title: Inflation in Multidimensional Quantum Cosmology

abstract:
  We extend to multidimensional cosmology Vilenkin's prescription of tunnelling
from nothing for the quantum origin of the observable Universe. Our model
consists of a $D+4$-dimensional spacetime of topology ${\cal R}\times {\cal
S}^3 \times{\cal S}^D$, with a scalar field (``chaotic inflaton'') for the
matter component. Einstein gravity and Casimir compactification are assumed.
The resulting minisuperspace is 3--dimensional. Patchwise we find an
approximate analytic solution of the Wheeler--DeWitt equation through which we
discuss the tunnelling picture and the probability of nucleation of the
classical Universe with compactifying extra dimensions. Our conclusion is that
the most likely initial conditions, although they do not lead to the
compactification of the internal space, still yield (power-law) inflation for
the outer space. The scenario is physically acceptable because the inner space
growth is limited to $\sim 10^{11}$ in 100 e-foldings of inflation, starting
from the Planck scale.


title: Anisotropic Inflation from Extra Dimensions

abstract:
  Vacuum multidimensional cosmological models with internal spaces being
compact $n$-dimensional Lie group manifolds are considered. Products of
3-spheres and $SU(3)$ manifold (a novelty in cosmology) are studied. It turns
out that the dynamical evolution of the internal space drives an accelerated
expansion of the external world (power law inflation). This generic solution
(attractor in a phase space) is determined by the Lie group space without any
fine tuning or arbitrary inflaton potentials. Matter in the four dimensions
appears in the form of a number of scalar fields representing anisotropic scale
factors for the internal space. Along the attractor solution the volume of the
internal space grows logarithmically in time. This simple and natural model
should be completed by mechanisms terminating the inflationary evolution and
transforming the geometric scalar fields into ordinary particles.


title: A causal statistical family of dissipative divergence type fluids

abstract:
  In this paper we investigate some properties, including causality, of a
particular class of relativistic dissipative fluid theories of divergence type.
This set is defined as those theories coming from a statistical description of
matter, in the sense that the three tensor fields appearing in the theory can
be expressed as the three first momenta of a suitable distribution function. In
this set of theories the causality condition for the resulting system of
hyperbolic partial differential equations is very simple and allow to identify
a subclass of manifestly causal theories, which are so for all states outside
equilibrium for which the theory preserves this statistical interpretation
condition. This subclass includes the usual equilibrium distributions, namely
Boltzmann, Bose or Fermi distributions, according to the statistics used,
suitably generalized outside equilibrium. Therefore this gives a simple proof
that they are causal in a neighborhood of equilibrium. We also find a bigger
set of dissipative divergence type theories which are only pseudo-statistical,
in the sense that the third rank tensor of the fluid theory has the symmetry
and trace properties of a third momentum of an statistical distribution, but
the energy-momentum tensor, while having the form of a second momentum
distribution, it is so for a different distribution function. This set also
contains a subclass (including the one already mentioned) of manifestly causal
theories.


title: Spinning Black Holes in (2+1)-dimensional String and Dilaton Gravity

abstract:
  We present a new class of spinning black hole solutions in
$(2+1)$-dimensional general relativity minimally coupled to a dilaton with
potential $e^{b\phi}\Lambda$. When $b=4$, the corresponding spinning black hole
is a solution of low energy $(2+1)$-dimensional string gravity. Apart from the
limiting case of the $BTZ$ black hole, these spinning black holes have no inner
horizon and a curvature singularity only at the origin. We compute the mass and
angular momentum parameters of the solutions at spatial infinity, as well as
their temperature and entropy.


title: The Equivalence Principle and g-2 Experiments

abstract:
  We consider the possibility of using measurements of anomalous magnetic
moments of elementary particles as a possible test of the Einstein Equivalence
Principle (EEP). For the class non-metric theories of gravity described by the
\tmu formalism we find several novel mechanisms for breaking the EEP, and
discuss the possibilities of setting new empirical constraints on such effects.


title: Quantum Field Theory Constrains Traversable Wormhole Geometries

abstract:
  Recently a bound on negative energy densities in four-dimensional Minkowski
spacetime was derived for a minimally coupled, quantized, massless, scalar
field in an arbitrary quantum state. The bound has the form of an uncertainty
principle-type constraint on the magnitude and duration of the negative energy
density seen by a timelike geodesic observer. When spacetime is curved and/or
has boundaries, we argue that the bound should hold in regions small compared
to the minimum local characteristic radius of curvature or the distance to any
boundaries, since spacetime can be considered approximately Minkowski on these
scales. We apply the bound to the stress-energy of static traversable wormhole
spacetimes. Our analysis implies that either the wormhole must be only a little
larger than Planck size or that there is a large discrepancy in the length
scales which characterize the wormhole. In the latter case, the negative energy
must typically be concentrated in a thin band many orders of magnitude smaller
than the throat size. These results would seem to make the existence of
macroscopic traversable wormholes very improbable.


title:
Analytical Solving of Partial Differential Equations using Symbolic
  Computing

abstract:
  This work presents a brief discussion and a plan towards the analytical
solving of Partial Differential Equations (PDEs) using symbolic computing, as
well as an implementation of part of this plan as the PDEtools software-package
of commands.


title: Quantum Geometry and Gravity

abstract:
  The geometro-stochastic method of quantization provides a framework for
quantum general relativity, in which the principal frame bundles of local
Lorentz frames that underlie the fibre-theoretical approach to classical
general relativity are replaced by Poincar\'e-covariant quantum frame bundles.
In the semiclassical regime for quantum field theory in curved spacetime, where
the gravitational field is not quantized, the elements of these local quantum
frames are generalized coherent states, which emerge naturally from phase space
representations of the Poincar\'e group. Due to their informational
completeness, these quantum frames are capable of taking over the role played
by complete sets of observables in conventional quantum theory. The propagation
of quantum-geometric fields proceeds by path integral methods, based on
parallel transport along broken paths consisting of arcs of geodesics of the
Levi-Civita connection. The formulation of quantum gravity within this
framework necessitates the transition to quantum superframe bundles and a
quantum gravitational supergroup capable of incorporating diffeomorphism
invariance into the framework. This results in a geometric version of quantum
gravity which shares some conceptual features with covariant as well as with
canonical gravity, but which avoids the foundational and the mathematical
difficulties encountered by these two approaches.


title: Black hole solutions in 2+1 dimensions

abstract:
  We give circularly symmetric solutions for null fluid collapse in
2+1-dimensional Einstein gravity with a cosmological constant. The fluid
pressure $P$ and energy density $\rho$ are related by $P=k\rho$ $(k\le 1)$. The
long time limit of the solutions are black holes whose horizon structures
depend on the value of $k$. The $k=1$ solution is the
Banados-Teitelboim-Zanelli black hole metric in the long time static limit,
while the $k<1$ solutions give other, `hairy' black hole metrics in this limit.


title: Quantum Theory of Non-Relativistic Particles Interacting with Gravity

abstract:
  We investigate the effects of the gravitational field on the quantum dynamics
of non-relativistic particles. We consider N non-relativistic particles,
interacting with the linearized gravitational field. Using the Feynman - Vernon
influence functional technique, we trace out the graviton field, to obtain a
master equation for the system of particles to first order in $G$. The
effective interaction between the particles, as well as the self-interaction is
non-local in time and in general non-markovian. We show that the gravitational
self-interaction cannot be held responsible for decoherence of microscopic
particles due to the fast vanishing of the diffusion function. For macroscopic
particles though, it leads to diagonalization to the energy eigenstate basis, a
desirable feature in gravity induced collapse models. We finally comment on
possible applications.


title: Extreme Dilatonic Black Holes on a Torus

abstract:
  The interaction of maximally-charged dilatonic black holes on $R^{4}\times
T^{d}$ is studied in the low-velocity limit. In particular, the scattering of
two black holes on $R^{4}\times S^{1}$ is investigated.


title: FRW Cosmologies with Adiabatic Matter Creation

abstract:
  Some properties of cosmological models with matter creation are investigated
in the framework of the Friedman-Robertson-Walker (FRW) line element. For
adiabatic matter creation, as developed by Prigogine and coworkers, we derive a
simple expression relating the particle number density $n$ and energy density
$\rho$ which holds regardless of the matter creation rate. The conditions to
generate inflation are discussed and by considering the natural
phenomenological matter creation rate $\psi =3 \beta nH$, where $\beta$ is a
pure number of the order of unity and $H$ is the Hubble parameter, a minimally
modified hot big-bang model is proposed. The dynamic properties of such models
can be deduced from the standard ones simply by replacing the adiabatic index
$\gamma$ of the equation of state by an effective parameter $\gamma_{*} =
\gamma (1 - \beta)$. The thermodynamic behavior is determined and it is also
shown that ages large enough to agree with observations are obtained even given
the high values of $H$ suggested by recent measurements.


title: Complex lapse, complex action and path integrals

abstract:
  Imaginary time is often used in quantum tunnelling calculations. This article
advocates a conceptually sounder alternative: complex lapse. In the ``3+1''
action for the Einstein gravitational field minimally coupled to a Klein-Gordon
field, allowing the lapse function to be complex yields a complex action which
generates both the usual Lorentzian theory and its Riemannian analogue, and in
particular allows a change of signature between the two. The action and
variational equations are manifestly well defined in the Hamiltonian
representation, with the momentum fields consequently being complex. The
complex action interpolates between the Lorentzian and Riemannian actions as
they appear formally in the respective path integrals. Thus the complex-lapse
theory provides a unified basis for a path-integral quantum theory of gravity
involving both Lorentzian and Riemannian aspects. A major motivation is the
quantum-tunnelling scenario for the origin of the universe. Taken as an
explanation for the observed quantum tunnelling of particles, the complex-lapse
theory determines that the argument of the lapse for the universe now is
extremely small but negative.


title:
Stress-Energy-Momentum of Affine-Metric Gravity. Generalized Komar
  Superportential

abstract:
  In case of the Einstein's gravitation theory and its first order Palatini
reformulation, the stress-energy-momentum of gravity has been proved to reduce
to the Komar superpotential. We generalize this result to the affine-metric
theory of gravity in case of general connections and arbitrary Lagrangian
densities invariant under general covariant transformations. In this case, the
stress-energy-momentum of gravity comes to the generalized Komar superpotential
depending on a Lagrangian density in a precise way.


