title:
MATTERS OF GRAVITY, The newsletter of the APS Topical Group on
  Gravitation

abstract:
  Contents:
  -Report from the APS Topical Group in Gravitation, Beverly Berger
  -Some remarks on the passing of S. Chandrasekhar, Robert Wald
  -LIGO Project Status, Syd Meshkov and Stan Whitcomb
  -New Hyperbolic forms of the Einstein Equations, Andrew Abrahams
  -Massless Black Holes, Gary Horowitz
  -A plea for theoretical help from the gravity wave co-op, William Hamilton
  -Why Quantum Cosmologists are Interested in Quantum Mechanics, James Hartle
  -Probing the Early Universe with the Cosmic Microwave Background, Rahul Dave
  and Paul Steinhardt
  -G measurements, Riley Newman
  -Is general relativity about null surfaces?, Carlo Rovelli
  -ITP program solicitation, James Hartle
  -7th Gregynog workshop in general relativity, Miguel Alcubierre
  -Third Annual Penn State Conference: Astrophysical Sources of Gravitational
  Waves, Curt Cutler
  -General news from GR14, Abhay Ashtekar
  -VIth Canadian General Relativity Conference, Jack Gegenberg


title: Inflationary Solutions in Quantum Cosmology

abstract:
  We prove that in the Hartle-Hawking approach to quantum cosmology the
existence of an inflationary phase is a general property of minisuperspace
models given by a closed Friedmann-Robertson-Walker universe containing a
massless scalar field with a $\lambda\phi^{n}$ self-interaction. The evolution
in time of the cosmic scale factor and of the scalar field in the very early
universe is derived, together with the conditions to be satisfied in order to
solve the horizon and flatness problems.


title: The Singularity Problem for Space-Times with Torsion

abstract:
  The problem of a rigorous theory of singularities in space-times with torsion
is addressed. We define geodesics as curves whose tangent vector moves by
parallel transport. This is different from what other authors have done,
because their definition of geodesics only involves the Christoffel connection,
though studying theories with torsion. We propose a preliminary definition of
singularities which is based on timelike or null geodesic incompleteness, even
though for theories with torsion the paths of particles are not geodesics. The
study of the geodesic equation for cosmological models with torsion shows that
the definition has a physical relevance. It can also be motivated, as done in
the literature, remarking that the causal structure of a space-time with
torsion does not get changed with respect to general relativity. We then prove
how to extend Hawking's singularity theorem without causality assumptions to
the space-time of the ECSK theory. This is achieved studying the generalized
Raychaudhuri equation in the ECSK theory, the conditions for the existence of
conjugate points and properties of maximal timelike geodesics. Hawking's
theorem can be generalized, provided the torsion tensor obeys some conditions.
Thus our result can also be interpreted as a no-singularity theorem if these
additional conditions are not satisfied. In other words, it turns out that the
occurrence of singularities in closed cosmological models based on the ECSK
theory is less generic than in general relativity. Our work is to be compared
with previous papers in the literature. There are some relevant differences,
because we rely on a different definition of geodesics, we keep the field
equations of the ECSK theory in their original form rather than casting them in
a form similar to general relativity with a modified energy momentum tensor,


title:
Micro--universes and ``strong black holes'': a purely geometric approach
  to elementary particles

abstract:
  We present here a panoramic view of our unified, bi--scale theory of
gravitational and strong interactions [which is mathematically analogous to the
last version of N.Rosen's bi--metric theory; and yields physical results
similar to strong gravity's]. This theory, developed during the last 15 years,
is purely geometrical in nature, adopting the methods of General Relativity for
the description of hadron structure and strong interactions. In particular,
hadrons are associated with `` strong black--holes'', from the external point
of view, and with ``micro--universes'', from the internal point of view. Among
the results herein presented, let us mention the derivation: (i) of confinement
and (ii) asymptotic freedom for the hadron constituents; (iii) of the Yukawa
behaviour for the strong potential at the static limit; (iv) of the strong
coupling ``constant'', and (v) of mesonic mass spectra.


title: Density Fluctuations in Inflationary Models with Multiple Scalar Fields

abstract:
  Making use of the primordially isocurvature fluctuations, which are generated
in inflationary models with multiple scalar fields, we make a phenomenological
model that predicts formation of primordial black holes which can account for
the massive compact halo objects recently observed.


title:
Hamiltonian Structure of a Friedmann-Robertson-Walker Universe with
  Torsion

abstract:
  We study a $R^{2}$ model of gravity with torsion in a closed
Friedmann-Robertson-Walker universe. The model is cast in Hamiltonian form
subtracting from the original Lagrangian the total time derivative of
$f_{K}f_{R}$, where $f_{K}$ is proportional to the trace of the extrinsic
curvature tensor, and $f_{R}$ is obtained differentiating the Lagrangian with
respect to the highest derivative. Torsion is found to lead to a primary
constraint linear in the momenta and a secondary constraint quadratic in the
momenta, and the full field equations are finally worked out in detail.
Problems to be studied for further research are the solution of these equations
and the quantization of the model. One could then try to study a new class of
quantum cosmological models with torsion.


title:
Hamilton-Jacobi Equation for Brans-Dicke Theory and Its Long-wavelength
  Solution

abstract:
  Hamilton-Jacobi equation for Brans-Dicke theory is solved by using a
long-wavelength approximation. We examine the non-linear evolution of the
inhomogeneities in the dust fluid case and the cosmological constant case. In
the case of dust fluid, it turns out that the inhomogeneities of space-time
grow. In the case of cosmological constant, the inhomogeneities decay, which is
consistent with the cosmic no hair conjecture. The inhomogeneities of the
density perturbation and the gravitational constant behave similarly with that
of space-time.


title: Gravitational Instantons in Ashtekar's Formalism

abstract:
  Gravitational instantons of Bianchi type IX space are constructed in
Ashtekar's canonical formalism. Instead of solving the self-duality condition,
we fully solve the constraint on the ``initial surface'' and ``Hamiltonian
equations''. This formalism is applicable to the matter coupled system with
cosmological constant.


title: Pair creation rate for $U(1)^2$ black holes

abstract:
  I consider a truncation of low-energy string theory which contains two $U(1)$
gauge fields. After making some general comments on the theory, I describe a
previously-obtained instanton for the pair creation of black holes when both
gauge fields are non-zero, and obtain the pair creation rate by calculating its
action. This calculation agrees qualitatively with the earlier calculation of
the pair creation rate for black holes in Einstein-Maxwell theory. That is, the
pair creation is strongly suppressed in realizable circumstances, and it
reduces to the Schwinger result in the point-particle limit. The pair creation
of non-extreme black holes is enhanced over that of extreme black holes by
$e^{{\cal A}_{bh}/4}$.


title: Black Holes with Weyl Charge and Non-Riemannian Waves

abstract:
  A simple modification to Einstein's theory of gravity in terms of a
non-Riemannian connection is examined. A new tensor-variational approach yields
field equations that possess a covariance similar to the gauge covariance of
electromagnetism. These equations are shown to possess solutions analogous to
those found in the Einstein-Maxwell system. In particular one finds
gravi-electric and gravi-magnetic charges contributing to a spherically
symmetric static Reissner-Nordstr\"om metric. Such Weyl ``charges'' provide a
source for the non-Riemannian torsion and metric gradient fields instead of the
electromagnetic field. The theory suggests that matter may be endowed with
gravitational charges that couple to gravity in a manner analogous to
electromagnetic couplings in an electromagnetic field. The nature of
gravitational coupling to spinor matter in this theory is also investigated and
a solution exhibiting a plane-symmetric gravitational metric wave coupled via
non-Riemannian waves to a propagating spinor field is presented.


title: Formation of Black Holes from Collapsed Cosmic String Loops

abstract:
  The fraction of cosmic string loops which collapse to form black holes is
estimated using a set of realistic loops generated by loop fragmentation. The
smallest radius sphere into which each cosmic string loop may fit is obtained
by monitoring the loop through one period of oscillation. For a loop with
invariant length $L$ which contracts to within a sphere of radius $R$, the
minimum mass-per-unit length $\mu_{\rm min}$ necessary for the cosmic string
loop to form a black hole according to the hoop conjecture is $\mu_{\rm min} =
R /(2 G L)$. Analyzing $25,576$ loops, we obtain the empirical estimate $f_{\rm
BH} = 10^{4.9\pm 0.2} (G\mu)^{4.1 \pm 0.1}$ for the fraction of cosmic string
loops which collapse to form black holes as a function of the mass-per-unit
length $\mu$ in the range $10^{-3} \lesssim G\mu \lesssim 3 \times 10^{-2}$. We
use this power law to extrapolate to $G\mu \sim 10^{-6}$, obtaining the
fraction $f_{\rm BH}$ of physically interesting cosmic string loops which
collapse to form black holes within one oscillation period of formation.
Comparing this fraction with the observational bounds on a population of
evaporating black holes, we obtain the limit $G\mu \le 3.1 (\pm 0.7) \times
10^{-6}$ on the cosmic string mass-per-unit-length. This limit is consistent
with all other observational bounds.


title:
The variational theory of perfect fluid with intrinsic hypermomentum in
  space-time with nonmetricity

abstract:
  The variational theory of the perfect fluid with an intrinsic hypermomentum
is developed. The Lagrangian density of such fluid is stated and the equations
of motion of the fluid and the evolution equation of the hypermomentum tensor
are derived. The expressions of the matter currents of the fluid (the metric
stress-energy 4-form, the canonical energy-momentum 3-form and the
hypermomentum 3-form) are obtained.


title: Unified Relativistic Physics from a Standing Wave Particle Model

abstract:
  An extremely simple and unified base for physics comes out by starting all
over from a single postulate on the common nature of matter and stationary
forms of radiation quanta. Basic relativistic, gravitational (G) and quantum
mechanical properties of a standing wave particle model have been derived. This
has been done from just dual properties of radiation's and strictly homogeneous
relationships for nonlocal cases in G fields. This way reduces the number of
independent variables and puts into relief (and avoid) important inhomogeneity
errors of some G theories. It unifies and accounts for basic principles and
postulates physics. The results for gravity depend on linear radiation
properties but not on arbitrary field relations. They agree with the
conventional tests. However they have some fundamental differences with current
G theories. The particle model, at a difference of the conventional theories,
also fixes well-defined cosmological and astrophysical models that are
different from the rather conventional ones. They have been described and
tested with the astronomical observations. These tests have been resumed in a
separated work to be sent to the astro Archive.


