title: Two-Component Dust in Spherically Symmetric Motion

abstract:
  Two components of spherically symmetric, inhomogeneous dust penetrating each
other are introduced as a generalization of the well-known Tolman-Bondi dust
solution. The field equations of this model are formulated and general
properties are discussed. inhomogeneous Special solutions with additional
symmetries - an extra Killing- or homothetic vector - and their matching to the
corresponding Tolman-Bondi solution are investigated.


title:
Non-linear conformally invariant generalization of the Poisson equation
  to D>2 dimensions

abstract:
  I propound a non-linear generalization of the Poisson equation describing a
"medium" in D dimensions with a "dielectric constant" proportional to the field
strength to the power D-2. It is the only conformally invariant scalar theory
that is second order, and in which the scalar $phi$ couples to the sources
$\rho$ via a $\phi\rho$ contact term. The symmetry is used to generate
solutions for the field for some non-trivial configurations (e.g. for two
oppositely charged points). Systems comprising N point charges afford further
application of the symmetry. For these I derive e.g. exact expressions for the
following quantities: the general two-point-charge force; the energy function
and the forces in any three-body configuration with zero total charge; the
few-body force for some special configurations; the virial theorem for an
arbitrary, bound, many-particle system relating the time-average kinetic energy
to the particle charges. Possible connections with an underlying conformal
quantum field theory are mentioned.


title: Black holes with unusual topology

abstract:
  The Einstein's equations with a negative cosmological constant admit
solutions which are asymptotically anti-de Sitter space. Matter fields in
anti-de Sitter space can be in stable equilibrium even if the potential energy
is unbounded from below, violating the weak energy condition. Hence there is no
fundamental reason that black hole's horizons should have spherical topology.
In anti-de Sitter space the Einstein's equations admit black hole solutions
where the horizon can be a Riemann surface with genus $g$. The case $g=0$ is
the asymptotically anti-de Sitter black hole first studied by Hawking-Page,
which has spherical topology. The genus one black hole has a new free parameter
entering the metric, the conformal class to which the torus belongs. The genus
$g>1$ black hole has no other free parameters apart from the mass and the
charge. All such black holes exhibits a natural temperature which is identified
as the period of the Euclidean continuation and there is a mass formula
connecting the mass with the surface gravity and the horizon area of the black
hole. The Euclidean action and entropy are computed and used to argue that the
mass spectrum of states is positive definite.


title: Multidimensional sigma-models with composite electric p-branes

abstract:
  We consider a gravitational model on a manifold M = M_0 x M_1 x...x M_n with
oriented connected Einstein internal spaces M_1,...,M_n. The matter part of the
action contains several scalar fields and antisymmetric forms. With Ricci-flat
internal spaces, the model has a midisuperspace representation in form of a
sigma-model on M_0. The latter can be used to determine exact composite
electric p-brane solutions, which depend on a set of harmonic functions on M_0.


title: The Statistical Mechanics of Black Hole Thermodynamics

abstract:
  Although we have convincing evidence that a black hole bears an entropy
proportional to its surface (horizon) area, the ``statistical mechanical''
explanation of this entropy remains unknown. Two basic questions in this
connection are: what is the microscopic origin of the entropy, and why does the
law of entropy increase continue to hold when the horizon entropy is included?
After a review of some of the difficulties in answering these questions, I
propose an explanation of the law of entropy increase which comes near to a
proof in the context of the ``semi-classical'' approximation, and which also
provides a proof in full quantum gravity under the assumption that the latter
fulfills certain natural expectations, like the existence of a conserved energy
definable at infinity. This explanation seems to require a fundamental
spacetime discreteness in order for the entropy to be consistently finite, and
I recall briefly some of the ideas for what the discreteness might be. If such
ideas are right, then our knowledge of the horizon entropy will allow us to
``count the atoms of spacetime''.


title: Black Holes of Negative Mass

abstract:
  I demonstrate that, under certain circumstances, regions of negative energy
density can undergo gravitational collapse into a black hole. The resultant
exterior black hole spacetimes necessarily have negative mass and non-trivial
topology. A full theory of quantum gravity, in which topology-changing
processes take place, could give rise to such spacetimes.


title:
Wick Rotation, Regularization of Propagators by a Complex Metric and
  Multidimensional Cosmology

abstract:
  The Wick rotation in quantum field theory is considered in terms of
analytical continuation in the signature matrix parameter w = eta_00.
Regularization of propagators by a complex metric parameter in most cases
preserves (i) the convergence of Feynmann integrals (understood as Lebesgue
integrals) if the corresponding integrals of Euclidean theory are convergent;
(ii) the regularity of propagators in the coordinate representation if there is
regularity in the Euclidean case. The well-known covariant regularization by a
complex mass does not in general satisfy these conditions. Theories with a
large family of propagators regularized by complex metric were previously
considered by the author, and analogues of the
Bogoliubov-Parasiuk-Hepp-Zimmermann theorems were proved. [V.D.Ivashchuk, Izv.
Akad. Nauk Mold. SSR, Ser. Fiz.-Tekhn. i Math. Nauk, 3 (1987), 8; 1 (1988),
10]. This paper shows that in the case of multidimensional cosmology describing
the evolution of n spaces M_i, i = 1, ..., n, the Wick rotation in the
minisuperspace may be performed by analytical continuation in the dimensions
N_i = dim M_i or in the dimension of the time submanifold M_0.


title: Non-Integrability and Chaos in Classical Cosmology

abstract:
  A brief analysis of the dynamics of a Friedmann-Robertson-Walker universe
with a conformally coupled, real, self-interacting, massive scalar field, based
on the Painleve theory of differential equations, is presented. Our results
complete earlier works done within the framework of Dynamical System Theory. We
conclude that, in general, the system will not be integrable and that the chaos
that has been found in a previous work, arises from the presence of movable
logarithmic branch points in the solution in the complex plane of time.


title:
Rotating dust solutions of Einstein's equations with 3-dimensional
  symmetry groups; Part 1: Two Killing fields spanned on u^{\alpha} and
  w^{\alpha }

abstract:
  For a rotating dust with a 3-dimensional symmetry group all possible metric
forms can be classified and, within each class, explicitly written out. This is
made possible by the formalism of Pleba\'nski based on the Darboux theorem. In
the resulting coordinates, the Killing vector fields (if any exist) assume a
special form. Each Killing vector field may be either spanned on the fields of
velocity and rotation or linearly independent of them. By considering all such
cases one arrives at the classification. With respect to the structures of the
groups, this is just the Bianchi classification, but with all possible
orientations of the orbits taken into account. In this paper, which is part 1
of a 3-part series, all solutions are considered for which two Killing fields
are spanned on velocity and rotation. The solutions of Lanczos and G\"{o}del
are identified as special cases, and their new invariant definitions are
provided. In addition, a new invariant definition is given of the Ozsvath class
III solution.


title: Back Reaction of Hawking Radiation on Black Hole Geometry

abstract:
  We propose a model for the geometry of a dynamical spherical shell in which
the metric is asymptotically Schwarzschild, but deviates from Ricci-flatness in
a finite neighbourhood of the shell. Hence, the geometry corresponds to a
`hairy' black hole, with the hair originating on the shell. The metric is
regular for an infalling shell, but it bifurcates, leading to two disconnected
Schwarzschild-like spacetime geometries. The shell is interpreted as either
collapsing matter or as Hawking radiation, depending on whether or not the
shell is infalling or outgoing. In this model, the Hawking radiation results
from tunnelling between the two geometries. Using this model, the back reaction
correction from Hawking radiation is calculated.


title:
Thermodynamics of (3+1)-dimensional black holes with toroidal or higher
  genus horizons

abstract:
  We examine counterparts of the Reissner-Nordstrom-anti-de Sitter black hole
spacetimes in which the two-sphere has been replaced by a surface Sigma of
constant negative or zero curvature. When horizons exist, the spacetimes are
black holes with an asymptotically locally anti-de Sitter infinity, but the
infinity topology differs from that in the asymptotically Minkowski case, and
the horizon topology is not S^2. Maximal analytic extensions of the solutions
are given. The local Hawking temperature is found. When Sigma is closed, we
derive the first law of thermodynamics using a Brown-York type quasilocal
energy at a finite boundary, and we identify the entropy as one quarter of the
horizon area, independent of the horizon topology. The heat capacities with
constant charge and constant electrostatic potential are shown to be positive
definite. With the boundary pushed to infinity, we consider thermodynamical
ensembles that fix the renormalized temperature and either the charge or the
electrostatic potential at infinity. Both ensembles turn out to be
thermodynamically stable, and dominated by a unique classical solution.


title:
Canonical quantization of cylindrical gravitational waves with two
  polarizations

abstract:
  The canonical quantization of the essentially nonlinear midisuperspace model
describing cylindrically symmetric gravitational waves with two polarizations
is presented. A Fock space type representation is constructed. It is based on a
complete set of quantum observables. Physical expectation values may be
calculated in arbitrary excitations of the vacuum. Our approach provides a
non-linear generalization of the quantization of the collinearly polarized
Einstein-Rosen gravitational waves.


title: Radiative multipole moments of integer-spin fields in curved spacetime

abstract:
  Radiative multipole moments of scalar, electromagnetic, and linearized
gravitational fields in Schwarzschild spacetime are computed to third order in
v in a weak-field, slow-motion approximation, where v is a characteristic
velocity associated with the motion of the source. To zeroth order in v, a
radiative moment of order l is given by the corresponding source moment
differentiated l times with respect to retarded time. At second order in v,
additional terms appear inside the spatial integrals. These are near-zone
corrections which depend on the detailed behavior of the source. At third order
in v, the correction terms occur outside the spatial integrals, so that they do
not depend on the detailed behavior of the source. These are wave-propagation
corrections which are heuristically understood as arising from the scattering
of the radiation by the spacetime curvature surrounding the source. Our
calculations show that the wave-propagation corrections take a universal form
which is independent of multipole order and field type. We also show that in
general relativity, temporal and spatial curvatures contribute equally to the
wave-propagation corrections.