title:
Geometric Interpretation and Classification of Global Solutions in
  Generalized Dilaton Gravity

abstract:
  Two dimensional gravity with torsion is proved to be equivalent to special
types of generalized 2d dilaton gravity. E.g. in one version, the dilaton field
is shown to be expressible by the extra scalar curvature, constructed for an
independent Lorentz connection corresponding to a nontrivial torsion.
Elimination of that dilaton field yields an equivalent torsionless theory,
nonpolynomial in curvature. These theories, although locally equivalent exhibit
quite different global properties of the general solution. We discuss the
example of a (torsionless) dilaton theory equivalent to the $R^2 + T^2$--model.
Each global solution of this model is shown to split into a set of global
solutions of generalized dilaton gravity. In contrast to the theory with
torsion the equivalent dilaton one exhibits solutions which are asymptotically
flat in special ranges of the parameters. In the simplest case of ordinary
dilaton gravity we clarify the well known problem of removing the Schwarzschild
singularity by a field redefinition.


title: Kinematics and Dynamics of $f(R)$ Theories of Gravity

abstract:
  We generalise the equations governing relativistic fluid dynamics given by
Ehlers and Ellis for general relativity, and by Maartens and Taylor for
quadratic theories, to generalised $f(R)$ theories of gravity. In view of the
usefulness of this alternative framework to general relativity, its
generalisation can be of potential importance for deriving analogous results to
those obtained in general relativity. We generalise, as an example, the results
of Maartens and Taylor to show that within the framework of general $f(R)$
theories, a perfect fluid spacetime with vanishing vorticity, shear and
acceleration is Friedmann--Lema\^{\i}tre--Robertson--Walker only if the fluid
has in addition a barotropic equation of state. It then follows that the
Ehlers--Geren--Sachs theorem and its ``almost'' extension also hold for $f(R)$
theories of gravity.


title: Exact solutions for null fluid collapse

abstract:
  Exact non-static spherically symmetric solutions of the Einstein equations
for a null fluid source with pressure $P$ and density $\rho$ related by $P =
k\rho^a$ are given. The $a=1$ metrics are asymptotically flat for $1/2<k\le 1$
and cosmological for $0<k<1/2$. The $k=1$ metric is the known charged Vaidya
solution. In general the metrics have multiple apparent horizons. In the long
time limit, the asymptotically flat metrics are hairy black hole solutions that
`fall between' the Schwarzschild and Reissner-Nordstrom metrics.


title: Thermodynamics of Dilatonic Black Holes in $n$ Dimensions

abstract:
  We present a formalism for studying the thermodynamics of black holes in
dilaton gravity. The thermodynamic variables are defined on a quasilocal
surface surrounding the black hole system and are obtained from a general class
of Lagrangians involving a dilaton. The formalism thus accommodates a large
number of possible theories and black hole spacetimes. Many of the
thermodynamic quantities are identified from the contribution of the action on
the quasilocal boundary. The entropy is found using path integral techniques,
and a first law of thermodynamics is obtained. As an illustration, we calculate
the thermodynamic quantities for two black hole solutions in $(1+1)$
dimensions: one obtained from a string inspired theory and the other being a
Liouville black hole in the ``$R=\kappa T$'' theory with a Liouville field.


title: Moebius Inverse Problem for Distorted Black Holes

abstract:
  Hawking ``thermal'' radiation could be a means to detect black holes of
micron sizes, which may be hovering through the universe. We consider these
micro-black holes to be distorted by the presence of some distribution of
matter representing a convolution factor for their Hawking radiation. One may
hope to determine from their Hawking signals the temperature distribution of
their material shells by the inverse black body problem. In 1990, Nan-xian Chen
has used a so-called modified M\"{o}bius transform to solve the inverse black
body problem. We discuss and apply this technique to Hawking radiation of
distorted micro-black holes. Some comments on supersymmetric applications of
M\"{o}bius function and transform are also added.


title: Quantum Potential and Quantum Gravity

abstract:
  The quantum potential approach makes it possible to construct a complementary
picture of quantum mechanical evolution which reminds classical equation of
motion. The only difference as compared to equations of motion for the
underlying classical system is the presence of an additional potential term
being a functional of the real part of the wavefunction. In the present paper
this approach is applied to the quantum theory of gravity based on Wheeler --
De Witt equation. We describe the derivation of the `quantum Einstein equation'
and discuss the new features of their solutions.


title: Cosmic String in Scalar-Tensor Gravity

abstract:
  The gravitational properties of a local cosmic string in the framework of
scalar-tensor gravity are examined. We find the metric in the weak-field
approximation and we show that, contrary to the General Relativity case, the
cosmic string in scalar-tensor gravitation exerces a force on non-relativistic,
neutral test particle. This force is proportional to the derivative of the
conformal factor $A^{2}(\phi)$ and it is always attractive. Moreover, this
force could have played an important role at the Early Universe, although
nowadays it can be neglegible. It is also shown that the angular separation
$\delta\varphi$ remains unaltered for scalar-tensor cosmic strings.


title: $D$-Dimensional Gravity from $(D+1)$ Dimensions

abstract:
  We generalise Wesson's procedure, whereby vacuum $(4+1)-$dimensional field
equations give rise to $(3+1)-$dimensional equations with sources, to arbitrary
dimensions. We then employ this generalisation to relate the usual
$(3+1)-$dimensional vacuum field equations to $(2+1)-$dimensional field
equations with sources and derive the analogues of the classes of solutions
obtained by Ponce de Leon. This way of viewing lower dimensional gravity
theories can be of importance in establishing a relationship between such
theories and the usual 4-dimensional general relativity, as well as giving a
way of producing exact solutions in $(2+1)$ dimensions that are naturally
related to the vacuum $(3+1)-$dimensional solutions. An outcome of this
correspondence, regarding the nature of lower dimensional gravity, is that the
intuitions obtained in $(3+1)$ dimensions may not be automatically
transportable to lower dimensions.
  We also extend a number of physically motivated solutions studied by Wesson
and Ponce de Leon to $(D+1)$ dimensions and employ the equivalence between the
$(D+1)$ Kaluza-Klein theories with empty $D-$dimensional Brans-Dicke theories
(with $\omega=0$) to throw some light on the solutions derived by these
authors.


title:
New limits on the violation of the Strong Equivalence Principle in
  strong field regimes

abstract:
  The Strong Equivalence Principle (SEP) demands, besides the validity of the
Einstein Equivalence Principle, that all self-gravitating bodies feel the same
acceleration in an external gravitational field. It has been found that metric
theories of gravity other that than general relativity typically predict a
violation of the SEP. In case of the Earth-Moon system (weak field system) this
violation is called the Nordtvedt effect. It has been shown by Damour and
Sch\"afer, that small-eccentricity long-orbital-period binary pulsars with a
white dwarf companion provide excellent conditions to test the SEP in strong
field regimes. Based on newly discovered binary pulsars this paper investigates
a possible violation of the SEP in strong field regimes. New limits with an
improved confidence level are presented. The results of this paper lead to
constrains on the combination $\epsilon/2-\zeta$ of the only two
(post)$^2$-Newtonian parameters $\epsilon$ and $\zeta$ that arise from the
(post)$^2$-Newtonian approximation of the tensor-multi-scalar theory of Damour
and Esposito-Far{\`e}se.


title: Do Naked Singularities Form?

abstract:
  A naked singularity is formed by the collapse of a Sine-Gordon soliton in 1+1
dimensional dilaton gravity with a negative cosmological constant. We examine
the quantum stress tensor resulting from the formation of the singularity.
Consistent boundary conditions require that the incoming soliton is accompanied
by a flux of incoming radiation across past null infinity, but neglecting the
back reaction of the spacetime leads to the absurd conclusion that the total
energy entering the system by the time the observer is able to receive
information from the singularity is infinite. We conclude that the back
reaction must prevent the formation of the naked singularity.


title: Two-point Functions and Quantum Fields in de Sitter Universe

abstract:
  We present a theory of general two-point functions and of generalized free
fields in d-dimensional de Sitter space-time which closely parallels the
corresponding minkowskian theory. The usual spectral condition is now replaced
by a certain geodesic spectral condition, equivalent to a precise thermal
characterization of the corresponding ``vacuum''states. Our method is based on
the geometry of the complex de Sitter space-time and on the introduction of a
class of holomorphic functions on this manifold, called perikernels, which
reproduce mutatis mutandis the structural properties of the two-point
correlation functions of the minkowskian quantum field theory. The theory
contains as basic elementary case the linear massive field models in their
``preferred'' representation. The latter are described by the introduction of
de Sitter plane waves in their tube domains which lead to a new integral
representation of the two-point functions and to a Fourier-Laplace type
transformation on the hyperboloid. The Hilbert space structure of these
theories is then analysed by using this transformation. In particular we show
the Reeh-Schlieder property. For general two-point functions, a substitute to
the Wick rotation is defined both in complex space-time and in the complex mass
variable, and substantial results concerning the derivation of Kallen-Lehmann
type representation are obtained.


title: The Embedding Model of Induced Gravity with Bosonic Sources

abstract:
  We consider a theory in which spacetime is an n-dimensional surface $V_n$
embedded in an $N$-dimensional space $V_N$. In order to enable also the
Kaluza-Klein approach we admit $n > 4$. The dynamics is given by the minimal
surface action in a curved embedding space. The latter is taken, in our
specific model, as being a conformally flat space. In the quantization of the
model we start from a generalization of the Howe-Tucker action which depends on
the embedding variables ${\eta}^a (x)$ and the (intrinsic) induced metric
$g_{\mu \nu}$ on $V_n$. If in the path integral we perform only the functional
integration over ${\eta}^a (x)$, we obtain the effective action which
functionally depends on $g_{\mu \nu}$ and contains the Ricci scalar $R$ and its
higher orders $R^2$ etc. But due to our special choice of the conformal factor
in $V_N$ enterig our original action, it turns out that the effective action
contains also the source term. The latter is in general that of a
$p$-dimensional membrane ($p$-brane); in particular we consider the case of a
point particle. Thus, starting from the basic fields ${\eta}^a (x)$, we induce
not only the kinetic term for $g_{\mu \nu}$, but also the "matter" source term.