title: Renormalization of the charged scalar field in curved space

abstract:
  The DeWitt-Schwinger proper time point-splitting procedure is applied to a
massive complex scalar field with arbitrary curvature coupling interacting with
a classical electromagnetic field in a general curved spacetime. The scalar
field current is found to have a linear divergence. The presence of the
external background gauge field is found to modify the stress-energy tensor
results of Christensen for the neutral scalar field by adding terms of the form
$(eF)^2$ to the logarithmic counterterms. These results are shown to be
expected from an analysis of the degree of divergence of scalar quantum
electrodynamics.


title:
Renormalization Group Calculation of the Galaxy-Galaxy Correlation
  Function

abstract:
  The observable Universe is described by a collection of equal mass galaxies
linked into a common unit by their mutual gravitational interaction. The
partition function of this system is cast in terms of Ising model spin
variables and maps exactly onto a three-dimensional stochastic scalar classical
field theory. The full machinery of the renormalization group and critical
phenomena is brought to bear on this field theory allowing one to calculate the
galaxy-galaxy correlation function, whose critical exponent is predicted to be
between 1.530 to 1.862, compared to the phenomenological value of 1.6 to 1.8


title: String Gravity and Cosmology: Some new ideas

abstract:
  String theory provides the only consistent framework so far that unifies all
interactions including gravity. We discuss gravity and cosmology in string
theory. Conventional notions from general relativity like geometry, topology
etc. are well defined only as low energy approximations in string theory. At
small distances physics deviates from the field theoretic intuition. We present
several examples of purely stringy phenomena which imply that the physics at
strong curvatures can be quite different from what one might expect from field
theory. They indicate new possibilities in the context of quantum cosmology.


title: On Pseudospherically Symmetric Repulsive Gravitational Field

abstract:
  Solutions of Einstein vacuum equations, for a static pseudospherically
symmetric system, are presented. They describe a naked singularity and a
singular solution with many resemblances to the Schwartzschild solution but
with two major differences: its static region, lying inside the null horizon,
sees the singularity, and its effective gravitational field is repulsive. We
shortly discuss on the phenomenological plausibility of this last solution as a
self-consistent system living on a space-time domain, and discuss some features
of particle geodesics in its gravitational field.


title:
Variable rest masses in 5-dimensional gravitation confronted with
  experimental data

abstract:
  Cosmological solutions of Einstein equation for a \mbox{5-dimensional}
space-time, in the case of a dust-filled universe, are presented. With these
solutions we are able to test a hypothetical relation between the rest mass of
a particle and the $5^{\rm th}$ dimension. Comparison with experiment strongly
refutes the implied dependence of the rest mass on the cosmological time.


title:
Black hole collisions from Brill-Lindquist initial data: predictions of
  perturbation theory

abstract:
  The Misner initial value solution for two momentarily stationary black holes
has been the focus of much numerical study. We report here analytic results for
an astrophysically similar initial solution, that of Brill and Lindquist (BL).
Results are given from perturbation theory for initially close holes and are
compared with available numerical results. A comparison is made of the
radiation generated from the BL and the Misner initial values, and the physical
meaning is discussed.


title: Gauge-invariance in one-loop quantum cosmology

abstract:
  We study the problem of gauge-invariance and gauge-dependence in one-loop
quantum cosmology. We formulate some requirements which should be satisfied by
boundary conditions in order to give gauge-independent path integral. The case
of QED is studied in some detail. We outline difficulties in gauge-invariant
quantization of gravitational field in a bounded region.


title: Stars of WIMPs

abstract:
  A class of boson-fermion stars, whose spin-0 and spin-1/2 constituents
interact through a U(1) current-current term in the Lagrangian density, is
analysed. It is shown that it describes the low-energy behavior of a system of
weakly interacting massive particles (WIMPs) from the leptonic sector of the
minimal supersymmetric standard model. In this case the effective coupling
constant $\lambda$ is related to the Fermi constant $G_F$.


title:
Spontaneous Symmetry Breaking of Rapidly Rotating Stars in General
  Relativity

abstract:
  We investigate the effects of general relativity upon the non-axisymmetric
``bar'' mode secular instability of rapidly rotating stars, i.e. the
relativistic and compressible analog of the transition from Maclaurin spheroids
to Jacobi ellipsoids. Our method consists in perturbing a stationary
axisymmetric configuration, constructed by a 2-D general relativistic numerical
code, and taking into account only the dominant terms in the non-axisymmetric
part of the 3-D relativistic equations. For a polytropic equation of state, we
have determined, as a function of the degree of relativity, the critical
adiabatic index $\gamma_{\rm crit}$ above which rapidly rotating stars can
break their axial symmetry. A by-product of the present study is the
confirmation of the Newtonian value $\gamma_{\rm crit} = 2.238$ obtained by
James (1964). We have also considered neutron star models contructed upon
twelve nuclear matter equations of state taken from the literature. We found
that five equations of state from this sample allow the symmetry breaking for
sufficiently high rotation velocities. For the others, the Keplerian velocity
(mass-shedding from the equator) is reached before the axisymmetry is broken.
Rotating neutron stars that break their axial symmetry can be an important
source of gravitational waves for the LIGO/VIRGO interferometric detectors.


title: Statistical Mechanics and Black Hole Entropy

abstract:
  I review a new (and still tentative) approach to black hole thermodynamics
that seeks to explain black hole entropy in terms of microscopic quantum
gravitational boundary states induced on the black hole horizon.


title: Symmetries of pp-Waves with Distributional Profile

abstract:
  We generalize the classification of (non-vacuum) pp-waves \cite{JEK} based on
the Killing-algebra of the space-time by admitting distribution-valued profile
functions. Our approach is based on the analysis of the (infinite-dimensional)
group of ``normal-form-preserving'' diffeomorphisms.


title: On Relativistic Material Reference Systems

abstract:
  This work closes certain gaps in the literature on material reference systems
in general relativity. It is shown that perfect fluids are a special case of
DeWitt's relativistic elastic media and that the velocity--potential formalism
for perfect fluids can be interpreted as describing a perfect fluid coupled to
a fleet of clocks. A Hamiltonian analysis of the elastic media with clocks is
carried out and the constraints that arise when the system is coupled to
gravity are studied. When the Hamiltonian constraint is resolved with respect
to the clock momentum, the resulting true Hamiltonian is found to be a
functional only of the gravitational variables. The true Hamiltonian is
explicitly displayed when the medium is dust, and is shown to depend on the
detailed construction of the clocks.


title:
On the Evolution of Scalar Metric Perturbations in an Inflationary
  Cosmology

abstract:
  We further clarify how scalar metric perturbations are amplified in an
inflationary cosmology. We first construct a simple, analytic model of an
inflationary cosmology in which the expansion scale factor evolves continuously
from an inflationary era to a radiation-dominated era. From this model, it is
clear to see how scalar perturbations are amplified. Second, we examine the
recent claims of Grishchuk, and the reply by Deruelle and Mukhanov, regarding
the evolution of scalar perturbations through an abrupt transition in the
equation of state of the cosmological fluid. We demonstrate that the ``standard
results'' regarding the amplification of scalar, density perturbations from
inflation are valid.


title: A Hamiltonian Formulation of Nonsymmetric Gravitational Theories

abstract:
  The dynamics of a class of nonsymmetric gravitational theories is presented
in Hamiltonian form. The derivation begins with the first-order action,
treating the generalized connection coefficients as the canonical coordinates
and the densitised components of the inverse of the fundamental tensor as
conjugate momenta. The phase space of the symmetric sector is enlarged compared
to the conventional treatments of General Relativity (GR) by a canonical pair
that represents the metric density and its conjugate, removable by imposing
strongly an associated pair of second class constraints and introducing Dirac
brackets. The lapse and shift functions remain undetermined Lagrange
multipliers that enforce the diffeomorphism constraints in the standard form of
the NGT Hamiltonian. Thus the dimension of the physical constraint surface in
the symmetric sector is not enlarged over that of GR. In the antisymmetric
sector, all six components of the fundamental tensor contribute conjugate pairs
for the massive theory, and the absence of additional constraints gives six
configuration space degrees of freedom per spacetime point in the antisymmetric
sector. For the original NGT action (or, equivalently, Einstein's Unified Field
Theory), the U(1) invariance of the action is shown to remove one of these
antisymmetric sector conjugate pairs through an additional first class
constraint, leaving five degrees of freedom. The restriction of the dynamics to
GR configurations is considered, as well as the form of the surface terms that
a rise from the variation of the Hamiltonian. In the resulting Hamiltonian
system for the massive theory, singular behavior is found in the relations that
determine some of the Lagrange multipliers near GR and certain NGT spacetimes.
What this implies about the dynamics of the theory is not clearly understood at


title: Gauge Fields with Quasinilpotent Gauge Group

abstract:
  We investigate non-linear generalization of Maxwell theory of electromagnetic
field keeping the gauge invariance of Lagrangian. New theory, which is standard
Yang-Mills theory, is based on Harmonic Oscillator HO(4,R) gauge group. It's a
solvable Lie group with nilpotent normal subgroup of codimension 1. We write
down the Yang-Mills equation and point out their pecularities and connection
with standard Maxwell theory.


title: Solutions of Maxwell Equations for Hollow curved Wave Conductor

abstract:
  In the present paper the idea is proposed to solve Maxwell equations for a
curved hollow wave conductor by means of effective Riemannian space, in which
the lines of motion of fotons are isotropic geodesies for a 4-dimensional
space-time. The algorithm of constructing such a metric and curvature tensor
components are written down explicitly. The result is in accordance with
experiment.


title: Quenched Hawking Radiation and the Black Hole Pair-Creation Rate

abstract:
  The main topic of this talk is the Hawking effect when the black holes in
question are undergoing a uniform acceleration. The semiclassical effect of the
acceleration is most striking when the Hawking temperature equals the
acceleration temperature. Within the usual late-time approximation, the natural
black hole vacuum is then equivalent to the asymptotically empty Minkowskian
vacuum, and the accelerated black hole becomes semiclassically stable against
the familiar thermal evaporation. An important application of this phenomenon
is found in the problem of charged black hole pair-creation.