title: Quantum Ergoregion Instability

abstract:
  We have shown that, as in the case of black holes, an ergosphere itself with
no event horizon inside can evaporate spontaneously, giving energy radiation to
spatial infinity until the ergoregion disappears. However, the feature of his
quantum ergoregion instability is very much different from black hole
radiation. It is rather analogous to a laser amplification. This analysis is
based on the canonical quantization of a neutral scalar field in the presence
of unstable modes characterized by complex frequencies in a simple model for a
rapidly rotating star.


title:
Rotating Charged Solutions to Einstein-Maxwell-ChernSimons Theory in 2+1
  Dimensions

abstract:
  We obtain a class of rotating charged stationary circularly symmetric
solutions of Einstein-Maxwell theory coupled to a topological mass term for the
Maxwell field. These solutions are regular, have finite mass and angular
momentum, and are asymptotic to the uncharged extreme BTZ black hole.


title:
QSD III : Quantum Constraint Algebra and Physical Scalar Product in
  Quantum General Relativity

abstract:
  This paper deals with several technical issues of non-perturbative
four-dimensional Lorentzian canonical quantum gravity in the continuum that
arose in connection with the recently constructed Wheeler-DeWitt quantum
constraint operator. 1) The Wheeler-DeWitt constraint mixes the previously
discussed diffeomorphism superselection sectors which thus become spurious, 2)
Thus, the inner product for diffeomorphism invariant states can be fixed by
requiring that diffeomorphism group averaging is a partial isometry, 3) The
established non-anomalous constraint algebra is clarified by computing
commutators of duals of constraint operators, 4) The full classical constraint
algebra is faithfully implemented on the diffeomorphism invariant Hilbert space
in an appropriate sense, 5) The Hilbert space of diffeomorphism invariant
states can be made separable if a natural new superselection principle is
satisfied, 6) We propose a natural physical scalar product for quantum general
relativity by extending the group average approach to the case of
non-self-adjoint constraint operators like the Wheeler-DeWitt constraint and 7)
Equipped with this inner product, the construction of physical observables is
straightforward.


title:
QSD IV : 2+1 Euclidean Quantum Gravity as a model to test 3+1 Lorentzian
  Quantum Gravity

abstract:
  The quantization of Lorentzian or Euclidean 2+1 gravity by canonical methods
is a well-studied problem. However, the constraints of 2+1 gravity are those of
a topological field theory and therefore resemble very little those of the
corresponding Lorentzian 3+1 constraints. In this paper we canonically quantize
Euclidean 2+1 gravity for arbitrary genus of the spacelike hypersurface with
new, classically equivalent constraints that maximally probe the Lorentzian 3+1
situation. We choose the signature to be Euclidean because this implies that
the gauge group is, as in the 3+1 case, SU(2) rather than SU(1,1). We employ,
and carry out to full completion, the new quantization method introduced in
preceding papers of this series which resulted in a finite 3+1 Lorentzian
quantum field theory for gravity. The space of solutions to all constraints
turns out to be much larger than the one as obtained by traditional approaches,
however, it is fully included. Thus, by suitable restriction of the solution
space, we can recover all former results which gives confidence in the new
quantization methods. The meaning of the remaining "spurious solutions" is
discussed.


title:
QSD V : Quantum Gravity as the Natural Regulator of Matter Quantum Field
  Theories

abstract:
  It is an old speculation in physics that, once the gravitational field is
successfully quantized, it should serve as the natural regulator of infrared
and ultraviolet singularities that plague quantum field theories in a
background metric. We demonstrate that this idea is implemented in a precise
sense within the framework of four-dimensional canonical Lorentzian quantum
gravity in the continuum. Specifically, we show that the Hamiltonian of the
standard model supports a representation in which finite linear combinations of
Wilson loop functionals around closed loops, as well as along open lines with
fermionic and Higgs field insertions at the end points are densely defined
operators. This Hamiltonian, surprisingly, does not suffer from any
singularities, it is completely finite without renormalization. This property
is shared by string theory. In contrast to string theory, however, we are
dealing with a particular phase of the standard model coupled to gravity which
is entirely non-perturbatively defined and second quantized.


title:
QSD VI : Quantum Poincar\'e Algebra and a Quantum Positivity of Energy
  Theorem for Canonical Quantum Gravity

abstract:
  We quantize the generators of the little subgroup of the asymptotic
Poincar\'e group of Lorentzian four-dimensional canonical quantum gravity in
the continuum. In particular, the resulting ADM energy operator is densely
defined on an appropriate Hilbert space, symmetric and essentially
self-adjoint. Moreover, we prove a quantum analogue of the classical positivity
of energy theorem due to Schoen and Yau. The proof uses a certain technical
restriction on the space of states at spatial infinity which is suggested to us
given the asymptotically flat structure available. The theorem demonstrates
that several of the speculations regarding the stability of the theory,
recently spelled out by Smolin, are false once a quantum version of the
pre-assumptions underlying the classical positivity of energy theorem is
imposed in the quantum theory as well. The quantum symmetry algebra
corresponding to the generators of the little group faithfully represents the
classical algebra.


title:
Kinematical Hilbert Spaces for Fermionic and Higgs Quantum Field
  Theories

abstract:
  We extend the recently developed kinematical framework for diffeomorphism
invariant theories of connections for compact gauge groups to the case of a
diffeomorphism invariant quantum field theory which includes besides
connections also fermions and Higgs fields. This framework is appropriate for
coupling matter to quantum gravity. The presence of diffeomorphism invariance
forces us to choose a representation which is a rather non-Fock-like one : the
elementary excitations of the connection are along open or closed strings while
those of the fermions or Higgs fields are at the end points of the string.
Nevertheless we are able to promote the classical reality conditions to quantum
adjointness relations which in turn uniquely fixes the gauge and diffeomorphism
invariant probability measure that underlies the Hilbert space. Most of the
fermionic part of this work is independent of the recent preprint by Baez and
Krasnov and earlier work by Rovelli and Morales-Tec\'otl because we use new
canonical fermionic variables, so-called Grassman-valued half-densities, which
enable us to to solve the difficult fermionic adjointness relations.


title: Generalized Quantum Theory in Evaporating Black Hole Spacetimes

abstract:
  Quantum mechanics for matter fields moving in an evaporating black hole
spacetime is formulated in fully four-dimensional form according to the
principles of generalized quantum theory. The resulting quantum theory cannot
be expressed in a 3+1 form in terms of a state evolving unitarily or by
reduction through a foliating family of spacelike surfaces. That is because
evaporating black hole geometries cannot be foliated by a non-singular family
of spacelike surfaces. A four-dimensional notion of information is reviewed.
Although complete information may not be available on every spacelike surface,
information is not lost in a spacetime sense in an evaporating black hole
spacetime. Rather complete information is distributed about the
four-dimensional spacetime. Black hole evaporation is thus not in conflict with
the principles of quantum mechanics when suitably generally stated. (Talk
presented at Black Holes and Relativistic Stars: A Symposium in Honor of S.
Chandrasekhar, Chicago, Dec 14-15,1996.)


title: The Stability of Relativistic Neutron Stars in Binary Orbit

abstract:
  We analyze the stability of relativistic, quasi-equilibrium binary neutron
stars in synchronous circular orbit. We explore stability against radial
collapse to black holes prior to merger, and against orbital plunge. We apply
theorems based on turning points along uniformly rotating sequences of constant
angular momentum and rest mass to locate the onset of secular instabilities. We
find that inspiraling binary neutron stars are stable against radial collapse
to black holes all the way down to the innermost stable circular orbit.


title:
An Understanding of The Dark Matter in The Universe And The Variation of
  The Universal Gravitational Constant G With Time

abstract:
  Considering the fact that the present universe might have been formed out of
a system of ficticious self-gravitating particles, fermionic in nature, each of
mass $m$, we are able to obtain a compact expression for the radius $R_0$ of
the universe by using a model density distribution $\rho (r)$ for the particles
which is singular at the origin. This singularity in $\rho (r)$ can be
considered to be consistent with the socalled Big Bang theory of the universe.
By assuming that Mach's principle holds good in the evolution of the universe,
we determine the number of particles, $N$, of the universe and its $R_0$, which
are obtained in terms of the mass $m$ of the constituent particles and the
Universal Gravitational constant $G$ only. It is seen that for a mass of the
constituent particles $m\simeq 1.07\times 10^{-35} g$ the age of the present
universe,$\tau_0$, becomes $\tau_0 \simeq 20\times 10^9 yr$, or equivalently
$R_0 \simeq 1.9\times 10^{28} cm $. For this $m$, the total number of particles
costituting the present universe is found to be $N \simeq 2.4 \times 10^{91}$
and its total mass $(M \simeq 1.27916 \times 10^{23} M_{\odot})$, $M_{\odot}$
being the solar mass. All these numbers seem to be quantitatively agreeing with
those evaluated from other theories. Using the present theory, we have also
made an estimation of the variation of the universal gravitational constant $G$
with time which gives $({\dot G \over G}) =-9.6\times 10^{-11} yr^{-1}$. This
is again in extremely good agreement with the results of some of the most
recent calculations. Lastly, a plausible explanation for the Dark Matter
present in today's universe is given.


title: Two-component spinor Lie derivatives and spinor-gauge gravity

abstract: %auto-ignore This paper has been withdrawn by the authors.


title: On ``minimally curved spacetimes'' in general relativity

abstract:
  We consider a spacetime corresponding to uniform relativistic potential
analogus to Newtonian potential as an example of ``minimally curved
spacetime''. We also consider a radially symmetric analogue of the Rindler
spacetime of uniform proper acceleration relative to infinity.


title:
Solving the Darwin problem in the first post-Newtonian approximation of
  general relativity

abstract:
  We analytically calculate the equilibrium sequence of the corotating binary
stars of incompressible fluid in the first post-Newtonian(PN) approximation of
general relativity. By calculating the total energy and total angular momentum
of the system as a function of the orbital separation, we investigate the
innermost stable circular orbit for corotating binary(we call it ISCCO). It is
found that by the first PN effect, the orbital separation of the binary at the
ISCCO becomes small with increase of the compactness of each star, and as a
result, the orbital angular velocity at the ISCCO increases. These behaviors
agree with previous numerical works.