title: Solutions Stationnaires en Th\'eorie de Kaluza-Klein

abstract:
  Kaluza-Klein theory is a 5-dimensional Einstein general relativity; it has
the interest of describing on an equal footing the laws of gravitation and
electromagnetism in a geometrically unified way. We present it in Chapter 1,
and we generalize it by adding to the equations of the theory the Lanczos
tensor (endowed with the same physical properties as the Einstein tensor but
quadratic with respect to the Riemann tensor.) One has obtained in the last
decade all the spherically symmetric 2-stationary solutions (independent of
time and of the extra coordinate) of the ``special" Kaluza-Klein theory. The
study of the stability of these solutions against radial excitations is carried
out in Chapter 2. We begin by presenting the spherically symmetric 2-static
solutions; then we write and separate the perturbation-linearized equations of
the 5-metric. The problem of stability against small oscillations is reduced to
an eigenvalue problem which we discuss in detail in the static-solution
parameter space. We show that regular solutions of non-vanishing finite energy
(Kaluza-Klein solitons) --with non-euclidean spatial topology-- are stable. A
broad class of singular solutions, containing among others the Schwarzschild
solution, are also stable. Finally our stability results are compared to those
obtained previously by Tomimatsu for a less broad class of solutions. We search
in Chapter 3 for other exact stationary solutions, endowed this time with
cylindrical symmetry, thus actually 4-stationary (depending on only one
spacelike coordinate). First we obtain by a systematic study all the
4-stationary solutions of the special theory, some of which are interpreted as
neutral or charged distributional cosmic string sources. We generalize these
solutions in a following section by considering the Lanczos tensor, and we find


title: Multi-Black-Hole Geometries in (2+1)-Dimensional Gravity

abstract:
  Generalizations of the Black Hole geometry of Ba\~nados, Teitelboim and
Zanelli (BTZ) are presented. The theory is three-dimensional vacuum Einstein
theory with a negative cosmological constant. The $n$-black-hole solution has
$n$ asymptotically anti-de Sitter ``exterior" regions that join in one
``interior" region. The geometry of each exterior region is identical to that
of a BTZ geometry; in particular, each contains a black hole horizon that
surrounds (as judged from that exterior) all the other horizons. The interior
region acts as a closed universe containing $n$ black holes. The initial state
and its time development are discussed in some detail for the simple case when
the angular momentum parameters of all the black holes vanish. A procedure to
construct $n$ black holes with angular momentum (for $n \geq 4$) is also given.


title: Complex actions in two-dimensional topology change

abstract:
  We investigate topology change in (1+1) dimensions by analyzing the
scalar-curvature action $1/2 \int R dV$ at the points of metric-degeneration
that (with minor exceptions) any nontrivial Lorentzian cobordism necessarily
possesses. In two dimensions any cobordism can be built up as a combination of
only two elementary types, the ``yarmulke'' and the ``trousers.'' For each of
these elementary cobordisms, we consider a family of Morse-theory inspired
Lorentzian metrics that vanish smoothly at a single point, resulting in a
conical-type singularity there. In the yarmulke case, the distinguished point
is analogous to a cosmological initial (or final) singularity, with the
spacetime as a whole being obtained from one causal region of Misner space by
adjoining a single point. In the trousers case, the distinguished point is a
``crotch singularity'' that signals a change in the spacetime topology (this
being also the fundamental vertex of string theory, if one makes that
interpretation). We regularize the metrics by adding a small imaginary part
whose sign is fixed to be positive by the condition that it lead to a
convergent scalar field path integral on the regularized spacetime. As the
regulator is removed, the scalar density $1/2 \sqrt{-g} R$ approaches a
delta-function whose strength is complex: for the yarmulke family the strength
is $\beta -2\pi i$, where $\beta$ is the rapidity parameter of the associated
Misner space; for the trousers family it is simply $+2\pi i$. This implies that
in the path integral over spacetime metrics for Einstein gravity in three or
more spacetime dimensions, topology change via a crotch singularity is
exponentially suppressed, whereas appearance or disappearance of a universe via
a yarmulke singularity is exponentially enhanced.


title: Continuous Self-Similarity and $S$-Duality

abstract:
  We study the spherically symmetric collapse of the axion/dilaton system
coupled to gravity. We show numerically that the critical solution at the
threshold of black hole formation is continuously self-similar. Numerical and
analytical arguments both demonstrate that the mass scaling away from
criticality has a critical exponent of $\gamma = 0.264$.


title: Angular Momentum and Killing Potentials

abstract:
  When the Penrose-Goldberg (PG) superpotential is used to compute the angular
momentum of an axial symmetry, the Killing potential $Q_{(\varphi )}^{\mu\nu}$
for that symmetry is needed. Killing potentials used in the PG superpotential
must satisfy Penrose's equation. It is proved for the Schwarzschild and Kerr
solutions that the Penrose equation does not admit a $%Q_{(\varphi )}^{\mu\nu}$
at finite r and therefore the PG superpotential can only be used to compute
angular momentum asymptotically.


title: Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action

abstract:
  Barbero recently suggested a modification of Ashtekar's choice of canonical
variables for general relativity. Although leading to a more complicated
Hamiltonian constraint this modified version, in which the configuration
variable still is a connection, has the advantage of being real. In this
article we derive Barbero's Hamiltonian formulation from an action, which can
be considered as a generalization of the ordinary Hilbert-Palatini action.


title: Are there metric theories of gravity other than General Relativity?

abstract:
  Current generalizations of the classical Einstein-Hilbert Lagrangian
formulation of General Relativity are reviewed. Some alternative variational
principles are known to reproduce Einstein's gravitational equations, and
should therefore be regarded as equivalent descriptions of the same physical
model, while other variational principles ("Scalar-tensor theories" and
"Higher-derivative theories") are commonly presented as truly alternative
physical theories. Such theories, however, are also known to admit a
reformulation which is formally identical to General Relativity (with auxiliary
fields). The physical significance of this change of variables has been
questioned by several authors in recent years. Here, we investigate to which
extent purely affine, metric-affine, scalar-tensor and purely metric theories
can be regarded as physically equivalent to GR; we show that in general this
depends on which metric tensorfield is assumed to represent the true physical
space-time geometry. For purely metric theories where the Lagrangian is a
nonlinear function f(R) of the curvature scalar, we present an argument based
on the definition of the physical energy, which leads one to regard the
rescaled metric (Einstein frame) as the true physical one. As a direct
consequence, the physical content of such "alternative" models is reset to
coincide with General Relativity, and the "Nonlinear Gravity Theories" become
nothing but exotic reformulations of General Relativity in terms of unphysical
variables.


title: The Equivalence Principle and Anomalous Magnetic Moment Experiments

abstract:
  We investigate the possibility of testing of the Einstein Equivalence
Principle (EEP) using measurements of anomalous magnetic moments of elementary
particles. We compute the one loop correction for the $g-2$ anomaly within the
class of non metric theories of gravity described by the \tmu formalism. We
find several novel mechanisms for breaking the EEP whose origin is due purely
to radiative corrections. We discuss the possibilities of setting new empirical
constraints on these effects.


title: Correlations of Quantum Fields on Robertson-Walker Spacetimes

abstract:
  It is a well known fact that quantum fields on Minkowski spacetime are
correlated for each pair of spacetime regions. In Robertson-Walker spacetimes
there are spacelike separated regions with disjoint past horizons but the
absence of correlations in that case was never proved. We derive in this paper
formulae for correlations of quantum fields on Robertson-Walker spacetimes.
Such correlations could have reasonably influenced the formation of structure
in the early universe. We use methods of algebraic and constructive quantum
field theory.


title: Spectrum of the Volume Operator in Quantum Gravity

abstract:
  The volume operator is an important kinematical quantity in the
non-perturbative approach to four-dimensional quantum gravity in the connection
formulation. We give a general algorithm for computing its spectrum when acting
on four-valent spin network states, evaluate some of the eigenvalue formulae
explicitly, and discuss the role played by the Mandelstam constraints.


title:
Centaurus A as a source of extragalactic cosmic rays with arrival
  energies well beyond the GZK cutoff

abstract:
  The ultra--high energy cosmic rays recently detected by several air shower
experiments could have an extragalactic origin. In this case, the nearest
active galaxy Centaurus A might be the source of the most energetic particles
ever detected on Earth. We have used recent radio observations in order to
estimate the arrival energy of the protons accelerated by strong shock fronts
in the outer parts of this southern radio source. We expect detections
corresponding to particles with energies up to $\sim 2.2 \times 10^{21}$ eV and
an arrival direction of ($l \approx 310^{\circ}$, $b \approx 20^{\circ}$) in
galactic coordinates. The future Southern Hemisphere Pierre Auger Observatory
might provide a decisive test for extragalactic models of the origin of the
ultra--high energy cosmic rays.


title:
Search templates for gravitational waves from inspiraling binaries:
  Choice of template spacing

abstract:
  It has long been known that the search for gravitational waves from
inspiraling binaries must be aided by signal processing methods, and that the
technique of matched filtering is the most likely to be used for the detection
of inspiral ``chirps''. This means that the output of an interferometer must be
cross- correlated with many waveform templates to dig out faint signals buried
in the noise. The templates are characterized by several parameters which vary
continuously over some finite range; but because the amount of computing power
available to perform the cross-correlations of the search templates with the
output is finite, the actual templates used must be picked with certain
discrete values of these parameters, which will have some finite spacing. If
the spacing is too small, the number of templates (and therefore the computing
power) needed to perform an on-line search becomes prohibitive; if the spacing
is too large, many chirps will not be detected because the values of their
parameters lie too far from those of the nearest template. In this paper I use
differential geometry to extend the earlier formalism of Sathyaprakash and
Dhurandhar to estimate the template spacing, number of templates, and computing
power required for a single-pass, on-line search of the output of a single
interferometer in terms of the fraction of events lost to parameter
discretization. My formalism obtains these results with little numerical
computation, and is valid for arbitrary noise spectra and template
parameterizations. I find that the computing power needed for the most
computationally intensive, reasonable search is of order several hundred
Gigaflops. This will be feasible by the time LIGO is operational, but it is
worth pursuing methods of reducing this number.


title: First Order Corrections to the Unruh Effect

abstract:
  First order corrections to the Unruh effect are calculated from a model of an
accelerated particle detector of finite mass. We show that quantum smearing of
the trajectory and large recoil essentially do not modify the Unruh effect.
Nevertheless, we find corrections to the thermal distribution and to the Unruh
temperature. In a certain limit, when the distribution at equilibrium remains
exactly thermal, the corrected temperature is found to be $T = T_U( 1 -
T_U/M)$, where $T_U$ is the Unruh temperature. We estimate the consequent
corrections to the Hawking temperature and the black hole entropy, and comment
on the relationship to the problem of trans-planckian frequencies.


