title: Nonzero $\Omega_{\Lambda}$ and a new type of the dissipative structure

abstract:
  We revisit the proposed theoretical model for a small but nonzero
cosmological constant which seems supported increasingly better by recent
observations. The model features two scalar fields which interact with each
other through a specifically chosen nonlinear potential. We find a very
sensitive dependence of the solutions of the scalar field equations on the
initial values. We discuss how the behavior is similar to and different from
those in well-known chaotic systems, coming to suggest an interesting new type
of the dissipative structure.


title:
On the relationship between the angular deficit and the internal
  structure of straight cosmic strings

abstract:
  We give a brief discussion on the limitations involving the expression mu
={angular deficit}/(8*pi),(G=c=1), which relates the string linear energy
density ''mu'' to the conical deficit angle. Then, we establish a new equation
between the angular deficit and another physical attribute of the string which
shows that the angular deficit is determined not only by the amount of proper
matter of the string but also, in a Newtonian sense, by its internal
gravitational field.


title: Superluminal travel requires negative energies

abstract:
  The content of gr-qc/9805003 and gr-qc/9806091 now appears in a single paper
in the archive under gr-qc/9805003, since these appeared as a single
publication in Physical Review Letters.


title: What can we do on gravity with antihydrogens?

abstract:
  We discuss the implications of the proposed gravitational redshift experiment
on antihydrogens. We show that the result should be the same as on hydrogens in
spite of different free-fall accelerations (WEP violation) which may occur if
there is a vector fifth-force field. We emphasize the experiment is unique in
the sense that it tests the Equivalence Principle expressed in its ultimate
form, proposed to be called UEP, directly without being disturbed by the effect
of possible presence of a scalar fifth-force field.


title:
Interaction of Hawking radiation with static sources outside a
  Schwarzschild black hole

abstract:
  We show that the response rate of (i) a static source interacting with
Hawking radiation of massless scalar field in Schwarzschild spacetime (with the
Unruh vacuum) and that of (ii) a uniformly accelerated source with the same
proper acceleration in Minkowski spacetime (with the Minkowski vacuum) are
equal. We show that this equality will not hold if the Unruh vacuum is replaced
by the Hartle-Hawking vacuum. It is verified that the source responds to the
Hawking radiation near the horizon as if it were at rest in a thermal bath in
Minkowski spacetime with the same temperature. It is also verified that the
response rate in the Hartle-Hawking vacuum approaches that in Minkowski
spacetime with the same temperature far away from the black hole. Finally, we
compare our results with others in the literature.


title:
On the construction of global models describing rotating bodies;
  uniqueness of the exterior gravitational field

abstract:
  The problem of constructing global models describing isolated axially
symmetric rotating bodies in equilibrium is analyzed. It is claimed that,
whenever the global spacetime is constructed by giving boundary data on the
limiting surface of the body and integrating Einstein's equations both inside
and ouside the body, the problem becomes overdetermined. Similarly, when the
spacetime describing the interior of the body is explicitly given,the problem
of finding the exterior vacuum solution becomes overdetermined. We discuss in
detail the procedure to be followed in order to construct the exterior vacuum
field created by a given but arbitrary distribution of matter. Finally, the
uniqueness of the exterior vacuum gravitational field is proven by exploiting
the harmonic map formulation of the vacuum equations and the boundary
conditions prescribed from the matching.


title: A rotating incompressible perfect fluid space-time

abstract:
  A rigidly rotating incompressible perfect fluid solution of Einstein's
gravitational equations is discussed. The Petrov type is D, and the metric
admits a four-parameter isometry group. The Gaussian curvature of the
constant-pressure surfaces is positive and they have two ring-shaped cusps.


title: Wormholes in String Theory

abstract:
  A wormhole is constructed by cutting and joining two spacetimes satisfying
the low energy string equations with a dilaton field. In spacetimes described
by the "string metric" the dilaton energy-momentum tensor need not satisfy the
weak or dominant energy conditions. In the cases considered here the dilaton
field violates these energy conditions and is the source of the exotic matter
required to maintain the wormhole. There is also a surface stress-energy, that
must be produced by additional matter, where the spacetimes are joined. It is
shown that wormholes can be constructed for which this additional matter
satisfies the weak and dominant energy conditions, so that it could be a form
of "normal" matter. Charged dilaton wormholes with a coupling between the
dilaton and the electromagnetic field that is more general than in string
theory are also briefly discussed.


title: Gravitational Lensing in Inhomogeneous Universes

abstract:
  I describe a new approach (developed in collaboration with D.E. Holz) to
calculating the statistical distributions for magnification, shear, and
rotation of images of cosmological sources due to gravitational lensing by mass
inhomogeneities on galactic and smaller scales. Our approach is somewhat
similar to that used in ``Swiss cheese'' models, but the ``cheese'' has been
completely eliminated, the matter distribution in the ``voids'' need not be
spherically symmetric, the total mass in each void need equal the corresponding
Robertson-Walker mass only on average, and we do not impose an ``opaque
radius'' cutoff. In our approach, we integrate the geodesic deviation equation
backwards in time until the desired redshift is reached, using a Monte Carlo
procedure wherein each photon beam in effect ``creates its own universe'' as it
propagates. Our approach fully takes into account effects of multiple
encounters with gravitational lenses and is much easier to apply than ``ray
shooting'' methods.


title: Scalar Field Cosmologies and the Initial Space-Time Singularity

abstract:
  The singularity structure of cosmological models whose matter content
consists of a scalar field with arbitrary non-negative potential is discussed.
The special case of spatially flat FRW space-time is analysed in detail using a
dynamical systems approach which may readily be generalised to more complicated
space-times. It is shown that for a very large and natural class of models a
simple and regular past asymptotic structure exists. More specifically, there
exists a family of solutions which is in continuous 1-1 correspondence with the
exactly integrable massless scalar field cosmologies, this correspondence being
realised by a unique asymptotic approximation. The set of solutions which do
not fall into this class has measure zero. The significance of this result to
the cosmological initial value problem is briefly discussed.


title:
Local anisotropy of space in a frame of reference co-moving with the
  Earth

abstract:
  We consider, in the framework of General Relativity, the linear approximation
of the gravitational field of the Earth taking into account its mass, its
quadrupole moment, its shape and its diurnal rotation.
  We conclude that in the frame of reference co-moving with the Earth the local
anisotropy of the space is of the order of $10^{-12}-10^{-13}$ and could be
observed.


title: Brans-Dicke wormholes endowed with torsion

abstract:
  A two-way traversable wormhole solution in Brans-Dicke theory with torsion is
obtained using the method of massive thin shells. The solution goes over
general relativity for an infinite large value of the coupling parameter,
however, the Brans-Dicke scalar could never be the ``carrier'' of exoticity
that threads the wormhole throat.


title: From classical chaos to decoherence in Robertson-Walker cosmology

abstract:
  We analyse the relationship between classical chaos and particle creation in
Robertson-Walker cosmological models with gravity coupled to a scalar field.
Within our class of models chaos and particle production are seen to arise in
the same cases. Particle production is viewed as the seed of decoherence, which
both enables the quantum to classical transition, and ensures that the
correspondence between the quantum and classically chaotic models will be valid


title: Gravitating Brane Systems: Some General Theorems

abstract:
  Multidimensional gravity interacting with intersecting electric and magnetic
$p$-branes is considered for fields depending on a single variable. Some
general features of the system behaviour are revealed without solving the field
equations. Thus, essential asymptotic properties of isotropic cosmologies are
indicated for different signs of spatial curvature; a no-hair-type theorem and
a single-time theorem for black holes are proved (the latter makes sense in
models with multiple time coordinates). The validity of the general
observations is verified for a class of exact solutions known for the cases
when certain vectors, built from the input parameters of the model, are either
orthogonal in minisuperspace, or form mutually orthogonal subsystems. From the
non-existence of Lorentzian wormholes, a universal restriction is obtained,
applicable to orthogonal or block-orthogonal subsystems of any $p$-brane
system.


title:
Calculating initial data for the conformal Einstein equations by
  pseudo-spectral methods

abstract:
  We present a numerical scheme for determining hyperboloidal initial data sets
for the conformal field equations by using pseudo-spectral methods. This
problem is split into two parts. The first step is the determination of a
suitable conformal factor which transforms from an initial data set in physical
space-time to a hyperboloidal hypersurface in the ambient conformal manifold.
This is achieved by solving the Yamabe equation, a non-linear second order
equation. The second step is a division by the conformal factor of certain
fields which vanish on $\scri$, the zero set of the conformal factor. The
challenge there is to numerically obtain a smooth quotient. Both parts are
treated by pseudo-spectral methods. The non-linear equation is solved
iteratively while the division problem is treated by transforming the problem
to the coefficient space, solving it there by the QR-factorisation of a
suitable matrix, and then transforming back. These hyperboloidal initial data
can be used to generate general relativistic space-times by evolution with the
conformal field equations.


title: (2+1) dimensional stars

abstract:
  We investigate, in the framework of (2+1) dimensional gravity, stationary,
rotationally symmetric gravitational sources of the perfect fluid type,
embedded in a space of arbitrary cosmological constant. We show that the
matching conditions between the interior and exterior geometries imply
restrictions on the physical parameters of the solutions. In particular,
imposing finite sources and absence of closed timelike curves privileges
negative values of the cosmological constant, yielding exterior vacuum
geometries of rotating black hole type. In the special case of static sources,
we prove the complete integrability of the field equations and show that the
sources' masses are bounded from above and, for vanishing cosmological
constant, generally equal to one. We also discuss and illustrate the stationary
configurations by explicitly solving the field equations for constant
mass--energy densities. If the pressure vanishes, we recover as interior
geometries Godel like metrics defined on causally well behaved domains, but
with unphysical values of the mass to angular momentum ratio. The introduction
of pressure in the sources cures the latter problem and leads to physically
more relevant models.


title: Quantization of pure gravitational plane waves

abstract:
  Pure gravitational plane waves are considered as a special case of spacetimes
with two commuting spacelike Killing vector fields. Starting with a
midisuperspace that describes this kind of spacetimes, we introduce
gauge-fixing and symmetry conditions that remove all non-physical degrees of
freedom and ensure that the classical solutions are plane waves. In this way,
we arrive at a reduced model with no constraints and whose only degrees of
freedom are given by two fields. In a suitable coordinate system, the reduced
Hamiltonian that generates the time evolution of this model turns out to
vanish, so that all relevant information is contained in the symplectic
structure. We calculate this symplectic structure and particularize our
discussion to the case of linearly polarized plane waves. The reduced phase
space can then be described by an infinite set of annihilation and creation
like variables. We finally quantize the linearly polarized model by introducing
a Fock representation for these variables.