title:
Solving the Darwin problem in the first post-Newtonian approximation of
  general relativity: compressible model

abstract:
  Using the ellipsoidal model for the density configuration, we calculate the
equilibrium sequence of the corotating binary stars of the polytropic equation
of state in the first post-Newtonian approximation of general relativity. After
we calibrate this model by comparing with previous numerical results, we
perform the stability analysis by calculating the energy and the angular
momentum of the system as a function of the orbital separation. We find that
the orbital angular velocity at the energy and/or momentum minimum increases
with the increase of the compactness of each star, and this fact holds
irrespective of the polytropic index. These features agree with those in
previous numerical works. We also show that due to the influence of the tidal
field from the companion star, the central density of each star slightly
decreases.


title: Colliding plane waves with W=M=0

abstract:
  It is shown that there are three vacuum and one electrovacuum solutions of
diagonal plane waves with M=0 and constant Maxwell scalars. Namely, these are
the single wave, Stoyanov, Babala and Bell-Szekeres solutions. A comparison is
made with the planar solutions of Taub.


title: General Solution for Self-Gravitating Spherical Null Dust

abstract:
  We find the general solution of equations of motion for self-gravitating
spherical null dust as a perturbative series in powers of the outgoing matter
energy-momentum tensor, with the lowest order term being the Vaidya solution
for the ingoing matter. This is done by representing the null-dust model as a
2d dilaton gravity theory, and by using a symmetry of a pure 2d dilaton gravity
to fix the gauge. Quantization of this solution would provide an effective
metric which includes the back-reaction for a more realistic black hole
evaporation model than the evaporation models studied previously.


title: Geometric interpretation of Thiemann's generalized Wick transform

abstract:
  In the Ashtekar and geometrodynamic formulations of vacuum general
relativity, the Euclidean and Lorentzian sectors can be related by means of the
generalized Wick transform discovered by Thiemann. For some vacuum
gravitational systems in which there exists an intrinsic time variable which is
not invariant under constant rescalings of the metric, we show that, after such
a choice of time gauge and with a certain identification of parameters, the
generalized Wick transform can be understood as an analytic continuation in the
explicit time dependence. This result is rigorously proved for the Gowdy model
with the topology of a three-torus and for a whole class of cosmological models
that describe expanding universes. In these gravitational systems, the analytic
continuation that reproduces the generalized Wick transform after gauge fixing
turns out to map the Euclidean line element to the Lorentzian one multiplied by
an imaginary factor; this transformation rule differs from that expected for an
inverse Wick rotation in a complex rescaling of the four-metric. We then prove
that this transformation rule for the line element continues to be valid in the
most general case of vacuum gravity with no model reduction nor gauge fixing.
In this general case, it is further shown that the action of the generalized
Wick transform on any function of the gravitational phase space variables, the
shift vector, and the lapse function can in fact be interpreted as the result
of an inverse Wick rotation and a constant, imaginary conformal transformation.


title: Distributional curvature of time-dependent cosmic strings

abstract:
  Colombeau's theory of generalised functions is used to calculate the
contributions, at the rotation axis, to the distributional curvature for a
time-dependent radiating cosmic string, and hence the mass per unit length of
the string source. This mass per unit length is compared with the mass at null
infinity, giving evidence for a global energy conservation law.


title: Cauchy-characteristic extraction in numerical relativity

abstract:
  We treat the calculation of gravitational radiation using the mixed
timelike-null initial value formulation of general relativity. The
determination of an exterior radiative solution is based on boundary values on
a timelike worldtube $\Gamma$ and on characteristic data on an outgoing null
cone emanating from an initial cross-section of $\Gamma$. We present the
details of a 3-dimensional computational algorithm which evolves this initial
data on a numerical grid, which is compactified to include future null infinity
as finite grid points. A code implementing this algorithm is calibrated in the
quasispherical regime. We consider the application of this procedure to the
extraction of waveforms at infinity from an interior Cauchy evolution, which
provides the boundary data on $\Gamma$. This is a first step towards
Cauchy-characteristic matching in which the data flow at the boundary $\Gamma$
is two-way, with the Cauchy and characteristic computations providing exact
boundary values for each other. We describe strategies for implementing
matching and show that for small target error it is much more computationally
efficient than alternative methods.


title:
Gravitational waves from inspiraling compact binaries: Second
  post-Newtonian waveforms as search templates

abstract:
  We ascertain the effectiveness of the second post-Newtonian approximation to
the gravitational waves emitted during the adiabatic inspiral of a compact
binary system as templates for signal searches with kilometer-scale
interferometric detectors. The reference signal is obtained by solving the
Teukolsky equation for a small mass moving on a circular orbit around a large
nonrotating black hole. Fitting factors computed from this signal and these
templates, for various types of binary systems, are all above the 90% mark.
According to Apostolatos' criterion, second post-Newtonian waveforms should
make acceptably effective search templates.


title: Description of Friedmann Observables in Quantum Universe

abstract:
  The solution of the problem of describing the Friedmann observables (the
Hubble law, the red shift, etc.) in quantum cosmology is proposed on the basis
of the method of gaugeless Hamiltonian reduction in which the gravitational
part of the energy constraint is considered as a new momentum. We show that the
conjugate variable corresponding to the new momentum plays a role of the
invariant time parameter of evolution of dynamical variables in the sector of
the Dirac observables of the general Hamiltonian approach. Relations between
these Dirac observables and the Friedmann observables of the expanding Universe
are established for the standard Friedmann cosmological model with dust and
radiation. The presented reduction removes an infinite factor from the
functional integral, provides the normalizability of the wave function of the
Universe and distinguishes the conformal frame of reference where the Hubble
law is caused by the alteration of the conformal dust mass.


title: Dirac and Friedmann Observables in Quantum Universe with Radiation

abstract:
  Relations between the Friedmann observables of the expanding Universe and the
Dirac observables in the generalized Hamiltonian approach are established for
the Friedmann cosmological model of the Universe with the field excitations
imitating radiation. A full separation of the physical sector from the gauge
one is fulfilled by the method of the gaugeless reduction in which the
gravitational part of the energy constraint is considered as a new momentum. We
show that this reduction removes an infinite factor from the Hartle -- Hawking
functional integral, provides the normalizability of the Wheeler -- DeWitt wave
function, clarifies its relation to the observational cosmology, and picks out
a conformal frame of Narlikar.


title: Black hole : Equipartition of matter and potential energy

abstract:
  Black hole horizon is usually defined as the limit for existence of timelike
worldline or when a spatially bound surface turns oneway (it is crossable only
in one direction). It would be insightful and physically appealing to find its
characterization involving an energy consideration. By employing the Brown-York
[1] quasilocal energy we propose a new and novel characterization of the
horizon of static black hole. It is the surface at which the Brown-York energy
equipartitions itself between the matter and potential energy. It is also
equivalent to equipartitioning of the binding energy and the gravitational
charge enclosed by the horizon.


title:
Inhomogeneous imperfect fluid spherical models without Big-Bang
  singularity

abstract:
  So far all known singularity-free cosmological models are cylindrically
symmetric. Here we present a new family of spherically symmetric non-singular
models filled with imperfect fluid and radial heat flow, and satisfying the
weak and strong energy conditions. For large $t$ anisotropy in pressure and
heat flux tend to vanish leading to a perfect fluid. There is a free function
of time in the model, which can be suitably chosen for non-singular behaviour
and there exist multiplicity of such choices.


title: Irreducible decompositions in metric-affine gravity models

abstract:
  The irreducible decomposition technique is applied to the study of classical
models of metric-affine gravity (MAG). The dynamics of the gravitational field
is described by a 12-parameter Lagrangian encompassing a Hilbert-Einstein term,
torsion and nonmetricity square terms, and one quadratic curvature piece that
is built up from Weyl's segmental curvature. Matter is represented by a
hyperfluid, a continuous medium the elements of which possess classical
momentum and hypermomentum. With the help of irreducible decompositions, we are
able to express torsion and traceless nonmetricity explicitly in terms of the
spin and the shear current of the hyperfluid. Thereby the field equations
reduce to an effective Einstein theory describing a metric coupled to the Weyl
1-form (a Proca-type vector field) and to a spin fluid. We demonstrate that a
triplet of torsion and nonmetricity 1-forms describes the general and unique
vacuum solution of the field equations of MAG. Finally, we study homogeneous
cosmologies with an hyperfluid. We find that the hypermomentum affects
significantly the cosmological evolution at very early stages. However, unlike
spin, shear does not prevent the formation of a cosmological singularity.


title: Path Integral Approach to Noncommutative Space-Times

abstract:
  We propose a path integral formulation of noncommutative generalizations of
spacetime manifold in even dimensions, characterized by a length scale
$\lambda_P$. The commutative case is obtained in the limit $\lambda_P=0$.


title: Quantum Fluctuations of Scalar Field in Conical Space

abstract:
  We consider vacuum polarization effect of a conformally coupled massless
scalar field in the background produced by an idealized straight cosmic string.
Using previous criterion we show the calculation of back reaction of the field
to the metric in the context of semiclassical gravity theory is not valid , in
some regions due to large quantum fluctuations in the conical space.


title:
Implications of Spontaneous Glitches in the Mass and Angular Momentum in
  Kerr Space-Time

abstract:
  The outward-pointing principal null direction of the Schwarzschild Riemann
tensor is null hypersurface-forming. If the Schwarzschild mass spontaneously
jumps across one such hypersurface then the hypersurface is the history of an
outgoing light-like shell. The outward-- pointing principal null direction of
the Kerr Riemann tensor is asymptotically (in the neighbourhood of future null
infinity) null hypersurface-forming. If the Kerr parameters of mass and angular
momentum spontaneously jump across one such asymptotic hypersurface then the
asymptotic hypersurface is shown to be the history of an outgoing light-like
shell and a wire singularity-free spherical impulsive gravitational wave.


title: Quantum Cosmology and Grand Unification

abstract:
  Quantum cosmology may restrict the class of gauge models which unify
electroweak and strong interactions. In particular, if one studies the
normalizability criterion for the one-loop wave function of the universe in a
de Sitter background one finds that the interaction of inflaton and matter
fields, jointly with the request of normalizability at one-loop order, picks
out non-supersymmetric versions of unified gauge models.