title: Causal structure and diffeomorphismsm in Ashtekar's gravity

abstract:
  A manifestly diffeomorphism invariant extension of Einstein gravity is
constructed, which includes singular metrics, and whose ADM formulation is
Ashtekar's gravity. The latter is shown to be locally equivalent to the
covariant theory. It turns out that exactly those kinds of degenerate four
dimensional metrics are allowed which do not destroy the causal structure of
spacetime. It is also shown that Ashtekar's gravity possesses an extension that
provides a local SO(3,C) invariance, without complexifying or changing the
signature of the metric.


title: Dirac Equation in Gauge and Affine-Metric Gravitation Theories

abstract:
  We show that the covariant derivative of Dirac fermion fields in the presence
of a general linear connection on a world manifold is universal for Einstein's,
gauge and affine-metric gravitation theories.


title:
On a class of consistent linear higher spin equations on curved
  manifolds

abstract:
  We analyze a class of linear wave equations for odd half spin that have a
well posed initial value problem. We demonstrate consistency of the equations
in curved space-times. They generalize the Weyl neutrino equation. We show that
there exists an associated invariant exact set of spinor fields indicating that
the characteristic initial value problem on a null cone is formally solvable,
even for the system coupled to general relativity. We derive the general
analytic solution in flat space by means of Fourier transforms. Finally, we
present a twistor contour integral description for the general analytic
solution and assemble a representation of the group $O(4,4)$ on the solution
space.


title: Unitarity Condition on Quantum Fields in Semiclassical Gravity

abstract:
  The condition for the unitarity of a quantum field is investigated in
semiclassical gravity from the Wheeler-DeWitt equation. It is found that the
quantum field preserves unitarity asymptotically in the Lorentzian universe,
but does not preserve unitarity completely in the Euclidean universe. In
particular we obtain a very simple matter field equation in the basis of the
generalized invariant of the matter field Hamiltonian whose asymptotic solution
is found explicitly.


title: New Asymptotic Expanstion Method for the Wheeler-DeWitt Equation

abstract:
  A new asymptotic expansion method is developed to separate the Wheeler-DeWitt
equation into the time-dependent Schr\"{o}dinger equation for a matter field
and the Einstein-Hamilton-Jacobi equation for the gravitational field including
the quantum back-reaction of the matter field. In particular, the nonadiabatic
basis of the generalized invariant for the matter field Hamiltonian separates
the Wheeler-DeWitt equation completely in the asymptotic limit of $m_p^2$
approaching infinity. The higher order quantum corrections of the gravity to
the matter field are found. The new asymptotic expansion method is valid
throughout all regions of superspace compared with other expansion methods with
a certain limited region of validity. We apply the new asymptotic expansion
method to the minimal FRW universe.


title: Perturbations of a Universe Filled with Dust and Radiation

abstract:
  A first-order perturbation approach to $k=0$ Friedmann cosmologies filled
with dust and radiation is developed. Adopting the coordinate gauge comoving
with the perturbed matter, and neglecting the vorticity of the radiation, a
pair of coupled equations is obtained for the trace $h$ of the metric
perturbations and for the velocity potential $v$. A power series solution with
upwards cutoff exists such that the leading terms for large values of the
dimensionless time $\xi$ agree with the relatively growing terms of the dust
solution of Sachs and Wolfe.


title:
Stress-Energy-Momentum Tensors in Lagrangian Field Theory. Part 2.
  Gravitational Superpotential

abstract:
  Our investigation of differential conservation laws in Lagrangian field
theory is based on the first variational formula which provides the canonical
decomposition of the Lie derivative of a Lagrangian density by a projectable
vector field on a bundle (Part 1: gr-qc/9510061). If a Lagrangian density is
invariant under a certain class of bundle isomorphisms, its Lie derivative by
the associated vector fields vanishes and the corresponding differential
conservation laws take place. If these vector fields depend on derivatives of
parameters of bundle transformations, the conserved current reduces to a
superpotential. This Part of the work is devoted to gravitational
superpotentials. The invariance of a gravitational Lagrangian density under
general covariant transformations leads to the stress-energy-momentum
conservation law where the energy-momentum flow of gravity reduces to the
corresponding generalized Komar superpotential. The associated energy-momentum
(pseudo) tensor can be defined and calculated on solutions of metric and
affine-metric gravitational models.


title: What is the Velocity of Gravitational Waves?

abstract:
  We present a new field theory of gravity. It incorporates a great part of
General Relativity (GR) and can be interpreted in the standard geometrical way
like GR as far as the interaction of matter to gravity is concerned. However,
it differs from GR when treating gravity to gravity interaction. The most
crucial distinction concerns the velocity of propagation of gravitational
waves. Since there is a large expectation that the detection of gravitational
waves will occur in the near future the question of which theory describes
Nature better will probably be settled soon.


title: A rigorous solution of the quantum Einstein equations

abstract:
  We show that the second coefficient of the Conway knot polynomial is
annihilated by the Hamiltonian constraint of canonically quantized general
relativity in the loop representation. The calculations are carried out in a
fully regularized lattice framework. Crucial to the calculation is the explicit
form of the skein relations of the second coefficient, which relate it to the
Gauss linking number. Contrary to the lengthy formal continuum calculation, the
rigorous lattice version can be summarized in a few pictures.


title: Almost-homogeneity of the universe in higher-order gravity

abstract:
  In the $R+\alpha R^2$ gravity theory, we show that if freely propagating
massless particles have an almost isotropic distribution, then the spacetime is
almost Friedmann-Robertson-Walker (FRW). This extends the result proved
recently in general relativity ($\alpha=0$), which is applicable to the
microwave background after photon decoupling. The higher-order result is in
principle applicable to a massless species that decouples in the early
universe, such as a relic graviton background. Any future observations that
show small anisotropies in such a background would imply that the geometry of
the early universe were almost FRW.


title: Quadrupole anisotropy from photon quantum effects

abstract:
  We consider quantum effects of an electromagnetic field in a
radiation-dominated almost FRW spacetime. The dominant non-local quantum
correction to the photon distribution is a quadrupole moment, corresponding to
an effective anisotropic pressure in the energy-momentum tensor.


title: Inhomogeneous universes in observational coordinates

abstract:
  Isotropic inhomogeneous dust universes are analysed via observational
coordinates based on the past light cones of the observer's galactic worldline.
The field equations are reduced to a single first--order {\sc ode} in
observational variables on the past light cone, completing the observational
integration scheme. This leads naturally to an explicit exact solution which is
locally nearly homogeneous (i.e. {\sc frw}), but at larger redshift develops
inhomogeneity. New observational characterisations of homogeneity ({\sc frw}
universes) are also given.


title:
Back-Reaction on the Topological Degrees of Freedom in (2+1)-Dimensional
  Spacetime

abstract:
  We investigate the back-reaction effect of the quantum field on the
topological degrees of freedom in (2+1)-dimensional toroidal universe, ${\cal
M} \simeq T^2\times {\bf R}$. Constructing a homogeneous model of the toroidal
universe, we examine explicitly the back-reaction effect of the Casimir energy
of a massless, conformally coupled scalar field, with a conformal vacuum. The
back-reaction causes an instability of the universe: The torus becomes thinner
and thinner as it evolves, while its total 2-volume (area) becomes smaller and
smaller. The back-reaction caused by the Casimir energy can be compared with
the influence of the negative cosmological constant: Both of them make the
system unstable and the torus becomes thinner and thinner in shape. On the
other hand, the Casimir energy is a complicated function of the Teichm\"uller
parameters $(\tau^1, \tau^2)$ causing highly non-trivial dynamical evolutions,
while the cosmological constant is simply a constant.
  Since the spatial section is a 2-torus, we shall write down the partition
function of this system, fixing the path-integral measure for gravity modes,
with the help of the techniques developed in string theories. We show
explicitly that the partition function expressed in terms of the canonical
variables corresponding to the (redundantly large) original phase space, is
reduced to the partition function defined in terms of the physical-phase-space
variables with a standard Liouville measure. This result is compatible with the
general theory of the path integral for the 1st-class constrained systems.


title: Classical Trace Anomaly

abstract:
  We seek an analogy of the mathematical form of the alternative form of
Einstein's field equations for Lovelock's field equations. We find that the
price for this analogy is to accept the existence of the trace anomaly of the
energy-momentum tensor even in classical treatments. As an example, we take
this analogy to any generic second order Lagrangian and exactly derive the
trace anomaly relation suggested by Duff. This indicates that an intrinsic
reason for the existence of such a relation should perhaps be, classically,
somehow related to the covariance of the form of Einstein's equations.


title: Two lectures on Two-Dimensional Gravity

abstract:
  (from the talk:) I shall here speak on gravity in (1+1)-dimensional
space-time --- lineal gravity. The purpose of studying lower dimensional
theories, and specifically lower dimensional gravity, is to gain insight into
difficult conceptional issues, which are present and even more opaque in the
physical (3+1)-dimensional world. Perhaps lessons learned in the
lower-dimensional setting can be used to explicate physical problems. Moreover,
if we are lucky, the lower-dimensional theories can have a direct physical
relevance to modelling phenomena that is actually dynamically confined to the
lower dimensionality. This is what happened with (2+1)-dimensional gravity:
gravitational physics in the presence of cosmic strings (infinitely long,
perpendicular to a plane) is adequately described planar gravity. Indeed the
recently discussed causality puzzles raised by ``Gott time machines'' were
resolved with the help of the lower-dimensional model...


title: An account of transforms on \bar {{\cal A}/{\cal G}}

abstract:
  In this article we summarize and describe the recently found transforms for
theories of connections modulo gauge transformations associated with compact
gauge groups. Specifically, we put into a coherent picture the so-called loop
transform, the inverse loop transform, the coherent state transform and finally
the Wick rotation transform which is the appropriate transform that
incorporates the correct reality conditions of quantum gravity when formulated
as a dynamical theory of connections while preserving the simple algebraic form
of the Hamiltonian constraint.