title: Free Fields for Chiral 2D Dilaton Gravity

abstract:
  We give an explicit canonical transformation which transforms a generic
chiral 2D dilaton gravity model into a free field theory.


title: Chaos in the Kepler System

abstract:
  The long-term dynamical evolution of a Keplerian binary orbit due to the
emission and absorption of gravitational radiation is investigated. This work
extends our previous results on transient chaos in the planar case to the three
dimensional Kepler system. Specifically, we consider the nonlinear evolution of
the relative orbit due to gravitational radiation damping as well as external
gravitational radiation that is obliquely incident on the initial orbital
plane. The variation of orbital inclination, especially during resonance
capture, turns out to be very sensitive to the initial conditions. Moreover, we
discuss the novel phenomenon of chaotic transition.


title: Post-Newtonian Approximation

abstract:
  We discuss various aspects of the post-Newtonian approximation in general
relativity. After presenting the foundation based on the Newtonian limit, we
use the (3+1) formalism to formulate the post-Newtonian approximation for the
perfect fluid. As an application we show the method for constructing the
equilibrium configuration of nonaxisymmetric uniformly rotating fluid. We also
discuss the gravitational waves including tail from post-Newtonian systems.


title: Signature Change, Inflation, and the Cosmological Constant

abstract:
  Colombeau's generalized functions are used to adapt the distributional
approach to singular hypersurfaces in general relativity with signature change.
Equations governing the dynamics of singular hypersurface is obtained and it is
shown that matching leads to de Sitter space for the Lorentzian region. The
matching is possible for different sections of the de Sitter hyperboloid. A
relation between the radius of $S^4$, as the Euclidean manifold, and the
cosmological constant leading to inflation after signature change is obtained.


title: Gravity on a parallelizable manifold. Exact solutions

abstract:
  The wave type field equation $\square \vt^a=\la \vt^a$, where $\vt^a$ is a
coframe field on a space-time, was recently proposed to describe the gravity
field. This equation has a unique static, spherical-symmetric,
asymptotically-flat solution, which leads to the viable Yilmaz-Rosen metric. We
show that the wave type field equation is satisfied by the pseudo-conformal
frame if the conformal factor is determined by a scalar 3D-harmonic function.
This function can be related to the Newtonian potential of classical gravity.
So we obtain a direct relation between the non-relativistic gravity and the
relativistic model: every classical exact solution leads to a solution of the
field equation. With this result we obtain a wide class of exact, static
metrics. We show that the theory of Yilmaz relates to the pseudo-conformal
sector of our construction. We derive also a unique cosmological (time
dependent) solution of the described type.


title: Nonsingular Dilaton Cosmology

abstract:
  We study spatially homogeneous and isotropic solutions to the equations of
motion derived from dilaton gravity, in the presence of a special combination
of higher derivative terms in the gravitational action. All solutions are
nonsingular. For initial conditions resembling those in the pre-big-bang
scenario, there are solutions corresponding to a spatially flat, bouncing
Universe originating in a dilaton-dominated contracting phase and emerging as
an expanding Friedmann Universe.


title: Self-Similar Collapse of Scalar Field in Higher Dimensions

abstract:
  This paper constructs continuously self-similar solution of a spherically
symmetric gravitational collapse of a scalar field in n dimensions. The
qualitative behavior of these solutions is explained, and closed-form answers
are provided where possible. Equivalence of scalar field couplings is used to
show a way to generalize minimally coupled scalar field solutions to the model
with general coupling.


title: Scalar Field Cosmological Models With Hard Potential Walls

abstract:
  The global behavior of scalar field cosmological models with very hard
potential walls is investigated via the simple example of an exponentially
steep potential well. It is found that the solutions exhibit a non-trivial
oscillatory behavior in the approach to an initial space-time singularity. This
behavior can be interpreted as being due to the inability of the scalar field
to negotiate the walls of the steep potential well.


title: Uniformly accelerated sources in electromagnetism and gravity

abstract:
  Electromagnetic field produced by magnetic multipoles in hyperbolic motion is
derived and compared with electromagnetic field produced by electric multipoles
in hyperbolic motion. The resulting fields are related by duality symmetry.
Radiative properties of these solutions are demonstrated. In the second part an
analogous, uniformly accelerated source of gravitational radiation is studied,
within exact Einstein's theory. Radiative characteristics of the corresponding
solution as flux of the radiation and the total mass-energy of the system are
calculated and graphically illustrated.


title: Apparent horizons, black hole entropy and loop quantum gravity

abstract:
  In recent work on black hole entropy in non-perturbative quantum gravity, an
action for the black hole sector of the phase space is introduced and
(partially) quantized. We give a number of observations on this and related
works. In particular we show that (I) the entropy calculation applies without
change to generally covariant theories having no black hole solutions, (II) the
phase space constraint used to select the black hole sector is not the apparent
horizon equation, which is the natural phase space constraint separating
trapped and untrapped regions on an initial data surface, and (III) there
appears to be at least one other phase space constraint which leads to the
conclusion that the entropy associated with a bounding two-dimensional surface
is proportional to its area.


title: Alternative Lagrangians for Einstein Metrics

abstract:
  We shall use the variational decomposition technique in order to calculate
equations of motion and Noether energy-momentum complex for some classes of
non-linear gravitational Lagrangians within the first-order (Palatini)
formalism. In particular, a complex space-time appears as a solution of our
variational problem.


title: The No-defect Conjecture: Cosmological Implications

abstract:
  When the topology of the universe is non trivial, it has been shown that
there are constraints on the network of domain walls, cosmic strings and
monopoles. I generalize these results to textures and study the cosmological
implications of such constraints. I conclude that a large class of
multi-connected universes with topological defects accounting for structure
formation are ruled out by observation of the cosmic microwave background.


title:
Superradiance and the Statistical-Mechanical Entropy of Rotating BTZ
  Black Holes

abstract:
  We have considered the divergence structure in the brick-wall model for the
statistical mechanical entropy of a quantum field in thermal equilibrium with a
black hole which {\it rotates}. Especially, the contribution to entropy from
superradiant modes is carefully incorporated, leading to a result for this
contribution which corrects some previous errors in the literature. It turns
out that the previous errors were due to an incorrect quantization of the
superradiant modes. Some of main results for the case of rotating BTZ black
holes are that the entropy contribution from superradiant modes is positive
rather than negative and also has a leading order divergence as that from
nonsuperradiant modes. The total entropy, however, can still be identified with
the Bekenstein-Hawking entropy of the rotating black hole by introducing a
universal brick-wall cutoff. Our correct treatment of superradiant modes in the
``angular-momentum modified canonical ensemble'' also removes unnecessary
introductions of regulating cutoff numbers as well as ill-defined expressions
in the literature.


title: An overview of canonical quantum gravity

abstract:
  This is a summary of a talk delivered at the workshop ``Quantum gravity in
the Southern Cone II''. We present a very brief review of current results on
canonical quantization of general relativity using Ashtekar's variables and
loop quantization.


title:
The fermionic contribution to the spectrum of the area operator in
  nonperturbative quantum gravity

abstract:
  The role of fermionic matter in the spectrum of the area operator is analyzed
using the Baez--Krasnov framework for quantum fermions and gravity. The result
is that the fermionic contribution to the area of a surface $S$ is equivalent
to the contribution of purely gravitational spin network's edges tangent to
$S$. Therefore, the spectrum of the area operator is the same as in the pure
gravity case.


title: The projector on physical states in loop quantum gravity

abstract:
  We construct the operator that projects on the physical states in loop
quantum gravity. To this aim, we consider a diffeomorphism invariant functional
integral over scalar functions. The construction defines a covariant,
Feynman-like, spacetime formalism for quantum gravity and relates this theory
to the spin foam models. We also discuss how expectation values of physical
quantity can be computed.


title: Midi-superspace Models of Canonical Quantum Gravity

abstract:
  A midi-superspace model is a field theory obtained by symmetry reduction of a
parent gravitational theory. Such models have proven useful for exploring the
classical and quantum dynamics of the gravitational field. I present 3 recent
classes of results pertinent to canonical quantization of vacuum general
relativity in the context of midi-superspace models. (1) I give necessary and
sufficient conditions such that a given symmetry reduction can be performed at
the level of the Lagrangian or Hamiltonian. (2) I discuss the Hamiltonian
formulation of models based upon cylindrical and toroidal symmetry. In
particular, I explain how these models can be identified with parametrized
field theories of wave maps, thus a natural strategy for canonical quantization
is available. (3) The quantization of a parametrized field theory, such as the
midi-superspace models considered in (2), requires construction of a quantum
field theory on a fixed (flat) spacetime that allows for time evolution along
arbitrary foliations of spacetime. I discuss some recent results on the
possibility of finding such a quantum field theory.


title: Spacetime Embedding Diagrams for Black Holes

abstract:
  We show that the 1+1 dimensional reduction (i.e., the radial plane) of the
Kruskal black hole can be embedded in 2+1 Minkowski spacetime and discuss how
features of this spacetime can be seen from the embedding diagram. The purpose
of this work is educational: The associated embedding diagrams may be useful
for explaining aspects of black holes to students who are familiar with special
relativity, but not general relativity.


title: An explanation of the Newman-Janis Algorithm

abstract:
  After the original discovery of the Kerr metric, Newman and Janis showed that
this solution could be ``derived'' by making an elementary complex
transformation to the Schwarzschild solution. The same method was then used to
obtain a new stationary axisymmetric solution to Einstein's field equations now
known as the Kerr-newman metric, representing a rotating massive charged black
hole. However no clear reason has ever been given as to why the Newman-Janis
algorithm works, many physicist considering it to be an ad hoc procedure or
``fluke'' and not worthy of further investigation. Contrary to this belief this
paper shows why the Newman-Janis algorithm is successful in obtaining the
Kerr-Newman metric by removing some of the ambiguities present in the original
derivation. Finally we show that the only perfect fluid generated by the
Newman-Janis algorithm is the (vacuum) Kerr metric and that the only Petrov
typed D solution to the Einstein-Maxwell equations is the Kerr-Newman metric.