title:
Physical Interpretation of Cylindrically Symmetric Static Gravitational
  Fields

abstract:
  The explicit relationship is determined between the interior properties of a
static cylindrical matter distribution and the metric of the exterior
space-time according to Einstein gravity for space-time dimensionality larger
or equal to four. This is achieved through use of a coordinate system isotropic
in the transverse coordinates. As a corollary, similar results are obtained for
a spherical matter distribution in Brans-Dicke gravity for dimensions larger
than or equal to three. The approach used here leads to consistency conditions
for those parameters characterizing the exterior metric. It is shown that these
conditions are equivalent to the requirement of hydrostatic equilibrium of the
matter distribution (generalized Oppenheimer-Volkoff equations). These
conditions lead to a consistent Newtonian limit where pressures and the
gravitational constant go to zero at the same rate.


title:
New cosmological solutions and stability analysis in full extended
  thermodynamics

abstract:
  The Einstein's field equations of FRW universes filled with a dissipative
fluid described by full theory of causal transport equations are analyzed. New
exact solutions are found using a non-local transformations on the nonlinear
differential equation for the Hubble factor. The stability of the de Sitter and
asymptotically friedmannian solutions are analyzed using Lyapunov function
method.


title:
Integrable Multicomponent Perfect Fluid Multidimensional Cosmology II:
  Scalar Fields

abstract:
  We consider anisotropic cosmological models with an universe of dimension 4
or more, factorized into n>1 Ricci-flat spaces, containing an m-component
perfect fluid of m non-interacting homogeneous minimally coupled scalar fields
under special conditions. We describe the dynamics of the universe: It has a
Kasner-like behaviour near the singularity and isotropizes during the expansion
to infinity.
  Some of the considered models are integrable, and classical as well as
quantum solutions are found. Some solutions produce inflation from "nothing".
There exist classical asymptotically anti-de Sitter wormholes, and quantum
wormholes with discrete spectrum.


title: Wave Function of Evaporating Black Holes

abstract:
  We study some quantum mechanical aspects of dynamical black holes where the
Vaidya metric is used as a model representing evaporating black holes. It is
shown that in this model the Wheeler-DeWitt equation is solvable in whole
region of spacetime, provided that one considers the ingoing (or outgoing)
Vaidya metric and selects a suitable coordinate frame. This wave function has
curious features in that near the curvature singularity it oscillates violently
owing to large quantum effects while in the other regions the wave function
exhibits a rather benign and completely regular behavior. The general formula
concerning the black hole radiation, which reduces to the Hawking's
semiclassical result when $r = 2M$ is chosen, is derived by means of purely
quantum mechanical approach. The present formulation can be applied essentially
to any system with a spherically symmetric black hole in an arbitrary spacetime
dimension.


title: Can Inflation be Falsified?

abstract:
  Despite its central role in modern cosmology, doubts are often expressed as
to whether cosmological inflation is really a falsifiable theory. We
distinguish two facets of inflation, one as a theory of initial conditions for
the hot big bang and the other as a model for the origin of structure in the
Universe. We argue that the latter can readily be excluded by observations, and
that there are also a number of ways in which the former can find itself in
conflict with observational data. Both aspects of the theory are indeed
falsifiable.


title: Gravitational Particle Production in Spinning Cosmic String Spacetimes

abstract:
  The spontaneous loss of angular momentum of a spinning cosmic string due to
particle emission is discussed. The rate of particle production between two
assymptotic spacetimes: the spinning cosmic string spacetime in the infinite
past and a non-spinning cosmic string spacetime in the infinite future is
calculated.


title: On a New Non-Geometric Element in Gravity

abstract:
  In this essay a generalized notion of flavor-oscillation clocks is
introduced. The generalization contains the element that various superimposed
mass eigenstates may have different relative orientation of the component of
their spin with respect to the rotational axis of the the gravitational source.
It is found that these quantum mechanical clocks do not always redshift
identically when moved from the gravitational environment of a non-rotating
source to the field of a rotating source. The non-geometric contributions to
the redshifts may be interpreted as quantum mechanically induced fluctuations
over a geometric structure of space-time.


title: Mass for the graviton

abstract:
  Can we give the graviton a mass? Does it even make sense to speak of a
massive graviton? In this essay I shall answer these questions in the
affirmative. I shall outline an alternative to Einstein Gravity that satisfies
the Equivalence Principle and automatically passes all classical weak-field
tests (GM/r approx 10^{-6}). It also passes medium-field tests (GM/r approx
1/5), but exhibits radically different strong-field behaviour (GM/r approx 1).
Black holes in the usual sense do not exist in this theory, and large-scale
cosmology is divorced from the distribution of matter. To do all this we have
to sacrifice something: the theory exhibits {*prior geometry*}, and depends on
a non-dynamical background metric.


title: Hamiltonian structures for compact homogeneous universes

abstract:
  Hamiltonian structures for spatially compact locally homogeneous vacuum
universes are investigated, provided that the set of dynamical variables
contains the \Teich parameters, parameterizing the purely global geometry. One
of the key ingredients of our arguments is a suitable mathematical expression
for quotient manifolds, where the universal cover metric carries all the
degrees of freedom of geometrical variations, i.e., the covering group is
fixed. We discuss general problems concerned with the use of this expression in
the context of general relativity, and demonstrate the reduction of the
Hamiltonians for some examples. For our models, all the dynamical degrees of
freedom in Hamiltonian view are unambiguously interpretable as geometrical
deformations, in contrast to the conventional open models.


title: Quantum Gravity:the axiomatic approach, a possible interpretation

abstract:
  Twenty years ago, by extending the Wightman axiom framework, it has been
found possible to quantize only a conformal factor of the gravitational field.
Gravitons being excluded from this quantum scalar field theory, numerous
attempts were done to give a valuable description of what could be quantum
gravity. In this talk we present a familly of Lorentz manifolds which can be
foliated by isotropic hypersurfaces and pose severe restrictions on the form of
the energy-momentum tensor in Einstein's equations. They can be associated to
gravitational waves "without gravitons" in a vacuum described by two
cosmological functions, but not to a massless particle flow. From this
cross-checking with the previous remark, a "very" primordial quantum
cosmological scenario is proposed.


title: Classical Nature of the Inflaton Field with Self-Interaction

abstract:
  Taking into account the effect of self-interaction, the dynamics of the
quantum fluctuations of the inflaton field with $\lambda\phi^4$ potential is
studied in detail. We find that the self interaction efficiently drives the
initial pure state into a mixed one, which can be understood as a statistical
ensemble. Further, the expectation value of the squared field operator is found
to be converted into the variance of this statistical ensemble without giving
any significant change in its amplitude. These results verify the ansatz of the
quantum-to-classical transition that has been assumed in the standard
evaluation of the amplitude of the primordial fluctuations of the universe.


title: Diagonalization of pp-waves

abstract:
  A coordinate transformation is found which diagonalizes the axisymmetric
pp-waves. Its effect upon concrete solutions, including impulsive and shock
waves, is discussed.


title: Nonaxisymmetric Neutral Modes in Rotating Relativistic Stars

abstract:
  We study nonaxisymmetric perturbations of rotating relativistic stars.
modeled as perfect-fluid equilibria. Instability to a mode with angular
dependence $\exp(im\phi)$ sets in when the frequency of the mode vanishes. The
locations of these zero-frequency modes along sequences of rotating stars are
computed in the framework of general relativity. We consider models of
uniformly rotating stars with polytropic equations of state, finding that the
relativistic models are unstable to nonaxisymmetric modes at significantly
smaller values of rotation than in the Newtonian limit. Most strikingly, the
m=2 bar mode can become unstable even for soft polytropes of index $N \leq
1.3$, while in Newtonian theory it becomes unstable only for stiff polytropes
of index $N \leq 0.808$. If rapidly rotating neutron stars are formed by the
accretion-induced collapse of white dwarfs, instability associated with these
nonaxisymmetric, gravitational-wave driven modes may set an upper limit on
neutron-star rotation. Consideration is restricted to perturbations that
correspond to polar perturbations of a spherical star. A study of axial
perturbations is in progress.


title: Are naked singularites forbidden by the second law of thermodynamics?

abstract:
  By now, many examples of naked singularities in classical general relativity
are known. It may however be that a physical principle over and above the
general theory prevents the occurrence of such singularities in nature.
Assuming the validity of the Weyl curvature hypothesis, we propose that naked
singularities are forbidden by the second law of thermodynamics.


title: Universal Spin Structure in Gauge Gravitation Theory

abstract:
  Building on the universal covering group of the general linear group, we
introduce the composite spinor bundle whose subbundles are Lorentz spin
structures associated with different gravitational fields. General covariant
transformations of this composite spinor bundle are canonically defined.


title: The Immirzi parameter in quantum general relativity

abstract:
  Barbero has generalized the Ashtekar canonical transformation to a
one-parameter scale transformation $U(\iota)$ on the phase space of general
relativity. Immirzi has noticed that in loop quantum gravity this
transformation alters the spectra of geometrical quantities. We show that
$U(\iota)$ is a canonical transformation that cannot be implement unitarily in
the quantum theory. This implies that there exists a one-parameter quantization
ambiguity in quantum gravity, namely a free parameter that enters the
construction of the quantum theory. The purpose of this letter is to elucidate
the origin and the role of this free parameter.


title: Naked singularities and the Weyl Curvature Hypothesis

abstract:
  We examine the growth of the Weyl curvature in two examples of naked
singularity formation in spherical gravitational collapse - dust and the Vaidya
spacetime. We find that the Weyl scalar diverges along outgoing radial null
geodesics as they meet the naked singularity in the past. The implications of
this result for the Weyl curvature hypothesis are discussed. We mention the
possibility that although classical general relativity admits naked singularity
solutions arising from gravitational collapse, the second law of thermodynamics
could forbid their occurrence in nature. The method can also be used to compare
the relative importance of initial data and that of the energy-momentum tensor
in deciding the metric solution in any general case.


title: Colliding axisymmetric pp-waves

abstract:
  An exact solution is found describing the collision of axisymmetric pp-waves
with M=0. They are impulsive in character and their coordinate singularities
become point curvature singularities at the boundaries of the interaction
region. The solution is conformally flat. Concrete examples are given,
involving an ultrarelativistic black hole against a burst of pure radiation or
two colliding beam- like waves.


title: Supersymmetric Action for FRW Model with Complex Matter Field

abstract:
  On the basis of the local n=2 supersymmetry we construct the supersymmetric
action for a set of complex scalar supermultiplets in the FRW model. This
action corresponds to the dilaton-axion and chiral components of supergravity
theory.


