title: Energy conservation for point particles undergoing radiation reaction

abstract:
  For smooth solutions to Maxwell's equations sourced by a smooth
charge-current distribution $j_a$ in stationary, asymptotically flat
spacetimes, one can prove an energy conservation theorem which asserts the
vanishing of the sum of (i) the difference between the final and initial
electromagnetic self-energy of the charge distribution, (ii) the net
electromagnetic energy radiated to infinity (and/or into a black hole/white
hole), and (iii) the total work done by the electromagnetic field on the charge
distribution via the Lorentz force. A similar conservation theorem can be
proven for linearized gravitational fields off of a stationary, asymptotically
flat background, with the second order Einstein tensor playing the role of an
effective stress-energy tensor of the linearized field. In this paper, we prove
the above theorems for smooth sources and then investigate the extent to which
they continue to hold for point particle sources. The ``self-energy'' of point
particles is ill defined, but in the electromagnetic case, we can consider
situations where, initially and finally, the point charges are stationary and
in the same spatial position, so that the self-energy terms should cancel.
Under certain assumptions concerning the decay behavior of source-free
solutions to Maxwell's equations, we prove the vanishing of the sum of the net
energy radiated to infinity and the net work done on the particle by the
DeWitt-Brehme radiation reaction force. We also obtain a similar conservation
theorem for angular momentum in an axisymmetric spacetime. In the gravitational
case, we argue that similar conservation results should hold for freely falling
point masses whose orbits begin and end at infinity.


title: Some Identities for the Quantum Measure and its Generalizations

abstract:
  After a brief review of classical probability theory (measure theory), we
present an observation (due to Sorkin) concerning an aspect of probability in
quantum mechanics. Following Sorkin, we introduce a generalized measure theory
based on a hierarchy of ``sum-rules.'' The first sum-rule yields classical
probability theory, and the second yields a generalized probability theory that
includes quantum mechanics as a special case. We present some algebraic
relations involving these sum-rules. This may be useful for the study of the
higher-order sum-rules and possible generalizations of quantum mechanics. We
conclude with some open questions and suggestions for further work.


title: Cosmological model in 5D, stationarity, yes or no

abstract:
  We consider cosmological model in 4+1 dimensions with variable scale factor
in extra dimension and static external space. The time scale factor is
changing. Variations of light velocity, gravity constant, mass and pressure are
determined with four-dimensional projection of this space-time. Data obtained
by space probes Pioneer 10/11 and Ulysses are analyzed within the framework of
this model.


title: Evolution of Fluctuations during Graceful Exit in String Cosmology

abstract:
  We study the evolution of fluctuations in a universe dominated by a scalar
field coupled to the Gauss-Bonnet term. During the graceful exit, we found
non-negligible enhancements of both curvature perturbation and gravitational
wave in the long wavelength limit, and we also found a short wavelength
instability for steep background superinflation just after the completion of
the graceful exit. This result for one possible graceful exit mechanism would
provide a significant implication on the primordial spectrum from the string
cos mology.


title:
Isotropic cosmological singularities 3: The Cauchy problem for the
  inhomogeneous conformal Einstein-Vlasov equations

abstract:
  We consider the conformal Einstein equations for massless collisionless gas
cosmologies which admit an isotropic singularity. It is shown that the Cauchy
problem for these equations is well-posed with data consisting of the limiting
particle distribution function at the singularity.


title: On the r-mode spectrum of relativistic stars

abstract:
  We present a mathematically rigorous proof that the r-mode spectrum of
relativistic stars to the rotational lowest order has a continuous part. A
rigorous definition of this spectrum is given in terms of the spectrum of a
continuous linear operator. This study verifies earlier results by Kojima
(1998) about the nature of the r-mode spectrum.


title:
Axisymmetric electrovacuum spacetimes with a translational Killing
  vector at null infinity

abstract:
  By using the Bondi-Sachs-van der Burg formalism we analyze the asymptotic
properties at null infinity of axisymmetric electrovacuum spacetimes with a
translational Killing vector and, in general, an infinite ``cosmic string''
(represented by a conical singularity) along the axis. Such spacetimes admit
only a local null infinity. There is a non-vanishing news function due to the
existence of the string even though there is no radiation.
  We prove that if null infinity has a smooth compact cross section and the
spacetime is not flat in a neighbourhood of null infinity, then the
translational Killing vector must be timelike and the spacetime is stationary.
The other case in which an additional symmetry of axisymmetric spacetimes
admits compact cross sections of null infinity is the boost symmetry, which
leads to radiative spacetimes representing ``uniformly accelerated objects''.
These cases were analyzed in detail in our previous works. If the translational
Killing vector is spacelike or null, corresponding to cylindrical or plane
waves, some complete generators of null infinity are ``singular'' but null
infinity itself can be smooth apart from these generators.
  As two explicit examples of local null infinity, Schwarzschild spacetime with
a string and a class of cylindrical waves with a string are discussed in detail
in the Appendix.


title:
Self-gravitating fluid shells and their non-spherical oscillations in
  Newtonian theory

abstract:
  We summarize the general formalism describing surface flows in
three-dimensional space in a form which is suitable for various astrophysical
applications. We then apply the formalism to the analysis of non-radial
perturbations of self-gravitating spherical fluid shells.
  Spherically symmetric gravitating shells (or bubbles) have been used in
numerous model problems especially in general relativity and cosmology. A
radially oscillating shell was recently suggested as a model for a variable
cosmic object. Within Newtonian gravity we show that self-gravitating static
fluid shells are unstable with respect to linear non-radial perturbations. Only
shells (bubbles) with a negative mass (or with a charge the repulsion of which
is compensated by a tension) are stable.


title: Tilted String Cosmologies

abstract:
  Global symmetries of the string effective action are employed to generate
tilted, homogeneous Bianchi type VI_h string cosmologies from a previously
known stiff perfect fluid solution to Einstein gravity. The dilaton field is
not constant on the surfaces of homogeneity. The future asymptotic state of the
models is interpreted as a plane wave and is itself an exact solution to the
string equations of motion to all orders in the inverse string tension. An
inhomogeneous generalization of the Bianchi type III model is also found.


title: Two-spinor Formulation of First Order Gravity coupled to Dirac Fields

abstract:
  Two-spinor formalism for Einstein Lagrangian is developed. The gravitational
field is regarded as a composite object derived from soldering forms. Our
formalism is geometrically and globally well-defined and may be used in
virtually any 4m-dimensional manifold with arbitrary signature as well as
without any stringent topological requirement on space-time, such as
parallelizability. Interactions and feedbacks between gravity and spinor fields
are considered. As is well known, the Hilbert-Einstein Lagrangian is second
order also when expressed in terms of soldering forms. A covariant splitting is
then analysed leading to a first order Lagrangian which is recognized to play a
fundamental role in the theory of conserved quantities. The splitting and
thence the first order Lagrangian depend on a reference spin connection which
is physically interpreted as setting the zero level for conserved quantities. A
complete and detailed treatment of conserved quantities is then presented.


title:
The Apparent Anomalous, Weak, Long-Range Acceleration of Pioneer 10 and
  11

abstract:
  Recently we reported that radio Doppler data generated by NASA's Deep Space
Network (DSN) from the Pioneer 10 and 11 spacecraft indicate an apparent
anomalous, constant, spacecraft acceleration with a magnitude $\sim 8.5\times
10^{-8}$ cm s$^{-2}$, directed towards the Sun (gr-qc/9808081). Analysis of
similar Doppler and ranging data from the Galileo and Ulysses spacecraft
yielded ambiguous results for the anomalous acceleration, but it was useful in
that it ruled out the possibility of a systematic error in the DSN Doppler
system that could easily have been mistaken as a spacecraft acceleration. Here
we present some new results, including a critique suggestions that the
anomalous acceleration could be caused by collimated thermal emission. Based
partially on a further data for the Pioneer 10 orbit determination, the data
now spans January 1987 to July 1998, our best estimate of the average Pioneer
10 acceleration directed towards the Sun is $\sim 7.5 \times 10^{-8}$ cm
s$^{-2}$.


title:
Quantum mechanics forbids an initial or final singularity in a closed
  FRW universe

abstract:
  The existence of singularities in a closed FRW universe depends on the
assumption that general relativity is valid for distances less than the Planck
length. However, stationary state wave functions of the Schrodinger equation
for a closed radiation-dominated FRW universe derived by Elbaz et al (General
Relativity and Gravitation 29, 481, 1997) are zero at zero radius of curvature.
Thus, even if general relativity is assumed valid at distances less than the
Planck length, quantum mechanics seems to forbid singularities in a closed FRW
universe.


title: Quantum Fields in Nonstatic background: A Histories Perspective

abstract:
  For a quantum field living on a non - static spacetime no instantaneous
Hamiltonian is definable, for this generically necessitates a choice of
inequivalent representation of the canonical commutation relations at each
instant of time. This fact suggests a description in terms of time - dependent
Hilbert spaces, a concept that fits naturally in a (consistent) histories
framework. Our primary tool for the construction of the quantum theory in a
continuous -time histories format is the recently developed formalism based on
the notion of the history group . This we employ to study a model system
involving a 1+1 scalar field in a cavity with moving boundaries.
  The instantaneous (smeared) Hamiltonian and a decoherence functional are then
rigorously defined so that finite values for the time - averaged particle
creation rate are obtainable through the study of energy histories. We also
construct the Schwinger - Keldysh closed- time - path generating functional as
a ``Fourier transform'' of the decoherence functional and evaluate the
corresponding n - point functions.