title: Ricci Fall-off in Static, Globally Hyperbolic, Non-singular Spacetimes

abstract:
  What restrictions are there on a spacetime for which the Ricci curvature is
such as to produce convergence of geodesics (such as the preconditions for the
Singularity Theorems) but for which there are no singularities? We answer this
question for a restricted class of spacetimes: static, geodesically complete,
and globally hyperbolic. The answer is that, in at least one spacelike
direction, the Ricci curvature must fall off at a rate inversely quadratic in a
naturally-occurring Riemannian metric on the space of static observers. Along
the way, we establish some global results on the static observer space,
regarding its completeness and its behavior with respect to universal covering
spaces.


title:
Non-Linear Affine Embedding of the Dirac Field from the
  Multiplicity-Free SL(4,R) Unirreps

abstract:
  The correspondence between the linear multiplicity-free unirreps of SL(4, R)
studied by Ne'eman and {\~{S}}ija{\~{c}}ki and the non-linear realizations of
the affine group is worked out. The results obtained clarify the inclusion of
spinorial fields in a non-linear affine gauge theory of gravitation.


title:
Criticality and Bifurcation in the Gravitational Collapse of a
  Self-Coupled Scalar Field

abstract:
  We examine the gravitational collapse of a non-linear sigma model in
spherical symmetry. There exists a family of continuously self-similar
solutions parameterized by the coupling constant of the theory. These solutions
are calculated together with the critical exponents for black hole formation of
these collapse models. We also find that the sequence of solutions exhibits a
Hopf-type bifurcation as the continuously self-similar solutions become
unstable to perturbations away from self-similarity.


title: Time-Symmetric Initial Data for Multi-Body Solutions in Three Dimensions

abstract:
  Time-symmetric initial data for two-body solutions in three dimensional
anti-deSitter gravity are found. The spatial geometry has constant negative
curvature and is constructed as a quotient of two-dimensional hyperbolic space.
Apparent horizons correspond to closed geodesics. In an open universe, it is
shown that two black holes cannot exist separately, but are necessarily
enclosed by a third horizon. In a closed universe, two separate black holes can
exist provided there is an additional image mass.


title: Black hole and the adiabatic phase

abstract:
  An open system consisting of a scalar field bound to a Kerr black hole whose
mass ($M$) and specific angular momentum ($a$) are slowly (adiabatically)
perturbed is considered. The adiabatically induced phase and the conditions for
the validity of the adiabatic approximation are obtained. The effect of closed
cycles in parameter space ($a$, $M$ plane) on the energy levels of both stable
and unstable scalar field bound states, together with other quantities of
interest, is illustrated. Lastly it is noted that the black hole wavefunction
will acquire an equal and opposite phase to that of matter thus leading to a
change of its effective action (entropy).


title:
Primordial Nucleosynthesis as a test of variable rest masses
  5-dimensional cosmology

abstract:
  The deviation of primordial Helium production due to a variation on the
difference between the rest masses of the nucleons is presented. It is found an
upper bound $\delta (M_{_n} - M_{_p}) \alt 0.129$ MeV, between the present and
nucleosynthesis epochs. This bound is used to analyze Wesson's theory of
gravitation; as a result, it is ruled out by observation.


title:
On the Algebraic Structure of Second Order Symmetric Tensors in
  5-Dimensional Space-times

abstract:
  A new approach to the algebraic classification of second order symmetric
tensors in 5-dimensional space-times is presented. The possible Segre types for
a symmetric two-tensor are found. A set of canonical forms for each Segre type
is obtained. A theorem which collects together some basic results on the
algebraic structure of the Ricci tensor in 5-dimensional space-times is also
stated.


title:
Reality conditions inducing transforms for quantum gauge field theory
  and quantum gravity

abstract:
  For various theories, in particular gauge field theories, the algebraic form
of the Hamiltonian simplifies considerably if one writes it in terms of certain
complex variables. Also general relativity when written in the new canonical
variables introduced by Ashtekar belongs to that category, the Hamiltonian
being replaced by the so-called scalar (or Wheeler-DeWitt) constraint. In order
to ensure that one is dealing with the correct physical theory one has to
impose certain reality conditions on the classical phase space which generally
are algebraically quite complicated and render the task of finding an
appropriate inner product into a difficult one. This article shows, for a
general theory, that if we prescribe first a {\em canonical} complexification
and second a $^*$ representation of the canonical commutation relations in
which the real connection is diagonal, then there is only one choice of a
holomorphic representation which incorporates the correct reality conditions
{\em and} keeps the Hamiltonian (constraint) algebraically simple ! We derive a
canonical algorithm to obtain this holomorphic representation and in particular
explicitly compute it for quantum gravity in terms of a {\em Wick rotation
transform}.


title:
On Regularization Scheme Dependence of Predictions in Inflationary
  Cosmology

abstract:
  We show that there exists a large class of regularization schemes for
probabilistic predictions in the theory of a self-reproducing inflationary
univere, all of which eliminate the apparent dependence on the time
reparametrization. However, all these schemes lead to different answers for
relative probabilities of finding various types of post-inflationary universes.
Besides, all these schemes fail to be reparametrization invariant beyond the
range of the inflaton field close to end of inflation boundary. Therefore, we
argue that at the current level of understanding, the simple regularization
schemes associated with cutoffs at equal time hypersurfaces are as good as the
recently proposed more complicated procedures which try to fix the
time-reparametrization dependence.


title: Consistent Evolution with Different Time-Slicings in Quantum Gravity

abstract:
  Rovelli's `` quantum mechanics without time'' motivates an intrinsically
time-slicing independent picture of reduced phase space quantum gravity, which
may be described as ``quantization after evolution''. Sufficient criteria for
carrying out quantization after evolution are developed in terms of a general
concept of the classical limit of quantum mechanics. If these criteria are
satisfied then it is possible to have consistent unitary evolution of
operators, with respect to an infinite parameter family of time-slicings (and
probably all time-slicings), with the correct classical limit. The criteria are
particularly amenable to study in (2+1)-dimensional gravity, where the reduced
phase space is finite dimensional.


title:
The Symplectic Structure of General Relativity in the Double-Null (2+2)
  Formalism

abstract:
  In the (2+2) formulation of general relativity spacetime is foliated by a
two-parameter family of spacelike 2-surfaces (instead of the more usual
one-parameter family of spacelike 3-surfaces). In a partially gauge-fixed
setting (double-null gauge), I write down the symplectic structure of general
relativity in terms of intrinsic and extrinsic quantities associated with these
2-surfaces. This leads to an identification of the reduced phase space degrees
of freedom. In particular, I show that the two physical degrees of freedom of
general relativity are naturally encoded in a quantity closely related to the
twist of the pair of null normals to the 2-surfaces. By considering the
characteristic initial-value problem I establish a canonical transformation
between these and the more usually quoted conformal 2-metric (or shear) degrees
of freedom. (This paper is based on a talk given at the Fifth Midwest
Relativity Conference, Milwaukee, USA.)


title: Open-Flux Solutions to the Constraints for Plane Gravity Waves

abstract:
  The metric for plane gravitational waves is quantized using the Ashtekar
field variables. The z axis (direction of travel of the waves) is taken to be
the entire real line. Solutions to the constraints are proposed; they involve
open-ended flux lines running along the entire z axis. These solutions are
annihilated by the constraints except at the two boundary points, where the
Gauss constraint does not annihilate the solutions. This result is in sharp
contrast to the situation in the general, 3+1 dimensional case without planar
symmetry, where the Gauss constraints do not contribute at boundaries because
the Lagrange multipliers for the Gauss constraints vanish there. The
constraints annihilate the solutions if classical matter is included (so that
flux lines are terminated on the matter). The SU(2) holonomy matrices used in
the solutions are (2j+1) dimensional, where j may be any spin, not necessarily
j = 1/2. In this respect the solutions resemble the spin network states
recently constructed by Rovelli and Smolin in loop space.


title:
Effect of gravitational radiation reaction on nonequatorial orbits
  around a Kerr black hole

abstract:
  The effect of gravitational radiation reaction on orbits around a spinning
black hole is analyzed. Such orbits possess three constants of motion: $\iota$,
$e$, and $a$, which correspond, in the Newtonian limit of the orbit being an
ellipse, to the inclination angle of the orbital plane to the hole's equatorial
plane, the eccentricity, and the semi-major axis length, respectively. First,
it is argued that circular orbits ($e=0$) remain circular under gravitational
radiation reaction. Second, for elliptical orbits (removing the restriction of
$e=0$), the evolution of $\iota$, $e$, and $a$ is computed to leading order in
$S$ (the magnitude of the spin angular momentum of the hole) and in $M/a$,
where $M$ is the mass of the black hole. As $a$ decreases, $\iota$ increases
and $e$ decreases.


title: A Specimen of Theory Construction from Quantum Gravity

abstract:
  I describe the history of my attempts to arrive at a discrete substratum
underlying the spacetime manifold, culminating in the hypothesis that the basic
structure has the form of a partial-order (i.e. that it is a causal set).


title:
Spatially self-similar locally rotationally symmetric perfect fluid
  models

abstract:
  Einstein's field equations for spatially self-similar locally rotationally
symmetric perfect fluid models are investigated. The field equations are
rewritten as a first order system of autonomous ordinary differential
equations. Dimensionless variables are chosen in such a way that the number of
equations in the coupled system of differential equations is reduced as far as
possible. The system is subsequently analyzed qualitatively for some of the
models. The nature of the singularities occurring in the models is discussed.


title: Particle Creation in the Bell-Szekeres Spacetime

abstract:
  The quantization of a real massless scalar field in a spacetime produced in a
collision of two electromagnetic plane waves with constant wave fronts is
considered. The background geometry in the interaction region, the
Bell-Szekeres solution, is locally isometric to the conformally flat
Bertotti-Robinson universe filled with a uniform electric field. It is shown
that before the waves interact the Bogoliubov coefficients relating different
observers are trivial and no vacuum polarization takes place. In the non-
singular interaction region neutral scalar particles are produced with number
of created particles and spectrum typical of gravitational wave collision.


title: Scalar Field Inhomogeneous Cosmologies

abstract:
  Some exact solutions for the Einstein field equations corresponding to
inhomogeneous $G_2$ cosmologies with an exponential-potential scalar field
which generalize solutions obtained previously are considered. Several
particular cases are studied and the properties related to generalized
inflation and asymptotic behaviour of the models are discussed.


title: Density perturbations in Kaluza--Klein theories during a de Sitter phase

abstract:
  In the context of Kaluza-Klein theories, we consider a model in which the
universe is filled with a perfect fluid described by a barotropic equation of
state. An analysis of density perturbations employing the synchronous gauge
shows that there are cases where these perturbations have an exponential growth
during a de Sitter phase evolution in the external space.