title: Canonical Quantization and Expanding Metrics

abstract:
  The canonical formalism for expanding metrics scenarios is presented.
Non-unitary time evolution implied by expanding geometry is described as a
trajectory over unitarily inequivalent representations at different times of
the canonical commutation relations. Thermal properties of inflating Universe
are also discussed.


title:
Inequalities relating area, energy, surface gravity and charge of black
  holes

abstract:
  The Penrose-Gibbons inequality for charged black holes is proved in spherical
symmetry, assuming that outside the black hole there are no current sources,
meaning that the charge e is constant, with the remaining fields satisfying the
dominant energy condition. Specifically, for any achronal hypersurface which is
asymptotically flat at spatial or null infinity and has an outermost marginal
surface of areal radius r, the asymptotic mass m satisfies 2m >= r + e^2/r.
Replacing m by a local energy, the inequality holds locally outside the black
hole. A recent definition of dynamic surface gravity k also satisfies
inequalities 2k <= 1/r - e^2/r^3 and m >= r^2 k + e^2/r. All these inequalities
are sharp in the sense that equality is attained for the Reissner-Nordstrom
black hole.


title:
Toda Chains with Type Am Lie Algebra for Multidimensional Classical
  Cosmology with Intersecting p-Branes

abstract:
  We consider a D-dimensional cosmological model describing an evolution of
(n+1) Einstein factor spaces in the theory with several dilatonic scalar fields
and generalized electro-magnetic forms, admitting an interpretation in terms of
intersecting p-branes. The equations of motion of the model are reduced to the
Euler-Lagrange equations for the so called pseudo-Euclidean Toda-like system.
We consider the case, when characteristic vectors of the model, related to
p-branes configuration and their couplings to the dilatonic fields, may be
interpreted as the root vectors of a Lie algebra of the type Am. The model is
reduced to the open Toda chain and integrated. The exact solution is presented
in the Kasner-like form.


title:
Gravitational radiation from corotating binary neutron stars of
  incompressible fluid in the first post-Newtonian approximation of general
  relativity

abstract:
  We analytically study gravitational radiation from corotating binary neutron
stars composed of incompressible, homogeneous fluid in circular orbits. The
energy and the angular momentum loss rates are derived up to the first
post-Newtonian (1PN) order beyond the quadrupole approximation including
effects of the finite size of each star of binary. It is found that the leading
term of finite size effects in the 1PN order is only $O(GM_{\ast}/c^2
a_{\ast})$ smaller than that in the Newtonian order, where $GM_{\ast}/c^2
a_{\ast}$ means the ratio of the gravitational radius to the mean radius of
each star of binary, and the 1PN term acts to decrease the Newtonian finite
size effect in gravitational radiation.


title: On the Motion of Free Material Test Particles in Arbitrary Spatial Flows

abstract:
  We show how the motion of free material test particles in arbitrary spatial
flows is easily determined within the context of ordinary vector calculus. This
may be useful for everyone, including engineers and other non-specialists, when
thinking about gravitational problems. It already has valid application to
simple problems such as the problems of motion in rotating and accelerating
frames and to the gravitational problem of the single spherically symmetric
attractor. When applied to the two body gravitational problem, it may help us
determine the actual direction of the flow.


title: Lagrangian planetary equations in Schwarzschild space--time

abstract:
  We have developed a method to study the effects of a perturbation to the
motion of a test point--like object in a Schwarzschild spacetime. Such a method
is the extension of the Lagrangian planetary equations of classical celestial
mechanics into the framework of the full theory of general relativity. The
method provides a natural approach to account for relativistic effects in the
unperturbed problem in an exact way.


title: Truncated post-Newtonian neutron star model

abstract:
  As a preliminary step towards simulating binary neutron star coalescing
problem, we test a post-Newtonian approach by constructing a single neutron
star model. We expand the Tolman-Oppenheimer-Volkov equation of hydrostatic
equilibrium by the power of $c^{-2}$, where $c$ is the speed of light, and
truncate at the various order. We solve the system using the polytropic
equation of state with index $\Gamma=5/3, 2$ and 3, and show how this
approximation converges together with mass-radius relations. Next, we solve the
Hamiltonian constraint equation with these density profiles as trial functions,
and examine the differences in the final metric. We conclude the second
`post-Newtonian' approximation is close enough to describe general relativistic
single star. The result of this report will be useful for further binary
studies.
  (Note to readers) This paper was accepted for publication in Physical Review
D. [access code dsj637]. However, since I was strongly suggested that the
contents of this paper should be included as a section in our group's future
paper, I gave up the publication.


title:
Non stationary Einstein-Maxwell fields interacting with a
  superconducting cosmic string

abstract:
  Non stationary cylindrically symmetric exact solutions of the
Einstein-Maxwell equations are derived as single soliton perturbations of a
Levi-Civita metric, by an application of Alekseev inverse scattering method. We
show that the metric derived by L. Witten, interpreted as describing the
electrogravitational field of a straight, stationary, conducting wire may be
recovered in the limit of a `wide' soliton. This leads to the possibility of
interpreting the solitonic solutions as representing a non stationary
electrogravitational field exterior to, and interacting with, a thin, straight,
superconducting cosmic string. We give a detailed discussion of the
restrictions that arise when appropiate energy and regularity conditions are
imposed on the matter and fields comprising the string, considered as `source',
the most important being that this `source' must necessarily have a non-
vanishing minimum radius. We show that as a consequence, it is not possible,
except in the stationary case, to assign uniquely a current to the source from
a knowledge of the electrogravitational fields outside the source. A discussion
of the asymptotic properties of the metrics, the physical meaning of their
curvature singularities, as well as that of some of the metric parameters, is
also included.


title: The Action of Instantons with Nut Charge

abstract:
  We examine the effect of a non-trivial nut charge on the action of
non-compact four-dimensional instantons with a U(1) isometry. If the instanton
action is calculated by dimensionally reducing along the isometry, then the nut
charge is found to make an explicit non-zero contribution. For metrics
satisfying AF, ALF or ALE boundary conditions, the action can be expressed
entirely in terms of quantities (including the nut charge) defined on the fixed
point set of the isometry. A source (or sink) of nut charge also implies the
presence of a Misner string coordinate singularity, which will have an
important effect on the Hamiltonian of the instanton.


title:
Constraints on spacetime manifold in Euclidean supergravity in terms of
  Dirac eigenvalues

abstract:
  We generalize previous work on Dirac eigenvalues as dynamical variables of
Euclidean supergravity. The most general set of constraints on the curvatures
of the tangent bundle and on the spinor bundle of the spacetime manifold under
which spacetime admits Dirac eigenvalues as observables, are derived.


title:
Extended particle models based on hollow singular hypersurfaces in
  general relativity: Classical and quantum aspects of charged textures

abstract:
  In present paper we construct classical and quantum models of an extended
charged particle. One shows that consecutive modelling can be based on the
hollow thin-wall charged texture (in the hydrodynamical approach of a perfect
fluid) which acquires gravitational mass due to Einstein-Maxwell interaction.
We demonstrate that such a model has equilibrium states at the radius equal to
the established classical radius of a charged particle. Also we consider
quantum aspects of the theory and obtain the (internal) Dirac sea conception in
a natural way. Besides, the phenomenological unification on the mass level of
the two families of elementary particles, charged pions and electrons and
positrons, evidently arises as the effect induced by classical and quantum
gravity prior to Standard Model.
  Finally, in the cosmological connection our model proposes the answer on the
important question, what are the real sources of texture matter. Besides, the
texture hypothesis means that in the early Universe the topological texture
foam phase existed before the lepton-hadron one.


title: Basis states for gravitons in non-perturbative loop representation space

abstract:
  A relation between the non-perturbative loop representation space and the
semi-classical loop representation space is studied. A sector of (approximate)
states and a sector of operators in the non-perturbative loop representation
space are made related respectively to the physical states and the basic
variables of the semi-classical loop representation space through a
transformation. This transformation makes a construction of graviton states
within the non-perturbative theory possible although the notion of gravitons
originally emerged from semi-classical perturbative treatments. This
transformation is ``exact'' in the sense that it does not contain an error
term, a fact contrast to the previous construction of a similar transformation.
This fact allows the interpretation that these graviton states represent free
gravitons even after introducing the self-interaction of gravitons into the
theory; the presence of an error term of order of possible perturbative
self-interaction would spoil this interpretation. The existence of such an
``exact'' relation of the two theories supports the potential ability of the
non-perturbative loop representation quantum gravity to address the physics of
gravitons, namely quanta for large scale small fluctuations of gravitational
field in the flat background spacetime.


title: General Relativistic Solitons (II)

abstract:
  We investigate the possible existence of non-topological solitons in
string-like theories, or in other completions of Einstein theory, by examining
a simple extension of standard theory that describes a non-linear scalar field
interacting with the Einstein, Maxwell and Weyl (dilaton) fields. The Einstein
and Maxwell couplings are standard while the dilatonic coupling is taken to
agree with string models. The non-linear scalar potential is quite general. It
is found to be impossible to satisfy the dilatonic boundary conditions.
Excluding the dilaton field we find a variety of solitonic structures differing
in ways that depend on the non-linear potential. In general the excited states
exhibit a discrete mass spectrum. At large distances the gravitational field
approaches the Reissner-Nordstrom solution.


title:
How unique is the expected stress-energy tensor of a massive scalar
  field?

abstract:
  We show that the set of ambiguities in the renormalized expected
stress-energy tensor allowed by the Wald axioms is much larger for a massive
scalar field (an infinite number of free parameters) than for a massless scalar
field (two free parameters). We also use the closed-time-path effective action
formalism of Schwinger to calculate the expected value of the stress-energy
tensor in the incoming vacuum state, for a massive scalar field, on any
spacetime which is a linear perturbation off Minkowski spacetime. This result
generalizes an earlier result of Horowitz and also Jordan in the massless case,
and can be used as a testbed for comparing different calculational methods.


title: Coasting cosmologies with time dependent cosmological constant

abstract:
  The effect of a time dependent cosmological constant is considered in a
family of scalar tensor theories. Friedmann-Robertson-Walker cosmological
models for vacumm and perfect fluid matter are found. They have a linear
expansion factor, the so called coasting cosmology, the gravitational
"constant" decreace inversely with time; this model satisfy the Dirac
hipotesis. The cosmological "constant" decreace inversely with the square of
time, therefore we can have a very small value for it at present time.