title:
Heisenberg-picture approach to the evolution of the scalar fields in an
  expanding universe

abstract:
  We present the Heisenberg-picture approach to the quantum evolution of the
scalar fields in an expanding FRW universe which incorporates relatively simply
the initial quantum conditions such as the vacuum state, the thermal
equilibrium state, and the coherent state. We calculate the Wightman function,
two-point function, and correlation function of a massive scalar field. We find
the quantum evolution of fluctuations of a self-interacting field
perturbatively and discuss the renormalization of field equations.


title:
Bayesian Bounds on Parameter Estimation Accuracy for Compact Coalescing
  Binary Gravitational Wave Signals

abstract:
  A global network of laser interferometric gravitational wave detectors is
projected to be in operation by around the turn of the century. Here, the noisy
output of a single instrument is examined. A gravitational wave is assumed to
have been detected in the data and we deal with the subsequent problem of
parameter estimation. Specifically, we investigate theoretical lower bounds on
the minimum mean-square errors associated with measuring the parameters of the
inspiral waveform generated by an orbiting system of neutron stars/black holes.
Three theoretical lower bounds on parameter estimation accuracy are considered:
the Cramer-Rao bound (CRB); the Weiss-Weinstein bound (WWB); and the Ziv-Zakai
bound (ZZB). We obtain the WWB and ZZB for the Newtonian-form of the coalescing
binary waveform, and compare them with published CRB and numerical Monte-Carlo
results. At large SNR, we find that the theoretical bounds are all identical
and are attained by the Monte-Carlo results. As SNR gradually drops below 10,
the WWB and ZZB are both found to provide increasingly tighter lower bounds
than the CRB. However, at these levels of moderate SNR, there is a significant
departure between all the bounds and the numerical Monte-Carlo results.


title: Pure states don't wear black

abstract:
  Recently, string theory has provided some remarkable new insights into the
microphysics of black holes. I argue that a simple and important lesson is also
provided with regards to the information loss paradox, namely, pure quantum
states do not form black holes! Thus it seems black hole formation, as well as
evaporation, must be understood within the framework of quantum decoherence.


title:
Canonical Structure of Locally Homogeneous Systems on Compact Closed
  3-Manifolds of Types $E^3$, Nil and Sol

abstract:
  In this paper we investigate the canonical structure of diffeomorphism
invariant phase spaces for spatially locally homogeneous spacetimes with
3-dimensional compact closed spaces. After giving a general algorithm to
express the diffeomorphism-invariant phase space and the canonical structure of
a locally homogeneous system in terms of those of a homogeneous system on a
covering space and a moduli space, we completely determine the canonical
structures and the Hamiltonians of locally homogeneous pure gravity systems on
orientable compact closed 3-spaces of the Thurston-type $E^3$, $\Nil$ and
$\Sol$ for all possible space topologies and invariance groups. We point out
that in many cases the canonical structure becomes degenerate in the moduli
sectors, which implies that the locally homogeneous systems are not canonically
closed in general in the full diffeomorphism-invariant phase space of generic
spacetimes with compact closed spaces.


title: Black Holes and Causal Structure in Anti-de Sitter Isometric Spacetimes

abstract:
  The observation that the 2+1 dimensional BTZ black hole can be obtained as a
quotient space of anti-de Sitter space leads one to ask what causal behaviour
other such quotient spaces can display. In this paper we answer this question
in 2+1 and 3+1 dimensions when the identification group has one generator.
Among other things we find that there does not exist any 3+1 generalization of
the rotating BTZ hole. However, the non-rotating generalization exists and
exhibits some unexpected properties. For example, it turns out to be non-static
and to possess a non-trivial apparent horizon.


title:
Darboux parameter for empty FRW quantum universes and quantum
  cosmological singularities

abstract:
  I present the factorization(s) of the Wheeler-DeWitt equation for vacuum FRW
minisuperspace universes of arbitrary Hartle-Hawking factor ordering, including
the so-called strictly isospectral supersymmetric method. By the latter means,
one can introduce an infinite class of singular FRW minisuperspace
wavefunctions characterized by a Darboux parameter that mathematically speaking
is a Riccati integration constant, while physically determines the position of
these strictly isospectral singularities on the Misner time axis


title: Gravity and the Tenacious Scalar Field

abstract:
  Scalar fields have had a long and controversial life in gravity theories,
having progressed through many deaths and resurrections. The first scientific
gravity theory, Newton's, was that of a scalar potential field, so it was
natural for Einstein and others to consider the possibility of incorporating
gravity into special relativity as a scalar theory. This effort, though
fruitless in its original intent, nevertheless was useful in leading the way to
Einstein's general relativity, a purely two-tensor field theory. However, a
universally coupled scalar field again appeared, both in the context of Dirac's
large number hypothesis and in five dimensional unified field theories as
studied by Fierz, Jordan, and others. While later experimentation seems to
indicate that if such a scalar exists its influence on solar system size
interactions is negligible, other reincarnations have been proposed under the
guise of dilatons in string theory and inflatons in cosmology. This paper
presents a brief overview of this history.


title:
General Relativistic Energy Conditions: The Hubble expansion in the
  epoch of galaxy formation

abstract:
  The energy conditions of Einstein gravity (classical general relativity) are
designed to extract as much information as possible from classical general
relativity without enforcing a particular equation of state for the
stress-energy. This systematic avoidance of the need to specify a particular
equation of state is particularly useful in a cosmological setting --- since
the equation of state for the cosmological fluid in a
Friedmann-Robertson-Walker type universe is extremely uncertain. I shall show
that the energy conditions provide simple and robust bounds on the behaviour of
both the density and look-back time as a function of red-shift. I shall show
that current observations suggest that the so-called strong energy condition
(SEC) is violated sometime between the epoch of galaxy formation and the
present. This implies that no possible combination of ``normal'' matter is
capable of fitting the observational data.


title: Understanding initial data for black hole collisions

abstract:
  Numerical relativity, applied to collisions of black holes, starts with
initial data for black holes already in each other's strong field. The initial
hypersurface data typically used for computation is based on mathematical
simplifying prescriptions, such as conformal flatness of the 3-geometry and
longitudinality of the extrinsic curvature. In the case of head on collisions
of equal mass holes, there is evidence that such prescriptions work reasonably
well, but it is not clear why, or whether this success is more generally valid.
Here we study these questions by considering the ``particle limit'' for head on
collisions of nonspinning holes. Einstein's equations are linearized in the
mass of the small hole, and described by a single gauge invariant spacetime
function psi, for each multipole. The resulting equations have been solved by
numerical evolution for collisions starting from various initial separations,
and the evolution is studied on a sequence of hypersurfaces. In particular, we
extract hypersurface data, that is psi and its time derivative, on surfaces of
constant background Schwarzschild time. These evolved data can then be compared
with ``prescribed'' data, evolved data can be replaced by prescribed data on
any hypersurface, and evolved further forward in time, a gauge invariant
measure of deviation from conformal flatness can be evaluated, etc. The main
findings of this study are: (i) For holes of unequal mass the use of prescribed
data on late hypersurfaces is not successful. (ii) The failure is likely due to
the inability of the prescribed data to represent the near field of the smaller
hole. (iii) The discrepancy in the extrinsic curvature is more important than
in the 3-geometry. (iv) The use of the more general conformally flat
longitudinal data does not notably improve this picture.


title: Time in Cosmology

abstract:
  The notion of time in cosmology is revealed through an examination of
transition matrix elements of radiative processes occurring in the cosmos. To
begin with, the very concept of time is delineated in classical physics in
terms of correlations between the succession of configurations which describe a
process and a standard trajectory called the clock. The total is an isolated
system of fixed energy. This is relevant for cosmology in that the universe is
an isolated system which we take to be homogeneous and isotropic. Furthermore,
in virtue of the constraint which arises from reparametrization invariance of
time, it has total energy zero. Therefore the momentum of the scale factor is
determined from the energy of matter. In the quantum theory this is exploited
through use of the WKB approximation for the wave function of the scale factor,
justified for a large universe. The formalism then gives rise to matrix
elements describing matter processes. These are shown to take on the form of
usual time dependent quantum amplitudes wherein the temporal dependence is
given by a background which is once more fixed by the total energy of matter.


title:
Gravitational Radiation Reaction to a Particle Motion II: Spinning
  Particle

abstract:
  We discuss the leading order correction to the equation of motion of a
particle with spin on an arbitrary spacetime. A particle traveling in a curved
spacetime is known to trace a geodesic of the background spacetime if the mass
of the particle is negligibly small. For a spinning particle, it is known that
there appears a term due to the coupling of the spin and the Riemann tensor of
the background spacetime. Recently we have found the equation of motion of a
non-spinning particle which includes the effect of gravitational radiation
reaction. This paper is devoted to discussion of a consistent derivation of the
equation of motion which is corrected both by the spin-Riemann coupling and the
gravitational radiation reaction.


title: Geodesics in Lewis Spacetime

abstract:
  The geodesic equations are integrated for the Lewis metric and the effects of
the different parameters appearing in the Weyl class on the motion of test
particles are brought out. Particular attention deserves the appearance of a
force parallel to the axial axis and without Newtonian analogue.


title: Divergences in the Effective Action for Acausal Spacetimes

abstract:
  The 1--loop effective Lagrangian for a massive scalar field on an arbitrary
causality violating spacetime is calculated using the methods of Euclidean
quantum field theory in curved spacetime. Fields of spin 1/2, spin 1 and
twisted field configurations are also considered. In general, we find that the
Lagrangian diverges to minus infinity at each of the nth polarised
hypersurfaces of the spacetime with a structure governed by a DeWitt-Schwinger
type expansion.