title:
Comment on the Calculation of the Angular Momentum and Mass for the
  (Anti-) Self Dual Charged Spinning $BTZ$ Black Hole

abstract:
  A recent paper [M. Kamata and T. Koikawa, Phys. Lett. {\bf B353} (1995) 196.]
claimed to obtain the charged version of the $(2+1)$-dimensional spinning $BTZ$
black hole solution by assuming a (anti-) self dual condition imposed on the
electric and magnetic fields. We point out that the angular momentum and mass
diverge at spatial infinity and as a consequence the solution is unphysical


title: Gravitational and electromagnetic fields of a charged tachyon

abstract:
  An axially symmetric exact solution of the Einstein-Maxwell equations is
obtained and is interpreted to give the gravitational and electromagnetic
fields of a charged tachyon. Switching off the charge parameter yields the
solution for the uncharged tachyon which was earlier obtained by Vaidya. The
null surfaces for the charged tachyon are discussed.


title: Energy and momentum of cylindrical gravitational waves. II

abstract:
  Recently Nathan Rosen and the present author obtained the energy and momentum
densities of cylindrical gravitational waves in Einstein's prescription and
found them to be finite and reasonable. In the present paper we calculate the
same in prescriptions of Tolman as well as Landau and Lifshitz and discuss the
results.


title: Geodesic and Path Motion in the Nonsymmetric Gravitational Theory

abstract:
  We study the problem of test-particle motion in the Nonsymmetric
Gravitational Theory (NGT) assuming the four-velocity of the particle is
parallel-transported along the trajectory. The predicted motion is studied on a
static, spherically symmetric background field, with particular attention paid
to radial and circular motions. Interestingly, it is found that the proper time
taken to travel between any two non-zero radial positions is finite. It is also
found that circular orbits can be supported at lower radii than in General
Relativity for certain forms of motion.
  We present three interactions which could be used as alternate methods for
coupling a test-particle to the antisymmetric components of the NGT field. One
of these takes the form of a Yukawa force in the weak-field limit of a static,
spherically symmetric field, which could lead to interesting phenomenology.


title:
A Bisognano-Wichmann-like Theorem in a Certain Case of a Non Bifurcate
  Event Horizon related to an Extreme Reissner-Nordstr\"om Black Hole

abstract:
  Thermal Wightman functions of a massless scalar field are studied within the
framework of a ``near horizon'' static background model of an extremal R-N
black hole. This model is built up by using global Carter-like coordinates over
an infinite set of Bertotti-Robinson submanifolds glued together. The
analytical extendibility beyond the horizon is imposed as constraints on
(thermal) Wightman's functions defined on a Bertotti-Robinson sub manifold. It
turns out that only the Bertotti-Robinson vacuum state, i.e. $T=0$, satisfies
the above requirement. Furthermore the extension of this state onto the whole
manifold is proved to coincide exactly with the vacuum state in the global
Carter-like coordinates. Hence a theorem similar to Bisognano-Wichmann theorem
for the Minkowski space-time in terms of Wightman functions holds with
vanishing ``Unruh-Rindler temperature''. Furtermore, the Carter-like vacuum
restricted to a Bertotti-Robinson region, resulting a pure state there, has
vanishing entropy despite of the presence of event horizons. Some comments on
the real extreme R-N black hole are given.


title:
Time and Time Functions in Parametrized Non-Relativistic Quantum
  Mechanics

abstract:
  The ``evolving constants'' method of defining the quantum dynamics of
time-reparametrization-invariant theories is investigated for a particular
implementation of parametrized non-relativistic quantum mechanics (PNRQM). The
wide range of time functions that are available to define evolving constants
raises issues of interpretation, consistency, and the degree to which the
resulting quantum theory coincides with, or generalizes, the usual
non-relativistic theory. The allowed time functions must be restricted for the
predictions of PNRQM to coincide with those of usual quantum theory. They must
be restricted to have a notion of quantum evolution in a time-parameter
connected to spacetime geometry. They must be restricted to prevent the theory
from making inconsistent predictions for the probabilities of histories.
Suitable restrictions can be introduced in PNRQM but these seem unlikely to
apply to a reparametrization invariant theory like general relativity.


title: Singularities in a Scalar Field Quantum Cosmology

abstract:
  The quantum theory of a spatially flat Friedmann-Robertson-Walker universe
with a massless scalar field as source is further investigated. The classical
model is singular, and in the framework of the Arnowitt-Deser-Misner canonical
quantization formalism a discussion is made of the cosmic evolution,
particularly of the quantum gravitational collapse problem. It is shown that in
a matter-time gauge such that time is identified with the scalar field the
classical model is singular either at $t=-\infty$ or at $t=+\infty$, but the
quantum model is nonsingular. The latter behavior disproves a conjecture
according to which quantum cosmological singularities are predetermined on the
classical level by the choice of time.


title: On the Obstructions to non-Cliffordian Pin Structures

abstract:
  We derive the topological obstructions to the existence of non-Cliffordian
pin structures on four-dimensional spacetimes. We apply these obstructions to
the study of non-Cliffordian pin-Lorentz cobordism. We note that our method of
derivation applies equally well in any dimension and in any signature, and we
present a general format for calculating obstructions in these situations.
Finally, we interpret the breakdown of pin structure and discuss the relevance
of this to aspects of physics.


title: Quantum Potential Approach to Class of Cosmological Models

abstract:
  In this paper we discuss the quantum potential approach of Bohm in the
context of quantum cosmological model. This approach makes it possible to
convert the wavefunction of the universe to a set of equations describing the
time evolution of the universe. Following Ashtekar et.\ al., we make use of
quantum canonical transformation to cast a class of quantum cosmological models
to a simple form in which they can be solved explicitly, and then we use the
solutions do recover the time evolution.


title: Quantization of 2+1 Gravity on the Torus

abstract:
  We use the polygon representation of 2+1--dimensional gravity to explicitly
carry out the canonical quantization of a universe with the topology of a
torus. The mapping-class-invariant wave function for a quantum ''big bounce'',
is reminiscent of the interference patterns of linear gratings. We consider the
``problem of time'' of quantum gravity: for one choice of internal time the
universe recovers a semiclassical interpretation after the bounce, with a wave
packet centered at a single geometry; for another choice of internal time, the
quantum solutions involve interference between macroscopically distinct
universes.


title:
Coincidence detection of broadband signals by networks of the planned
  interferometric gravitational wave detectors

abstract:
  We describe how the six planned detectors (2 LIGOs, VIRGO, GEO, AIGO, TAMA)
can be used to perform coincidence experiments for the detection of broadband
signals from either coalescing compact binaries or burst sources. We make
comparisons of the achievable sensitivities of these detectors under different
optical configurations and find that a meaningful coincidence experiment for
the detection of coalescing binary signals can only be performed by a network
where the LIGOs and VIRGO are operated in power recycling mode and other medium
scale detectors are operated in dual recycling mode. For the model of burst
waveform considered by us (i.e. uniform power upto 2000Hz), we find that the
relative sensitivity of the power-recycled VIRGO is quite high as compared to
others with their present design parameters and thus coincidence experiment
performed by including VIRGO in the network would not be a meaningful one. We
also calculate optimized values for the time-delay window sizes for different
possible networks. The effect of filtering on the calculation of thresholds has
also been discussed. We set the thresholds for different detectors and find out
the volume of sky that can be covered by different possible networks and the
corresponding rate of detection of coalescing binaries in the beginning of the
next century. We note that a coincidence experiment of power-recycled LIGOs and
VIRGO and dual-recycled GEO and AIGO can increase the volume of the sky covered
by 3.2 times as compared with only the power-recycled LIGO detectors and by 1.7
times the sky covered by the power-recycled LIGO-VIRGO network. These values
are far less than the range that can be covered by only the LIGO-VIRGO network
with dual recycling operation at a later stage, but the accuracy in the
determination of direction, distance and other source parameters will be much


title: Four Dimensional Elasticity and General Relativity

abstract:
  It has been shown that the extension of the elasticity theory in more than
three dimensions allows a description of space-time as a properly stressed
medium, even recovering the Minkowski metric in the case of uniaxial stress.
The fundamental equation for the metric in the theory is shown to be the
equilibrium equation for the medium. Examples of spherical and cylindrical
symmetries in four dimensions are considered, evidencing convergencies and
divergencies with the classical general relativity theory. Finally the possible
meaning of the dynamics of the four dimensional elastic medium is discussed.


title: Unified Analysis of Cosmological Perturbations in Generalized Gravity

abstract:
  In a class of generalized Einstein's gravity theories we derive the equations
and general asymptotic solutions describing the evolution of the perturbed
universe in unified forms. Our gravity theory considers general couplings
between the scalar field and the scalar curvature in the Lagrangian, thus
includes broad classes of generalized gravity theories resulting from recent
attempts for the unification. We analyze both the scalar-type mode and the
gravitational wave in analogous ways. For both modes the large scale evolutions
are characterized by the same conserved quantities which are valid in the
Einstein's gravity. This unified and simple treatment is possible due to our
proper choice of the gauges, or equivalently gauge invariant combinations.


title: Thermodynamic Features of Black Holes Dressed with Quantum Fields

abstract:
  The thermal properties of black holes in the presence of quantum fields can
be revealed through solutions of the semi-classical Einstein equation. We
present a brief but self-contained review of the main features of the
semi-classical back reaction problem for a black hole in the microcanonical
ensemble. The solutions, obtained for conformal scalars, massless spinors and
U(1) gauge bosons, are used to calculate the $O(\hbar)$ corrections to the
temperature and thermodynamical entropy of a Schwarzschild black hole. In each
spin case considered, the entropy corrections $\Delta S(r)$, are positive
definite and monotone increasing with increasing distance $r$ from the hole,
and are of the same order as the naive flat space radiation entropy.


title: Topology and Causal Structure

abstract:
  We investigate the causal structure of spacetimes $(M, g)$ for which the
metric $g$ is singular on a set of points.


title:
On the interpretation of time-reparametrization-invariant quantum
  mechanics

abstract:
  The classical and quantum dynamics of simple time-reparametrization-
invariant models containing two degrees of freedom are studied in detail.
Elimination of one ``clock'' variable through the Hamiltonian constraint leads
to a description of time evolution for the remaining variable which is
essentially equivalent to the standard quantum mechanics of an unconstrained
system. In contrast to a similar proposal of Rovelli, evolution is with respect
to the geometrical proper time, and the Heisenberg equation of motion is exact.
The possibility of a ``test clock'', which would reveal time evolution while
contributing negligibly to the Hamiltonian constraint is examined, and found to
be viable in the semiclassical limit of large quantum numbers.