title: How the Change in Horizon Area Drives Black Hole Evaporation

abstract:
  We rephrase the derivation of black hole radiation so as to take into
account, at the level of transition amplitudes, the change of the geometry
induced by the emission process. This enlarged description reveals that the
dynamical variables which govern the emission are the horizon area and its
conjugate time variable. Their conjugation is established through the boundary
term at the horizon which must be added to the canonical action of general
relativity in order to obtain a well defined action principle when the area
varies. These coordinates have already been used by Teitelboim and
collaborators to compute the partition function of a black hole. We use them to
show that the probability to emit a particle is given by $e^{- \Delta A/4}$
where $\Delta A$ is the decrease in horizon area induced by the emission. This
expression improves Hawking result which is governed by a temperature (given by
the surface gravity) in that the specific heat of the black hole is no longer
neglected. The present derivation of quantum black hole radiation is based on
the same principles which are used to derive the first law of classical black
hole thermodynamics. Moreover it also applies to quantum processes associated
with cosmological or acceleration horizons. These two results indicate that not
only black holes but all event horizons possess an entropy which governs
processes according to quantum statistical thermodynamics.


title: Electrically Charged Cold Black Holes in Scalar-Tensor Theories

abstract:
  We study the possible existence of charged and neutral black holes in the
Bergmann-Wagoner class of scalar-tensor theories (STT) of gravity in four
dimensions. The existence of black holes is shown for anomalous versions of
these theories, with a negative kinetic term in the Lagrangian. The Hawking
temperature of these holes is zero, while the horizon area is (in most cases)
infinite. As a special case, the Brans-Dicke theory is studied in more detail,
and two kinds of infinite-area black holes are revealed, with finite and
infinite proper time needed for an infalling particle to reach the horizon;
among them, analyticity properties select a discrete subfamily of solutions,
parametrized by two integers, which admit an extension beyond the horizon. The
causal structure and stability of these solutions with respect to small radial
perturbations is discussed. As a by-product, the stability properties of all
spherically symmetric electrovacuum STT solutions are outlined.


title: Comment on the quantum modes of the scalar field on AdS_{d+1} spacetime

abstract:
  The problem of the quantum modes of the scalar free field on anti-de Sitter
backgrounds with an arbitrary number of space dimensions is considered. It is
shown that this problem can be solved by using the same quantum numbers as
those of the nonrelativistic oscillator and two parameters which give the
energy quanta and respectively the ground state energy. This last one is known
to be just the conformal dimension of the boundary field theory of the AdS/CFT
conjecture.


title: A Conformal Hyperbolic Formulation of the Einstein Equations

abstract:
  We propose a re-formulation of the Einstein evolution equations that cleanly
separates the conformal degrees of freedom and the non-conformal degrees of
freedom with the latter satisfying a first order strongly hyperbolic system.
The conformal degrees of freedom are taken to be determined by the choice of
slicing and the initial data, and are regarded as given functions (along with
the lapse and the shift) in the hyperbolic part of the evolution.
  We find that there is a two parameter family of hyperbolic systems for the
non-conformal degrees of freedom for a given set of trace free variables. The
two parameters are uniquely fixed if we require the system to be ``consistently
trace-free'', i.e., the time derivatives of the trace free variables remains
trace-free to the principal part, even in the presence of constraint violations
due to numerical truncation error. We show that by forming linear combinations
of the trace free variables a conformal hyperbolic system with only physical
characteristic speeds can also be constructed.


title: Quasinormal Modes of Dirty Black Holes

abstract:
  Quasinormal mode (QNM) gravitational radiation from black holes is expected
to be observed in a few years. A perturbative formula is derived for the shifts
in both the real and the imaginary part of the QNM frequencies away from those
of an idealized isolated black hole. The formulation provides a tool for
understanding how the astrophysical environment surrounding a black hole, e.g.,
a massive accretion disk, affects the QNM spectrum of gravitational waves. We
show, in a simple model, that the perturbed QNM spectrum can have interesting
features.


title: Perturbative Approach to the Quasinormal Modes of Dirty Black Holes

abstract:
  Using a recently developed perturbation theory for uasinormal modes (QNM's),
we evaluate the shifts in the real and imaginary parts of the QNM frequencies
due to a quasi-static perturbation of the black hole spacetime. We show the
perturbed QNM spectrum of a black hole can have interesting features using a
simple model based on the scalar wave equation.


title:
The Thermal Response of a Pulsar Glitch : The Non-spherical Symmetric
  Case

abstract:
  We study the thermal evolution of a pulsar after a glitch in which the energy
is released from a relative compact region. A set of relativistic thermal
transport and energy balance equations is used to study the thermal evolution,
without making the assumption of spherical symmetry. We use an exact cooling
model to solve this set of differential equtions. Our results differ
significantly from those obtained under the assumption of spherical symmetry.
Even for young pulsars with a hot core like the Vela pulsar, we find that a
detectable hot spot can be observed after a glitch. The results suggest that
the intensity variation and the relative phases of hard X-ray emissions in
different epoches can provide important information on the equation of state.


title: General-Relativistic Thomas-Fermi model

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


title: Triggers for the Detection of Gravitational Wave Bursts

abstract:
  We present several filtering methods which can be used as triggers for the
detection of gravitational wave bursts in interferometric detectors. All the
methods are compared to matched filtering with the help of a figure of merit
based on the detection of supernovae signals simulated by Zwerger and Muller.


title:
Stability of inflationary solutions driven by a changing dissipative
  fluid

abstract:
  In this paper the second Lyapunov method is used to study the stability of
the de Sitter phase of cosmic expansion when the source of the gravitational
field is a viscous fluid. Different inflationary scenarios related with
reheating and decay of mini-blackholes into radiation are investigated using an
effective fluid described by time--varying thermodynamical quantities.


title: Topological Reverberations in Flat Space-times

abstract:
  We study the role played by multiply-connectedness in the time evolution of
the energy E(t) of a radiating system that lies in static flat space-time
manifolds M_4 whose t=const spacelike sections M_3 are compact in at least one
spatial direction. The radiation reaction equation of the radiating source is
derived for the case where M_3 has any non-trivial flat topology, and an exact
solution is obtained. We also show that when the spacelike sections are
multiply-connected flat 3-manifolds the energy E(t) exhibits a reverberation
pattern with discontinuities in the derivative of E(t) and a set of relative
minima and maxima, followed by a growth of E(t). It emerges from this result
that the compactness in at least one spatial direction of Minkowski space-time
is sufficient to induce this type of topological reverberation, making clear
that our radiating system is topologically fragile. An explicit solution of the
radiation reaction equation for the case where M_3 = R^2 x S^1 is discussed,
and graphs which reveal how the energy varies with the time are presented and
analyzed.


title: Lightcone reference for total gravitational energy

abstract:
  We give an explicit expression for gravitational energy, written solely in
terms of physical spacetime geometry, which in suitable limits agrees with the
total Arnowitt-Deser-Misner and Trautman-Bondi-Sachs energies for
asymptotically flat spacetimes and with the Abbot-Deser energy for
asymptotically anti-de Sitter spacetimes. Our expression is a boundary value of
the standard gravitational Hamiltonian. Moreover, although it stands alone as
such, we derive the expression by picking the zero-point of energy via a
``lightcone reference.''


title: The $\omega\to\infty$ limit of Brans-Dicke gravity revisited

abstract:
  The $\omega\to\infty$ limit of Brans-Dicke theory is studied with the help of
the conformal transformation approach without resorting, however, to the
conformal invariance property of this formalism, that is shown to be spurious.


title: On the relation between 2+1 Einstein gravity and Chern Simons theory

abstract:
  A simple example is given to show that the gauge equivalence classes of
physical states in Chern Simons theory are not in one-to-one correspondence
with those of Einstein gravity in three spacetime dimensions. The two theories
are therefore not equivalent. It is shown that including singular metrics into
general relativity has more, and in fact a quite counter-intuitive, impact on
the theory than one naively expects.


title: Is the Schwarzschild black hole spurious?

abstract:
  A point of view is presented, according to which, the well known picture with
the Schwarzschild black hole in canonical general relativity is one in a whole
class of conformal representations of the same physical situation, that are
physically equivalent. Symmetry arguments are presented that favour a conformal
picture without singularity instead of the Schwarzschild one.


title: Stability of the r-modes in white dwarf stars

abstract:
  Stability of the r-modes in rapidly rotating white dwarf stars is
investigated. Improved estimates of the growth times of the
gravitational-radiation driven instability in the r-modes of the observed DQ
Her objects are found to be longer (probably considerably longer) than 6x10^9y.
This rules out the possibility that the r-modes in these objects are emitting
gravitational radiation at levels that could be detectable by LISA. More
generally it is shown that the r-mode instability can only be excited in a very
small subset of very hot (T>10^6K), rather massive (M>0.9M_sun) and very
rapidly rotating (P_min<P<1.2P_min) white dwarf stars. Further, the growth
times of this instability are so long that these conditions must persist for a
very long time (t>10^9y) to allow the amplitude to grow to a dynamically
significant level. This makes it extremely unlikely that the r-mode instability
plays a significant role in any real white dwarf stars.


title:
Real sector of the nonminimally coupled scalar field to self-dual
  gravity

abstract:
  A scalar field nonminimally coupled to gravity is studied in the canonical
framework, using self-dual variables. The corresponding constraints are first
class and polynomial. To identify the real sector of the theory, reality
conditions are implemented as second class constraints, leading to three real
configurational degrees of freedom per space point. Nevertheless, this
realization makes non-polynomial some of the constraints. The original complex
symplectic structure reduces to the expected real one, by using the appropriate
Dirac brackets. For the sake of preserving the simplicity of the constraints,
an alternative method preventing the use of Dirac brackets, is discussed. It
consists of converting all second class constraints into first class by adding
extra variables. This strategy is implemented for the pure gravity case.