title: Hyperfast Interstellar Travel in General Relativity

abstract:
  The problem is discussed of whether a traveller can reach a remote object and
return back sooner than a photon would when taken into account that the
traveller can partly control the geometry of his world. It is argued that under
some reasonable assumptions in globally hyperbolic spacetimes the traveller
cannot hasten reaching the destination. Nevertheless, it is perhaps possible
for him to make an arbitrarily long round-trip within an arbitrarily short
(from the point of view of a terrestrial observer) time.


title:
The Problem of Classical Limit in Quantum Cosmology: The effective
  action language

abstract:
  The tool of functional averaging over some ``large'' diffeomorphisms is used
to describe quantum systems with constraints, in particular quantum cosmology,
in the language of quantum Effective Action. Simple toy models demonstrate a
supposedly general phenomenon: the presence of a constraint results in
``quantum repel'' from the classical mass shell.


title: Vacuum Spacetimes with Future Trapped Surfaces

abstract:
  In this article we show that one can construct initial data for the Einstein
equations which satisfy the vacuum constraints. This initial data is defined on
a manifold with topology $R^3$ with a regular center and is asymptotically
flat. Further, this initial data will contain an annular region which is
foliated by two-surfaces of topology $S^2$. These two-surfaces are future
trapped in the language of Penrose. The Penrose singularity theorem guarantees
that the vacuum spacetime which evolves from this initial data is future null
incomplete.


title: Expanding Spherically Symmetric Models without Shear

abstract:
  The integrability properties of the field equation $L_{xx} = F(x)L^2$ of a
spherically symmetric shear--free fluid are investigated. A first integral,
subject to an integrability condition on $F(x)$, is found, giving a new class
of solutions which contains the solutions of Stephani (1983) and Srivastava
(1987) as special cases. The integrability condition on $F(x)$ is reduced to a
quadrature which is expressible in terms of elliptic integrals in general.
There are three classes of solution and in general the solution of $L_{xx} =
F(x)L^2$ can only be written in parametric form. The case for which $F=F(x)$
can be explicitly given corresponds to the solution of Stephani (1983). A Lie
analysis of $L_{xx} = F(x) L^2$ is also performed. If a constant $\alpha$
vanishes, then the solutions of Kustaanheimo and Qvist (1948) and of this paper
are regained. For $\alpha \neq 0$ we reduce the problem to a simpler,
autonomous equation. The applicability of the Painlev\'e analysis is also
briefly considered.


title: Cosmologies with Two-Dimensional Inhomogeneity

abstract:
  We present a new generating algorithm to construct exact non static solutions
of the Einstein field equations with two-dimensional inhomogeneity. Infinite
dimensional families of $G_1$ inhomogeneous solutions with a self interacting
scalar field, or alternatively with perfect fluid, can be constructed using
this algorithm. Some families of solutions and the applications of the
algorithm are discussed.


title: Universality of Einstein's General Relativity

abstract:
  Among relativistic theories of gravitation the closest ones to general
relativity are the scalar-tensor ones and these with Lagrangians being any
function f(R) of the curvature scalar. A complete chart of relationships
between these theories and general relativity can be delineated. These theories
are mathematically (locally) equivalent to general relativity plus a minimally
coupled self-interacting scalar field. Physically they describe a massless
spin-2 field (graviton) and a spin-0 component of gravity. It is shown that
these theories are either physically equivalent to general relativity plus the
scalar or flat space is classically unstable (or at least suspected of being
unstable). In this sense general relativity is universal: it is an isolated
point in the space of gravity theories since small deviations from it either
carry the same physical content as it or give rise to physically untenable
theories.


title:
Statistics of the Microwave Background Anisotropies Caused by
  Cosmological Perturbations of Quantum-Mechanical Origin

abstract:
  The genuine quantum gravity effects can already be around us. It is likely
that the observed large-angular-scale anisotropies in the microwave background
radiation are induced by cosmological perturbations of quantum-mechanical
origin. Such perturbations are placed in squeezed vacuum quantum states and,
hence, are characterized by large variances of their amplitude. The statistical
properties of the anisotropies should reflect the underlying statistics of the
squeezed vacuum quantum states. In this paper, the theoretical variances for
the temperature angular correlation function are described in detail. It is
shown that they are indeed large and must be present in the observational data,
if the anisotropies are truly caused by the perturbations of quantum-mechanical
origin. Unfortunately, these large theoretical statistical uncertainties will
make the extraction of cosmological information from the measured anisotropies
a much more difficult problem than we wanted it to be. This contribution to the
Proceedings is largely based on references~[42,8]. The Appendix contains an
analysis of the ``standard'' inflationary formula for density perturbations.


title:
Correlation Dynamics of Quantum Fields and Black Hole Information
  Paradox

abstract:
  In recent years a statistical mechanics description of particles, fields and
spacetime based on the concept of quantum open systems and the influence
functional formalism has been introduced. It reproduces in full the established
theory of quantum fields in curved spacetime and contains also a microscopic
description of their statistical properties, such as noise, fluctuations,
decoherence, and dissipation. This new framework allows one to explore the
quantum statistical properties of spacetime at the interface between the
semiclassical and quantum gravity regimes, as well as important non-equilibrium
processes in the early universe and black holes, such as particle creation,
entropy generation, galaxy formation, Hawking radiation, gravitational
collapse, backreaction and the black hole end-state and information lost
issues. Here we give a summary of the theory of correlation dynamics of quantum
fields and describe how this conceptual scheme coupled with scaling behavior
near the infrared limit can shed light on the black hole information paradox.


title: Cosmology as `Condensed Matter' Physics

abstract:
  We note that in general there exist two basic aspects in any branch of
physics, including cosmology - one dealing with the attributes of basic
constituents and forces of nature, the other dealing with how structures arise
from them and how they evolve. Current research in quantum and superstring
cosmology is directed mainly towards the first aspect, even though a viable
theory of the underlying interactions is lacking. We call the attention to the
development of the second aspect, i.e., on the organization and processing of
the basic constituents of matter (in classical cosmology) and spacetime (in
quantum cosmology). Many newly developed concepts and techniques in condensed
matter physics stemming from the investigation of disordered, dynamical and
complex systems can guide us in asking the right questions and formulating new
solutions to existing and developing cosmological issues, thereby broadening
our view of the universe both in its formative and present state.


title: Semiclassical Gravity and Mesoscopic Physics

abstract:
  Developments in theoretical cosmology in the recent decades show a close
connection with particle physics, quantum gravity and unified theories. Answers
or hints to many fundamental questions in cosmology like the homogeneity and
isotropy of the Universe, the sources of structure formation and entropy
generation, and the initial state of the Universe can be traced back to the
activities of quantum fields and the dynamics of spacetime from the Grand
Unification time to the Planck time at $10^{-43} sec$. A closer depiction of
this primordial state of the Universe requires at least a semiclassical theory
of gravity and the consideration of non-equilibrium statistical processes
involving quantum fields. This critical state is intermediate between the
well-known classical epoch successfully described by Einstein's Theory of
General Relativity and the completely unknown realm of quantum gravity. Many
issues special to this stage such as the transition from quantum to classical
spacetime via decoherence, cross-over behavior at the Planck scale, tunneling
and particle creation, or growth of density contrast from vacuum fluctuations
share some basic concerns of mesoscopic physics for condensed matter, atoms or
nuclei, in the quantum/classical and the micro/macro interfaces, or the
discrete/continuum and the stochastic/ deterministic transitions. We point out
that underlying these issues are three main factors: quantum coherence,
fluctuations and correlation. We discuss how a deeper understanding of these
aspects of fields and spacetimes can help one to address some basic problems,
such as Planck scale metric fluctuations, cosmological phase transition and
structure formation, and the black hole entropy, end-state and information
paradox.


title: Stochastic semiclassical equations for weakly inhomogeneous cosmologies

abstract:
  Semiclassical Einstein-Langevin equations for arbitrary small metric
perturbations conformally coupled to a massless quantum scalar field in a
spatially flat cosmological background are derived. Use is made of the fact
that for this problem the in-in or closed time path effective action is simply
related to the Feynman and Vernon influence functional which describes the
effect of the ``environment'', the quantum field which is coarse grained here,
on the ``system'', the gravitational field which is the field of interest. This
leads to identify the dissipation and noise kernels in the in-in effective
action, and to derive a fluctuation-dissipation relation. A tensorial Gaussian
stochastic source which couples to the Weyl tensor of the spacetime metric is
seen to modify the usual semiclassical equations which can be viewed now as
mean field equations. As a simple application we derive the correlation
functions of the stochastic metric fluctuations produced in a flat spacetime
with small metric perturbations due to the quantum fluctuations of the matter
field coupled to these perturbations.


title: Statistical Mechanics and Quantum Cosmology

abstract:
  Statistical mechanical concepts and processes such as decoherence,
correlation, and dissipation can prove to be of basic importance to
understanding some fundamental issues of quantum cosmology and theoretical
physics such as the choice of initial states, quantum to classical transition
and the emergence of time. Here we summarize our effort in 1) constructing a
unified theoretical framework using techniques in interacting quantum field
theory such as influence functional and coarse-grained effective action to
discuss the interplay of noise, fluctuation, dissipation and decoherence; and
2) illustrating how these concepts when applied to quantum cosmology can alter
the conventional views on some basic issues. Two questions we address are 1)
the validity of minisuperspace truncation, which is usually assumed without
proof in most discussions, and 2) the relevance of specific initial conditions,
which is the prevailing view of the past decade. We also mention how some
current ideas in chaotic dynamics, dissipative collective dynamics and
complexity can alter our view of the quantum nature of the universe.


title: Making quantum gravity calculable

abstract:
  We describe recent attempts at discretizing canonical quantum gravity in four
dimensions in terms of a connection formulation. This includes a general
introduction, a comparison between the real and complex connection approach,
and a discussion of some open problems. (Contribution to the proceedings of the
workshop ``Recent mathematical developments in classical and quantum gravity",
Sintra, Portugal, July 1995.)