title: Some applications of differential topology in general relativity

abstract:
  Recently, there have been several applications of differential and algebraic
topology to problems concerned with the global structure of spacetimes. In this
paper, we derive obstructions to the existence of spin-Lorentz and pin-Lorentz
cobordisms and we show that for compact spacetimes with non-empty boundary
there is no relationship between the homotopy type of the Lorentz metric and
the causal structure. We also point out that spin-Lorentz and tetrad cobordism
are equivalent. Furthermore, because the original work [7] on metric homotopy
and causality may not be known to a wide audience, we present an overview of
the results here.


title: Quantum information and information loss in General Relativity

abstract:
  When it comes to performing thought experiments with black holes,
Einstein-Bohr like discussions have to be re-opened. For instance one can ask
what happens to the quantum state of a black hole when the wave function of a
single ingoing particle is replaced by an other one that is orthogonal to the
first, while keeping the total energy and momentum unaffected. Observers at
$t\rightarrow\infty$ will not notice any difference, or so it seems in certain
calculational schemes.
  If one argues that this cannot be correct for the complete theory because a
black hole should behave in accordance with conventional quantum mechanics,
implying a unitary evolution, one is forced to believe that local quantum field
theory near the black hole horizon is very different from what had hitherto
been accepted. This would give us very valuable information concerning physics
in the Planck length region, notably a mathematical structure very close to
that of super string theory, but it does lead to conceptual difficulties.
  An approach that is somewhat related to this is to suspect a breakdown of
General Relativity for quantum mechanical systems. It is to some extent
unavoidable that Hilbert space is not invariant under general coordinate
transformations because such transformations add and remove some states.
Finally the cosmological constant problem also suggests that flat space-time
has some special significance in a quantum theory. We suggest that a new
causality principle could lead to further clues on how to handle this problem.


title:
Diffeomorphism invariant eigenvalue problem for metric perturbations in
  a bounded region

abstract:
  We suggest a method of construction of general diffeomorphism invariant
boundary conditions for metric fluctuations. The case of $d+1$ dimensional
Euclidean disk is studied in detail. The eigenvalue problem for the Laplace
operator on metric perturbations is reduced to that on $d$-dimensional vector,
tensor and scalar fields. Explicit form of the eigenfunctions of the Laplace
operator is derived. We also study restrictions on boundary conditions which
are imposed by hermiticity of the Laplace operator.


title: Signature Change at Material Layers and Step Potentials

abstract:
  For a contravariant 4-metric which changes signature from Lorentzian to
Riemannian across a spatial hypersurface, the mixed Einstein tensor is
manifestly non-singular. In Gaussian normal coordinates, the metric contains a
step function and the Einstein tensor contains the Dirac delta function with
support at the junction. The coefficient of the Dirac function is a linear
combination of the second fundamental form (extrinsic curvature) of the
junction. Thus, unless the junction has vanishing extrinsic curvature, the
physical interpretation of the metric is that it describes a layer of matter
(with stresses but no energy or momentum) at the junction. In particular, such
metrics do not satisfy the vacuum Einstein equations, nor the
Einstein-Klein-Gordon equations and so on. Similarly, the d'Alembertian of a
Klein-Gordon field contains the Dirac function with coefficient given by the
momentum of the field. Thus, if the momentum of the field does not vanish at
the junction, the physical interpretation is that there is a source (with step
potential) at the junction. In particular, such fields do not satisfy the
massless Klein-Gordon equation. These facts contradict claims in the
literature.


title: Cosmological perturbations and classical change of signature

abstract:
  Cosmological perturbations on a manifold admitting signature change are
studied. The background solution consists in a Friedmann-Lemaitre-Robertson-
Walker (FLRW) Universe filled by a constant scalar field playing the role of a
cosmological constant. It is shown that no regular solution exist satisfying
the junction conditions at the surface of change. The comparison with similar
studies in quantum cosmology is made.


title: Strong Decoherence

abstract:
  We introduce a condition for the strong decoherence of a set of alternative
histories of a closed quantum-mechanical system such as the universe. The
condition applies, for a pure initial state, to sets of homogeneous histories
that are chains of projections, generally branch-dependent. Strong decoherence
implies the consistency of probability sum rules but not every set of
consistent or even medium decoherent histories is strongly decoherent. Two
conditions characterize a strongly decoherent set of histories: (1) At any time
the operators that effectively commute with generalized records of history up
to that moment provide the pool from which -- with suitable adjustment for
elapsed time -- the chains of projections extending history to the future may
be drawn. (2) Under the adjustment process, generalized record operators acting
on the initial state of the universe are approximately unchanged. This
expresses the permanence of generalized records. The strong decoherence
conditions (1) and (2) guarantee what we call ``permanence of the past'' -- in
particular the continued decoherence of past alternatives as the chains of
projections are extended into the future. Strong decoherence is an idealization
capturing in a general way this and other aspects of realistic physical
mechanisms that destroy interference, as we illustrate in a simple model. We
discuss the connection between the reduced density matrices that have often
been used to characterize mechanisms of decoherence and the more general notion
of strong decoherence. The relation between strong decoherence and a measure of
classicality is briefly described.


title: Internal Time Formalism for Spacetimes with Two Killing Vectors

abstract:
  The Hamiltonian structure of spacetimes with two commuting Killing vector
fields is analyzed for the purpose of addressing the various problems of time
that arise in canonical gravity. Two specific models are considered: (i)
cylindrically symmetric spacetimes, and (ii) toroidally symmetric spacetimes,
which respectively involve open and closed universe boundary conditions. For
each model canonical variables which can be used to identify points of space
and instants of time, {\it i.e.}, internally defined spacetime coordinates, are
identified. To do this it is necessary to extend the usual ADM phase space by a
finite number of degrees of freedom. Canonical transformations are exhibited
that identify each of these models with harmonic maps in the parametrized field
theory formalism. The identifications made between the gravitational models and
harmonic map field theories are completely gauge invariant, that is, no
coordinate conditions are needed. The degree to which the problems of time are
resolved in these models is discussed.


title:
Chronology Protection and Quantized Fields: Complex Automorphic Scalar
  Field in Misner Space

abstract:
  The renormalized stress-energy tensor $\langle T_{\mu\nu}\rangle$ of the
quantized complex massless scalar field which obeys the automorphic condition
in Misner space is obtained. It is shown that there exists the special value of
the automorphic parameter for which $\langle T_{\mu\nu}\rangle$ is regular on
the chronology horizon and, so, can not act as a protector of chronology
through a back reaction on a spacetime metric. However, it is shown that, at
the same time, the value of field square $\langle\phi^2\rangle$, which
characterizes the quantum field fluctuations, is divergent on the chronology
horizon. The assumption is suggested that the infinitely growing quantum field
fluctuations, which appear if a (self)interaction of the scalar field is taken
into account, would prevent the chronology horizon formation.


title: Quantum Field Theory in Curved Spacetime

abstract:
  We review the mathematically rigorous formulation of the quantum theory of a
linear field propagating in a globally hyperbolic spacetime. This formulation
is accomplished via the algebraic approach, which, in essence, simultaneously
admits all states in all possible (unitarily inequivalent) Hilbert space
constructions. The physically nonsingular states are restricted by the
requirement that their two-point function satisfy the Hadamard condition, which
insures that the ultra-violet behavior of the state be similar to that of the
vacuum state in Minkowski spacetime, and that the expected stress-energy tensor
in the state be finite. We briefly review the Unruh and Hawking effects from
the perspective of the theoretical framework adopted here. A brief discussion
also is given of several open issues and questions in quantum field theory in
curved spacetime regarding the treatment of ``back-reaction", the validity of
some version of the ``averaged null energy condition'', and the formulation and
properties of quantum field theory in causality violating spacetimes.


title: $R + R^2$ Gravity as $R +$ Backreaction

abstract:
  Quadratic theory of gravity is a complicated constraint system. We
investigate some consequences of treating quadratic terms perturbatively
(higher derivative version of backreaction effects). This approach is shown to
overcome some well known problems associated with higher derivative theories,
i.e., the physical gravitational degree of freedom remains unchanged from those
of Einstein gravity.
  Using such an interpretation of $R + \beta R^2$ gravity, we investigate a
classical and Wheeler DeWitt evolution of $R + \beta R^2$ gravity for a
particular sign of $\beta$, corresponding to non- tachyon case. Matter is
described by a phenomenological $\rho \propto a(t)^{-n}$. It is concluded that
both the Friedmann potential $U(a)$ ($ {\dot a}^2 + 2U(a) = 0 $) and the
Wheeler DeWitt potential $W(a)$ ($\left[-{\partial^2\over \partial a^2} +
2W(a)\right]\psi (a) =0 $) develop repulsive barriers near $a\approx 0$ for
$n>4$ (i.e., $ p > {1\over 3}\rho $). The interpretations is clear. Repulsive
barrier in $U(a)$ implies that a contracting FRW universe ($k>0, k=0, k<0$)
will bounce to an expansion phase without a total gravitational collapse.
Repulsive barrier in $W(a)$ means that $a \approx 0$ is a classically forbidden
region. Therefore, probability of finding a universe with the big bang
singularity ($a=0$ ) is exponentially suppressed.


title: Implementing Markov's Limiting Curvature Hypothesis

abstract:
  The effective action for gravity at high curvatures is likely to contain
higher derivative terms. These corrections may have profound consequences for
the singularity structure of space-time and for early Universe cosmology. In
this contribution, recent work is reviewed which demonstrates that it is
possible to construct a class of effective gravitational actions for which all
solutions with sufficient symmetries have limited curvature and are
nonsingular. Near the limiting curvature, the coupling between matter and
gravity goes to zero and in this sense the theory is asymptotically free.


title: Gravitational scattering on a global monopole reexamined

abstract:
  We critically reexamine the gravitational scattering of scalar particles on a
global monopole studied recently. The original investigation of Mazur and
Papavassiliou is extended by considering different couplings of the scalar
field to the space-time curvature and by varying the dimension of the
space-time where the Klein-Gordon (KG) field lives. A universal behavior of the
leading term in the scattering amplitude as a function of this dimension is
revealed.


title: Is there analogy between quantized vortex and black hole?