title: Quantum Reference Frames, Time and Measurements

abstract:
  We argue that correct account of the quantum properties of macroscopic
objects which form reference frames (RF) demand the change of the standard
space-time picture accepted in Quantum Mechanics. The presence of RF free
quantum motion in the form of wave packet smearing results in formal
nonapplicability of Galilean or Lorentz space-time transformations in this
case. For the description of the particles states transformations between
different quantum RF the special quantum space-time transformations are
formulated. Consequently it results in corrections to Schrodinger or Klein-
Gordon equations which depends on the RF mass. RF proper time becomes the
operator depending of momentums spread in RF wave packet ,from the point of
view of other observer. The experiments with macroscopic coherent states are
proposed in which this effects can be tested.}


title:
zeta-function regularization and one-loop renormalization of field
  fluctuations in curved space-times

abstract:
  A method to regularize and renormalize the fluctuations of a quantum field in
a curved background in the $\zeta$-function approach is presented. The method
produces finite quantities directly and finite scale-parametrized counterterms
at most. These finite couterterms are related to the presence of a particular
pole of the effective-action $\zeta$ function as well as to the heat kernel
coefficients. The method is checked in several examples obtaining known or
reasonable results. Finally, comments are given for as it concerns the recent
proposal by Frolov et al. to get the finite Bekenstein-Hawking entropy from
Sakharov's induced gravity theory.


title:
Rotating dust solutions of Einstein's equations with 3-dimensional
  symmetry groups, Part 2: One Killing field spanned on u^{\alpha} and
  w^{\alpha}

abstract:
  This is the second part of a series of 3 papers. Using the same method and
the same coordinates as in part 1, rotating dust solutions of Einstein's
equations are investigated that possess 3-dimensional symmetry groups, under
the assumption that only one of the Killing fields is spanned on the fields of
velocity $u^{\alpha}$ and rotation $w^{\alpha}$, while the other two define
vectors that are linearly independent of $u^{\alpha}$ and $w^{\alpha}$ at every
point of the spacetime region under consideration. The Killing fields are found
and the Killing equations solved for the components of the metric tensor in
every case that arises. The Einstein equations are simplified in a few cases,
three (most probably) new solutions are found, and several classes of solutions
known earlier are identified in the present scheme. They include those by
Ozsv\'ath, Maitra, Ellis, King and Vishveshwara and Winicour.
  PACS numbers 04.20.-q, 04.20.Cv, 04.20.Jb, 04.40.+c


title: Shear-free Null Quasi-Spherical Spacetimes

abstract:
  The residual gauge freedom within the null quasi-spherical coordinate
condition is studied, for spacetimes admitting an expanding, shear-free null
foliation. The freedom consists of a boost and rotation at each coordinate
sphere, corresponding to a specification of inertial frame at each sphere.
Explicit formulae involving arbitrary functions of two variables are obtained
for the accelerated Minkowski, Schwarzschild, and Robinson-Trautman spacetimes.
These examples will be useful as test metrics in numerical relativity.


title: SU(2)-invariant reduction of the 3+1 dimensional Ashtekar's gravity

abstract:
  We consider a space-time with spatial sections isomorphic to the group
manifold of SU(2). Triad and connection fluctuations are assumed to be
SU(2)-invariant. Thus, they form a finite dimensional phase space. We perform
non-perturbative path integral quantization of the model. Contarary to previous
claims the path integral measure appeared to be non-singular near
configurations admitting additional Killing vectors. In this model we are able
to calculate the generating functional of Green functions of the reduced phase
space variables exactly.


title:
Accuracy of the relativistic Cowling approximation in slowly rotating
  stars

abstract:
  We have calculated the non-radial oscillation in slowly rotating relativistic
stars with the Cowling approximation. The frequencies are compared with those
based on the complete linearized equations of general relativity. It is found
that the results with the approximation differ by less than about $20 %$ for
typical relativistic stellar models. The approximation is more accurate for
higher-order modes as in the Newtonian case.


title: Density Perturbations in String Cosmology

abstract:
  We discuss the generation and evolution of density perturbations during the
large curvature phase of string cosmology. We find that perturbations in the
scalar components of the metric evolve with cosmic time as $\exp (\gamma H_st)$
where $H_s$ is the Hubble constant during the string phase and $\gamma$ is a
constant which is determined by an algebraic equation involving all orders in
the string coupling $\alpha '$. The seed for the perturbations can be provided
by massive string modes.


title: On Poisson Structure and Curvature

abstract:
  We consider a curved space-time whose algebra of functions is the commutative
limit of a noncommutative algebra and which has therefore an induced Poisson
structure. In a simple example we determine a relation between this structure
and the Riemann tensor.


title:
Regularized Algebraic Nets for General Covariant QFT on Differentiable
  Manifolds

abstract:
  Quantum general relativity may be considered as generally covariant QFT on
differentiable manifolds, without any a priori metric structure. The
kinematically covariance group acts by general diffeomorphisms on the manifold
and by automorphisms on the isotonic net of *-algebras encoding the QFT, while
the algebra of observables is covariant under the dynamical subgroup of the
general diffeomorphism group.
  Here, I focus on an algebraic implementation of the dynamical subgroup of
dilations. Introducing an small and large scale cutoffs algebraically, their
usual a priori conflict with general covariance is avoided. Thereby, a
commutant duality between the minimal and maximal algebra is proposed. This
allows to extract the modular structure, which is again related to the
dilations.


title: An operationalistic reformulation of Einstein's equivalence principle

abstract:
  The Einstein's equivalence principle is formulated in terms of the accuracy
of measurements and its dependence of the size of the area of measurement. It
is shown that different refinements of the statement 'the spacetime is locally
flat' lead to different conculsions about the spacetime geometry.


title:
Perturbations in the Kerr-Newman Dilatonic Black Hole Background: I.
  Maxwell waves

abstract:
  In this paper we analyze the perturbations of the Kerr-Newman dilatonic black
hole background. For this purpose we perform a double expansion in both the
background electric charge and the wave parameters of the relevant quantities
in the Newman-Penrose formalism. We then display the gravitational, dilatonic
and electromagnetic equations, which reproduce the static solution (at zero
order in the wave parameter) and the corresponding wave equations in the Kerr
background (at first order in the wave parameter and zero order in the electric
charge). At higher orders in the electric charge one encounters corrections to
the propagations of waves induced by the presence of a non-vanishing dilaton.
An explicit computation is carried out for the electromagnetic waves up to the
asymptotic form of the Maxwell field perturbations produced by the interaction
with dilatonic waves. A simple physical model is proposed which could make
these perturbations relevant to the detection of radiation coming from the
region of space near a black hole.


title: O(N) Quantum fields in curved spacetime

abstract:
  For the O(N) field theory with lambda Phi^4 self-coupling, we construct the
two-particle-irreducible (2PI), closed-time-path (CTP) effective action in a
general curved spacetime. From this we derive a set of coupled equations for
the mean field and the variance. They are useful for studying the
nonperturbative, nonequilibrium dynamics of a quantum field when full back
reactions of the quantum field on the curved spacetime, as well as the
fluctuations on the mean field, are required. Applications to phase transitions
in the early Universe such as the Planck scale or in the reheating phase of
chaotic inflation are under investigation.


title: Forks in the Road, on the Way to Quantum Gravity

abstract:
  In seeking to arrive at a theory of ``quantum gravity'', one faces several
choices among alternative approaches. I list some of these ``forks in the
road'' and offer reasons for taking one alternative over the other. In
particular, I advocate the following: the sum-over-histories framework for
quantum dynamics over the ``observable and state-vector'' framework; relative
probabilities over absolute ones; spacetime over space as the gravitational
``substance'' (4 over 3+1); a Lorentzian metric over a Riemannian
(``Euclidean'') one; a dynamical topology over an absolute one; degenerate
metrics over closed timelike curves to mediate topology-change; ``unimodular
gravity'' over the unrestricted functional integral; and taking a discrete
underlying structure (the causal set) rather than the differentiable manifold
as the basis of the theory.
  In connection with these choices, I also mention some results from unimodular
quantum cosmology, sketch an account of the origin of black hole entropy,
summarize an argument that the quantum mechanical measurement scheme breaks
down for quantum field theory, and offer a reason why the cosmological constant
of the present epoch might have a magnitude of around $10^{-120}$ in natural
units.


title:
Toward a Complete Analysis of the Global Structure of Kerr-Newman
  Spacetime

abstract:
  An attempt is made to supplement Carter's partial investigation of the global
structure of Kerr-Newman spacetime on the symmetry axis. Namely, the global
structure of \theta = const. timelike submanifolds of Kerr-Newman metric
starting from the symmetry axis all the way down to the equatorial plane are
studied by introducing a new time coordinate slightly different from the usual
Boyer-Lindquist time coordinate. It turns out that the maximal anaytic
extension of \theta = \theta_0 (0 \leq \theta_0 < \pi/2) submanifolds is the
same as that of the symmetry axis first studied by Carter whereas \theta =
\pi/2 equatorial plane has the topology identical to that of the
Reissner-Nordstrom spacetime. General applicability of this method to
Kerr-Newman-type black hole solutions in other gravity theories is discussed as
well.


title: Can extreme black holes have (long) Abelian Higgs hair?

abstract:
  It has been argued that a black hole horizon can support the long range
fields of a Nielsen-Olesen string, and that one can think of such a vortex as
black hole ``hair''. In this paper, we examine the properties of an Abelian
Higgs vortex in the presence of a charged black hole as we allow the hole to
approach extremality. Using both analytical and numerical techniques, we show
that the magnetic field lines (as well as the scalar field) of the vortex are
completely expelled from the black hole in the extreme limit. This was to be
expected, since extreme black holes in Einstein-Maxwell theory are known to
exhibit such a ``Meissner effect'' in general. This would seem to imply that a
vortex does not want to be attached to an extreme black hole. We calculate the
total energy of the vortex fields in the presence of an extreme black hole.
When the hole is small relative to the size of the vortex, it is energetically
favoured for the hole to remain inside the vortex region, contrary to the
intuition that the hole should be expelled. However, as we allow the extreme
horizon radius to become very large compared to the radius of the vortex, we do
find evidence of an instability. This proves that it is energetically
unfavourable for a thin vortex to interact with a large extreme black hole.
This would seem to dispel the notion that a black hole can support `long'
abelian Higgs hair in the extreme limit. We show that these considerations do
not go through in the near extreme limit. Finally, we discuss whether this has
implications for strings that end at black holes.


title:
Statistical mechanics of Kerr-Newman dilaton black holes and the
  bootstrap condition

abstract:
  The Bekenstein-Hawking ``entropy'' of a Kerr-Newman dilaton black hole is
computed in a perturbative expansion in the charge-to-mass ratio. The most
probable configuration for a gas of such black holes is analyzed in the
microcanonical formalism and it is argued that it does not satisfy the
equipartition principle but a bootstrap condition. It is also suggested that
the present results are further support for an interpretation of black holes as
excitations of extended objects.