title:
Numerical evolution of matter in dynamical axisymmetric black hole
  spacetimes. I. Methods and tests

abstract:
  We have developed a numerical code to study the evolution of self-gravitating
matter in dynamic black hole axisymmetric spacetimes in general relativity. The
matter fields are evolved with a high-resolution shock-capturing scheme that
uses the characteristic information of the general relativistic hydrodynamic
equations to build up a linearized Riemann solver. The spacetime is evolved
with an axisymmetric ADM code designed to evolve a wormhole in full general
relativity. We discuss the numerical and algorithmic issues related to the
effective coupling of the hydrodynamical and spacetime pieces of the code, as
well as the numerical methods and gauge conditions we use to evolve such
spacetimes. The code has been put through a series of tests that verify that it
functions correctly. Particularly, we develop and describe a new set of testbed
calculations and techniques designed to handle dynamically sliced,
self-gravitating matter flows on black holes, and subject the code to these
tests. We make some studies of the spherical and axisymmetric accretion onto a
dynamic black hole, the fully dynamical evolution of imploding shells of dust
with a black hole, the evolution of matter in rotating spacetimes, the
gravitational radiation induced by the presence of the matter fields and the
behavior of apparent horizons through the evolution.


title: Quantization of Gravity Based on a Condensed Matter Model

abstract:
  One way the ultraviolet problem may be solved is explicit physical
regularization. In this scenario, QFT is only the long distance limit of some
unknown non-Poincare-invariant microscopic theory. One can ask how complex and
contrived such microscopic theories should be.
  We show that condensed matter in standard Newtonian framework is sufficient
to obtain gravity. We derive a metrical theory of gravity with two additional
to GR cosmological constants. The observable difference is similar to
homogeneously distributed dark matter with p = -1/3 epsilon. resp. p = epsilon.
The gravitational collapse stops before horizon formation and evaporates by
Hawking radiation. The cutoff is not the Planck length, but expanding together
with the universe. Thus, in some cosmological future microscopic effects become
observable.


title: Can Naked Singularities Yield Gamma Ray Bursts?

abstract:
  Gamma-ray bursts are believed to be the most luminous objects in the
Universe. There has been some suggestion that these arise from quantum
processes around naked singularities. The main problem with this suggestion is
that all known examples of naked singularities are massless and hence there is
effectively no source of energy. It is argued that a globally naked singularity
coupled with quantum processes operating within a distance of the order of
Planck length of the singularity will probably yield energy burst of the order
of M_pc^2\approx2\times 10^{16} ergs, where M_p is the Planck mass.


title: Kinematic cosmology in conformally flat spacetime

abstract:
  In a recent series of papers Endean examines the properties of spatially
homogeneous and isotropic (FLRW) cosmological models filled with dust in the
``conformally flat spacetime presentation of cosmology'' (CFS cosmology). This
author claims it is possible to resolve a certain number of the difficulties
the standard model exhibits when confronted to observations, if the theoretical
predictions are obtained in the special framework of CFS cosmology. As a
by-product of his analysis Endean claims that no initial (big-bang) nor final
(big-crunch) singularities occur in the closed FLRW model. In this paper we
show up the fallacious arguments leading to Endean's conclusions and we
consistently reject his CFS cosmology.


title:
Universality Principle for Orbital Angular Momentum and Spin in Gravity
  with Torsion

abstract:
  We argue that compatibility with elementary particle physics requires
gravitational theories with torsion to be unable to distinguish between orbital
angular momentum and spin. An important consequence of this principle is that
spinless particles must move along autoparallel trajectories, not along
geodesics.


title:
The (In)stability of Bianchi IX Dynamics: Geodesic Deviation Equations
  in Finsler Spaces

abstract:
  We explore the dynamical stability of the minisuperspace Hamiltonian of the
Bianchi IX cosmological models, giving a gauge-invariant and unapproximated
description of the full continuous dynamics, achieved through a geometrical
description of the equations of motion in the framework of the theory of
Finsler Spaces. The numerical integrations of the geodesics and geodesic
deviation equations show clearly the absence of any "traditional" signature of
Chaos, while suggesting a chaotic scattering dynamics scenario.


title:
Loss of Quantum Coherence and Positivity of Energy Density in
  Semiclassical Quantum Gravity

abstract:
  In the semiclassical quantum gravity derived from the Wheeler-DeWitt
equation, the energy density of a matter field loses quantum coherence due to
the induced gauge potential from the parametric interaction with gravity in a
non-static spacetime. It is further shown that the energy density takes only
positive values and makes superposition principle hold true. By studying a
minimal massive scalar field in a FRW spacetime background, we illustrate the
positivity of energy density and obtain the classical Hamiltonian of a complex
field from the energy density in coherent states.


title: Noise induced transitions in semiclassical cosmology

abstract:
  A semiclassical cosmological model is considered which consists of a closed
Friedmann-Robertson-Walker in the presence of a cosmological constant, which
mimics the effect of an inflaton field, and a massless, non-conformally coupled
quantum scalar field. We show that the back-reaction of the quantum field,
which consists basically of a non local term due to gravitational particle
creation and a noise term induced by the quantum fluctuations of the field, are
able to drive the cosmological scale factor over the barrier of the classical
potential so that if the universe starts near zero scale factor (initial
singularity) it can make the transition to an exponentially expanding de Sitter
phase. We compute the probability of this transition and it turns out to be
comparable with the probability that the universe tunnels from "nothing" into
an inflationary stage in quantum cosmology. This suggests that in the presence
of matter fields the back-reaction on the spacetime should not be neglected in
quantum cosmology.


title:
Solar System Experiments and the Interpretation of Saa's Model of
  Gravity with Propagating Torsion as a Theory with Variable Plank "Constant"

abstract:
  It is shown that the recently proposed interpretation of the transposed
equi-affine theory of gravity as a theory with variable Plank "constant" is
inconsistent with basic solar system gravitational experiments.


title:
The role of the quantum properties of gravitational radiation in the
  dete ction of gravitational waves

abstract:
  The role that the quantum properties of a gravitational wave could play in
the detection of gravitational radiation is analyzed. It is not only
corroborated that in the current laser-interferometric detectors the resolution
of the experimental apparatus could lie very far from the corresponding quantum
threshold (thus the backreaction effect of the measuring device upon the
gravitational wave is negligible), but it is also suggested that the
consideration of the quantum properties of the wave could entail the definition
of dispersion of the measurement outputs. This dispersion would be a function
not only of the sensitivity of the measuring device, but also of the
interaction time (between measuring device and gravitational radiation) and of
the arm length of the corresponding laser- interferometer. It would have a
minimum limit, and the introduction of the current experimental parameters
insinuates that the dispersion of the existing proposals could lie very far
from this minimum, which means that they would show a very large dispersion.


title: Higher-Dimensional Geometric Sigma Models

abstract:
  Geometric $\sigma$-models have been defined as purely geometric theories of
scalar fields coupled to gravity. By construction, these theories possess
arbitrarily chosen vacuum solutions. Using this fact, one can build a
Kaluza--Klein geometric $\sigma$-model by specifying the vacuum metric of the
form $M^4\times B^d$. The obtained higher dimensional theory has vanishing
cosmological constant but fails to give massless gauge fields after the
dimensional reduction. In this paper, a modified geometric $\sigma$-model is
suggested, which solves the above problem.


title: A New Look at the Ashtekar-Magnon Energy Condition

abstract:
  In 1975, Ashtekar and Magnon showed that an energy condition selects a unique
quantization procedure for certain observers in general, curved spacetimes. We
generalize this result in two important ways, by eliminating the need to assume
a particular form for the (quantum) Hamiltonian, and by considering the
surprisingly nontrivial extension to nonminimal coupling.


title:
Treating instabilities in a hyperbolic formulation of Einstein's
  equations

abstract:
  We have recently constructed a numerical code that evolves a spherically
symmetric spacetime using a hyperbolic formulation of Einstein's equations. For
the case of a Schwarzschild black hole, this code works well at early times,
but quickly becomes inaccurate on a time scale of 10-100 M, where M is the mass
of the hole. We present an analytic method that facilitates the detection of
instabilities. Using this method, we identify a term in the evolution equations
that leads to a rapidly-growing mode in the solution. After eliminating this
term from the evolution equations by means of algebraic constraints, we can
achieve free evolution for times exceeding 10000M. We discuss the implications
for three-dimensional simulations.


title: Quantum Mechanics in General Relativity

abstract:
  Having started with the general formulation of the quantum theory of the real
scalar field (QFT) in the general Riemannian space--time $ V_{1,3} $, the
general--covariant quasinonrelativistic quantum mechanics of a point-like
spinless particle in $ V_{1,3} $ is constructed. To this end, for any normal
geodesic 1+3--foliation of $ V_{1,3} $, a space $\Phi^-$ of asymptotic in
$c^{-1}$ solutions of the field equation is specified, which can be mapped to a
space $\Psi$ of solutions of a Schr\"odinger equation with an (asymptotically)
Hermitean hamiltonian and the Born probabilistic interpretation of the vectors
of $\Psi$. The basic operators of the momentum and the spatial position of the
particle acting in $\Psi$ generated by the corresponding observables of QFT
include relativistic corrections, and therefore differ generally from those
which follow for the geodesic motion in $ V_{1,3} $ from the canonical
postulates of quantization. In particular, the operators of coordinates do not
commute as well as the operators of the conjugate momenta, except the cases of
Cartesian coordinates in the Minkowski space--time or of the exact
nonrelativistic limit $(c^{-1} = 0)$. This approach provides QFT in the general
$ V_{1,3} $ in the Fock representation with a particle interpretation based on
the Born interpretation of wave functions.


title: Global Structure of Evaporating Black Holes

abstract:
  By extending the charged Vaidya metric to cover all of spacetime, we obtain a
Penrose diagram for the formation and evaporation of a charged black hole. In
this construction, the singularity is time-like. The entire spacetime can be
predicted from initial conditions if boundary conditions at the singularity are
known.