abstract:
  An attempt is made to promote an analogy between quantized vortex in
condensed matter and black hole: both compact objects have fermion zero modes
which induce the finite temperature of these objects. The motion of the
quantized vortex lines in Fermi superfluids and superconductors leads to the
spectral flow of fermion zero mode. This results in finite temperature and
entropy of the moving vortex. The tunneling transition rate between the
fermionic levels under the influence of the vortex motion suggests the
effective temperature of the vortex core $T_{\rm eff}=(2/\pi) p_Fv_L$, where
$v_L$ is the velocity of the vortex with respect to the heat bath reference
frame and $p_F$ the Fermi momentum. This is an analogue of the Unruh
temperature of the accelerating object in the relativistic system. For the
vortex ring with the radius $R$ this leads to the Hawking type temperature
$T_{\rm vortex~ring}=(\hbar v_F / 2\pi R) \ln (R/r_c)$, where $v_F$ is the
Fermi velocity and $r_c$ is the radius of the vortex core. The corresponding
"Hawking" entropy of the vortex ring of radius $R$ and area $A=\pi R^2$ appears
to be ${\cal S}_{\rm vortex ~ring}=(1/6) A p_F^2$. Similar expression but with
different numerical factor is obtained for the instanton action for the quantum
nucleation of the vortex loop from the homogeneous vacuum, and also for the
"Bekenstein" entropy obtained by counting the number of fermionic bound states
which appear when the vortex loop is created. For the superfluid $^3$He-A,
where some components of the order parameter play the part of the gravitational
field, the Fermi momentum $p_F$ corresponds to the Planck scale for this
effective gravity. The effective action for the gravity field is obtained after
integration over the fermion fields in correspondence with the Sakharov


title: Stochastic Theory of Accelerated Detectors in a Quantum Field

abstract:
  We analyze the statistical mechanical properties of n-detectors in arbitrary
states of motion interacting with each other via a quantum field. We use the
open system concept and the influence functional method to calculate the
influence of quantum fields on detectors in motion, and the mutual influence of
detectors via fields. We discuss the difference between self and mutual
impedance and advanced and retarded noise. The mutual effects of detectors on
each other can be studied from the Langevin equations derived from the
influence functional, as it contains the backreaction of the field on the
system self-consistently. We show the existence of general fluctuation-
dissipation relations, and for trajectories without event horizons,
correlation-propagation relations, which succinctly encapsulate these quantum
statistical phenomena. These findings serve to clarify some existing confusions
in the accelerated detector problem. The general methodology presented here
could also serve as a platform to explore the quantum statistical properties of
particles and fields, with practical applications in atomic and optical physics
problems.


title: Nucleation of vacuum phase transitions by topological defects

abstract:
  The Euclidean action is calculated in the thin-wall approximation for a
first-order vacuum phase transition in which the bubble appears symmetrically
around either a global monopole or a gauge cosmic string. The bubble is assumed
to be much larger than the core size of the monopole or string. In both cases
the value of the Euclidean action is shown to be reduced below the $O(4)$
symmetric action value, indicating that the topological defects act as
effective nucleation sites for vacuum decay.


title:
Comment on Ricci Collineations of Static Spherically Symmetric
  Spacetimes

abstract:
  We present a counter example to a theorem given by Amir {\em et al.} J. Math.
Phys. {\bf 35}, 3005 (1994). We also comment on a misleading statements of the
same reference.


title:
Statistical Mechanics of Charged Particles in Einstein-Maxwell-Scalar
  Theory

abstract:
  We consider an $N$-body system of charged particle coupled to gravitational,
electromagnetic, and scalar fields. The metric on moduli space for the system
can be considered if a relation among the charges and mass is satisfied, which
includes the BPS relation for monopoles and the extreme condition for charged
black holes. Using the metric on moduli space in the long distance
approximation, we study the statistical mechanics of the charged particles at
low velocities. The partition function is evaluated as the leading order of the
large $d$ expansion, where $d$ is the spatial dimension of the system and will
be substituted finally as $d=3$.


title: Topology and Time Reversal

abstract:
  In this lecture we address some topological questions connected with the
existence on a general spacetime manifold of diffeomorphisms connected to the
identity which reverse the time-orientation.


title: On Quantum-Geometric Connections and Propagators in Curved Spacetime

abstract:
  The basic properties of Poincare gauge invariant Hilbert bundles over
Lorentzian manifolds are derived. Quantum connections are introduced in such
bundles, which govern a parallel transport that is shown to satisfy the strong
equivalence principle in the quantum regime. Path-integral expressions are
presented for boson propagators in Hilbert bundles over globally hyperbolic
curved spacetimes. Their Poincare gauge covariance is proven, and their special
relativistic limit is examined. A method for explicitly computing such
propagators is presented for the case of cosmological models with
Robertson-Walker metric.


title: Strong Energy Condition in $R + R^2$ Gravity

abstract:
  In this paper, we study Raychaudhuri's equation in the background of $R +
\beta R^2$ gravity with a phenomenological matter ($\rho \propto a(t)^{-n}$).
We conclude that even though the Strong Energy Condition (S.E.C.) for
Einstein's gravity, which guarantees singularity, is $n\geq 2$ for $\rho
\propto a(t)^{-n}$, a perturbative analysis of Raychaudhuri's equation in the
background of $R + \beta R^2$ gravity reveals that the big bang singularity may
not be guaranteed for $n > 4$. We derive the following Strong Energy Conditions
for $R + \beta R^2$ ($\beta \not= 0$):
  1) For $k<0$ FRW metric, S.E.C. is ($0\leq n\leq 4$)
  i.e., $-\rho_n \leq p_n \leq {1\over 3}\rho_n$.
  2) For $k=0$ FRW metric, S.E.C. is ( $1\leq n\leq 4$)
  i.e., $-{2\over 3}\rho_n \leq p_n \leq {1\over 3}\rho_n$.
  3) For $k>0$ FRW metric, S.E.C. is ($2\leq n\leq 4$)
  i.e., $-{1\over 3}\rho_n \leq p_n \leq {1\over 3}\rho_n$.


title: Solutions of the Einstein equations with matter

abstract:
  Recent results on solutions of the Einstein equations with matter are
surveyed and a number of open questions are stated. The first group of results
presented concern asymptotically flat spacetimes, both stationary and
dynamical. Then there is a discussion of solutions of the equations describing
matter in special relativity and Newtonian gravitational theory and their
relevance for general relativity. Next spatially compact solutions of the
Einstein-matter equations are presented. Finally some remarks are made on the
methods which have been used, and could be used in the future, to study
solutions of the Einstein equations with matter.


title:
Application of gradient expansion to non-linear gravitational wave in
  plane-symmetric universe

abstract:
  As an application of Gradient Expansion (long-wavelength) approximation, we
studied the inhomogeneous universe including the gravitational wave(GW). For a
plane-symmetric cosmological model, we could implement the 2nd order expansion
and analyze the purely non-linear perturbation of GW. The result indicates that
the non-linear effect plays an important role in anisotropic stage of the
universe. We also confirm that the perturbation from the linear source term in
gradient expansion is consistent with the result of linear perturbation.


title: Radiation from the extremal black holes

abstract:
  The radiation from extreme Reissner-Nordstr\"{o}m black holes is computed by
explicitly considering the collapse of a spherical charged shell. No neutral
scalar radiation is found but there is emission of charged particles, provided
the charge to mass ratio be different from one. The absence of thermal effects
is in accord with the predictions of the euclidean theory but since the body
emits charged particles the entropy issue is not the same as for eternal
extreme black holes.


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

abstract:
  Black hole solutions in the context of a generic matter-coupled
two-dimensional dilaton gravity theory are discussed both at the classical and
semiclassical level. Starting from general assumptions, a criterion for the
existence of black holes is given. The relationship between conformal anomaly
and Hawking radiation is extended to a broad class of two-dimensional dilaton
gravity models. A general and simple formula relating the magnitude of the
Hawking effect to the dilaton potential evaluated on the horizon is derived.


title: Normal frames for non-Riemannian connections

abstract:
  The principal properties of geodesic normal coordinates are the vanishing of
the connection components and first derivatives of the metric components at
some point. It is well-known that these hold only at points where the
connection has vanishing torsion and non-metricity. However, it is shown that
normal frames, possessing the essential features of normal coordinates, can
still be constructed when the connection is non-Riemannian.


title:
Simulations of Nonaxisymmetric Instability in a Rotating Star: A
  Comparison Between Eulerian and Smooth Particle Hydrodynamics

abstract:
  We have carried out 3-D numerical simulations of the dynamical bar
instability in a rotating star and the resulting gravitational radiation using
both an Eulerian code written in cylindrical coordinates and a smooth particle
hydrodynamics (SPH) code. The star is modeled initially as a polytrope with
index $n = 3/2$ and $T_{\rm rot}/|W| \approx 0.30$, where $T_{\rm rot}$ is the
rotational kinetic energy and $|W|$ is the gravitational potential energy. In
both codes the gravitational field is purely Newtonian, and the gravitational
radiation is calculated in the quadrupole approximation.
  We have run 3 simulations with the Eulerian code, varying the number of
angular zones and the treatment of the boundary between the star and the
vacuum. Using the SPH code we did 7 runs, varying the number of particles, the
artificial viscosity, and the type of initial model. We compare the growth rate
and rotation speed of the bar, the mass and angular momentum distributions, and
the gravitational radiation quantities. We highlight the successes and
difficulties of both methods, and make suggestions for future improvements.


title:
Killing vectors in asymptotically flat space-times: I. Asymptotically
  translational Killing vectors and the rigid positive energy theorem

abstract:
  We study Killing vector fields in asymptotically flat space-times. We prove
the following result, implicitly assumed in the uniqueness theory of stationary
black holes. If the conditions of the rigidity part of the positive energy
theorem are met, then in such space-times there are no asymptotically null
Killing vector fields except if the initial data set can be embedded in
Minkowski space-time. We also give a proof of the non-existence of non-singular
(in an appropriate sense) asymptotically flat space-times which satisfy an
energy condition and which have a null ADM four-momentum, under conditions
weaker than previously considered.


title:
Hessling's Quantum Equivalence Principle and the Temperature of an
  Extremal Reissner-Nordstr\"{o}m Black Hole

abstract:
  The Hessling improvement of the Haag, Narnhofer and Stein principle is
analysed in the case of a massless scalar field propagating outside of an
extremal R-N black hole. It is found that this sort of ``Quantum (Einstein's)
Equivalence Principle'' selects only the R-N vacuum as a physically sensible
state, i.e., it selects the temperature $T=0$ only.