title: Quantum inequalities in two dimensional Minkowski spacetime

abstract:
  We generalize some results of Ford and Roman constraining the possible
behaviors of renormalized expected stress-energy tensors of a free massless
scalar field in two dimensional Minkowski spacetime. Ford and Roman showed that
the energy density measured by an inertial observer, when averaged with respect
to that observers proper time by integrating against some weighting function,
is bounded below by a negative lower bound proportional to the reciprocal of
the square of the averaging timescale. However, the proof required a particular
choice for the weighting function. We extend the Ford-Roman result in two ways:
(i) We calculate the optimum (maximum possible) lower bound and characterize
the state which achieves this lower bound; the optimum lower bound differs by a
factor of three from the bound derived by Ford and Roman for their choice of
smearing function. (ii) We calculate the lower bound for arbitrary, smooth
positive weighting functions. We also derive similar lower bounds on the
spatial average of energy density at a fixed moment of time.


title:
Classicality, Matter-Antimatter Asymmetry, and Quantum-Gravity Deformed
  Uncertainty Relations

abstract:
  Some of the recent work on quantum gravity has involved modified uncertainty
relations such that the products of the uncertainties of certain pairs of
observables increase with time. It is here observed that this type of modified
uncertainty relations would lead to quantum decoherence, which could explain
the classical behavior of macroscopic systems, and CPT violation, which coud
provide the seed for the emergence of a matter-antimatter asymmetry.


title: Particle creation and non-adiabatic transitions in quantum cosmology

abstract:
  The aim of this paper is to compute transitions amplitudes in quantum
cosmology, and in particular pair creation amplitudes and radiative
transitions. To this end, we apply a double adiabatic development to the
solutions of the Wheeler-DeWitt equation restricted to mini-superspace wherein
gravity is described by the scale factor $a$. The first development consists in
working with instantaneous eigenstates, in $a$, of the matter Hamiltonian. The
second development is applied to the gravitational part of the wave function
and generalizes the usual WKB approximation. We then obtain an exact equation
which replaces the Wheeler-DeWitt equation and determines the evolution, i.e.
the dependence in $a$, of the coefficients of this double expansion. When
working in the gravitational adiabatic approximation, the simplified equation
delivers the unitary evolution of transition amplitudes occurring among
instantaneous eigenstates. Upon abandoning this approximation, one finds that
there is an additional coupling among matter states living in expanding and
contracting universes. Moreover one has to face also the Klein paradox, i.e.
the generation of backward waves from an initially forward wave. The
interpretation and the consequences of these unusual features are only sketched
in the present paper. Finally, the examples of pair creation and radiative
transitions are analyzed in detail to establish when and how the above
mentioned unitary evolution coincides with the Schr\" odinger evolution.


title:
On the structure of the energy-momentum and the spin currents in Dirac's
  electron theory

abstract:
  We consider a classical Dirac field in flat Minkowski spacetime. We perform a
Gordon decomposition of its canonical energy-momentum and spin currents,
respectively. Thereby we find for each of these currents a convective and a
polarization piece. The polarization pieces can be expressed as exterior
covariant derivatives of the two-forms $\check M_\alpha$ and
$M_{\alpha\beta}=-M_{\beta\alpha}$, respectively. In analogy to the magnetic
moment in electrodynamics, we identify these two-forms as gravitational moments
connected with the translation group and the Lorentz group, respectively. We
point out the relation between the Gordon decomposition of the energy-momentum
current and its Belinfante-Rosenfeld symmetrization. In the non-relativistic
limit, the translational gravitational moment of the Dirac field is found to be
proportional to the spin covector of the electron.


title: Pulsation modes for increasingly relativistic polytropes

abstract:
  We present the results of a numerical study of the fluid $f$, $p$ and the
gravitational $w$ modes for increasingly relativistic nonrotating polytropes.
The results for $f$ and $w$-modes are in good agreement with previous data for
uniform density stars, which supports an understanding of the nature of the
gravitational wave modes based on the uniform density data. We show that the
$p$-modes can become extremely long-lived for some relativistic stars. This
effect is attributed to the change in the perturbed density distribution as the
star becomes more compact.


title: Quantum Decay of Domain Walls In Cosmology I: Instanton Approach

abstract:
  This paper studies the decay of a large, closed domain wall in a closed
universe. Such walls can form in the presence of a broken, discrete symmetry.
We introduce a novel process of quantum decay for such a wall, in which the
vacuum fluctuates from one discrete state to another throughout one half of the
universe, so that the wall decays into pure field energy. Equivalently, the
fluctuation can be thought of as the nucleation of a second domain wall of zero
size, followed by its growth by quantum tunnelling and its collision with the
first wall, annihilating both. The barrier factor for this quantum tunneling is
calculated by guessing and verifying a Euclidean instanton for the two-wall
system. We also discuss the classical origin and evolution of closed,
topologically spherical domain walls in the early universe, through a
"budding-off" process involving closed domain walls larger than the Hubble
radius. This paper is the first of a series on this subject.


title: Lorentz Invariance and the Cosmological Constant

abstract:
  Non-trivial solutions in string field theory may lead to the spontaneous
breaking of Lorentz invariance and to new tensor-matter interactions. It is
argued that requiring the contribution of the vacuum expectation values of
Lorentz tensors to account for the vacuum energy up to the level that
$\Omega_{0}^{\Lambda} = 0.5$ implies the new interactions range is $\lambda
\sim 10^{-4} m$. These conjectured violations of the Lorentz symmetry are
consistent with the most stringent experimental limits.


title: Singularities and asymptotic behavior of the Tolman-Bondi model

abstract:
  The Bondi formula for calculation of the invariant mass in the Tolman- Bondi
(TB) model is interprated as a transformation rule on the set of co-moving
coordinates. The general procedure by which the three arbitrary functions of
the TB model are determined explicitly is presented. The properties of the TB
model, produced by the transformation rule are studied. Two applications are
studied: for the falling TB flat model the equation of motion of two
singularities hypersurfaces are obtained; for the expanding TB flat model the
dependence of size of area with friedmann-like solution on initial conditions
is studied in the limit $t \to +\infty$.


title:
Stability Analysis of Spherically Symmetric Star in Scalar-Tensor
  Theories of Gravity

abstract:
  A stability analysis of a spherically symmetric star in scalar-tensor
theories of gravity is given in terms of the frequencies of quasi-normal modes.
The scalar-tensor theories have a scalar field which is related to gravitation.
There is an arbitrary function, the so-called coupling function, which
determines the strength of the coupling between the gravitational scalar field
and matter. Instability is induced by the scalar field for some ranges of the
value of the first derivative of the coupling function. This instability leads
to significant discrepancies with the results of binary-pulsar-timing
experiments and hence, by the stability analysis, we can exclude the ranges of
the first derivative of the coupling function in which the instability sets in.
In this article, the constraint on the first derivative of the coupling
function from the stability of relativistic stars is found. Analysis in terms
of the quasi-normal mode frequencies accounts for the parameter dependence of
the wave form of the scalar gravitational waves emitted from the
Oppenheimer-Snyder collapse. The spontaneous scalarization is also discussed.


title:
Cylindrical analogue of NUT space: spacetime of a line gravomagnetic
  monopole

abstract:
  Using the quasi-Maxwell form of the vacuum Einstein equations and demanding
the presence of a cylindrically symmetric radial gravomagnetic field, we find
the solution to the Einstein equations which represents the gravity field of a
line gravomagnetic monopole. We show that this is the generalization of the
Levi-Civita's cylindrically symmetric static spacetime, in the same way that
the NUT metric is the empty space generalization of the Schwarzschild metric.
  Some of the features of this metric as well as its relation to other metrics
are discussed.


title:
Quantum Squeezing and Late Time Classical Behavior of Massive Fields in
  Expanding Robertson-Walker Universe

abstract:
  A Schroedinger picture analysis of time dependent quantum oscillators, in a
manner of Guth and Pi, clearly identifies two physical mechanisms for possible
decoherence of vacuum fluctuations in early universe: turning of quantum
oscillators upside-down, and rapid squeezing of upside-right oscillators so
that certain squeezing factor diverges. In inflationary cosmology the former
mechanism explains the stochastic evolution of light inflatons and the
classical nature of density perturbations in most of inflationary models, while
the later one is responsible for the classical evolution of relatively heavy
fields, with masses in a narrow range above the Hubble parameter: 2 < (m/H_0)^2
< 9/4. The same method may be applied to study of the decoherence of quantum
fluctuations in any Robertson-Walker cosmology.


title: Nucleosynthesis Constraints on Scalar-Tensor Theories of Gravity

abstract:
  We study the cosmological evolution of massless single-field scalar-tensor
theories of gravitation from the time before the onset of $e^+e^-$ annihilation
and nucleosynthesis up to the present. The cosmological evolution together with
the observational bounds on the abundances of the lightest elements (those
mostly produced in the early universe) place constraints on the coefficients of
the Taylor series expansion of $a(\phi)$, which specifies the coupling of the
scalar field to matter and is the only free function in the theory. In the case
when $a(\phi)$ has a minimum (i.e., when the theory evolves towards general
relativity) these constraints translate into a stronger limit on the
Post-Newtonian parameters $\gamma$ and $\beta$ than any other observational
test. Moreover, our bounds imply that, even at the epoch of annihilation and
nucleosynthesis, the evolution of the universe must be very close to that
predicted by general relativity if we do not want to over- or underproduce
$^{4}$He. Thus the amount of scalar field contribution to gravity is very small
even at such an early epoch.


title: Accelerated Detectors and Temperature in (Anti) de Sitter Spaces

abstract:
  We show, in complete accord with the usual Rindler picture, that detectors
with constant acceleration $a$ in de Sitter (dS) and Anti de Sitter (AdS)
spaces with cosmological constants $\Lambda$ measure temperatures $2\pi
T=(\Lambda/3+a^{2})^{1/2}\equiv a_{5}$, the detector "5-acceleration" in the
embedding flat 5-space. For dS, this recovers a known result; in AdS, where
$\Lambda$ is negative, the temperature is well defined down to the critical
value $a_{5}=0$, again in accord with the underlying kinematics. The existence
of a thermal spectrum is also demonstrated for a variety of candidate wave
functions in AdS backgrounds.