title: On a Class of Riemann-Cartan Space-times of G\"odel Type

abstract:
  A class of Riemann-Cartan G\"odel-type space-times is examined by using the
equivalence problem techniques, as formulated by Fonseca-Neto et al. and
embodied in a suite of computer algebra programs called TCLASSI. A
coordinate-invariant description of the gravitational field for this class of
space-times is presented. It is also shown that these space-times can admit a
group $G_{r}$ of affine-isometric motions of dimensions $r=2, 4, 5$. The
necessary and sufficient conditions for space-time (ST) homogeneity of this
class of space-times are derived, extending previous works on G\"odel-type
space-times. The equivalence of space-times in the ST homogeneous subclass is
studied, recovering recent results under different premises. The results of the
limiting Riemannian case are also recovered.


title:
Plane-Symmetric Vacuum Solutions with Null Singularities for
  Inhomogeneous Models and Colliding Gravitational Waves

abstract:
  New exact vacuum solutions with various singularities in the plane-symmetric
spacetime are shown, and they are applied to the analysis of inhomogeneous
cosmological models and colliding gravitational waves. One of the singularities
can be true null singularities, whose existence was locally clarified by Ori.
These solutions may be interesting from the viewpoint of the variety of
cosmological singularities and the instability problem of Cauchy horizons
inside black holes.


title: Self-Gravitating Non-Abelian Cosmic String Solution

abstract:
  The coupled Einstein-Yang-Mills equations on a time dependent axially
symmetric spacetime are investigated, without a priori any conditions on the
gauge field. There is numerical evidence for the existence of a regular
solution with the desired asymptotic features. Just as in the supermassive
abelian counterpart model, the formation of a singularity at finite distance of
the core of the string depends critically on a parameter of the model, i.e.,
the constant value of one of the magnetic components of the YM potentials. The
multiple-scale method could supply decisive answers concerning the stability of
the solution.


title: Black Holes with Yang-Mills Hair

abstract:
  In Einstein-Maxwell theory black holes are uniquely determined by their mass,
their charge and their angular momentum. This is no longer true in
Einstein-Yang-Mills theory. We discuss sequences of neutral and charged SU(N)
Einstein-Yang-Mills black holes, which are static spherically symmetric and
asymptotically flat, and which carry Yang-Mills hair. Furthermore, in
Einstein-Maxwell theory static black holes are spherically symmetric. We
demonstrate that, in contrast, SU(2) Einstein-Yang-Mills theory possesses a
sequence of black holes, which are static and only axially symmetric.


title: Gravitational waves from rapidly rotating white dwarfs

abstract:
  Rapidly rotating white dwarfs in cataclysmic variable systems may be emitting
gravitational radiation due to the recently discovered relativistic r-mode
instability. Assuming that the four most rapidly rotating known systems are
limited in rotation rate by the instability, the amplitude of the emitted
gravitational waves is determined at Earth for both known rapid rotators and
for a model background caused by a galactic population of such systems. The
proposed LISA and OMEGA space-based interferometer gravitational wave detectors
could observe such signals and determine whether the r-mode instability plays a
significant role in white dwarf systems.


title:
Chaos and a Resonance Mechanism for Structure Formation in Inflationary
  Models

abstract:
  We exhibit a resonance mechanism of amplification of density perturbations in
inflationary mo-dels, using a minimal set of ingredients (an effective
cosmological constant, a scalar field minimally coupled to the gravitational
field and matter), common to most models in the literature of inflation. This
mechanism is based on the structure of homoclinic cylinders, emanating from an
unstable periodic orbit in the neighborhood of a saddle-center critical point,
present in the phase space of the model. The cylindrical structure induces
oscillatory motions of the scales of the universe whenever the orbit visits the
neighborhood of the saddle-center, before the universe enters a period of
exponential expansion. The oscillations of the scale functions produce, by a
resonance mechanism, the amplification of a selected wave number spectrum of
density perturbations, and can explain the hierarchy of scales observed in the
actual universe. The transversal crossings of the homoclinic cylinders induce
chaos in the dynamics of the model, a fact intimately connected to the
resonance mechanism occuring immediately before the exit to inflation.


title: Final fate of the spherically symmetric collapse of a perfect fluid

abstract:
  The final fate of the spherically symmetric collapse of a perfect fluid which
follows the $\gamma$-law equation of state and adiabatic condition is
investigated. Full general relativistic hydrodynamics is solved numerically
using a retarded time coordinate, the so-called observer time coordinate.
Thanks to this coordinate, the causal structure of the resultant space-time is
automatically constructed. Then, it is found that a globally naked,
shell-focusing singularity can occur at the center from relativistically
high-density, isentropic and time symmetric initial data if $\gamma \alt 1.01$
within the numerical accuracy. The result is free from the assumption of
self-similarity. The upper limit of $\gamma$ with which a naked singularity can
occur from generic initial data is consistent with the result of Ori and Piran
based on the assumption of self-similarity.


title:
A possible Newtonian interpretation of relativistic cosmological
  perturbation theory

abstract:
  Cosmological perturbations with wavelengths smaller than Hubble radius can be
handled in the context of Newtonian theory with very high accuracy. The
application of this Newtonian approximation, however, is restricted to
nonrelativistic matter and cannot be used for relativistic matter. Recently, by
modifying the continuity equation, Lima, et. al., extended the domain of
applicability of Newtonian cosmology to radiation dominated phase. We adopted
this continuity equation to re-examine linear cosmological perturbation theory
for a two fluid universe with uniform pressure. We study the evolution
equations for density contrasts and their validity in different epochs and on
scales larger than Hubble radius and compare the results with the full
relativistic approach. The comparison shows the high accuracy of this
approximation.


title: String Cosmology

abstract:
  An overview is given of the formulation of low-energy string cosmologies
together with examples of particular solutions, successes and problems of the
theory.


title: Hamiltonian Time Evolution for General Relativity

abstract:
  Hamiltonian time evolution in terms of an explicit parameter time is derived
for general relativity, even when the constraints are not satisfied, from the
Arnowitt-Deser-Misner-Teitelboim-Ashtekar action in which the slicing density
$\alpha(x,t)$ is freely specified while the lapse $N=\alpha g^{1/2}$ is not.
The constraint ``algebra'' becomes a well-posed evolution system for the
constraints; this system is the twice-contracted Bianchi identity when
$R_{ij}=0$. The Hamiltonian constraint is an initial value constraint which
determines $g^{1/2}$ and hence $N$, given $\alpha$.


title: Black hole interacting with matter as a simple dynamical system

abstract:
  Recently, a variational principle has been derived from Einstein-Hilbert and
a matter Lagrangian for the spherically symmetric system of a dust shell and a
black hole. The so-called physical region of the phase space, which contains
all physically meaningful states of the system defined by the variational
principle, is specified; it has a complicated boundary. The principle is then
transformed to new variables that remove some problems of the original
formalism: the whole phase space is covered (in particular, the variables are
regular at all horizons), the constraint has a polynomial form, and the
constraint equation is uniquely solvable for two of the three conserved
momenta. The solutions for the momenta are written down explicitly. The
symmetry group of the system is studied. The equations of motion are derived
from the transformed principle and are shown to be equivalent to the previous
ones. Some lower-dimensional systems are constructed by exclusion of cyclic
variables, and some of their properties are found.


title: Symmetries of Taub-NUT Dual Metrics

abstract:
  In this paper we study the symmetries of the dual Taub-NUT metrics. Generic
and non-generic symmetries of dual Taub-NUT metrics are investigated.
  The existence of the Runge-Lenz type symmetry is analyzed for dual Taub-NUT
metrics.
  We find that in some cases the symmetries of the dual metrics are the same
with the symmetries of Taub-NUT metric.


title:
Answer to Question 55: Are there pictorial examples that distinguish
  covariant and contravariant vectors?

abstract:
  We present pictorial means of distinguishing contravariant vectors (or simply
vectors) from covariant vectors (or linear forms). When one depicts vector as
the directed segment, then the pictorial image of a linear form is a family of
equidistant parallel planes with an arrow joining the neighbouring planes and
showing the direction of increase of the form. First of these planes is the
linear subspace of dimension two on which the linear form gives value zero.
Several examples of physical quantities are given which are naturally vectors,
and others which are naturally linear forms.


title: Black Hole Entropy and Quantum Gravity

abstract:
  An elementary introduction is given to the problem of black hole entropy as
formulated by Bekenstein and Hawking. The information theoretic basis of
Bekenstein's formulation is briefly reviewed and compared with Hawking's
approach. The issue of calculating the entropy by actual counting of
microstates is taken up next within two currently popular approaches to quantum
gravity, viz., string theory and canonical quantum gravity. The treatment of
the former assay is confined to a few remarks, mainly of a critical nature,
while some of the computational techniques of the latter approach are
elaborated. We conclude by trying to find commonalities between these two
rather disparate directions of work.


title: Innermost stable circular orbits around relativistic rotating stars

abstract:
  We investigate the innermost stable circular orbit (ISCO) of a test particle
moving on the equatorial plane around rotating relativistic stars such as
neutron stars. First, we derive approximate analytic formulas for the angular
velocity and circumferential radius at the ISCO making use of an approximate
relativistic solution which is characterized by arbitrary mass, spin, mass
quadrupole, current octapole and mass $2^4$-pole moments. Then, we show that
the analytic formulas are accurate enough by comparing them with numerical
results, which are obtained by analyzing the vacuum exterior around numerically
computed geometries for rotating stars of polytropic equation of state. We
demonstrate that contribution of mass quadrupole moment for determining the
angular velocity and, in particular, the circumferential radius at the ISCO
around a rapidly rotating star is as important as that of spin.


title:
Cauchy-perturbative matching and outer boundary conditions:
  computational studies

abstract:
  We present results from a new technique which allows extraction of
gravitational radiation information from a generic three-dimensional numerical
relativity code and provides stable outer boundary conditions. In our approach
we match the solution of a Cauchy evolution of the nonlinear Einstein field
equations to a set of one-dimensional linear equations obtained through
perturbation techniques over a curved background. We discuss the validity of
this approach in the case of linear and mildly nonlinear gravitational waves
and show how a numerical module developed for this purpose is able to provide
an accurate and numerically convergent description of the gravitational wave
propagation and a stable numerical evolution.


title:
Integration of Einstein's Equations in the Weak Field Domain Using the
  "Einstein" Gauge

abstract:
  We propose a new alternative gauge for the Einstein equations instead of the
de Donder gauge, which allows in the limit of weak fields a straightforward
integration of these equations. The Newtonian potential plays a new interesting
role in this framework. The calculations are demonstrated explicitely for 2
simple astrophysical models.