title:
Scale Factor Duality and Hidden Supersymmetry in Scalar--Tensor
  Cosmology

abstract:
  It is shown that spatially flat, isotropic cosmologies derived from the
Brans--Dicke gravity action exhibit a scale factor duality invariance. This
classical duality is then associated with a hidden $N=2$ supersymmetry at the
quantum level and the supersymmetric quantum constraints are solved exactly.
These symmetries also apply to a dimensionally reduced version of vacuum
Einstein gravity.


title: Photon propagation in a stationary warp drive space-time

abstract:
  We simplify the warp drive space-time so that it becomes stationary and the
distorsion becomes one-dimensional and static. We use this simplified warp
drive space-time as a background for a photon field. We shall especially use
the Drummond\&Hathrell action in order to investigate the velocity effects on
photons in this background. Finally, we discuss the limitations of this model.


title: Multi-plaquette solutions for discretized Ashtekar gravity

abstract:
  A discretized version of canonical quantum gravity proposed by Loll is
investigated. After slightly modifying Loll's discretized Hamiltonian
constraint, we encode its action on the spin network states in terms of
combinatorial topological manipulations of the lattice loops. Using this
topological formulation we find new solutions to the discretized Wheeler-Dewitt
equation. These solutions have their support on the connected set of
plaquettes. We also show that these solutions are not normalizable with respect
to the induced heat-kernel measure on $SL(2,{\bf C})$ gauge theories.


title: Essential self-adjointness in one-loop quantum cosmology

abstract:
  The quantization of closed cosmologies makes it necessary to study squared
Dirac operators on closed intervals and the corresponding quantum amplitudes.
This paper proves self-adjointness of these second-order elliptic operators.


title: Dilaton Gravity with a Non-Minimally Coupled Scalar Field

abstract:
  We discuss the two-dimensional dilaton gravity with a scalar field as the
source matter. The coupling between the gravity and the scalar, massless, field
is presented in an unusual form. We work out two examples of these couplings,
and solutions with black-hole behaviour are discussed and compared with those
found in the literature.


title: The Group of Large Diffeomorphisms in General Relativity

abstract:
  We investigate the group of large diffeomorphisms fixing a frame at a point
for general closed 3-manifolds. We derive some general structural properties of
these groups which relate to the picture of the manifold as being composed of
extended `objects' (geons).


title:
Mass Superselection, Canonical Gauge Transformations, and Asymptotically
  Flat Variational Principles

abstract:
  The phase space reduction of Schwarzschild black holes by Thiemann and
Kastrup and by Kucha\v{r} is reexamined from a different perspective on gauge
freedom. This perspective introduces additional gauge transformations which
correspond to asymptotically nontrivial diffeomorphisms. Various subtleties
concerning variational principles for asymptotically flat systems are addressed
which allow us to avoid the usual conclusion that treating such transformations
as gauge implies the vanishing of corresponding total charges. Instead,
superselection rules are found for the (nonvanishing) ADM mass at the
asymptotic boundaries. The addition of phenomenological clocks at each
asymptotic boundary is also studied and compared with the `parametrization
clocks' of Kucha\v{r}.


title: Is there a problem with quantum wormhole states in N=1 Supergravity?

abstract:
  The issue concerning the existence of wormhole states in locally
supersymmetric minisuperspace models with matter is addressed. Wormhole states
are apparently absent in models obtained from the more general theory of N=1
supergravity with supermatter. A Hartle-Hawking type solution can be found,
even though some terms (which are scalar field dependent) cannot be determined
in a satisfactory way. A possible cause is investigated here. As far as the
wormhole situation is concerned, we argue here that the type of Lagrange
multipliers and fermionic derivative ordering used can make a difference. A
proposal is made for supersymmetric quantum wormholes to also be invested with
a Hilbert space structure, associated with a maximal analytical extension of
the corresponding minisuperspace.is concerned, we argue here that the type of
Lagrange multipliers and fermionic derivative ordering used can make a
difference. A proposal is made for supersymmetric quantum wormholes to also be
invested with a Hilbert space structure, associated with a maximal analytical
extension of the corresponding minisuperspace.


title: Spinning charged BTZ black holes and self-dual particle-like solutions

abstract:
  We generate from the static charged BTZ black hole a family of spinning
charged solutions to the Einstein-Maxwell equations in 2+1 dimensions. These
solutions go over, in a suitable limit, to self-dual spinning charged
solutions, which are horizonless and regular, with logarithmically divergent
mass and spin. To cure this divergence, we add a topological Chern-Simons term
to the gauge field action. The resulting self-dual solution is horizonless,
regular, and asymptotic to the extreme BTZ black hole.


title: Expansion of Bubbles in Inflationary Universe

abstract:
  We show that particle production during the expansion of bubbles of true
vacuum in the sea of false vacuum is possible and calculate the resulting rate.
As a result the nucleated bubbles cannot expand due to the transfer of false
vacuum energy to the created particles inside the bubbles. Therefore all the
inflationary models dealing with the nucleation and expansion of the bubbles
(including extended inflation) may not be viable.


title:
Classical and Quantum Solutions and the Problem of Time in $R^2$
  Cosmology

abstract:
  We have studied various classical solutions in $R^2$ cosmology. Especially we
have obtained general classical solutions in pure $R^2$\ cosmology. Even in the
quantum theory, we can solve the Wheeler-DeWitt equation in pure $R^2$\
cosmology exactly. Comparing these classical and quantum solutions in $R^2$\
cosmology, we have studied the problem of time in general relativity.


title:
The symplectic geometry of a parametrized scalar field on a curved
  background

abstract:
  We study the real, massive Klein-Gordon field on a $C^\infty$
globally-hyperbolic background space-time with compact Cauchy hypersurfaces. In
particular, the parametrization of this system as initiated by Dirac and
Kucha\v{r} is put on a rigorous basis. The discussion is focussed on the
structure of the set of spacelike embeddings of the Cauchy manifold into the
space-time, and on the associated $e$-tensor density bundles and their tangent
and cotangent bundles. The dynamics of the field is expressed as a set of
automorphisms of the space of initial data in which each pair of embeddings
defines one such automorphism. Using these results, the extended phase space of
the system is shown to be a weak-symplectic manifold, and the Kucha\v{r}
constraint is shown to define a smooth constraint submanifold which is foliated
smoothly by the constraint orbits. The pull-back of the symplectic form to the
constraint surface is a presymplectic form which is singular on the tangent
spaces to the constraint orbits. Thus, the geometric structure of this
infinite-dimensional system is analogous to that of a finite-dimensional,
first-class parametrized system, and hence many of the results for the latter
can be transferred to the infinite-dimensional case without difficulty.


title: The Solar Test of the Equivalence Principle

abstract:
  The Earth, Mars, Sun, Jupiter system allows for a sensitive test of the
strong equivalence principle (SEP) which is qualitatively different from that
provided by Lunar Laser Ranging. Using analytic and numerical methods we
demonstrate that Earth-Mars ranging can provide a useful estimate of the SEP
parameter $\eta$. Two estimates of the predicted accuracy are derived and
quoted, one based on conventional covariance analysis, and another (called
``modified worst case'' analysis) which assumes that systematic errors dominate
the experiment. If future Mars missions provide ranging measurements with an
accuracy of $\sigma$ meters, after ten years of ranging the expected accuracy
for the SEP parameter $\eta$ will be of order $(1-12)\times 10^{-4}\sigma$.
These ranging measurements will also provide the most accurate determination of
the mass of Jupiter, independent of the SEP effect test.


title:
Minisuperspace Examples of Quantization Using Canonical Variables of the
  Ashtekar Type: Structure and Solutions

abstract:
  The Ashtekar variables have been use to find a number of exact solutions in
quantum gravity and quantum cosmology. We investigate the origin of these
solutions in the context of a number of canonical transformations (both complex
and real) of the basic Hamiltonian variables of general relativity. We are able
to present several new solutions in the minisuperspace (quantum cosmology)
sector. The meaning of these solutions is then discussed.


title: Energy extremality in the presence of a black hole

abstract:
  We derive the so-called first law of black hole mechanics for variations
about stationary black hole solutions to the Einstein--Maxwell equations in the
absence of sources. That is, we prove that $\delta M=\kappa\delta
A+\omega\delta J+VdQ$ where the black hole parameters $M, \kappa, A, \omega, J,
V$ and $Q$ denote mass, surface gravity, horizon area, angular velocity of the
horizon, angular momentum, electric potential of the horizon and charge
respectively. The unvaried fields are those of a stationary, charged, rotating
black hole and the variation is to an arbitrary `nearby' black hole which is
not necessarily stationary. Our approach is 4-dimensional in spirit and uses
techniques involving Action variations and Noether operators. We show that the
above formula holds on any asymptotically flat spatial 3-slice which extends
from an arbitrary cross-section of the (future) horizon to spatial
infinity.(Thus, the existence of a bifurcation surface is irrelevant to our
demonstration. On the other hand, the derivation assumes without proof that the
horizon possesses at least one of the following two (related)properties: ($i$)
it cannot be destroyed by arbitrarily small perturbations of the metric and
other fields which may be present, ($ii$) the expansion of the null geodesic
generators of the perturbed horizon goes to zero in the distant future.)


title: Quantum Origin of the Early Universe and the Energy Scale of Inflation

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


title: Against the Wheeler-DeWitt equation

abstract:
  The ADM approach to canonical general relativity combined with Dirac's method
of quantizing constrained systems leads to the Wheeler-DeWitt equation. A
number of mathematical as well as physical difficulties that arise in
connection with this equation may be circumvented if one employs a covariant
Hamiltonian method in conjunction with a recently developed, mathematically
rigorous technique to quantize constrained systems using Rieffel induction. The
classical constraints are cleanly separated into four components of a covariant
momentum map coming from the diffeomorphism group of spacetime, each of which
is linear in the canonical momenta, plus a single finite-dimensional quadratic
constraint that arises in any theory, parametrized or not. The new quantization
method is carried through in a minisuperspace example, and is found to produce
a ``wavefunction of the universe". This differs from the proposals of both
Vilenkin and Hartle-Hawking for a closed FRW universe, but happens to coincide
with the latter in the open case.