title: Photon Stars

abstract:
  We discuss numerical solutions of Einstein's field equation describing
static, spherically symmetric conglomerations of a photon gas. These equations
imply a back reaction of the metric on the energy density of the photon gas
according to Tolman's equation. The 3-fold of solutions corresponds to a class
of physically different solutions which is parameterized by only two
quantities, e.g. mass and surface temperature. The energy density is typically
concentrated on a shell because the center contains a repelling singularity,
which can, however, not be reached by timelike or null geodesics. The physical
relevance of these solutions is completely open, although their existence may
raise some doubts w.r. to the stability of black holes.


title: Quantum spacetime: what do we know?

abstract:
  This is a contribution to a book on quantum gravity and philosophy. I discuss
nature and origin of the problem of quantum gravity. I examine the knowledge
that may guide us in addressing this problem, and the reliability of such
knowledge. In particular, I discuss the subtle modification of the notions of
space and time engendered by general relativity, and how these might merge into
quantum theory. I also present some reflections on methodological questions,
and on some general issues in philosophy of science which are are raised by, or
a relevant for, the research on quantum gravity.


title:
Completeness principle and quantum field theory on nonglobally
  hyperbolic spacetimes

abstract:
  We analyse in details the problems which one faces trying to quantize a
scalar field on the spacelike cylinder being the simple example of a spacetime
with closed timelike curves. Our analysis brings to light the fact that the
usual set of positive and negative frequency solutions of the field equation
turns out to be incomplete. The consequence of this fact is that the usual
formulation of quantum field theory breaks down on such a spacetime. We
postulate the completeness principle and build on its basis the modified
quantization procedure. As an example, the Hadamard function and $<\phi^2>$ for
the scalar field on the spacelike cylinder are calculated. It is shown that the
``naive'' method of images gives the same results of calculation.


title: On the General Covariance in the Bohmian Quantum Gravity

abstract:
  It is shown explicitly that in the framework of Bohmian quantum gravity, the
equations of motion of the space-time metric are Einstein's equations plus some
quantum corrections. It is observed that these corrections are not covariant.
So that in the framework of Bohmian quantum gravity the general covariance
principle breaks down at the individual level. This principle is restored at
the statistical level.


title: Nonlocal Effects in Quantum Gravity


title: Conformal Transformations and Quantum Gravity

abstract:
  Recently\cite{BQG}, it was shown that quantum effects of matter could be
identified with the conformal degree of freedom of the space-time metric.
Accordingly, one can introduce quantum effects either by making a scale
transformation (i.e. changing the metric), or by making a conformal
transformation (i.e. changing all physical quantities). These two ways are
investigated and compared. Also, it is argued that, the ultimate formulation of
such a quantum gravity theory should be in the framework of the scalar-tensor
theories.


title: Scalar-Tensor Theories and Quantum Gravity

abstract:
  Recently, it was shown that the quantum effects of the matter, could be used
to determine the conformal degree of freedom of the space-time metric. So both
gravity and quantum are geometrical features. Gravity determines the causal
structure of the space-time, while quantum determines the scale of the
space-time. In this article, it is shown that it is possible to use the
scalar-tensor framework to build a unified theory in which both quantum and
gravitational effects are present.


title:
Canonical Quantization and the Statistical Entropy of the Schwarzschild
  Black Hole

abstract:
  The canonical quantization of a Schwarzschild black hole yields a picture of
the black hole that is shown to be equivalent to a collection of oscillators
whose density of levels is commensurate with that of the statistical bootstrap
model. Energy eigenstates of definite parity exhibit the Bekenstein mass
spectrum, $M \sim \sqrt{\cal N} M_p$, where ${\cal N} \in {\bf N}$. From the
microcanonical ensemble, we derive the statistical entropy of the black hole by
explicitly counting the microstates corresponding to a macrostate of fixed
total energy.


title: Classical roots of the Unruh and Hawking effects

abstract:
  Although the Unruh and Hawking phenomena are commonly linked to field
quantization in "accelerated" coordinates or in curved spacetimes, we argue
that they are deeply rooted at the classical level. We maintain in particular
that these effects should be best understood by considering how the
special-relativistic notion of "particle" gets blurred when employed in
theories including accelerated observers or in general-relativistic theories,
and that this blurring is an instantiation of a more general behavior arising
when the principle of equivalence is used to generalize classical or quantum
special-relativistic theories to curved spacetimes or accelerated observers. A
classical analogue of the Unruh effect, stemming from the non-invariance of the
notion of "electromagnetic radiation" as seen by inertial and accelerated
observers, is illustrated by means of four gedanken-experimente. The issue of
energy balance in the various cases is also briefly discussed.


title: Large Scale Structures in the Universe

abstract:
  In this brief communication we show why superclusters would naturally arise
in the universe.


title:
Probes of the vacuum structure of quantum fields in classical
  backgrounds

abstract:
  We compare the different approaches presently available in literature to
probe the vacuum structure of quantum fields in classical electromagnetic and
gravitational backgrounds. We compare the results from the Bogolubov
transformations and the effective Lagrangian approach with the response of
monopole detectors (of the Unruh-DeWitt type) in non-inertial frames in flat
spacetime and in inertial frames in different types of classical
electromagnetic backgrounds. We also carry out such a comparison in inertial
and rotating frames when boundaries are present in flat spacetime. We find that
the results from these different approaches do not, in general, agree with each
other. We attempt to identify the origin of these differences and then go on to
discuss its implications for classical gravitational backgrounds.


title: Quantum interest for scalar fields in Minkowski spacetime

abstract:
  The quantum interest conjecture of Ford and Roman states that any negative
energy flux in a free quantum field must be preceded or followed by a positive
flux of greater magnitude, and the surplus of positive energy grows the further
the positive and negative fluxes are apart. In addition, the maximum possible
separation between the positive and negative energy decreases the larger the
amount of negative energy. We prove that the quantum interest conjecture holds
for arbitrary fluxes of non-interacting scalar fields in 4D Minkowski
spacetime, and discuss the consequences in attempting to violate the second law
of thermodynamics using negative energy. We speculate that quantum interest may
also hold for the Electromagnetic and Dirac fields, and might be applied to
certain curved spacetimes.


title: Post-Newtonian Cosmology

abstract:
  Newtonian Cosmology is commonly used in astrophysical problems, because of
its obvious simplicity when compared with general relativity. However it has
inherent difficulties, the most obvious of which is the non-existence of a
well-posed initial value problem. In this paper we investigate how far these
problems are met by using the post-Newtonian approximation in cosmology.


title:
On the uniqueness of the expected stress-energy tensor in renormalizable
  field theories

abstract:
  It is argued that the ambiguity introduced by the renormalization in the
effective action of a four-dimensional renormalizable quantum field theory is
at most a local polynomial action of canonical dimension four. The allowed
ambiguity in the expected stress-energy tensor of a massive scalar field is
severely restricted by this fact.


title:
Comparing solar-system, binary-pulsar, and gravitational-wave tests of
  gravity

abstract:
  This talk is based on my work in collaboration with Thibault Damour. We
compare the probing power of different classes of gravity experiments:
solar-system tests (weak-field regime), binary-pulsar tests (strong-field
regime), and future gravitational-wave observations of inspiralling binaries
(strong-field effects detected in our weak-gravitational-field conditions).
This is done within the most natural class of alternative theories to general
relativity, namely tensor-scalar theories, in which the gravitational
interaction is mediated by one tensor field (g_munu) together with one or
several scalar fields (phi). Our main conclusion is that strong-field tests are
qualitatively different from weak-field experiments: They constrain theories
which are strictly indistinguishable from general relativity in the solar
system. We also show that binary-pulsar data are so precise that they already
rule out the theories for which scalar effects could have been detected with
LIGO or VIRGO. This proves that it is therefore sufficient to compute the
`chirp' templates within general relativity.


title: Thick self-gravitating plane-symmetric domain walls

abstract:
  We investigate a self-gravitating thick domain wall for a $\lambda \Phi^4$
potential. The system of scalar and Einstein equations admits two types of
non-trivial solutions: domain wall solutions and false vacuum-de Sitter
solutions. The existence and stability of these solutions depends on the
strength of the gravitational interaction of the scalar field, which is
characterized by the number $\epsilon$. For $\epsilon \ll 1$, we find a domain
wall solution by expanding the equations of motion around the flat spacetime
kink. For ``large'' $\epsilon$, we show analytically and numerically that only
the de Sitter solution exists, and that there is a phase transition at some
$\epsilon_{\rm max}$ which separates the two kinds of solution. Finally, we
comment on the existence of this phase transition and its relation to the
topology of the domain wall spacetime.


title: The Quantum Tetrahedron in 3 and 4 Dimensions

abstract:
  Recent work on state sum models of quantum gravity in 3 and 4 dimensions has
led to interest in the `quantum tetrahedron'. Starting with a classical phase
space whose points correspond to geometries of the tetrahedron in R^3, we use
geometric quantization to obtain a Hilbert space of states. This Hilbert space
has a basis of states labeled by the areas of the faces of the tetrahedron
together with one more quantum number, e.g. the area of one of the
parallelograms formed by midpoints of the tetrahedron's edges. Repeating the
procedure for the tetrahedron in R^4, we obtain a Hilbert space with a basis
labelled solely by the areas of the tetrahedron's faces. An analysis of this
result yields a geometrical explanation of the otherwise puzzling fact that the
quantum tetrahedron has more degrees of freedom in 3 dimensions than in 4
dimensions.


title: Topological Censorship

abstract:
  Classically, all topologies are allowed as solutions to the Einstein
equations. However, one does not observe any topological structures on medium
range distance scales, that is scales that are smaller than the size of the
observed universe but larger than the microscopic scales for which quantum
gravity becomes important. Recently, Friedman, Schleich and Witt have proven
that there is topological censorship on these medium range distance scales: the
Einstein equations, locally positive energy, and local predictability of
physics imply that any medium distance scale topological structures cannot be
seen. More precisely, we show that the topology of physically reasonable
isolated systems is shrouded from distant observers, or in other words there is
a topological censorship principle.