title: Generalized r-Modes of the Maclaurin Spheroids

abstract:
  Analytical solutions are presented for a class of generalized r-modes of
rigidly rotating uniform density stars---the Maclaurin spheroids---with
arbitrary values of the angular velocity. Our analysis is based on the work of
Bryan; however, we derive the solutions using slightly different coordinates
that give purely real representations of the r-modes. The class of generalized
r-modes is much larger than the previously studied `classical' r-modes. In
particular, for each l and m we find l-m (or l-1 for the m=0 case) distinct
r-modes. Many of these previously unstudied r-modes (about 30% of those
examined) are subject to a secular instability driven by gravitational
radiation. The eigenfunctions of the `classical' r-modes, the l=m+1 case here,
are found to have particularly simple analytical representations. These r-modes
provide an interesting mathematical example of solutions to a hyperbolic
eigenvalue problem.


title: Two kinds of extreme black holes and their classification

abstract:
  According to different topological configurations, we suggest that there are
two kinds of extreme black holes in the nature. We find that the Euler
characteristic plays an essential role to classify these two kinds of extreme
black holes. For the first kind of extreme black holes, Euler characteristic is
zero, and for the second kind, Euler characteristic is two or one provided they
are four dimensional holes or two dimensional holes respectively.


title:
Third rank Killing tensors in general relativity. The (1+1)-dimensional
  case

abstract:
  Third rank Killing tensors in (1+1)-dimensional geometries are investigated
and classified. It is found that a necessary and sufficient condition for such
a geometry to admit a third rank Killing tensor can always be formulated as a
quadratic PDE, of order three or lower, in a Kahler type potential for the
metric. This is in contrast to the case of first and second rank Killing
tensors for which the integrability condition is a linear PDE. The motivation
for studying higher rank Killing tensors in (1+1)-geometries, is the fact that
exact solutions of the Einstein equations are often associated with a first or
second rank Killing tensor symmetry in the geodesic flow formulation of the
dynamics. This is in particular true for the many models of interest for which
this formulation is (1+1)-dimensional, where just one additional constant of
motion suffices for complete integrability. We show that new exact solutions
can be found by classifying geometries admitting higher rank Killing tensors.


title:
Detection of Scalar Particles in Gravitational Waves from Resonant-Mass
  Detectors of Spherical Shape

abstract:
  We report on some recent work, which points out the relevance of future
measurements of gravitational waves by resonant-mass detectors of spherical
shape for theories of gravity of non-Einstein type.


title: Quantum entropy of two-dimensional extreme charged dilaton black hole

abstract:
  By using Hawking's treatment as well as Zaslavskii's treatment respectively
and the brick wall model, two different values of classical entropy and quantum
entropy of scalar fields in the two-dimensional extreme charged dilaton black
hole backgrounds have been obtained. A new divergent term emerges in the
quantum entropy under the extreme limit for Zaslavskii's treatment and its
connection with the phase transition has been addressed.


title: Energy-Momentum and Gauge Conservation Laws

abstract:
  We treat energy-momentum conservation laws as particular gauge conservation
laws when generators of gauge transformations are horizontal vector fields on
fibre bundles. In particular, the generators of general covariant
transformations are the canonical horizontal prolongations of vector fields on
a world manifold. This is the case of the energy-momentum conservation laws in
gravitation theories. We find that, in main gravitational models, the
corresponding energy-momentum flows reduce to the generalized Komar
superpotential. We show that the superpotential form of a conserved flow is the
common property of gauge conservation laws if generators of gauge
transformations depend on derivatives of gauge parameters. At the same time,
dependence of conserved flows on gauge parameters make gauge conservation laws
form-invariant under gauge transformations.


title:
On the Asymptotic Behaviour of Cosmological Models in Scalar-Tensor
  Theories of Gravity

abstract:
  We study the qualitative properties of cosmological models in scalar-tensor
theories of gravity by exploiting the formal equivalence of these theories with
general relativity minimally coupled to a scalar field under a conformal
transformation and field redefinition. In particular, we investigate the
asymptotic behaviour of spatially homogeneous cosmological models in a class of
scalar-tensor theories which are conformally equivalent to general relativistic
Bianchi cosmologies with a scalar field and an exponential potential whose
qualitative features have been studied previously. Particular attention is
focussed on those scalar-tensor theory cosmological models, which are shown to
be self-similar, that correspond to general relativistic models that play an
important r\^{o}le in describing the asymptotic behaviour of more general
models (e.g., those cosmological models that act as early-time and late-time
attractors).


title: Novel Instability in Superstring Cosmology

abstract:
  As a most promising candidate for quantum theory of the gravity, the
superstring theory has attracted many researchers including cosmologists. It is
expected that the cosmological initial singularity is avoided within the
context of the superstring theory. Indeed, Antoniadis et. al. found an
interesting example of the non-singular cosmological solutions by considering
the string one-loop correction. Here, we will discuss the stability of this
model and find a new kind of instability in the graviton modes. We also argue
this instability will persist even in the non-perturbative regime. The
instability we have found might provide a mechanism to produce the primodial
black holes.


title:
Towards N=2 $SUSY$ Homogeneous Quantum Cosmology; Einstein--Yang--Mills
  systems

abstract:
  The application of N=2 supersymmetric quantum mechanics for the quantization
of homogeneous systems coupled with gravity is discussed. Starting with the
superfield formulation of an N=2 SUSY sigma model, Hermitian self-adjoint
expressions for quantum Hamiltonians and Lagrangians for any signature of a
sigma-model metric are obtained. This approach is then applied to coupled SU(2)
Einstein-Yang-Mills (EYM) systems in axially symmetric $Bianchi$-type I, II,
VIII, IX, $Kantowski-Sachs$, and closed $Friedmann-Robertson-Walker$
cosmological models. It is shown that all these models admit the embedding into
the N=2 SUSY sigma model with the explicit expressions for superpotentials
being direct sums of gravitational and Yang-Mills (YM) parts. In addition, the
YM parts of superpotentials exactly coincide with the corresponding
Chern-Simons terms. The spontaneous SUSY breaking caused by YM instantons in
EYM systems is discussed in a number of examples.


title: Rotating perfect fluid sources of the NUT metric

abstract:
  Locally rotationally symmetric perfect fluid solutions of Einstein's
gravitational equations are matched along the hypersurface of vanishing
pressure with the NUT metric. These rigidly rotating fluids are interpreted as
sources for the vacuum exterior which consists only of a stationary region of
the Taub-NUT space-time. The solution of the matching conditions leaves
generally three parameters in the global solution. Examples of perfect fluid
sources are discussed.


title: A remark on differentiability of Cauchy horizons

abstract:
  In a recent paper Kr\'olak and Beem have shown differentiability of Cauchy
horizons at all points of multiplicity one. In this note we give a simpler
proof of this result.


title:
Nonsingular Bianchi type I cosmological solutions from 1-loop
  superstring effective action

abstract:
  Non-singular Bianchi type I solutions are found from the effective action
with a superstring-motivated Gauss-Bonnet term. These anisotropic non-singular
solutions evolve from the asymptotic Minkowski region, subsequently
super-inflate, and then smoothly continue either to Kasner-type (expanding in
two directions and shrinking in one direction) or to Friedmann-type (expanding
in all directions) solutions. We also found a new kind of singularity which
arises from the fact that the anisotropic expansion rates are multiple-valued
function of time. The initial singularity in the isotropic limit of this model
belongs to this new kind of singularity. In our analysis the anisotropic
solutions are likely to be singular when the super-inflation is steep.


title: Semiclassical Limits of Extended Racah Coefficients

abstract:
  We explore the geometry and asymptotics of extended Racah coeffecients. The
extension is shown to have a simple relationship to the Racah coefficients for
the positive discrete unitary representation series of SU(1,1) which is
explicitly defined. Moreover, it is found that this extension may be
geometrically identified with two types of Lorentzian tetrahedra for which all
the faces are timelike.
  The asymptotic formulae derived for the extension are found to have a similar
form to the standard Ponzano-Regge asymptotic formulae for the SU(2) 6j symbol
and so should be viable for use in a state sum for three dimensional Lorentzian
quantum gravity.


title:
Causal Propagation of Constraints and the Canonical Form of General
  Relativity

abstract:
  Studies of new hyperbolic systems for the Einstein evolution equations show
that the ``slicing density'' $\alpha(t,x)$ can be freely specified while the
lapse $N = \alpha g^{1/2}$ cannot. Implementation of this small change in the
Arnowitt-Deser-Misner action principle leads to canonical equations that agree
with the Einstein equations whether or not the constraints are satisfied. The
constraint functions, independently of their values, then propagate according
to a first order symmetric hyperbolic system whose characteristic cone is the
light cone. This result follows from the twice-contracted Bianchi identity and
constitutes the central content of the constraint ``algebra'' in the canonical
formalism.


title: Rotating Cylindrical Systems and Gravitomagnetism

abstract:
  We discuss gravitomagnetism in connection with rotating cylindrical systems.
In particular, the gravitomagnetic clock effect is investigated for the
exterior vacuum field of an infinite rotating cylinder. The dependence of the
clock effect on the Weyl parameters of the stationary Lewis metric is
determined. We illustrate our results by means of the van Stockum spacetime.


title: Facets of Tunneling: Particle production in external fields

abstract:
  This paper presents a critical review of particle production in an uniform
electric field and Schwarzchild-like spacetimes. Both problems can be reduced
to solving an effective one-dimensional Schrodinger equation with a potential
barrier. In the electric field case, the potential is that of an inverted
oscillator -x^2 while in the case of Schwarchild-like spacetimes, the potential
is of the form -1/x^2 near the horizon. The transmission and reflection
coefficients can easily be obtained for both potentials. To describe particle
production, these coefficients have to be suitably interpreted. In the case of
the electric field, the standard Bogoliubov coefficients can be identified and
the standard gauge invariant result is recovered. However, for
Schwarzchild-like spacetimes, such a tunnelling interpretation appears to be
invalid. The Bogoliubov coefficients cannot be determined by using an
identification process similar to that invoked in the case of the electric
field. The reason for such a discrepancy appears to be that, in the tunnelling
method, the effective potential near the horizon is singular and symmetric. We
also provide a new and simple semi-classical method of obtaining Hawking's
result in the (t,r) co-ordinate system of the usual standard Schwarzchild
metric. We give a prescription whereby the singularity at the horizon can be
regularised with Hawking's result being recovered. This regularisation
prescription contains a fundamental asymmetry that renders both sides of the
horizon dissimilar. Finally, we attempt to interpret particle production by the
electric field as a tunnelling process between the two sectors of the Rindler
metric.