title:
Perennials and the Group-Theoretical Quantization of a Parametrized
  Scalar Field on a Curved Background

abstract:
  The perennial formalism is applied to the real, massive Klein-Gordon field on
a globally-hyperbolic background space-time with compact Cauchy hypersurfaces.
The parametrized form of this system is taken over from the accompanying paper.
Two different algebras ${\cal S}_{\text{can}}$ and ${\cal S}_{\text{loc}}$ of
elementary perennials are constructed. The elements of ${\cal S}_{\text{can}}$
correspond to the usual creation and annihilation operators for particle modes
of the quantum field theory, whereas those of ${\cal S}_{\text{loc}}$ are the
smeared fields. Both are shown to have the structure of a Heisenberg algebra,
and the corresponding Heisenberg groups are described. Time evolution is
constructed using transversal surfaces and time shifts in the phase space.
Important roles are played by the transversal surfaces associated with
embeddings of the Cauchy hypersurface in the space-time, and by the time shifts
that are generated by space-time isometries. The automorphisms of the algebras
generated by this particular type of time shift are calculated explicitly.


title: Comment on "Quantum bound states with zero binding energy"

abstract:
  The purpose of this Comment is to show that the solutions to the zero energy
Schr\"odinger equations for monomial central potentials discussed in a recently
published Letter, may also be obtained from the corresponding free particle
solutions in a straight forwardly way, using an algorithm previously devised by
us. New solutions to the zero energy Schr\"odinger equation are also exhibited.


title: How short can the hair of a black hole be?

abstract:
  We show that in all theories in which black hole hair has been discovered,
the region with non-trivial structure of the non-linear matter fields must
extend beyond $3/ 2$ the horizon radius, independently of all other parameters
present in the theory. We argue that this is a universal lower bound that
applies in every theory where hair is present. This {\it no short hair
conjecture} is then put forward as a more modest alternative to the now
debunked {\it no hair conjecture}.


title:
Conformal Decomposition of the Effective Action and Covariant Curvature
  Expansion

abstract:
  The class of effective actions exactly reproducing the conformal anomaly in
4D is considered. It is demonstrated that the freedom within this class can be
fixed by the choice of the conformal gauge. The conformal invariant part of the
generic one-loop effective action expanded in the covariant series up to third
order in the curvature is rewritten in the new conformal basis. The possible
applications of the obtained results are discussed.


title:
Quantum Field Theory at Finite Temperature and Cosmological
  Perturbations

abstract:
  It is shown how quantum field theory at finite temperature can be used to set
up self-consistent and gauge invariant equations for cosmological perturbations
sustained by an ultrarelativistic plasma. While in the collisionless case, the
results are equivalent to those obtained from the Einstein-Vlasov equations,
weak self-interactions in the plasma turn out to require the full machinery of
perturbative thermal field theories such as resummation of hard thermal loops.
Nevertheless it is still possible to use the same methods that yielded exact
solutions in the collisionless case.


title:
Comments on ''The Principle of Self-Consistency as a consequence of the
  Principle of Minimal Action''

abstract:
  The so called ''Principle of the self-consistency'' for space-time models
with causality violation, which was firstly formulated by I.D.Novikov, is
discussed for the test particle motion and for test scalar field. It is shown
that the constraints, which provide the self-concistensy of test particle
motion have pure geometrical (topological) nature. So, the recent statement
that ''The Principle of self-consistensy is a consiquence of the Principle of
minimal action'' is wrong.


title:
Covariant double-null dynamics: $(2+2)$-splitting of the Einstein
  equations

abstract:
  The paper develops a $(2+2)$-imbedding formalism adapted to a double
foliation of spacetime by a net of two intersecting families of lightlike
hypersurfaces. The formalism is two-dimensionally covariant, and leads to
simple, geometrically transparent and tractable expressions for the Einstein
field equations and the Einstein-Hilbert action, and it should find a variety
of applications. It is applied here to elucidate the structure of the
characteristic initial-value problem of general relativity.


title: The Oscillating Universe: an Alternative to Inflation

abstract:
  The aim of this paper is to show, that the 'oscillating universe' is a viable
alternative to inflation. We remind that this model provides a natural solution
to the flatness or entropy and to the horizon problem of standard cosmology. We
study the evolution of density perturbations and determine the power spectrum
in a closed universe. The results lead to constraints of how a previous cycle
might have looked like. We argue that most of the radiation entropy of the
present universe may have originated from gravitational entropy produced in a
previous cycle.
  We show that measurements of the power spectrum on very large scales could in
principle decide whether our universe is closed, flat or open.


title: Class of Einstein--Maxwell Dilatons

abstract:
  Three different classes of static solutions of the Einstein--Maxwell
equations non--minimally coupled to a dilaton field are presented. The
solutions are given in general in terms of two arbitrary harmonic functions and
involve among others an arbitrary parameter which determines their
applicability as charged black holes, dilaton black holes or strings. Most of
the known solutions are contained as special cases and can be non--trivially
generalized in different ways.


title: Newman-Penrose Formalism for Gravitational Shock Waves

abstract:
  First order perturbations for the fields with spin on the background metric
of the gravitational shock waves are discussed. Applying the Newman -- Penrose
formalism, exact solutions of the perturbation equations are obtained. For
particle physics, this would be one approach to the problem of scattering
paticle at Planck energy.


title: The Covariant Approach to LRS Perfect Fluid Spacetime Geometries

abstract:
  The dynamics of perfect fluid spacetime geometries which exhibit {\em Local
Rotational Symmetry} (LRS) are reformulated in the language of a $1+\,3$
"threading" decomposition of the spacetime manifold, where covariant fluid and
curvature variables are used. This approach presents a neat alternative to the
orthonormal frame formalism. The dynamical equations reduce to a set of
differential relations between purely scalar quantities. The consistency
conditions are worked out in a transparent way. We discuss their various
subcases in detail and focus in particular on models with higher symmetries
within the class of expanding spatially inhomogeneous LRS models, via a
consideration of functional dependencies between the dynamical variables.


title: Gravity, Gauges and Clocks

abstract:
  We discuss the definitions of standard clocks in theories of gravitation.
These definitions are motivated by the invariance of actions under different
gauge symmetries. We contrast the definition of a standard Weyl clock with that
of a clock in general relativity and argue that the historical criticisms of
theories based on non-metric compatible connections by Einstein, Pauli and
others must be considered in the context of Weyl's original gauge symmetry. We
argue that standard Einsteinian clocks can be defined in non-Riemannian
theories of gravitation by adopting the Weyl group as a local gauge symmetry
that {\it preserves the metric} and discuss the hypothesis that atomic clocks
may be adopted to measure proper time in the presence of non-Riemannian
gravitational fields. These ideas are illustrated in terms of a recently
developed model of gravitation based on a non-Riemannian space-time geometry.


title:
The dynamics of cosmological perturbations in thermal $\lambda\phi^4$
  theory

abstract:
  Using a recent thermal-field-theory approach to cosmological perturbations,
the exact solutions that were found for collisionless ultrarelativistic matter
are generalized to include the effects from weak self-interactions in a
$\lambda\phi^4$ model through order $\lambda^{3/2}$. This includes the effects
of a resummation of thermal masses and associated nonlocal gravitational
vertices, thus going far beyond classical kinetic theory. Explicit solutions
for all the scalar, vector, and tensor modes are obtained for a
radiation-dominated Einstein-de Sitter model containing a weakly interacting
scalar plasma with or without the admixture of an independent component of
perfect radiation fluid.


title: Asymptotically anti-de Sitter wormholes

abstract:
  Starting with a procedure for dealing with general asymptotic behaviors, we
construct a quantum theory for asymptotically anti-de Sitter wormholes. We
follow both the path integral formalism and the algebraic quantization program
proposed by Ashtekar. By adding suitable surface terms, the Euclidean action of
the asymptoically anti-de Sitter wormholes can be seen to be finite and gauge
invariant. This action determines an appropriate variational problem for
wormholes. We also obtain the wormhole wave functions of the gravitational
model and show that all the physical states of the quantum theory are
superpositions of wormhole states.


title:
Hamiltonian thermodynamics of two-dimensional vacuum dilatonic black
  holes

abstract:
  We consider the Hamiltonian dynamics and thermodynamics of the
two-dimensional vacuum dilatonic black hole in the presence of a timelike
boundary with a fixed value of the dilaton field. A~canonical transformation,
previously developed by Varadarajan and Lau, allows a reduction of the
classical dynamics into an unconstrained Hamiltonian system with one canonical
pair of degrees of freedom. The reduced theory is quantized, and a partition
function of a canonical ensemble is obtained as the trace of the analytically
continued time evolution operator. The partition function exists for any values
of the dilaton field and the temperature at the boundary, and the heat capacity
is always positive. For temperatures higher than $\beta_c^{-1} =
\hbar\lambda/(2\pi)$, the partition function is dominated by a classical black
hole solution, and the dominant contribution to the entropy is the
two-dimensional Bekenstein-Hawking entropy. For temperatures lower
than~$\beta_c^{-1}$, the partition function remains well-behaved and the heat
capacity is positive in the asymptotically flat space limit, in contrast to the
corresponding limit in four-dimensional spherically symmetric Einstein gravity;
however, in this limit, the partition function is not dominated by a classical
black hole solution.


title: Second order perturbations of a Schwarzschild black hole

abstract:
  We study the even-parity $\ell=2$ perturbations of a Schwarzschild black hole
to second order. The Einstein equations can be reduced to a single linear wave
equation with a potential and a source term. The source term is quadratic in
terms of the first order perturbations. This provides a formalism to address
the validity of many first order calculations of interest in astrophysics.


title: The Kauffman bracket and the Jones polynomial in quantum gravity

abstract:
  An analysis of the action of the Hamiltonian constraint of quantum gravity on
the Kauffman bracket and Jones knot polynomials is proposed. It is explicitely
shown that the Kauffman bracket is a formal solution of the Hamiltonian
constraint with cosmological constant ($\Lambda$) to third order in $\Lambda$.
The calculation is performed in the extended loop representation of quantum
gravity. The analysis makes use of the analytical expressions of the knot
invariants in terms of the two and three point propagators of the Chern-Simons
theory. Some particularities of the extended loop calculus are considered and
the implications of the results to the case of the conventional loop
representation are discussed.


title:
Is the third coefficient of the Jones knot polynomial a quantum state of
  gravity?