title:
Classical and Quantum Gravity in 1+1 Dimensions, Part II: The Universal
  Coverings

abstract:
  A set of simple rules for constructing the maximal (e.g. analytic) extensions
for any metric with a Killing field in an (effectively) two-dimensional
spacetime is formulated. The application of these rules is extremely
straightforward, as is demonstrated at various examples and illustrated with
numerous figures. Despite the resulting simplicity we also comment on some
subtleties concerning the concept of Penrose diagrams. Most noteworthy among
these, maybe, is that (smooth) spacetimes which have both degenerate and
non-degenerate (Killing) horizons do not allow for globally smooth Penrose
diagrams. Physically speaking this obstruction corresponds to an infinite
relative red/blueshift between observers moving across the two horizons. -- The
present work provides a further step in the classification of all global
solutions of the general class of two-dimensional gravity-Yang-Mills systems
introduced in Part I, comprising, e.g., all generalized (linear and nonlinear)
dilaton theories. In Part I we constructed the local solutions, which were
found to always have a Killing field; in this paper we provide all universal
covering solutions (the simply connected maximally extended spacetimes). A
subsequent Part III will treat the diffeomorphism inequivalent solutions for
all other spacetime topologies. -- Part II is kept entirely self-contained; a
prior reading of Part I is not necessary.


title: Radiation-Dominated Quantum Friedmann Models

abstract:
  Radiation-filled Friedmann-Robertson-Walker universes are quantized according
to the Arnowitt-Deser-Misner formalism in the conformal-time gauge. Unlike
previous treatments of this problem, here both closed and open models are
studied, only square-integrable wave functions are allowed, and the boundary
conditions to ensure self-adjointness of the Hamiltonian operator are
consistent with the space of admissible wave functions. It turns out that the
tunneling boundary condition on the universal wave function is in conflict with
self-adjointness of the Hamiltonian. The evolution of wave packets obeying
different boundary conditions is studied and it is generally proven that all
models are nonsingular. Given an initial condition on the probability density
under which the classical regime prevails, it is found that a closed universe
is certain to have an infinite radius, a density parameter $\Omega = 1$
becoming a prediction of the theory. Quantum stationary geometries are shown to
exist for the closed universe model, but oscillating coherent states are
forbidden by the boundary conditions that enforce self-adjointness of the
Hamiltonian operator.


title: A Generalized Wick Transform for Gravity

abstract:
  Using a key observation due to Thiemann, a generalized Wick transform is
introduced to map the constraint functionals of Riemannian general relativity
to those of the Lorentzian theory, including matter sources. This opens up a
new avenue within ``connection-dynamics'' where one can work, throughout, only
with real variables. The resulting quantum theory would then be free of
complicated reality conditions. Ramifications of this development to the
canonical quantization program are discussed.


title:
Low-Energy Interaction of a Cosmic String and an Extreme Dilatonic Black
  Hole

abstract:
  The interaction of a cosmic string and a maximally charged dilatonic black
hole is studied in the low-velocity limit. In particular, the string-black hole
scattering at a low velocity is investigated.


title: Hypersurfaces of Five Dimensional Space-times

abstract:
  It is shown that a space-time hypersurface of a 5-dimensional Ricci-flat
space-time has its energy momentum tensor algebrically related to its extrinsic
curvature and to the Riemann curvature of the embedding space. It is also seen
that the Einstein-Maxwell field does not arise naturally from this geometry, so
that a Kaluza-Klein model based on it would require further assumptions.


title: Numerical Investigation of Singularities

abstract:
  Numerical exploration of the properties of singularities could, in principle,
yield detailed understanding of their nature in physically realistic cases.
Examples of numerical investigations into the formation of naked singularities,
critical behavior in collapse, passage through the Cauchy horizon, chaos of the
Mixmaster singularity, and singularities in spatially inhomogeneous
cosmololgies are discussed.


title: Numerical Investigation of Cosmological Singularities

abstract:
  We describe a numerical approach to address the BKL conjecture that the
generic cosmological singularity is locally Mixmaster-like. We consider
application of a symplectic PDE solver to three models of increasing
complexity--spatially homogeneous (vacuum) Mixmaster cosmologies where we
compare the symplectic ODE solver to a Runge-Kutta one, the (plane symmetric,
vacuum) Gowdy universe on $T^3 \times R$ whose dynamical degrees of freedom
satisfy nonlinearly coupled PDE's in one spatial dimension and time, and U(1)
symmetric, vacuum cosmologies on $T^3 \times R$ which are the simplest
spatially inhomogeneous universes in which local Mixmaster dynamics is allowed.


title:
Comment on the chaotic singularity in some magnetic Bianchi VI$_0$
  cosmologies

abstract:
  Description of the magnetic Bianchi VI$_0$ cosmologies of LeBlanc, Kerr, and
Wainwright in the formalisms both of Belinskii, Khalatnikov, and Lifshitz, and
of Misner allows qualitative understanding of the Mixmaster-like singularity in
those models.


title: How to measure spatial distances?

abstract:
  The use of time--like geodesics to measure temporal distances is better
justified than the use of space--like geodesics for a measurement of spatial
distances. We give examples where a ''spatial distance'' cannot be
appropriately determined by the length of a space--like geodesic.


title: Consequences of the noncompactness of the Lorentz group

abstract:
  The following four statements have been proven decades ago already, but they
continue to induce a strange feeling:
  - All curvature invariants of a gravitational wave vanish - in spite of the
fact that it represents a nonflat spacetime.
  - The eigennullframe components of the curvature tensor (the Cartan
''scalars'') do not represent curvature scalars.
  - The Euclidean topology in the Minkowski spacetime does not possess a basis
composed of Lorentz--invariant neighbourhoods.
  - There are points in the de Sitter spacetime which cannot be joined to each
other by any geodesic.
  We explain that our feeling is influenced by the compactness of the rotation
group; the strangeness disappears if we fully acknowledge the noncompactness of
the Lorentz group. Output: Imaginary coordinate rotations from Euclidean to
Lorentzian signature are very dangerous.


title: Einstein's Energy-Free Gravitational Field

abstract:
  We show that Einstein's gravitational field has zero energy, momentum, and
stress. This conclusion follows directly from the gravitational field
equations, in conjunction with the differential law of energy-momentum
conservation $ T^{\mu\nu}_{;\nu} = 0 $. Einstein rejected this conservation law
despite the fact that it is generally covariant. We trace his rejection to a
misapplication of Gauss' divergence formula. Finally, we derive the formula
which pertains to energy-momentum conservation.


title:
Testing a Simplified Version of Einstein's Equations for Numerical
  Relativity

abstract:
  Solving dynamical problems in general relativity requires the full machinery
of numerical relativity. Wilson has proposed a simpler but approximate scheme
for systems near equilibrium, like binary neutron stars. We test the scheme on
isolated, rapidly rotating, relativistic stars. Since these objects are in
equilibrium, it is crucial that the approximation work well if we are to
believe its predictions for more complicated systems like binaries. Our results
are very encouraging.


title: Self-Similar Collapse of Conformally Coupled Scalar Fields

abstract:
  A massless scalar field minimally coupled to the gravitational field in a
simplified spherical symmetry is discussed. It is shown that, in this case, the
solution found by Roberts, describing a scalar field collapse, is in fact the
most general one. Taking that solution as departure point, a study of the
gravitational collapse for the self-similar conformal case is presented.


title: On the extended loop calculus

abstract:
  Some features of extended loops are considered. In particular, the behaviour
under diffeomorphism transformations of the wavefunctions with support on the
extended loop space are studied. The basis of a method to obtain analytical
expressions of diffeomorphism invariants via extended loops are settled.
Applications to knot theory and quantum gravity are considered.


title: Three Self-Consistent Kinematics in (1+1)D Special Relativity

abstract:
  When introducing special relativity, an elegant connection to familiar rules
governing Galilean constant acceleration can be made, by describing first the
discovery at high speeds that the clocks (as well as odometers) of different
travelers may proceed at different rates. One may then show how to parameterize
any given interval of constant acceleration with {\em either}: Newtonian
(low-velocity approximation) time, inertial relativistic (unaccelerated
observer) time, or traveler proper (accelerated observer) time, by defining
separate velocities for each of these three kinematics as well. Kinematic
invariance remains intact for proper acceleration since $m a_o = dE/dx$. This
approach allows students to solve relativistic constant acceleration problems
{\em with the Newtonian equations}! It also points up the self-contained and
special nature of the accelerated-observer kinematic, with its frame-invariant
time, 4-vector velocities which in traveler terms exceed Newtonian values and
the speed of light, and of course relativistic momentum conservation.


title:
Quasi-local energy-momentum and two-surface characterization of the
  pp-wave spacetimes

abstract:
  In the present paper the determination of the {\it pp}-wave metric form the
geometry of certain spacelike two-surfaces is considered. It has been shown
that the vanishing of the Dougan--Mason quasi-local mass $m_{\$}$, associated
with the smooth boundary $\$:=\partial\Sigma\approx S^2$ of a spacelike
hypersurface $\Sigma$, is equivalent to the statement that the Cauchy
development $D(\Sigma)$ is of a {\it pp}-wave type geometry with pure
radiation, provided the ingoing null normals are not diverging on $\$ $ and the
dominant energy condition holds on $D(\Sigma)$. The metric on $D(\Sigma)$
itself, however, has not been determined. Here, assuming that the matter is a
zero-rest-mass-field, it is shown that both the matter field and the {\it
pp}-wave metric of $D(\Sigma)$ are completely determined by the value of the
zero-rest-mass-field on $\$ $ and the two dimensional Sen--geometry of $\$ $
provided a convexity condition, slightly stronger than above, holds. Thus the
{\it pp}-waves can be characterized not only by the usual Cauchy data on a {\it
three} dimensional $\Sigma$ but by data on its {\it two} dimensional boundary
$\$ $ too. In addition, it is shown that the Ludvigsen--Vickers quasi-local
angular momentum of axially symmetric {\it pp}-wave geometries has the familiar
properties known for pure (matter) radiation.


title:
Kolmogorov Algorithmic Complexity and its Probability Interpretation in
  Quantum Gravity

abstract:
  The quantum gravity has great difficulties with application of the
probability notion. In given article this problem is analyzed according to
algorithmic viewpoint. According to A.N. Kolmogorov, the probability notion can
be connected with algorithmic complexity of given object. The paper proposes an
interpretation of quantum gravity, according to which an appearance of
something corresponds to its Kolmogorov's algorithmic complexity. By this
viewpoint the following questions are considered: the quantum transition with
supplementary coordinates splitting off, the algorithmic complexity of the
Schwarzschild black hole is estimated, the redefinition of the Feynman path
integral, the quantum birth of the Euclidean Universe with the following
changing of the metric signature.