title: Free Energy of Gravitating Fermions

abstract:
  We study a system of self-gravitating massive fermions in the framework of
the general-relativistic Thomas-Fermi model. We postulate the free energy
functional and show that its extremization is equivalent to solving the
Einstein's field equations. A self-gravitating fermion gas we then describe by
a set of Thomas-Fermi type self-consistency equations.


title:
Dynamics of a self-gravitating thin string in scalar-tensor theories of
  gravitation

abstract:
  We examine the dynamics of a self-gravitating string in the scalar-tensor
theories of gravitation by considering a thin tube of matter to describe it.
For a class of solutions, we obtain in the generic case that the extrinsic
curvature of the world sheet of the central line is null in the limit where the
radius of the string tends to zero. However, if we impose a specific constraint
on the behaviour of the solution then we find that only the mean curvature of
the world sheet of the central line vanishes which is just the Nambu-Goto
dynamics. This analysis can include the massless dilatonic theories of gravity.


title: Canonical Quantization Inside the Schwarzschild Black Hole

abstract:
  We propose a scheme for quantizing a scalar field over the Schwarzschild
manifold including the interior of the horizon. On the exterior, the timelike
Killing vector and on the horizon the isometry corresponding to restricted
Lorentz boosts can be used to enforce the spectral condition. For the interior
we appeal to the need for CPT invariance to construct an explicitly positive
definite operator which allows identification of positive and negative
frequencies. This operator is the translation operator corresponding to the
inexorable propagation to smaller radii as expected from the classical metric.
We also propose an expression for the propagator in the interior and express it
as a mode sum.


title:
Gauge Invariant Hamiltonian Formalism for Spherically Symmetric
  Gravitating Shells

abstract:
  The dynamics of a spherically symmetric thin shell with arbitrary rest mass
and surface tension interacting with a central black hole is studied. A careful
investigation of all classical solutions reveals that the value of the radius
of the shell and of the radial velocity as an initial datum does not determine
the motion of the shell; another configuration space must, therefore, be found.
A different problem is that the shell Hamiltonians used in literature are
complicated functions of momenta (non-local) and they are gauge dependent. To
solve these problems, the existence is proved of a gauge invariant
super-Hamiltonian that is quadratic in momenta and that generates the shell
equations of motion. The true Hamiltonians are shown to follow from the
super-Hamiltonian by a reduction procedure including a choice of gauge and
solution of constraint; one important step in the proof is a lemma stating that
the true Hamiltonians are uniquely determined (up to a canonical
transformation) by the equations of motion of the shell, the value of the total
energy of the system, and the choice of time coordinate along the shell. As an
example, the Kraus-Wilczek Hamiltonian is rederived from the super-Hamiltonian.
The super-Hamiltonian coincides with that of a fictitious particle moving in a
fixed two-dimensional Kruskal spacetime under the influence of two effective
potentials. The pair consisting of a point of this spacetime and a unit
timelike vector at the point, considered as an initial datum, determines a
unique motion of the shell.


title:
Do Vortex Filaments in a Superfluid Neutron Star Produce Gravimagnetic
  Forces ?

abstract:
  A general analysis of the gravitational dynamics of a medium with a
continuous distribution of vorticity indicates that the answer to the question
raised in the title is affirmative, contrary to a recent claim.


title: Cosmological CMBR dipole in open universes ?

abstract:
  The observed CMBR dipole is generally interpreted as a Doppler effect arising
from the motion of the Earth relative to the CMBR frame. An alternative
interpretation, proposed in the last years, is that the dipole results from
ultra-large scale isocurvature perturbations. We examine this idea in the
context of open cosmologies and show that the isocurvature interpretation is
not valid in an open universe, unless it is extremely close to a flat universe,
$|\Omega_0 -1|< 10^{-4}$.


title: Chaos in black holes surrounded by gravitational waves

abstract:
  The occurrence of chaos for test particles moving around Schwarzschild black
holes perturbed by a special class of gravitational waves is studied in the
context of the Melnikov method. The explicit integration of the equations of
motion for the homoclinic orbit is used to reduce the application of this
method to the study of simple graphics.


title: Generating New Perfect-fluid Solutions From Known Ones II

abstract:
  The properties of a transformation previously considered for generating new
perfect-fluid solutions from known ones are further investigated. It is assumed
that the four-velocity of the fluid is parallel to the stationary Killing
field, and also that the norm and the twist potential of the stationary Killing
field are functionally related. This case is complementary to the case studied
in our previous paper. The transformation can be applied to generate possibly
new perfect-fluid solutions from known ones only for the case of barotropic
equation of state rho+3p=0 or, alternatively, for the case of a static
spacetime. For static spacetimes our method recovers the Buchdahl
transformation. It is demonstrated, moreover, that Herlt's technique for
constructing stationary perfect-fluid solutions from static ones is, actually,
a special case of the method considered in the present paper.


title: Degenerate Metric Phase Boundaries

abstract:
  The structure of boundaries between degenerate and nondegenerate solutions of
Ashtekar's canonical reformulation of Einstein's equations is studied. Several
examples are given of such "phase boundaries" in which the metric is degenerate
on one side of a null hypersurface and non-degenerate on the other side. These
include portions of flat space, Schwarzschild, and plane wave solutions joined
to degenerate regions. In the last case, the wave collides with a planar phase
boundary and continues on with the same curvature but degenerate triad, while
the phase boundary continues in the opposite direction. We conjecture that
degenerate phase boundaries are always null.


title:
Gravitational Field of the Early Universe: I.Non-linear Scalar Field as
  the Source

abstract:
  In this review article we consider three most important sources of the
gravitational field of the Early Universe: self-interacting scalar field,
chiral field and gauge field. The correspondence between all of them are
pointed out. More attention is payed to nonlinear scalar field source of
gravity. The progress in finding the exact solutions in inflationary universe
is reviewed. The basic idea of `fine turning of the potential' method is
discussed and computational background is presented in details. A set of new
exact solutions for standard inflationary model and conformally-flat
space-times are obtained. Special attention payed to relations between `fine
turning of the potential' and Barrow's approaches. As the example of a
synthesis of both methods new exact solution is obtained.


title: Maximal Acceleration Is Nonrotating

abstract:
  In a stationary axisymmetric spacetime, the angular velocity of a stationary
observer that Fermi-Walker transports its acceleration vector is also the
angular velocity that locally extremizes the magnitude of the acceleration of
such an observer, and conversely if the spacetime is also symmetric under
reversing both t and phi together. Thus a congruence of Nonrotating
Acceleration Worldlines (NAW) is equivalent to a Stationary Congruence
Accelerating Locally Extremely (SCALE). These congruences are defined
completely locally, unlike the case of Zero Angular Momentum Observers (ZAMOs),
which requires knowledge around a symmetry axis. The SCALE subcase of a
Stationary Congruence Accelerating Maximally (SCAM) is made up of stationary
worldlines that may be considered to be locally most nearly at rest in a
stationary axisymmetric gravitational field. Formulas for the angular velocity
and other properties of the SCALEs are given explicitly on a generalization of
an equatorial plane, infinitesimally near a symmetry axis, and in a slowly
rotating gravitational field, including the weak-field limit, where the SCAM is
shown to be counter-rotating relative to infinity. These formulas are evaluated
in particular detail for the Kerr-Newman metric. Various other congruences are
also defined, such as a Stationary Congruence Rotating at Minimum (SCRAM), and
Stationary Worldlines Accelerating Radially Maximally (SWARM), both of which
coincide with a SCAM on an equatorial plane of reflection symmetry.
Applications are also made to the gravitational fields of maximally rotating
stars, the Sun, and the Solar System.


title: Black Hole Entropy: a spacetime foam approach

abstract:
  The spacetime foam structure is reviewed briefly (topogical fluctuations and
virtual black hole possibility; equation of state of the foam). A model of
space foam at the surface of the event horizon is introduced. The model is
applied to the calculus of the number of states of a black hole, of its entropy
and of other thermodynamical properties. A formula for the number of microholes
on the surface of the event horizon is derived. Thermodynamical properties of
the event horizon are extended to thermodynamical properties of the space. On
the basis of the previous results, the possibility of micro black holes
creation by the Unruh Effect is investigated.


title: New exact solutions in standard inflationary models

abstract:
  The exact solutions in the standard inflationary model based on the
self-interacting scalar field minimally coupled to gravity are considered. The
shape's freedom of the self-interacting potential $V(\phi)$ is postulated to
obtain a new set of the exact solutions in the framework of
Friedmann-Robertson-Walker Universes. The general solution was found in the
case of power law inflation. We obtained new solutions and compared them with
obtained ones earlir for the exponential type inflation.


title:
Abelian Higgs hair for extreme black holes and selection rules for
  snapping strings

abstract:
  It has been argued that a black hole horizon can support the long range
fields of a Nielsen-Olesen string, and that one can think of such a vortex as
black hole ``hair''. We show that the fields inside the vortex are completely
expelled from a charged black hole in the extreme limit (but not in the near
extreme limit). This would seem to imply that a vortex cannot be attached to an
extreme black hole. Furthermore, we provide evidence that it is energetically
unfavourable for a thin vortex to interact with a large extreme black hole.
This dispels the notion that a black hole can support `long' Abelian Higgs hair
in the extreme limit. We discuss the implications for strings that end at black
holes, as in processes where a string snaps by nucleating black holes.


title: Quantum Decay of Domain Walls in Cosmology II: Hamiltonian Approach

abstract:
  This paper studies the decay of a large, closed domain wall in a closed
universe. Such walls can form in the presence of a broken, discrete symmetry.
We study a novel process of quantum decay for such a wall, in which the vacuum
fluctuates from one discrete state to another throughout one half of the
universe, so that the wall decays into pure field energy. Equivalently, the
fluctuation can be thought of as the nucleation of a second closed domain wall
of zero size, followed by its growth by quantum tunnelling and its collision
with the first wall, annihilating both. We therefore study the 2-wall system
coupled to a spherically symmetric gravitational field. We derive a simple form
of the 2-wall action, use Dirac quantization, obtain the 2-wall wave function
for annihilation, find from it the barrier factor for this quantum tunneling,
and thereby get the decay probability. This is the second paper of a series.