title:
The Generalized Hartle-Hawking Initial State: Quantum Field Theory on
  Einstein Conifolds

abstract:
  Recent arguments have indicated that the sum over histories formulation of
quantum amplitudes for gravity should include sums over conifolds, a set of
histories with more general topology than that of manifolds. This paper
addresses the consequences of conifold histories in gravitational functional
integrals that also include scalar fields. This study will be carried out
explicitly for the generalized Hartle-Hawking initial state, that is the
Hartle-Hawking initial state generalized to a sum over conifolds. In the
perturbative limit of the semiclassical approximation to the generalized
Hartle-Hawking state, one finds that quantum field theory on Einstein conifolds
is recovered. In particular, the quantum field theory of a scalar field on de
Sitter spacetime with $RP^3$ spatial topology is derived from the generalized
Hartle-Hawking initial state in this approximation. This derivation is carried
out for a scalar field of arbitrary mass and scalar curvature coupling.
Additionally, the generalized Hartle-Hawking boundary condition produces a
state that is not identical to but corresponds to the Bunch-Davies vacuum on
$RP^3$ de Sitter spacetime. This result cannot be obtained from the original
Hartle-Hawking state formulated as a sum over manifolds as there is no Einstein
manifold with round $RP^3$ boundary.


title: Scale-factor duality in string Bianchi cosmologies

abstract:
  We apply the scale factor duality transformations introduced in the context
of the effective string theory to the anisotropic Bianchi-type models. We find
dual models for all the Bianchi-types [except for types $VIII$ and $IX$] and
construct for each of them its explicit form starting from the exact original
solution of the field equations. It is emphasized that the dual Bianchi class
$B$ models require the loss of the initial homogeneity symmetry of the
dilatonic scalar field.


title: Entropy bound for a charged object from the Kerr-Newman black hole

abstract:
  We derive again the upper entropy bound for a charged object by employing
thermodynamics of the Kerr-Newman black hole linearised with respect to its
electric charge


title: Theories of Space and Time Compatible with the Inertia Principle

abstract:
  A general formal definition of a theory of space and time compatible with the
inertia principle is given. The formal definition of reference frame and
inertial equivalence between reference frames are used to construct the class
of inertial frames. Then, suitable cocycle relations among the coefficients of
space-time transformations between inertial frames are established. The
kinematical meaning of coefficients and their reciprocity properties are
discussed in some detail. Finally, a rest frame map family is introduced as the
most general constitutive assumption to obtain the coefficients and to define a
theory of space and time. Four meaningful examples are then presented.


title:
Distance Measurement and $\kappa$-Deformed Propagation of Light and
  Heavy Probes

abstract:
  We investigate the implications for the measurability of distances of a
covariant dimensionful ``$\kappa$'' deformation of D=4 relativistic symmetries,
with quantum time coordinate and modified Heisenberg algebra. We show that the
structure of the deformed mass-shell condition has significant implications for
measurement procedures relying on light probes, whereas in the case of heavy
probes the most sizeable effect is due to the nontrivial commutation relation
between three-momenta and quantum time coordinate. We argue that these findings
might indicate that $\kappa$-Poincar\'e symmetries capture some aspects of the
physics of the Quantum-Gravity vacuum.


title: Bounds on 2m/R for static spherical objects

abstract:
  It is well known that a spherically symmetric constant density static star,
modeled as a perfect fluid, possesses a bound on its mass m by its radial size
R given by 2m/R \le 8/9 and that this bound continues to hold when the energy
density decreases monotonically. The existence of such a bound is intriguing
because it occurs well before the appearance of an apparent horizon at m = R/2.
However, the assumptions made are extremely restrictive. They do not hold in a
humble soap bubble and they certainly do not approximate any known
topologically stable field configuration. We show that the 8/9 bound is robust
by relaxing these assumptions. If the density is monotonically decreasing and
the tangential stress is less than or equal to the radial stress we show that
the 8/9 bound continues to hold through the entire bulk if m is replaced by the
quasi-local mass. If the tangential stress exceeds the radial stress and/or the
density is not monotonic we cannot recover the 8/9 bound. However, we can show
that 2m/R remains strictly bounded away from unity by constructing an explicit
upper bound which depends only on the ratio of the stresses and the variation
of the density.


title: Hyper-fast travel without negative energy

abstract:
  Olum (PRL 81 3567-3570, 1998) has defined "superluminality" as the ability of
a signal path to carry information faster than any neighbouring signal path,
and has suggested that this requires a negative energy-density. However, this
condition can be created without exotic matter if we are only sending
information along the delivery path in one particular direction, and restrict
ourselves to experiments that do not involve the speed of any
counterpropagating or return-trip signals. Although negative energy-densities
may be required for enhanced transit speeds in both directions along a single
path at the same time, a traveller will normally not need (or want!) to travel
in two opposing directions at once, so the condition of bidirectionality that
gives rise to the negative energy condition may be unnecessarily restrictive.


title: Testing string theory via black hole space-times

abstract:
  Charged black holes, both spherically symmetric and rotating, in the low
energy limit of string theory (Einstein-Maxwell-dilaton theory) are compared to
analogous geometries in pure general relativity. We describe various physical
differences and investigate some experiments which can distinguish between the
two theories. In particular we discuss the gyro-magnetic ratios of rotating
black holes and the propagation of light on black hole backgrounds. For the
former we obtain an expression in the Einstein frame (EF) which is different
from the one in the String frame (SF). This (and other results) can be used to
test the stringy nature of matter. For a binary system consisting of a star and
a rotating black hole, we give estimates of the damping of electro-magnetic
radiation coming from the star due to the existence of a scalar component of
gravity.


title: Timing Effects of Gravitational Waves from Localized Sources

abstract:
  Localized astronomical sources like a double stellar system, rotating neutron
star, or a massive black hole at the center of the Milky Way emit periodic
gravitational waves. For a long time only a far-zone contribution of
gravitational fields of the localized sources (plane-wave-front approximation)
were a matter of theoretical analysis. We demonstrate how this analysis can be
extended to take into account near-zone and intermediate-zone contributions as
well. The formalism is used to calculate gravitational-wave corrections to the
Shapiro time delay in binary pulsars and low-frequency (LF) pulsar timing noise
produced by an ensemble of double stars in our galaxy.


title: Gauss vs Coulomb and the Cosmological Mass-deficit Problem

abstract:
  In a previous work General Relativity has been presented as a microscopic
theory of finite and discrete point-like fields that we associate to a
classical description of gravitons. The standard macroscopic continuous field
is retrieved as an average-valued field through an integration over these
gravitons. Here we discuss extreme alternative (the Gauss's and the Coulomb's)
ways of obtaining and interpreting the averaged fields, how they depend on the
kind of measurements involved, and how do they fit with the experimental data.
The field measurements in the classical tests of general relativity correspond
to the Coulomb's mode whereas the determination of the overall spacetime
curvature in a cosmological scale is clearly a Gauss's mode. As a natural
consequence there is no missing mass and, therefore, no such a need of dark
mass as the value predicted by General Relativity, in the context of the
Gauss's mode, agrees with the observed one.


title: Spacetime and the Philosophical Challenge of Quantum Gravity

abstract:
  We survey some philosophical aspects of the search for a quantum theory of
gravity, emphasising how quantum gravity throws into doubt the treatment of
spacetime common to the two `ingredient theories' (quantum theory and general
relativity), as a 4-dimensional manifold equipped with a Lorentzian metric.
After an introduction, we briefly review the conceptual problems of the
ingredient theories and introduce the enterprise of quantum gravity We then
describe how three main research programmes in quantum gravity treat four
topics of particular importance: the scope of standard quantum theory; the
nature of spacetime; spacetime diffeomorphisms, and the so-called problem of
time. By and large, these programmes accept most of the ingredient theories'
treatment of spacetime, albeit with a metric with some type of quantum nature;
but they also suggest that the treatment has fundamental limitations. This
prompts the idea of going further: either by quantizing structures other than
the metric, such as the topology; or by regarding such structures as
phenomenological. We discuss this in Section \ref{Sec:TowardsQuST}.


title: The classical action for a Bianchi VI_h model

abstract:
  An estimate for the classical action for a Bianchi VI_h homogeneous spatially
closed cosmology is presented as a function of b, a parameter of the model that
is proportional to the relative rotation of the average inertial frame and the
bulk of matter in the universe. It is assumed (through the equation of state)
that a relativistic early universe is followed by a matter-dominated late
universe. The action is used in a saddlepoint approximation to a semiclassical
estimate for the wave function in quantum cosmology to explain why our inertial
frame seems not to rotate relative to the stars. The saddlepoint is at b=0, as
would be expected. Application of the saddlepoint approximation leads to the
result that only those classical geometries whose action differs from the
saddlepoint value for the action by an amount less than Planck's constant
contribute significantly to the integration to give the present value of the
wave function. Using estimates for our universe implies that only those
classical geometries for which the present relative rotation rate of inertial
frames and matter are less than about 10^(-130) radians per year contribute
significantly to the integration. This is well below the limit set by
experiment. The result depends on the ratio of the Hubble distance to the
Planck length, but does not depend on the details of the theory of quantum
gravity.


