmetric, and the spin network states are
orthonormal.