title: On Black Hole Horizon Fluctuations

abstract:
  A study of the high angular momentum particles 'atmosphere' near the
Schwarzschild black hole horizon suggested that strong gravitational
interactions occur at invariant distance of the order of $\sqrt[3]{M}$ (A.
Casher et. al). We present a generalization of this result to the Kerr-Newman
black hole case. It is shown that the larger charge and angular momentum black
hole bears, the larger invariant distance at which strong gravitational
interactions occur becomes. This invariant distance is of order
$\sqrt[3]{r_+^2/\hh}.$ This implies, that the Planckian structure of the
Hawking radiation of extreme black holes is completely broken.


title:
Does the non-minimal coupling of the scalar field improve or destroy
  inflation ?

abstract:
  The non-minimal coupling of a scalar field to the Ricci curvature in a curved
spacetime is unavoidable according to several authors. The coupling constant is
not a free parameter: the prescriptions for the value of the coupling constant
in specific scalar field and gravity theories (in particular in general
relativity) are studied. The results are applied to the most popular
inflationary scenarios of cosmology and their theoretical consistence is
analysed. Certain observational constraints on the coupling constant are also
discussed.


title:
Superluminal propagation of light in gravitational field and non-causal
  signals

abstract:
  It has been found in several papers that, because of quantum corrections,
light front can propagate with superluminal velocity in gravitational fields
and even in flat space-time across two conducting plates. We show that, if this
is the case, closed time-like trajectories would be possible and, in
particular, in certain reference frames photons could return to their source of
origin before they were produced there, in contrast to the opposite claim made
in the literature.


title: A nonlinear theory of tensor distributions

abstract:
  The coordinate invariant theory of generalised functions of Colombeau and
Meril is reviewed and extended to enable the construction of multi-index
generalised tensor functions whose transformation laws coincide with their
counterparts in classical distribution theory.


title: Quantization of singular systems and incomplete motions

abstract:
  The need for a mathematically rigorous quantization procedure of singular
spaces and incomplete motions is pointed out in connection with quantum
cosmology. We put our previous suggestion for such a procedure, based on the
theory of induced representations of C*-algebras, in the light of L. Schwartz'
theory of Hilbert subspaces. This turns out to account for the freedom in the
induction procedure, at the same time providing a basis for generalized
eigenfunction expansions pertinent to the needs of quantum cosmology.
Reinforcing our previous proposal for the wave-function of the Universe, we are
now able to add a concrete prescription for its calculation.


title: Spacetime Quantization from Non-abelian D-particle Dynamics

abstract:
  We describe the short-distance properties of the spacetime of a system of
D-particles by viewing their matrix-valued coordinates as coupling constants of
a deformed worldsheet $\sigma$-model. We show that the Zamolodchikov metric on
the associated moduli space naturally encodes properties of the non-abelian
dynamics, and from this we derive new spacetime uncertainty relations directly
from the quantum string theory. The non-abelian uncertainties exhibit
decoherence effects which suggest the interplay of quantum gravity in multiple
D-particle dynamics.


title: Perturbations in inflationary cosmologies with smooth exit

abstract:
  We give a comprehensive analysis of how scalar and tensor perturbations
evolve in cosmologies with a smooth transition from power-law-like and de
Sitter-like inflation to a radiation era. Analytic forms for the super-horizon
and sub-horizon perturbations in the inflationary and radiation dominated eras
are found.


title: Minimal Coupling and the Equivalence Principle in Quantum Mechanics

abstract:
  The role of the Equivalence Principle (EP) in classical and quantum mechanics
is reviewed. It is shown that the weak EP has a counterpart in quantum theory,
a Quantum Equivalence Principle (QEP). This implies that also in the quantum
domain the geometrisation of the gravitational interaction is an operational
procedure similar to the procedure in classical physics. This QEP can be used
for showing that it is only the usual Schr\"odinger equation coupled to
gravito--inertial fields which obeys our equivalence principle. In addition,
the QEP applied to a generalised Pauli equation including spin results in a
characterisation of the gravitational fields which can be identified with the
Newtonian potential and with torsion. Also, in the classical limit it is
possible to state beside the usual EP for the path an EP for the spin which
again may be used for introducing torsion as a gravitational field.


title: Tetrad Gravity: I) A New Formulation

abstract:
  A new version of tetrad gravity in globally hyperbolic, asymptotically flat
at spatial infinity spacetimes with Cauchy surfaces diffeomorphic to $R^3$ is
obtained by using a new parametrization of arbitrary cotetrads to define a set
of configurational variables to be used in the ADM metric action. Seven of the
fourteen first class constraints have the form of the vanishing of canonical
momenta. A comparison is made with other models of tetrad gravity and with the
ADM canonical formalism for metric gravity. The phase space expression of
various 4-tensors is explicitly given.


title: Tetrad Gravity: II) Dirac's Observables

abstract:
  After a study of the Hamiltonian group of gauge transformations of canonical
tetrad gravity on globally hyperbolic, asymptotically flat at spatial infinity,
spacetimes with Cauchy hypersurfaces $\Sigma_{\tau}$ diffeomorphic to $R^3, we
find the dependence of the cotriads on $\Sigma_{\tau}$ and of their momenta on
the six parameters associated with rotations and space diffeomorphisms. The
choice of 3-coordinates on $\Sigma_{\tau}$ is equivalent to the parametrization
of the cotriads with the last three degrees of freedom individuating the
3-geometries. The Shanmugadhasan canonical transformation, corresponding to the
choice of 3-orthogonal coordinates on $\Sigma_{\tau}$ and adapted to 13 of the
14 first class constraints, and the interpretation of the gauge transformations
are given. The gauge interpretation of tetrad gravity based on constraint
theory implies that a "Hamiltonian kinematical gravitational field" is an
equivalence class of pseudo-Riemannian spacetimes modulo the Hamiltonian group
of gauge transformations: it includes a conformal 3-geometry and all the
different 4-geometries (standard definition of a kinematical gravitational
field, $Riem M^4/Diff M^4$) connected to it by the gauge transformations. A
"Hamiltonian Einstein or dynamical gravitational field" is a kinematical one
which satisfies the Hamilton-Dirac equations generated by the ADM energy: it
coincides with the standard Einstein or dynamical gravitational field, namely a
4-geometry solution of Einstein's equations, since the Hilbert and ADM actions
both generate Einstein's equations so that the kinematical Hamiltonian gauge
transformations are dynamically restricted to the spacetime diffeomorphisms of
the solutions of Einstein's equations.


title: Operator ordering and consistency of the wavefunction of the Universe

abstract:
  We demonstrate in the context of the minisuperspace model consisting of a
closed Friedmann-Robertson-Walker universe coupled to a scalar field that
Vilenkin's tunneling wavefunction can only be consistently defined for
particular choices of operator ordering in the Wheeler-DeWitt equation. The
requirement of regularity of the wavefunction has the particular consequence
that the probability amplitude, which has been used previously in the
literature in discussions of issues such as the prediction of inflation, is
likewise ill-defined for certain choices of operator ordering with Vilenkin's
boundary condition. By contrast, the Hartle-Hawking no-boundary wavefunction
can be consistently defined within these models, independently of operator
ordering. The significance of this result is discussed within the context of
the debate about the predictions of semiclassical quantum cosmology. In
particular, it is argued that inflation cannot be confidently regarded as a
"prediction" of the tunneling wavefunction, for reasons similar to those
previously invoked in the case of the no-boundary wavefunction. A synthesis of
the no-boundary and tunneling approaches is argued for.


title: The problem of time in parametrized theories

abstract:
  A common feature of reparametrization invariant theories is the difficulty
involved in identifying an appropriate evolution parameter and in constructing
a Hilbert space on states. Two well known examples of such theories are the
relativistic point particle and the canonical formulation of quantum gravity.
The strong analogy between them (specially for minisuperspace models) is
considered in order to stress the correspondence between the ``localization
problem'' and the ``problem of time,'' respectively. A possible solution for
the first problem was given by the proper time formulation of relativistic
quantum mechanics. Thus, we extrapolate the main outlines of such a formalism
to the quantum gravity framework. As a consequence, a proposal to solve the
problem of time arises.


title:
Gravitational radiation from Schwarzschild black holes: the second order
  perturbation formalism

abstract:
  The perturbation theory of black holes has been useful recently for providing
estimates of gravitational radiation from black hole collisions. Second order
perturbation theory, relatively undeveloped until recently, has proved to be
important both for providing refined estimates and for indicating the range of
validity of perturbation theory. Here we present the second order formalism for
perturbations of Schwarzschild spacetimes. The emphasis is on practical methods
for carrying out second order computations of outgoing radiation. General
issues are illustrated throughout with examples from ``close-limit'' results,
perturbation calculations in which black holes start from small separation.


title:
Kinetic theory for nongeodesic particle motion: Selfinteracting
  equilibrium states and effective viscous fluid pressures

abstract:
  The particles of a classical relativistic gas are supposed to move under the
influence of a quasilinear (in the particle four-momenta), self-interacting
force inbetween elastic, binary collisions. This force which is completely
fixed by the equilibrium conditions of the gas, gives rise to an effective
viscous pressure on the fluid phenomenological level. Earlier results
concerning the possibility of accelerated expansion of the universe due to
cosmological particle production are reinterpreted. A phenomenon such as power
law inflation may be traced back to specific self-interacting forces keeping
the particles of a gas universe in states of generalized equilibrium.


title: Global properties of warped solutions in General Relativity

abstract:
  Assuming the four-dimensional space-time to be a general warped product of
two surfaces we reduce the four-dimensional Einstein equations to a
two-dimensional problem which can be solved. All global vacuum solutions are
explicitly constructed and analysed. The classification of the solutions
includes the Schwarzschild, the (anti-)de Sitter, and other well-known
solutions but also many exact ones whose detailed global properties to our
knowledge have not been discussed before. They have a natural physical
interpretation describing single or several wormholes, domain walls of
curvature singularities, cosmic strings, cosmic strings surrounded by domain
walls, solutions with closed timelike curves, etc.