title: Quantum Gravity - Testing Time for Theories

abstract:
  The extreme smallness of both the Planck length, on the one side, and the
ratio of the gravitational to the electrical forces between, say, two
electrons, on the other side has led to a widespread belief that the realm of
quantum gravity is beyond terrestrial experiments. A series of classical and
quantum arguments are put forward to dispel this view. It is concluded that
whereas the smallness of the Planck length and the ratio of gravitational to
electrical forces, does play its own essential role in nature, it does not make
quantum gravity a science where humans cannot venture to probe her secrets. In
particular attention is drawn to the latest neutron and atomic interferometry
experiments, and to gravity wave interferometers. The latter, as Giovanni
Amelino-Camelia argues [Nature 398, 216 (1999)], can be treated as probes of
space-time fuzziness down to Planck length for certain quantum-gravity models.


title: Wormholes and Flux Tubes in Kaluza-Klein Theory

abstract:
  In this work spherically symmetric solutions to 5D Kaluza-Klein theory, with
"electric" and/or "magnetic" fields are examined. Different relative strengths
of the "electric" and "magnetic" charges of the solutions are studied by
varying certain parameters in our metric ansatz. As the strengths of these two
charges are varied the resultant spacetime exhibits an interesting "evolution".


title: Canonical ``Loop'' Quantum Gravity and Spin Foam Models

abstract:
  The canonical ``loop'' formulation of quantum gravity is a mathematically
well defined, background independent, non perturbative standard quantization of
Einstein's theory of General Relativity. Some among the most meaningful results
of the theory are: 1) the complete calculation of the spectrum of geometric
quantities like the area and the volume and the consequent physical predictions
about the structure of the space-time at the Plank scale; 2) a microscopical
derivation of the Bekenstein-Hawking black-hole entropy formula. Unfortunately,
despite recent results, the dynamical aspect of the theory (imposition of the
Wheller-De Witt constraint) remains elusive.
  After a short description of the basic ideas and the main results of loop
quantum gravity we show in which sence the exponential of the super Hamiltonian
constraint leads to the concept of spin foam and to a four dimensional
formulation of the theory. Moreover, we show that some topological field
theories as the BF theory in 3 and 4 dimension admits a spin foam formulation.
We argue that the spin-foams/spin-networks formalism it is the natural
framework to discuss loop quantum gravity and topological field theory.


title: A simple shear-free non-singular spherical model with heat flux

abstract:
  We obtain an exact simple solution of the Einstein equation describing a
spherically symmetric cosmological model without the big-bang or any other kind
of singularity. The matter content of the model is shear free isotropic fluid
with radial heat flux and it satisfies the weak and strong energy conditions.
It is pressure gradient combined with heat flux that prevents occurrence of
singularity. So far all known non-singular models have non-zero shear. This is
the first shear free non-singular model, which is also spherically symmetric.


title:
Thermodynamics of charged anti-de Sitter black holes in canonical
  ensemble

abstract:
  As in the grand canonical treatment of Reissner - Nordstr\"{o}m black holes
in anti-de Sitter spacetime, the canonical ensemble formulation also shows that
non-extremal black holes tend to have lower action than extremal ones. However,
some small non-extremal black holes have higher action, leading to the
possibility of transitions between non-extremal and extremal black holes.


title: On the Detectability of Relic (Squeezed) Gravitational Waves

abstract:
  The expected amplitudes and spectral slopes of relic gravitational waves,
plus their specific correlation properties associated with the phenomenon of
squeezing, may allow the registration of relic (squeezed) gravitational waves
by the first generation of sensitive gravity-wave detectors.


title:
Gravity-wave interferometers as probes of a low-energy effective quantum
  gravity

abstract:
  The interferometry-based experimental tests of quantum properties of
space-time which the author sketched out in a recent short Letter [Nature 398
(1999) 216] are here discussed in self-contained fashion. Besides providing
detailed derivations of the results already announced in the previous Letter,
some new results are also derived; in particular, the analysis is extended to a
larger class of scenarios for space-time fuzziness and an absolute bound on the
measurability of the amplitude of a gravity wave is obtained. It is argued that
these studies could be helpful for the search of a theory describing a first
stage of partial unification of Gravity and Quantum Mechanics.


title: New Critical Behavior in Einstein-Yang-Mills Collapse

abstract:
  We extend the investigation of the gravitational collapse of a spherically
symmetric Yang-Mills field in Einstein gravity and show that, within the black
hole regime, a new kind of critical behavior arises which separates black holes
formed via Type I collapse from black holes formed through Type II collapse.
Further, we provide evidence that these new attracting critical solutions are
in fact the previously discovered colored black holes with a single unstable
mode.


title: Black hole collisions: how far can perturbation theory go?

abstract:
  The computation of gravitational radiation generated by the coalescence of
inspiralling binary black holes is nowdays one of the main goals of numerical
relativity. Perturbation theory has emerged as an ubiquitous tool for all those
dynamical evolutions where the two black holes start close enough to each
other, to be treated as single distorted black hole (close limit
approximation), providing at the same time useful benchmarks for full numerical
simulations. Here we summarize the most recent developments to study evolutions
of perturbations around rotating (Kerr) black holes. The final aim is to
generalize the close limit approximation to the most general case of two
rotating black holes in orbit around each other, and thus provide reliable
templates for the gravitational waveforms in this regime. For this reason it
has become very important to know if these predictions can actually be trusted
to larger separation parameters (even in the region where the holes have
distinct event horizons). The only way to extend the range of validity of the
linear approximation is to develop the theory of second order perturbations
around a Kerr hole, by generalizing the Teukolsky formalism.


title:
Naked Singularity of the Vaidya-deSitter Spacetime and Cosmic Censorship
  Hypothesis

abstract:
  We investigate the formation of a locally naked singularity in the collapse
of radiation shells in an expanding Vaidya-deSitter background. This is
achieved by considering the behaviour of non-spacelike and radial geodesics
originating at the singularity. A specific condition is determined for the
existence of radially outgoing, null geodesics originating at the singularity
which, when this condition is satisfied, becomes locally naked. This condition
turns out to be the same as that in the collapse of radiation shells in an
asymptotically flat background. Therefore, we have, at least for the case
considered here, established that the asymptotic flatness of the spacetime is
not essential for the development of a locally naked singularity. Our result
then unequivocally supports the view that no special role be given to
asymptotic observers (or, for that matter, any set of observers) in the
formulation of the Cosmic Censorship Hypothesis.


title: Quantum Gravity as a Dissipative Deterministic System

abstract:
  It is argued that the so-called holographic principle will obstruct attempts
to produce physically realistic models for the unification of general
relativity with quantum mechanics, unless determinism in the latter is
restored. The notion of time in GR is so different from the usual one in
elementary particle physics that we believe that certain versions of hidden
variable theories can -- and must -- be revived. A completely natural procedure
is proposed, in which the dissipation of information plays an essential role.
Unlike earlier attempts, it allows us to use strictly continuous and
differentiable classical field theories as a starting point (although discrete
variables, leading to fermionic degrees of freedom, are also welcome), and we
show how an effective Hilbert space of quantum states naturally emerges when
one attempts to describe the solutions statistically. Our theory removes some
of the mysteries of the holographic principle; apparently non-local features
are to be expected when the quantum degrees of freedom of the world are
projected onto a lower-dimensional black hole horizon. Various examples and
models illustrate the points we wish to make, notably a model showing that
massless, non interacting neutrinos are deterministic.


title:
Effect of a scale-dependent cosmological term on the motion of small
  test particles in a Schwarzschild background

abstract:
  It was recently suggested that the gravitational action could contain a
scale-dependent cosmological term, depending on the length or momentum scale
characteristic of the processes under consideration. In this work we explore a
simple possible consequence of this assumption. We compute the field generated
in empty space by a static spherical source (the Schwarzschild metric), using
the modified action. The resulting static potential turns out to contain a tiny
non-Newtonian component which depends on the size of the test particles. The
possible relevance of this small correction for the analysis of the recent
Pioneers data [J.D. Anderson et al., Phys. Rev. Lett. 81 (1998) 2858] is
briefly discussed.


title:
Exotic Spaces in Quantum Gravity I: Euclidean Quantum Gravity in Seven
  Dimensions

abstract:
  It is well known that in four or more dimensions, there exist exotic
manifolds; manifolds that are homeomorphic but not diffeomorphic to each other.
More precisely, exotic manifolds are the same topological manifold but have
inequivalent differentiable structures. This situation is in contrast to the
uniqueness of the differentiable structure on topological manifolds in one, two
and three dimensions. As exotic manifolds are not diffeomorphic, one can argue
that quantum amplitudes for gravity formulated as functional integrals should
include a sum over not only physically distinct geometries and topologies but
also inequivalent differentiable structures. But can the inclusion of exotic
manifolds in such sums make a significant contribution to these quantum
amplitudes? This paper will demonstrate that it will. Simply connected exotic
Einstein manifolds with positive curvature exist in seven dimensions. Their
metrics are found numerically; they are shown to have volumes of the same order
of magnitude. Their contribution to the semiclassical evaluation of the
partition function for Euclidean quantum gravity in seven dimensions is
evaluated and found to be nontrivial. Consequently, inequivalent differentiable
structures should be included in the formulation of sums over histories for
quantum gravity.


title:
Four Quantum Conservation Laws on Black Hole Equilibrium Radiation
  Process and Quantum Black Hole Entropy

abstract:
  The classical first law of thermodynamic for Kerr-Newmann black hole (KNBH)
is generalized to that in quantum form on event horizon. Then four quantum
conservation laws on the KNBH equilibrium radiation process are derived, and
Bekenstein-Hawking's relation S=A/4 is recovered. It can be argued that the
classical entropy of black hole arise from the quantum entropy of field quanta
or quasi-particles inside the hole.