title: Possible test of local Lorentz invariance from $\tau$ decays

abstract:
  We analyze the possibility of testing local Lorentz invariance from the
observation of tau decays. Future prospects of probing distances below the
electroweak characteristic scale are discussed.


title: The Static Gravitational Field of a Spherically Symmetric Body

abstract:
  We continue here the exam \cite{LuMa} of a theory of gravity that satisfies
the Einstein Equivalence Principle (EEP) for any kind of matter/energy, except
for the gravitational energy. This is part of a research program that intends
to re-examine the standard Feynman-Deser approach of field theoretical
derivation of Einstein\rq s General Relativity. The hypothesis implicit in such
precedent derivations \cite{Feynman} \cite{Deser} concerns the universality of
gravity interaction. Although there is a strong observational basis supporting
the universality of matter to gravity interaction, there is not an equivalent
situation that supports the hypothesis that gravity interacts with gravity as
any other form of non-gravitational energy. We analyse here a kind of
gravity-gravity interaction distinct from GR but, as we shall see, that
conforms with the actual status of observation. We exhibit the gravitational
field produced by a spherically symmetric static configuration as described in
this field theory of gravity. The values that we obtain for the standard PPN
parameters ($\alpha = \beta = \gamma = 1$) coincide with those of General
Relativity. Thus, as we pointed out in a previous paper, the main different
aspect of our theory and GR concerns the velocity of the gravitational waves.
Since there is a large expectation that the detection of gravitational waves
will occur in the near future, the question of which theory describes Nature
better will probably be settled soon.


title:
A semiclassical interpretation of the topological solutions for
  canonical quantum gravity

abstract:
  Ashtekar's formulation for canonical quantum gravity is known to possess the
topological solutions which have their supports only on the moduli space $\CN$
of flat $SL(2,C)$ connections. We show that each point on the moduli space
$\CN$ corresponds to a geometric structure, or more precisely the Lorentz group
part of a family of Lorentzian structures, on the flat (3+1)-dimensional
spacetime. A detailed analysis is given in the case where the spacetime is
homeomorphic to $R\times T^{3}$. Most of the points on the moduli space $\CN$
yield pathological spacetimes which suffers from singularities on each spatial
hypersurface or which violates the strong causality condition. There is,
however, a subspace of $\CN$ on which each point corresponds to a family of
regular spacetimes.


title:
Radiation-reaction-induced evolution of circular orbits of particles
  around Kerr Black Holes

abstract:
  It is demonstrated that, in the adiabatic approximation, non-Equatorial
circular orbits of particles in the Kerr metric (i.e. orbits of constant
Boyer-Lindquist radius) remain circular under the influence of gravitational
radiation reaction. A brief discussion is given of conditions for breakdown of
adiabaticity and of whether slightly non-circular orbits are stable against the
growth of eccentricity.


title:
Spherically symmetric solutions of gravitation equations on the
  background with spatial sections of constant curvature

abstract:
  We investigate the vacuum and charged spherically symmetric static solutions
of the Einstein equations on cosmological background. The background metric is
not flat, but curved, with constant - curvature spatial sections. Both vacuum
and charged cases contain two branches. The first branches transform into the
Schwarzschild and Reissner-Nordstr\"om solutions if the background metric goes
to the Minkovski one. The second branches describe wormholes and have no
Einstein limit.


title: Quantum deformation of quantum gravity

abstract:
  We describe a deformation of the observable algebra of quantum gravity in
which the loop algebra is extended to framed loops. This allows an alternative
nonperturbative quantization which is suitable for describing a phase of
quantum gravity characterized by states which are normalizable in the measure
of Chern-Simons theory. The deformation parameter, q, depends on the
cosmological constant. The Mandelstam identities are extended to a set of
relations which are governed by the Kauffman bracket so that the spin network
basis is deformed to a basis of SU(2)q spin networks. Corrections to the
actions of operators in non-perturbative quantum gravity may be readily
computed using recoupling theory; the example of the area observable is treated
here. Finally, eigenstates of the q-deformed Wilson loops are constructed,
which may make possible the construction of a q-deformed connection
representation through an inverse transform.


title: Gravitating Chern-Simons vortices

abstract:
  The construction of self-dual vortex solutions to the Chern-Simons-Higgs
model (with a suitable eighth-order potential) coupled to Einstein gravity in
(2 + 1) dimensions is reconsidered. We show that the self-duality condition may
be derived from the sole assumption $g_{00} = 1$. Next, we derive a family of
exact, doubly self-dual vortex solutions, which interpolate between the
symmetrical and asymmetrical vacua. The corresponding spacetimes have two
regions at spatial infinity. The eighth-order Higgs potential is positive
definite, and closed timelike curves are absent, if the gravitational constant
is chosen to be negative.


title:
Inequivalence of First and Second Order Formulations in D=2 Gravity
  Models

abstract:
  The usual equivalence between the Palatini and metric (or affinity and
vielbein) formulations of Einstein theory fails in two spacetime dimensions for
its "Kaluza--Klein" reduced (as well as for its standard) version. Among the
differences is the necessary vanishing of the cosmological constant in the
first order forms. The purely affine Eddington formulation of Einstein theory
also fails here.


title: Quasiclassical Dynamics in a Closed Quantum System

abstract:
  We consider Gell-Mann and Hartle's consistent histories formulation of
quantum cosmology in the interpretation in which one history, chosen randomly
according to the decoherence functional probabilities, is realised from each
consistent set. We show that in this interpretation, if one assumes that an
observed quasiclassical structure will continue to be quasiclassical, one
cannot infer that it will obey the predictions of classical or Copenhagen
quantum mechanics.


title: Introduction to the Effective Field Theory Description of Gravity

abstract:
  This is a pedagogical introduction to the treatment of general relativity as
a quantum effective field theory. Gravity fits nicely into the effective field
theory description and forms a good quantum theory at ordinary energies.


title: Probing the gravitational geon

abstract:
  The Brill-Hartle gravitational geon construct as a spherical shell of small
amplitude, high frequency gravitational waves is reviewed and critically
analyzed. The Regge-Wheeler formalism is used to represent gravitational wave
perturbations of the spherical background as a superposition of tensor
spherical harmonics and an attempt is made to build a non-singular solution to
meet the requirements of a gravitational geon. High-frequency waves are seen to
be a necessary condition for the geon and the field equations are decomposed
accordingly. It is shown that this leads to the impossibility of forming a
spherical gravitational geon. The attempted constructs of gravitational and
electromagnetic geons are contrasted. The spherical shell in the proposed
Brill-Hartle geon does not meet the regularity conditions required for a
non-singular source and hence cannot be regarded as an adequate geon construct.
Since it is the high frequency attribute which is the essential cause of the
geon non-viability, it is argued that a geon with less symmetry is an unlikely
prospect. The broader implications of the result are discussed with particular
reference to the problem of gravitational energy.


title: Time evolution and observables in constrained systems

abstract:
  The discussion is limited to first-class parametrized systems, where the
definition of time evolution and observables is not trivial, and to finite
dimensional systems in order that technicalities do not obscure the conceptual
framework. The existence of reasonable true, or physical, degrees of freedom is
rigorously defined and called {\em local reducibility}. A proof is given that
any locally reducible system admits a complete set of perennials. For locally
reducible systems, the most general construction of time evolution in the
Schroedinger and Heisenberg form that uses only geometry of the phase space is
described. The time shifts are not required to be 1symmetries. A relation
between perennials and observables of the Schroedinger or Heisenberg type
results: such observables can be identified with certain classes of perennials
and the structure of the classes depends on the time evolution. The time
evolution between two non-global transversal surfaces is studied. The problem
is posed and solved within the framework of the ordinary quantum mechanics. The
resulting non-unitarity is different from that known in the field theory
(Hawking effect): state norms need not be preserved so that the system can be
lost during the evolution of this kind.


title: Electromagnetism and Gravitation

abstract:
  The classical concept of "mass density" is not fundamental to the quantum
theory of matter. Therefore, mass density cannot be the source of gravitation.
Here, we treat electromagnetic energy, momentum, and stress as its source. The
resulting theory predicts that the gravitational potential near any charged
elementary particle is many orders of magnitude greater than the Newtonian
value.


title: A Fundamental Theorem of Space-times

abstract:
  The fundamental theorem of submanifolds is adapted to space-times. It is
shown that the integrability conditions for the existence of submanifolds of a
pseudo-Euclidean space contain the Einstein and Yang-Mills equations.


title:
Perfect-fluid cylinders and walls - sources for the Levi-Civita
  space-time

abstract:
  The diagonal metric tensor whose components are functions of one spatial
coordinate is considered. Einstein's field equations for a perfect-fluid source
are reduced to quadratures once a generating function, equal to the product of
two of the metric components, is chosen. The solutions are either static fluid
cylinders or walls depending on whether or not one of the spatial coordinates
is periodic. Cylinder and wall sources are generated and matched to the vacuum
(Levi--Civita) space--time. A match to a cylinder source is achieved for
$-\frac{1}{2}<\si<\frac{1}{2}$, where $\si$ is the mass per unit length in the
Newtonian limit $\si\to 0$, and a match to a wall source is possible for
$|\si|>\frac{1}{2}$, this case being without a Newtonian limit; the positive
(negative) values of $\si$ correspond to a positive (negative) fluid density.
The range of $\si$ for which a source has previously been matched to the
Levi--Civita metric is $0\leq\si<\frac{1}{2}$ for a cylinder source.


title: Nature of singularity in Einstein-massless scalar theory

abstract:
  We study the static and spherically symmetric exact solution of the
Einstein-massless scalar equations given by Janis, Newman and Winicour. We find
that this solution satisfies the weak energy condition and has strong globally
naked singularity.


title: Quantum Cosmology and the Constants of Nature

abstract:
  In models where the constants of Nature can take more than one set of values,
the cosmological wave function $\psi$ describes an ensemble of universes with
different values of the constants. The probability distribution for the
constants can be determined with the aid of the `principle of mediocrity' which
asserts that we are a `typical' civilization in this ensemble. I discuss the
implications of this approach for inflationary scenarios, the origin of density
fluctuations, and the cosmological constant.


title: Semiclassical collapse of a sphere of dust

abstract:
  The semiclassical collapse of a homogeneous sphere of dust is studied. After
identifying the independent dynamical variables, the system is 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. Further on neglecting
back--reaction effects, it is 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.