abstract:
  Some time ago it was conjectured that the coefficients of an expansion of the
Jones polynomial in terms of the cosmological constant could provide an
infinite string of knot invariants that are solutions of the vacuum Hamiltonian
constraint of quantum gravity in the loop representation. Here we discuss the
status of this conjecture at third order in the cosmological constant. The
calculation is performed in the extended loop representation, a generalization
of the loop representation. It is shown that the the Hamiltonian does not
annihilate the third coefficient of the Jones polynomal ($J_3$) for general
extended loops. For ordinary loops the result acquires an interesting
geometrical meaning and new possibilities appear for $J_3$ to represent a
quantum state of gravity.


title:
Junctions and thin shells in general relativity using computer algebra
  I: The Darmois-Israel Formalism

abstract:
  We present the GRjunction package which allows boundary surfaces and
thin-shells in general relativity to be studied with a computer algebra system.
Implementing the Darmois-Israel thin shell formalism requires a careful
selection of definitions and algorithms to ensure that results are generated in
a straight-forward way. We have used the package to correctly reproduce a wide
variety of examples from the literature. We present several of these
verifications as a means of demonstrating the packages capabilities. We then
use GRjunction to perform a new calculation - joining two Kerr solutions with
differing masses and angular momenta along a thin shell in the slow rotation
limit.


title: Using the Uncharged Kerr Black Hole as a Gravitational Mirror

abstract:
  We extend the study of the possibility to use the Schwarzschild black hole as
a gravitational mirror to the more general case of an uncharged Kerr black
hole. We use the null geodesic equation in the equatorial plane to prove a
theorem concerning the conditions the impact parameter has to satisfy if there
shall exist boomerang photons. We derive an equation for these boomerang
photons and an equation for the emission angle. Finally, the radial null
geodesic equation is integrated numerically in order to illustrate boomerang
photons.


title: Uncertainties of predictions in models of eternal inflation

abstract:
  In a previous paper \cite{MakingPredictions}, a method of comparing the
volumes of thermalized regions in eternally inflating universe was introduced.
In this paper, we investigate the dependence of the results obtained through
that method on the choice of the time variable and factor ordering in the
diffusion equation that describes the evolution of eternally inflating
universes. It is shown, both analytically and numerically, that the variation
of the results due to factor ordering ambiguity inherent in the model is of the
same order as their variation due to the choice of the time variable.
Therefore, the results are, within their accuracy, free of the spurious
dependence on the time parametrization.


title:
Principle of Mach, the Equivalence Principle and concepts of inertial
  mass

abstract:
  A study of kinematics of a 2-body system is used to show that the Mach
principle, previously rejected by general relativity, can still serve as an
alternative to the concept of absolute space, if one takes into account that
the background of distant stars (galaxies) determines {\it both} the inertial
and the gravitational masses of a body.


title:
The microlocal spectrum condition and Wick polynomials of free fields on
  curved spacetimes

abstract:
  Quantum fields propagating on a curved spacetime are investigated in terms of
microlocal analysis. We discuss a condition on the wave front set for the
corresponding n-point distributions, called ``microlocal spectrum condition''
($\mu$SC). On Minkowski space, this condition is satisfied as a consequence of
the usual spectrum condition. Based on Radzikowski's determination of the wave
front set of the two-point function of a free scalar field, satisfying the
Hadamard condition in the Kay and Wald sense, we construct in the second part
of this paper all Wick polynomials including the energy-momentum tensor for
this field as operator valued distributions on the manifold and prove that they
satisfy our microlocal spectrum condition.


title:
Evolution of Intra-Cavity Fields at Non-Steady State in Dual Recycled
  Interferometer

abstract:
  We describe how exactly the intra-cavity fields in a dual recycling cavity
build up their power before achieving a steady state value. We restricted our
analysis here to interferometers with lossless mirrors and beam-splitter. The
complete series representation of the intra-cavity lights at any stage of
evolution in non-steady state have been presented.


title: Long Range Effects of Cosmic String Structure

abstract:
  We combine and further develop ideas and techniques of Allen \& Ottewill,
Phys. Rev.D, {\bf 42}, 2669 (1990) and Kay \& Studer Commun. Math. Phys., {\bf
139}, 103 (1991) for calculating the long range effects of cosmic string cores
on classical and quantum field quantities far from an (infinitely long,
straight) cosmic string. We find analytical approximations for (a) the
gravity-induced ground state renormalized expectation values of $\hat\varphi^2$
and $\hat T_\mu{}^\nu$ for a non-minimally coupled quantum scalar field far
from a cosmic string (b) the classical electrostatic self force on a test
charge far from a superconducting cosmic string. Surprisingly -- even at
cosmologically large distances -- all these quantities would be very badly
approximated by idealizing the string as having zero thickness and imposing
regular boundary conditions; instead they are well approximated by suitably
fitted strengths of logarithmic divergence at the string core. Our formula for
${\langle {\hat \varphi}^2 \rangle}$ reproduces (with much less effort and much
more generality) the earlier numerical results of Allen \& Ottewill. Both
${\langle {\hat \varphi}^2 \rangle}$ and ${\langle {\hat T}_{\mu}{}^{\nu}
\rangle}$ turn out to be ``weak field topological invariants'' depending on the
details of the string core only through the minimal coupling parameter
``$\xi$'' (and the deficit angle). Our formula for the self-force (leaving
aside relatively tiny gravitational corrections) turns out to be attractive: We
obtain, for the self-potential of a test charge $Q$ a distance $r$ from a (GUT
scale) superconducting string, the formula $- Q^2/(16\epsilon_0r\ln(qr))$ where
$q$ is an (in principle, computable) constant of the order of the inverse
string radius.


title: Multidimensional generalization of Kasner solution

abstract:
  Full generalization of Kasner metric for the case of $n+1$ dimensions and
$m\le n+1$ essential variables is obtained. Any solution is defined by the
corresponding constant matrix of Kasner parameters. This parameters form in
euclidian space Casner hyperspheres and are connected by additional conditions.
General properties of obtained solutions are analyzed.


title: Lovelock Tensor as Generalized Einstein Tensor

abstract:
  We show that the splitting feature of the Einstein tensor, as the first term
of the Lovelock tensor, into two parts, namely the Ricci tensor and the term
proportional to the curvature scalar, with the trace relation between them is a
common feature of any other homogeneous terms in the Lovelock tensor. Motivated
by the principle of general invariance, we find that this property can be
generalized, with the aid of a generalized trace operator which we define, for
any inhomogeneous Euler-Lagrange expression that can be spanned linearly in
terms of homogeneous tensors. Then, through an application of this generalized
trace operator, we demonstrate that the Lovelock tensor analogizes the
mathematical form of the Einstein tensor, hence, it represents a generalized
Einstein tensor. Finally, we apply this technique to the scalar Gauss-Bonnet
gravity as an another version of string-inspired gravity.


title:
Stress-Energy-Momentum Tensors in Lagrangian Field Theory. Part 1.
  Superpotentials

abstract:
  Differential conservation laws in Lagrangian field theory are usually related
to symmetries of a Lagrangian density and are obtained if the Lie derivative of
a Lagrangian density by a certain class of vector fields on a fiber bundle
vanishes. However, only two field models meet this property in fact. In gauge
theory of exact internal symmetries, the Lie derivative by vertical vector
fields corresponding to gauge transformations is equal to zero. The
corresponding N\"oether current is reduced to a superpotential that provides
invariance of the N\"oether conservation law under gauge transformations. In
the gravitation theory, we meet the phenomenon of "hidden energy". Only the
superpotential part of energy-momentum of gravity and matter is observed when
the general covariant transformations are exact. Other parts of energy-momentum
display themselves if the invariance under general covariance transformations
is broken, e.g., by a background world metric. In this case, the Lie
derivatives of Lagrangian densities by vector fields which call into play the
stress-energy-momentum tensors fail to be equal to zero in general. We base our
analysis of differential conservation laws on the canonical decomposition of
the Lie derivative of a Lagrangian density $L$ by a projectable vector field on
a bundle and with respect to different Lepagian equivalents of $L$. Different
Lepagian equivalents lead to conserved quantities which differ from each other
in superpotential terms. We have different stress-energy-momentum tensors
depending on different lifts of vector fields on a base onto a bundle.
Moreover, different solutions of the same Euler-Lagrange equations may require
different energy-momentum tensors. We show that different
stress-energy-momentum tensors differ from each other in N\"oether currents. As


title: Classical mechanics with lapse

abstract:
  Mechanics is developed over a differentiable manifold as space of possible
positions. Time is considered to fill a one--dimensional Riemannian manifold,
so having the metric as lapse. Then the system is quantized with covariant
instead of partial derivatives in the Schr\"odinger operator. Consequences for
quantum cosmology are shortly discussed.


title: Structural Issues in Quantum Gravity

abstract:
  A discursive, non-technical, analysis is made of some of the basic issues
that arise in almost any approach to quantum gravity, and of how these issues
stand in relation to recent developments in the field. Specific topics include
the applicability of the conceptual and mathematical structures of both
classical general relativity and standard quantum theory. This discussion is
preceded by a short history of the last twenty-five years of research in
quantum gravity, and concludes with speculations on what a future theory might
look like.


title:
Time-Symmetrization and Isotropization of Stiff-Fluid Kantowski-Sachs
  Universes

abstract:
  It is shown that growing-entropy stiff-fluid Kantowski-Sachs universes become
time-symmetric (if they start with time-asymmetric phase) and isotropize.
Isotropization happens without any inflationary era during the evolution since
there is no cosmological term here. It seems that this approach is an
alternative to inflation since the universe gets bigger and bigger approaching
'flatness'.


title:
Hamiltonian Formulation of Bianchi Cosmological Models in Quadratic
  Theories of Gravity

abstract:
  We use Boulware's Hamiltonian formalism of quadratic gravity theories in
order to analyze the classical behaviour of Bianchi cosmological models for a
Lagrangian density containing quadratic terms in the curvature. For this
purpose we define a canonical transformation which leads to a clear distinction
between two main variants of the quadratic theory, namely the R-squared or
conformal Lagrangian densities. In this paper we restrict the study to the
first variant. For Bianchi type I and IX models we give the explicit forms of
the super-Hamiltonian constraint, of the ADM Hamiltonian density and of the
corresponding canonical equations. In the case of a pure R-squared theory we
solve these equations analytically for Bianchi I model. For Bianchi type IX
model, we reduce the first-order equations of the Hamiltonian system to three
coupled second-order equations for the true physical degrees of freedom. This
discussion is extended to isotropic FLRW models.