title: A Scheme to Numerically Evolve Data for the Conformal Einstein Equation

abstract:
  This is the second paper in a series describing a numerical implementation of
the conformal Einstein equation. This paper deals with the technical details of
the numerical code used to perform numerical time evolutions from a "minimal"
set of data.
  We outline the numerical construction of a complete set of data for our
equations from a minimal set of data. The second and the fourth order
discretisations, which are used for the construction of the complete data set
and for the numerical integration of the time evolution equations, are
described and their efficiencies are compared. By using the fourth order scheme
we reduce our computer resource requirements --- with respect to memory as well
as computation time --- by at least two orders of magnitude as compared to the
second order scheme.


title: Choice of Gauge in Quantum Gravity

abstract:
  This paper is an extended version of the talk given at 19th Texas Symposium
of Relativistic Astrophysics and Cosmology, Paris, 1998. It reviews of some
recent work; mathematical details are skipped. It is well-known that a choice
of gauge in generally covariant models has a twofold pupose: not only to render
the dynamics unique, but also to define the spacetime points. A geometric way
of choosing gauge that is not based on coordinate conditions---the so-called
covariant gauge fixing---is described. After a covariant gauge fixing, the
dynamics is unique and the background manifold points are well-defined, but the
description remains invariant with respect to all diffeomorphisms of the
background manifold. Transformations between different covariant gauge fixings
form the well-known Bergmann-Komar group. Each covariant gauge fixing
determines a so-called Kucha\v{r} decomposition. The construction of the
quantum theory is based on the Kucha\v{r} form of the action and the Dirac
method of operator constraints. It is demonstrated that the Bergmann-Komar
group is too large to be implementable by unitary maps in the quantum domain.


title:
The expansive nondecelerative universe - Gravitational effects and their
  manifestation in black holes evaporation and far-infrared spectra

abstract:
  The paper summarizes the background of Expensive Nondecelerative Universe
model and its main consequences for gravitation. Applying the Vaidya metrics,
the model allows for the localization and determination of the density and
quantity of gravitational energy created by a body with the mass m in the
distance r. The consequences are manifested both in a macrosystem (Hawking's
phenomenon of black holes evaporation) and microworld phenomenon (far-infrared
spectral properties)


title: On the fundamental length of quantum geometry and the black hole entropy

abstract:
  The geometric operators of area, volume, and length, depend on a fundamental
length l of quantum geometry which is a priori arbitrary rather than equal to
the Planck length l_P. The fundamental length l and the Immirzi parameter
$\gamma$ determine each other. With any l the entropy formula is rendered most
naturally in units of the length gap sqrt{{sqrt 3}/2} (sqrt{gamma} l).
  Independently of the choice of l, the black hole entropy derived from quantum
geometry in the limit of classical geometry is completely consistent with the
Bekenstein-Hawking form.
  The extremal limit of 1-puncture states of the quantum surface geometry
corresponds rather to an extremal string than to a classical horizon.


title: Quantum corrections to the geodesic equation

abstract:
  In this talk we will argue that, when gravitons are taken into account, the
solution to the semiclassical Einstein equations (SEE) is not physical. The
reason is simple: any classical device used to measure the spacetime geometry
will also feel the graviton fluctuations. As the coupling between the classical
device and the metric is non linear, the device will not measure the
`background geometry' (i.e. the geometry that solves the SEE). As a particular
example we will show that a classical particle does not follow a geodesic of
the background metric. Instead its motion is determined by a quantum corrected
geodesic equation that takes into account its coupling to the gravitons. This
analysis will also lead us to find a solution to the so-called gauge fixing
problem: the quantum corrected geodesic equation is explicitly independent of
any gauge fixing parameter.


title: On Killing vector fields and Newman-Penrose constants

abstract:
  Asymptotically flat spacetimes with one Killing vector field are considered.
The Killing equations are solved asymptotically using polyhomogeneous
expansions (i.e. series in powers of 1/r an ln r), and solved order by order.
The solution to the leading terms of these expansions yield the asymptotic form
of the Killing vector field. The possible classes of Killing fields are
discussed by analysing their orbits on null infinity. The integrability
conditions of the Killing equations are used to obtain constraints on the
components of the Weyl tensor (\Psi_0, \Psi_1, \Psi_2) and on the shear
(\sigma). The behaviour of the solutions to the constraint equations is
studied. It is shown that for Killing fields that are non-supertranslational
the characteristics of the constraint equations are the orbits of the
restriction of the Killing field to null infinity. As an application,
boost-rotation symmetric spacetimes are considered. The constraints on \Psi_0
are used to study the behaviour of the coefficients that give rise to the
Newman-Penrose constants, if the spacetime is non-polyhomogeneous, or the
logarithmic Newman-Penrose constants if the spacetime is polyhomogeneous.


title: Quintessence, the Gravitational Constant, and Gravity

abstract:
  Dynamical vacuum energy or quintessence, a slowly varying and spatially
inhomogeneous component of the energy density with negative pressure, is
currently consistent with the observational data. One potential difficulty with
the idea of quintessence is that couplings to ordinary matter should be
strongly suppressed so as not to lead to observable time variations of the
constants of nature. We further explore the possibility of an explicit coupling
between the quintessence field and the curvature. Since such a scalar field
gives rise to another gravity force of long range ($\simg H^{-1}_0$), the solar
system experiments put a constraint on the non-minimal coupling: $|\xi| \siml
10^{-2}$.


title: Qualitative Analysis of String Cosmologies

abstract:
  A qualitative analysis is presented for spatially flat, isotropic and
homogeneous cosmologies derived from the string effective action when the
combined effects of a dilaton, modulus, two-form potential and central charge
deficit are included. The latter has significant effects on the qualitative
dynamics. The analysis is also directly applicable to the anisotropic Bianchi
type I cosmology.


title:
Squared Weyl and Dirac fields with Sommers-Sen connection, associated
  with $V^4_3$ distribution

abstract:
  The generalization of Sommers--Sen spinor connection for spinor fields,
associated with a distribution $V_4^3$ and on this basis the equations for Weyl
and Dirac null vector fields on complexificated $V_4^3$ are obtained.
  We interpret the obtained results by examining the interaction of spinor
fields with the inertial forces.


title: The Quantization of Geodesic Deviation

abstract:
  There exists a two parameter action, the variation of which produces both the
geodesic equation and the geodesic deviation equation. In this paper it is
shown that this action can be quantized by the canonical method, resulting in
equations which generalize the Klein-Gordon equation. The resulting equations
might have applications, and also show that entirely unexpected systems can be
quantized. The possible applications of quantized geodesic deviation are to:
i)the spreading wave packet in quantum theory, ii)and also to the one particle
to many particle problem in second quantized quantum field theory.


title: On the differentiability of Cauchy horizons

abstract:
  Chrusciel and Galloway constructed a Cauchy horizon that is nondifferentiable
on a dense set. We prove that in a certain class of Cauchy horizons densely
nondifferentiable Cauchy horizons are generic. We show that our class of
densely nondifferentiable Cauchy horizons implies the existence of densely
nondifferentiable Cauchy horizons arising from partial Cauchy surfaces and also
the existence of densely nondifferentiable black hole event horizons.


title: Data Analysis for Continuous Gravitational-Wave Signals

abstract:
  The main problem that we will face in the data analysis for continuous
gravitational-wave sources is processing of a very long time series and a very
large parameter space. We present a number of analytic and numerical tools that
can be useful in such a data analysis. These consist of methods to calculate
false alarm probabilities, use of probabilistic algorithms, application of
signal splitting, and accurate estimation of parameters by means of
optimization algorithms.


title: The close-limit approximation to Neutron Star Collisions

abstract:
  We develop a close-limit approximation to the head-on collision of two
neutron stars similar to that used to treat the merger of black hole binaries .
This approximation can serve as a useful benchmark test for future fully
nonlinear studies. For neutron star binaries, the close-limit approximation
involves assuming that the merged object can be approximated as a perturbed,
stable neutron star during the ring-down phase of the coalescence. We introduce
a prescription for the construction of initial data sets, discuss the physical
plausibility of the various assumptions involved, and briefly investigate the
character of the gravitational radiation produced during the merger. The
numerical results show that several of the merged objects fluid pulsation modes
are excited to a significant level.


title: Detecting an association between Gamma Ray and Gravitational Wave Bursts

abstract:
  If $\gamma$-ray bursts (GRBs) are accompanied by gravitational wave bursts
(GWBs) the correlated output of two gravitational wave detectors evaluated in
the moments just prior to a GRB will differ from that evaluated at times not
associated with a GRB. We can test for this difference independently of any
model of the GWB signal waveform. If we invoke a model for the GRB source
population and GWB radiation spectral density we can find a confidence interval
or upper limit on the root-mean-square GWB signal amplitude in the detector
waveband. To illustrate we adopt a simple, physically motivated model and
estimate that initial LIGO detector observations coincident with 1000 GRBs
could lead us to exclude, with 95% confidence, associated GWBs with $h_{RMS}
\gtrsim 1.7 \times 10^{-22}$. This result does not require the detector noise
be Gaussian or that any inter-detector correlated noise be measured or
measurable; it does not require advanced or a priori knowledge of the source
waveform; and the limits obtained on the wave-strength improve with the number
of observed GRBs.


title:
The Laser Interferometer Gravitational-wave Observatory Scientific Data
  Archive

abstract:
  LIGO --- The Laser Interferometer Gravitational-Wave Observatory --- is one
of several large projects being undertaken in the United States, Europe and
Japan to detect gravitational radiation. The novelty and precision of these
instruments is such that large volumes of data will be generated in an attempt
to find a small number of weak signals, which can be identified only as subtle
changes in the instrument output over time. In this paper, I discuss the how
the nature of the LIGO experiment determines the size of the data archive that
will be produced, how the nature of the analyses that must be used to search
the LIGO data for signals determines the anticipated access patterns on the
archive, and how the LIGO data analysis system is designed to cope with the
problems of LIGO data analysis.