title:
Multidimensional Geometrical Model of the Renormalized Electrical Charge
  with Splitting off the Extra Coordinates

abstract:
  A geometrical model of electric charge is proposed. This model has ``naked''
charge screened with a ``fur - coat'' consisting of virtual wormholes. The 5D
wormhole solution in the Kaluza - Klein theory is the ``naked'' charge. The
splitting off of the 5D dimension happens on the two spheres (null surfaces)
bounding this 5D wormhole. This allows one to sew two Reissner - Nordstr\"om
black holes onto it on both sides. The virtual wormholes entrap a part of the
electrical flux lines coming into the ``naked'' charge. This effect essentially
changes the charge visible at infinity so that it satisfies the real relation
$m^2<e^2$.


title: Non-expanding impulsive gravitational waves

abstract:
  We investigate a class of impulsive gravitational waves which propagate
either in Minkowski or in the (anti-)de Sitter background. These waves are
constructed as impulsive members of the Kundt class $P(\Lambda)$ of
non-twisting, non-expanding type N solutions of vacuum Einstein equations with
a cosmological constant $\Lambda$. We show that the only non-trivial waves of
this type in Minkowski spacetime are impulsive pp-waves. For $\Lambda\not=0$ we
demonstrate that the canonical subclasses of $P(\Lambda)$, which are
invariantly different for smooth profiles, are all locally equivalent for
impulsive profiles. Also, we present coordinate system for these impulsive
solutions which is explicitly continuous.


title: On Conserved Quantities at Spatial Infinity

abstract:
  There is a well-known short list of asymptotic conserved quantities for a
physical system at spatial infinity. We search for new ones.This is carried
outwithin the asymptotic framework of Ashtekar and Romano, in which spatial
infinity is represented as a smooth boundary of space-time. We first introduce,
for physical fields on space-time,a characterization of their asymptotic
behavior as certain fields on this boundary. Conserved quantities at spatial
infinity, in turn, are constructed from these fields. We find,in Minkowski
space-time, that each of a Klein-Gordon field, a Maxwell field, and a
linearized gravitational field yields an entire hierarchy of conserved
quantities. Only certain quantities in this hierarchy survive into curved
space-time.


title: Black Hole Entropy and Exclusion Statistics

abstract:
  We compute the entropy of systems of quantum particles satisfying the
fractional exclusion statistics in the space-time of 2+1 dimensional black hole
by using the brick-wall method. We show that the entropy of each effective
quantum field theory with a Planck scale ultraviolet cutoff obeys the area law,
irrespective of the angular momentum of the black hole and the statistics
interpolating between Bose-Einstein and Fermi-Dirac statistics.


title:
GR without SR: A gravitational-domain description of first-order Doppler
  effects

abstract:
  Equivalence principles are a major part of modern relativity theory.
Gravitational shifts can already be calculated within the time domain as motion
shifts, and we examine the consequences of reversing this argument and
describing motion shifts outside the time domain, as effects of curvature
associated with relative velocity. This unusual "Doppler mass shift" approach
appears to resolve some of Einstein's own criticisms of the "SR+GR" model and
seems to remove some barriers to the reconciliation of classical and quantum
theory. The disadvantage of this model is that constant-velocity problems no
longer obey Euclidean geometry. By bypassing special relativity and the special
theory's flat-space assumptions, the model also suggests an alternative
non-transverse frequency-shift relationship. This difference should be
testable.


title: Decoherence and time emergence

abstract:
  In this work the possible role that Decoherence Model could play in the
emergence of the classical concept of time is analyzed. We take the case of a
Mixmaster universe with small anisotropy and construct its Halliwell
propagator. Afterwards we introduce in our system terms that comprise the
effects of Decoherence Model. This is done by means of the so called Restricted
Path Integral Formalism. We obtain Halliwell's modified propagator and find
that a gauge invariant physical time emerges as consequence of this process.


title: Wormholes and Flux Tubes in 5D Kaluza-Klein Theory

abstract:
  In this paper spherically symmetric solutions to 5D Kaluza-Klein theory, with
``electric'' and/or ``magnetic'' fields are investigated. It is shown that the
global structure of the spacetime depends on the relation between the
``electrical'' and ``magnetic'' Kaluza-Klein fields. For small ``magnetic''
field we find a wormhole-like solution. As the strength of the ``magnetic''
field is increased relative to the strength of the ``electrical'' field, the
wormhole-like solution evolves into a finite or infinite flux tube depending on
the strengths of the two fields. For the large ``electric'' field case we
conjecture that this solution can be considered as the mouth of a wormhole,
with the $G_{55}$, $G_{5t}$ and $G_{5\phi}$ components of the metric acting as
the source of the exotic matter necessary for the formation of the wormhole's
mouth. For the large ``magnetic'' field case a 5D flux tube forms, which is
similar to the flux tube between two monopoles in Type-II superconductors, or
the hypothesized color field flux tube between two quarks in the QCD vacuum.


title: The Quantum Modular Group in (2+1)-Dimensional Gravity

abstract:
  The role of the modular group in the holonomy representation of
(2+1)-dimensional quantum gravity is studied. This representation can be viewed
as a "Heisenberg picture", and for simple topologies, the transformation to the
ADM "Schr{\"o}dinger picture" may be found. For spacetimes with the spatial
topology of a torus, this transformation and an explicit operator
representation of the mapping class group are constructed. It is shown that the
quantum modular group splits the holonomy representation Hilbert space into
physically equivalent orthogonal ``fundamental regions'' that are interchanged
by modular transformations.


title:
General relativity on a null surface: Hamiltonian formulation in the
  teleparallel geometry

abstract:
  The Hamiltonian formulation of general relativity on a null surface is
established in the teleparallel geometry. No particular gauge conditons on the
tetrads are imposed, such as the time gauge condition. By means of a 3+1
decomposition the resulting Hamiltonian arises as a completely constrained
system. However, it is structurally different from the the standard
Arnowitt-Deser-Misner (ADM) type formulation. In this geometrical framework the
basic field quantities are tetrads that transform under the global SO(3,1) and
the torsion tensor.


title: Einstein-Yang-Mills solitons: towards new degrees of freedom

abstract:
  A recent progress in obtaining non-spherical and non-static solitons in the
four-dimensional Einstein--Yang--Mills (EYM) theory is discussed, and a
non-perturbative formulation of the stationary axisymmetric problem is
attempted. First a 2D dilaton gravity model is derived for the spherically
symmetric time-dependent configurations. Then a similar Euclidean
representation is constructed for the stationary axisymmetric non-circular
SU(2) EYM system using the (2+1)+1 reduction scheme suggested by Maeda, Sasaki,
Nakamura and Miyama. The crucial role in this reduction is played by the extra
terms entering the reduced Yang--Mills and Kaluza--Klein two-forms similarly to
Chern--Simons terms in the theories with higher rank antisymmetric tensor
fields. We also derive a simple 2D action describing static axisymmetric
magnetic EYM configurations and discuss a possibility of existence of
cylindrical EYM sphalerons.


title:
A characterization of the central shell-focusing singularity in
  spherical gravitational collapse

abstract:
  We give a characterization of the central shell-focusing curvature
singularity that can form in the spherical gravitational collapse of a bounded
matter distribution obeying the dominant energy condition. This
characterization is based on the limiting behaviour of the mass function in the
neighbourhood of the singularity. Depending on the rate of growth of the mass
as a function of the area radius R, the singularity may be either covered or
naked. The singularity is naked if this growth rate is slower than R, covered
if it is faster than R, and either naked or covered if the growth rate is same
as R.


title:
Einstein-Cartan-Maxwell Theory with Scalar Field through a
  Five-Dimensional Unification

abstract:
  A modification of Kaluza-Klein theory is proposed in which, as a result of a
symmetry breaking, five-dimensional space-time is partially parallelized
implying the appearance of torsion fields. A naturally chosen action functional
leads to the Einstein-Cartan-Maxwell theory where the electromagnetic field
strength is represented by the fifth component of the torsion 2-form.
Incorporation of a scalar field reveals that four-dimensional space-time
torsion is not induced by the scalar field.


title: Canonical general relativity: Matter fields in a general linear frame

abstract:
  Building on the results of previous work, we demonstrate how matter fields
are incorporated into the general linear frame approach to general relativity.
When considering the Maxwell one-form field, we find that the system that leads
naturally to canonical vierbein general relativity has the extrinsic curvature
of the Cauchy surface represented by gravitational as well as non-gravitational
degrees of freedom. Nevertheless the metric compatibility conditions are
undisturbed, and this apparent derivative-coupling is seen to be an effect of
working with (possibly orthonormal) linear frames. The formalism is adapted to
consider a Dirac Fermion, where we find that a milder form of this apparent
derivative-coupling appears.


title: Gravitation Theory with Propagating Torsion

abstract:
  We present a review of some recent models of gravitation theory with
propagating torsion based on the use of a torsion-dilaton field and propose one
more model of this type which promises to be more realistic. A proper universal
self-consistent minimal action principle yields the properties of this model
and predicts the interactions of torsion-dilaton field with the real matter.
The new model may be compatible with the string models with dilaton field and
gives a novel interpretation of the dilaton as a part of the space-time
torsion. A relation with some recent models of dilatonic gravity is also
possible.


title: Gravitational waves in an expanding Universe

abstract:
  We study the tensorial modes of the two-fluid model, where one of this fluids
has an equation of state $p = - \rho/3$ (variable cosmological constant, cosmic
string fluid, texture) or $p = - \rho$ (cosmological constant), while the other
fluid is an ordinary matter (radiation, stiff matter, incoherent matter). In
the first case, it is possible to have a closed Universe whose dynamics can be
that of an open Universe providing alternative solutions for the age and
horizon problems. This study of the gravitational waves is extended for all
values of the effective curvature $k_{eff}=k-\frac{8\pi G}{3}\rho_{0s}$, that
is, positive, negative or zero, $k$ being the curvature of the spacelike
section. In the second case, we restrict ourselves to a flat spatial section.
The behaviour of gravitational waves have, in each case, very particular
features, that can be reflected in the anisotropy spectrum of Cosmic Microwave
Background Radiation. We make also some considerations of these models as
candidate to dark matter models.