title:
Gravitational collapse of fluid bodies and cosmic censorship: analytic
  insights

abstract:
  The present analytical understanding on the nature of the singularities which
form at the endstate of gravitational collapse of massive fluid bodies
("stars") is reviewed. Special emphasis is devoted to the issue of physical
reasonability of the models.


title:
Group structure of the solution manifold of the hyperbolic Ernst
  equation --- general study of the subject and detailed elaboration of
  mathematical proofs

abstract:
  This is not for the faint of heart, for we here provide the full details
concerning the statement and proof of a generalized Geroch conjecture involving
not the usual analytic functions but instead functions that are merely C^3.


title: Binary Neutron Stars Systems: Irrotational Quasi-Equilibrium Sequences

abstract:
  We report on numerical results from an independent formalism to describe the
quasi-equilibrium structure of nonsynchronous binary neutron stars in general
relativity. This is an important independent test of controversial numerical
hydrodynamic simulations which suggested that nonsynchronous neutron stars in a
close binary can experience compression and even collapse prior to the last
stable circular orbit. We show that the interior density indeed increases as
irrotational binary neutron stars approach their last orbits for particular
values of the compaction ratio. The observed compression is however at a
significantly reduced level.


title:
Phenomenological scaling laws relating the observed galactic dimensions
  to Planck action constant

abstract:
  It is shown that the characteristic observed radius, velocity, and
temperature of a typical galaxy can be inferred from Planck action constant
through a phenomenological scaling law on all cosmological scales.


title: Gravitational radiation sources and signatures

abstract:
  The goal of these lecture notes is to introduce the developing research area
of gravitational-wave phenomenology. In more concrete terms, they are meant to
provide an overview of gravitational-wave sources and an introduction to the
interpretation of real gravitational wave detector data. They are, of course,
limited in both regards. Either topic could be the subject of one or more
books, and certainly more than the few lectures possible in a summer school.
Nevertheless, it is possible to talk about the problems of data analysis and
give something of their flavor, and do the same for gravitational wave sources
that might be observed in the upcoming generation of sensitive detectors. These
notes are an attempt to do just that.


title:
Observational Limit on Gravitational Waves from Binary Neutron Stars in
  the Galaxy

abstract:
  Using optimal matched filtering, we search 25 hours of data from the LIGO
40-meter prototype laser interferometric gravitational-wave detector for
gravitational-wave chirps emitted by coalescing binary systems within our
Galaxy. This is the first test of this filtering technique on real
interferometric data. An upper limit on the rate R of neutron star binary
inspirals in our Galaxy is obtained: with 90% confidence, R< 0.5/hour. Similar
experiments with LIGO interferometers will provide constraints on the
population of tight binary neutron star systems in the Universe.


title: Numerical hydrodynamics on light cones

abstract:
  Characteristic methods show excellent promise in the evolution of single
black hole spacetimes. The effective coupling with matter fields may help the
numerical exploration of important astrophysical systems such as neutron star
black hole binaries. To this end we investigate formalisms for numerical
relativistic hydrodynamics which can be adaptable to null (characteristic)
foliations of the spacetime. The feasibility of the procedure is demonstrated
with one-dimensional results on the evolution of self-gravitating matter
accreting onto a dynamical black hole.


title: Variations of G and SEE project

abstract:
  Problems of absolute G measurements, its temporal and range variations from
both experimental and theoretical points of view are discussed, and a new
universal space project for measuring G, G(r) and G-dot promising an
improvement of our knowledge of these quantities by 2-3 orders is advocated.


title: Quantum Cosmology in Scalar-Tensor Theories With Non Minimal Coupling

abstract:
  Quantization in the minisuperspace of non minimal scalar-tensor theories
leads to a partial differential equation which is non separable. Through a
conformal transformation we can recast the Wheeler-DeWitt equation in an
integrable form, which corresponds to the minimal coupling case, whose general
solution is known. Performing the inverse conformal transformation in the
solution so found, we can construct the corresponding one in the original
frame. This procedure can also be employed with the bohmian trajectories. In
this way, we can study the classical limit of some solutions of this quantum
model. While the classical limit of these solutions occurs for small scale
factors in the Einstein's frame, it happens for small values of the scalar
field non minimally coupled to gravity in the Jordan's frame, which includes
large scale factors.


title: A surface theoretic model of quantum gravity

abstract:
  A surface theoretic view of non-perturbative quantum gravity as "spin-foams"
was proposed by Baez. A possibility of constructing such a model was studied
some time ago based on (2+1) dimensional general relativity as a reformulation
of the Ponzano-Regge model in Riemannian spacetime. In the present work, a
model based on (3+1) dimensional general relativity in Riemannian spacetime is
presented. The construction is explicit and calculable in details. For a
physical application, a computation formula for spacetime volume density
correlations is presented. Remarks for further investigations are made.


title: Relic Gravitons, Dominant Energy Condition and Bulk Viscous Stresses

abstract:
  If the energy momentum tensor contains bulk viscous stresses violating the
dominant energy condition (DOC) the energy spectra of the relic gravitons
(produced at the time of the DOC's violation) increase in frequency in a
calculable way. In a general relativistic context we give examples where the
DOC is only violated for a limited amount of time after which the ordinary
(radiation dominated) evolution takes place. We connect our discussion to some
recent remarks of Grishchuk concerning the detectability of the stochastic
gravitational wave background by the forthcoming interferometric detectors.


title:
Quantum entropy of the general non-extreme stationary axisymmetric black
  hole due to minimally coupled quantum scalar field

abstract:
  By using the 't Hooft "brick wall" model and the Pauli-Villars regularization
scheme we calculate the statistical-mechanical entropy arising from the
minimally coupled scalar fields which rotate with the azimuthal angular
velocity $\Omega_0=\Omega_H$ ($\Omega_H$ is the angular velocity of the black
hole horizon) in the general four-dimensional non-extreme stationary
axisymmetric black hole space-time. We also show, for the Kerr-Newman and the
Einstein-Maxwell dilaton-axion black holes, that the statistical-mechanical
entropy obtained from our derivation and the quantum thermodynamical entropy by
the conical singularity method are equivalent.


title: The Energy-Momentum Tensor for the Gravitational Field

abstract:
  The field theoretical description of the general relativity (GR) is further
developed. The action for the gravitational field and its sources is given
explicitely. The equations of motion and the energy-momentum tensor for the
gravitational field are derived by applying the variational principle. We have
succeeded in constructing the unique gravitational energy-momentum tensor which
is 1) symmetric, 2) conserved due to the field equations, and 3) contains not
higher than the first order derivatives of the field variables. It is shown
that the Landau-Lifshitz pseudotensor is an object most closely related to the
derived energy-momentum tensor.


title:
On the Energy-Momentum Tensor of the Scalar Field in Scalar--Tensor
  Theories of Gravity

abstract:
  We study the dynamical description of gravity, the appropriate definition of
the scalar field energy-momentum tensor, and the interrelation between them in
scalar-tensor theories of gravity. We show that the quantity which one would
naively identify as the energy-momentum tensor of the scalar field is not
appropriate because it is spoiled by a part of the dynamical description of
gravity. A new connection can be defined in terms of which the full dynamical
description of gravity is explicit, and the correct scalar field
energy-momentum tensor can be immediately identified. Certain inequalities must
be imposed on the two free functions (the coupling function and the potential)
that define a particular scalar-tensor theory, to ensure that the scalar field
energy density never becomes negative. The correct dynamical description leads
naturally to the Einstein frame formulation of scalar-tensor gravity which is
also studied in detail.


title: Conformal classes of Brans-Dicke gravity

abstract:
  A classification of Brans-Dicke theories of gravitation, based on the
behaviour of the dimensionless gravitational coupling constant, is given. It is
noted that the discussion takes place in the current literature, about which of
the two distinguished conformal frames in which scalar-tensor theories of
gravity can be formulated: the Jordan frame and the Einstein frame, is the
physical one, may, in most cases, be meaningless for both frames may belong to
the same conformal class. It is also noted that the Jordan frame formulation of
Brans-Dicke gravity with ordinary matter nonminimally coupled, that is shown to
be just the Jordan frame formulation of general relativity, is scale-invariant,
unlike the situation with the Jordan frame representation of Brans-Dicke
gravity with matter minimally coupled (the original formulation of Brans-Dicke
theory), where the presence of nonzero mass ordinary matter breaks the
scale-invariance of the theory.


title: Hartle-Hawking state is a maximum of entanglement entropy

abstract:
  It is shown that the Hartle-Hawking state of a scalar field is a maximum of
entanglement entropy in the space of pure quantum states satisfying the
condition that backreaction is finite. In other words, the Hartle-Hawking state
is a curved-space analogue of the EPR state, which is also a maximum of
entanglement entropy.


title: The Physical Interpretation of the Lanczos Tensor

abstract:
  The field equations of general relativity can be written as first order
differential equations in the Weyl tensor, the Weyl tensor in turn can be
written as a first order differential equation in a three index tensor called
the Lanczos tensor. The Lanczos tensor plays a similar role in general
relativity to that of the vector potential in electro-magnetic theory. The
Aharonov-Bohm effect shows that when quantum mechanics is applied to
electro-magnetic theory the vector potential is dynamically significant, even
when the electro-magnetic field tensor $F_{ab}$ vanishes. Here it is assumed
that in the quantum realm the Lanczos tensor is dynamically significant, and
this leads to an attempt to quantize the gravitational field by pursuing the
analogy between the vector field and the Lanczos tensor.


title: Exact Nonnull Wavelike Solutions to Gravity with Quadratic Lagrangians

abstract:
  Solutions to gravity with quadratic Lagrangians are found for the simple case
where the only nonconstant metric component is the lapse $N$ and the Riemann
tensor takes the form $R^{t}_{.itj}=-k_{i}k_{j}, i,j=1,2,3$; thus these
solutions depend on cross terms in the Riemann tensor and therefore complement
the linearized theory where it is the derivatives of the Riemann tensor that
matter. The relationship of this metric to the null gravitational radiation
metric of Peres is given. Gravitaional energy Poynting vectors are construcetd
for the solutions and one of these, based on the Lanczos tensor, supports the
indication in the linearized theory that nonnull gravitational radiation can
occur.


title: Gravitation as a Supersymmetric Gauge Theory

abstract:
  We propose a gauge theory of gravitation. The gauge potential is a connection
of the Super SL(2,C) group. A MacDowell-Mansouri type of action is proposed
where the action is quadratic in the Super SL(2,C) curvature and depends purely
on gauge connection. By breaking the symmetry of the Super SL(2,C) topological
gauge theory to SL(2,C), a spinor metric is naturally defined. With an
auxiliary anti-commuting spinor field, the theory is reduced to general
relativity. The Hamiltonian variables are related to the ones given by
Ashtekar. The auxiliary spinor field plays the role of Witten spinor in the
positive energy proof for gravitation.


title: Non-linear Evolution of Rotating Relativistic Stars

abstract:
  We present first results of the non-linear evolution of rotating relativistic
stars obtained with an axisymmetric relativistic hydrodynamics code in a fixed
spacetime. As initial data we use stationary axisymmetric and perturbed
configurations. We find that, in order to prevent (numerical) angular momentum
loss at the surface layers of the star a high-resolution grid (or a numerical
scheme that retains high order at local extrema) is needed. For non-rotating
stars, we compute frequencies of radial and non-radial small-amplitude
oscillations, which are in excellent agreement with linear normal mode
frequencies computed in the Cowling approximation. As a first application of
our code, quasi-radial modes of rapidly rotating relativistic stars are
computed. By generalizing our numerical code to 3-D, we plan to study the
evolution and non-linear dynamics of toroidal oscillations (r-modes) of rapidly
rotating neutron stars, which are a promising source of gravitational waves.


title: Quasi-Stationary Binary Inspiral: Project Overview

abstract:
  I describe the current status of a collaboration with J.D. Romano, R.H.
Price, and W. Krivan to model the geometry of and gravitational radiation
emitted by a binary system of compact objects in the regime where
non-perturbative gravitational effects exist, but the rate of inspiral is still
small relative to the orbital frequency. The method of looking for a stationary
spacetime which approximates the evolving solution is initially being tested on
a simpler model with an additional translational symmetry. This report consists
of a general description of the method, followed by summaries of three
techniques in varying stages of development: the simplification of the Einstein
equations in the presence of two commuting Killing vectors which form a
non-orthogonally-transitive symmetry group, the boundary conditions appropriate
to the balance of ingoing and outgoing radiation needed to reconcile a
stationary radiating solution with conservation of energy, and the treatment of
gravitational waves far from the sources as linearized perturbations to the
Levi-Civita spacetime. The poster presentation with which this paper is
associated is available on line at http://www-itp.unibe.ch/~whelan/poster.ps.gz
and the current status of the project is described at
http://www-itp.unibe.ch/~whelan/qsbi.html


title: Binary-induced collapse of a compact, collisionless cluster

abstract:
  We improve and extend Shapiro's model of a relativistic, compact object which
is stable in isolation but is driven dynamically unstable by the tidal field of
a binary companion. Our compact object consists of a dense swarm of test
particles moving in randomly-oriented, initially circular, relativistic orbits
about a nonrotating black hole. The binary companion is a distant, slowly
inspiraling point mass. The tidal field of the companion is treated as a small
perturbation on the background Schwarzschild geometry near the hole; the
resulting metric is determined by solving the perturbation equations of Regge
and Wheeler and Zerilli in the quasi-static limit. The perturbed spacetime
supports Bekenstein's conjecture that the horizon area of a near-equilibrium
black hole is an adiabatic invariant. We follow the evolution of the system and
confirm that gravitational collapse can be induced in a compact collisionless
cluster by the tidal field of a binary companion.


title: Kerr-Schild Approach to the Boosted Kerr Solution

abstract:
  Using a complex representation of the Debney-Kerr-Schild (DKS) solutions and
the Kerr theorem we analyze the boosted Kerr geometries and give the exact and
explicit expressions for the metrics, the principal null congruences, the
coordinate systems and the location of the singularities for arbitrary value
and orientation of the boost with respect to the angular momentum. In the
limiting, ultrarelativistic case we obtain light-like solutions possessing
diverging and twisting principal null congruences and having, contrary to the
known pp-wave limiting solutions, a non-zero value of the total angular
momentum. The implications of the above results in various related fields are
discussed.


title: Gravitational Collapse of Gravitational Waves in 3D Numerical Relativity

abstract:
  We demonstrate that evolutions of three-dimensional, strongly non-linear
gravitational waves can be followed in numerical relativity, hence allowing
many interesting studies of both fundamental and observational consequences. We
study the evolution of time-symmetric, axisymmetric {\it and} non-axisymmetric
Brill waves, including waves so strong that they collapse to form black holes
under their own self-gravity. The critical amplitude for black hole formation
is determined. The gravitational waves emitted in the black hole formation
process are compared to those emitted in the head-on collision of two Misner
black holes.


title: Numerical Relativity As A Tool For Computational Astrophysics

abstract:
  The astrophysics of compact objects, which requires Einstein's theory of
general relativity for understanding phenomena such as black holes and neutron
stars, is attracting increasing attention. In general relativity, gravity is
governed by an extremely complex set of coupled, nonlinear, hyperbolic-elliptic
partial differential equations. The largest parallel supercomputers are finally
approaching the speed and memory required to solve the complete set of
Einstein's equations for the first time since they were written over 80 years
ago, allowing one to attempt full 3D simulations of such exciting events as
colliding black holes and neutron stars. In this paper we review the
computational effort in this direction, and discuss a new 3D multi-purpose
parallel code called ``Cactus'' for general relativistic astrophysics.
Directions for further work are indicated where appropriate.


title:
Errors on the inverse problem solution for a noisy spherical
  gravitational wave antenna

abstract:
  A single spherical antenna is capable of measuring the direction and
polarization of a gravitational wave. It is possible to solve the inverse
problem using only linear algebra even in the presence of noise. The simplicity
of this solution enables one to explore the error on the solution using
standard techniques. In this paper we derive the error on the direction and
polarization measurements of a gravitational wave. We show that the solid angle
error and the uncertainty on the wave amplitude are direction independent. We
also discuss the possibility of determining the polarization amplitudes with
isotropic sensitivity for any given gravitational wave source.


title: Quantum Flux from a Moving Spherical Mirror

abstract:
  We calculate the flux from a spherical mirror which is expanding or
contracting with nearly uniform acceleration. We find that the flux at an
exterior point (which could in principle be a functional of the mirror's past
history) is actually found to be a local function, depending on the first and
second time derivatives of acceleration at the retarded time.


title: Waves in Open Systems: Eigenfunction Expansions

abstract:
  An open system is not conservative because energy can escape to the outside.
An open system by itself is thus not conservative. As a result, the
time-evolution operator is not hermitian in the usual sense and the
eigenfunctions (factorized solutions in space and time) are no longer normal
modes but quasinormal modes (QNMs) whose frequencies $\omega$ are complex. QNM
analysis has been a powerful tool for investigating open systems. Previous
studies have been mostly system specific, and use a few QNMs to provide
approximate descriptions. Here we review recent developments which aim at a
unifying treatment. The formulation leads to a mathematical structure in close
analogy to that in conservative, hermitian systems. Many of the mathematical
tools for the latter can hence be transcribed. Emphasis is placed on those
cases in which the QNMs form a complete set for outgoing wavefunctions, so that
in principle all the QNMs together give an exact description of the dynamics.
Applications to optics in microspheres and to gravitational waves from black
holes are reviewed, and directions for further development are outlined.


title: Conformally Coupled Induced Gravity with Gradient Torsion

abstract:
  It is found that conformally coupled induced gravity with gradient torsion
gives a dilaton gravity in Riemann geometry. In the Einstein frame of the
dilaton gravity the conformal symmetry is hidden and a non-vanishing
cosmological constant is not plausible due to the constraint of the conformal
coupling.


title: Motion of Spinning Particles in Gravitational Fields

abstract:
  A new path equation in absolute parallelism (AP) geometry is derived. The
equation is a generalization of three path equations derived in a previous
work. It can be considered as a geodesic equation modified by a torsion term,
whose numerical coefficient jumps by steps of one half. The torsion term is
parametrized using the fine structure constant. It is suggested that the new
equation may describe the trajectories of spinning particles under the
influence of a gravitational field, and the torsion term represents a type of
interaction between the quantum spin of the moving particle and the background
field.
  Weak field limits of the new path equation show that the gravitational
potential felt by a spinning particle is different from that felt by a spinless
particle (or a macroscopic body).
  As a byproduct, and in order to derive the new path equation, the AP-space is
reconstructed using a new affine connexion preserving metricity. The new
AP-structure has non-vanishing curvature. In certain limits, the new
AP-structure can be reduced either to the ordinary Riemannian space, or to the
conventional AP-space.


title: Averaging Einstein's Equations: The Linearized Case

abstract:
  We introduce a simple and straight-forward averaging procedure, which is a
generalization of one which is commonly used in electrodynamics, and show that
it possesses all the characteristics we require for linearized averaging in
general relativity and cosmology -- for weak-field and perturbed FLRW
situations. In particular we demonstrate that it yields quantities which are
approximately tensorial in these situations, and that its application to an
exact FLRW metric yields another FLRW metric, to first-order in integrals over
the local coordinates. Finally, we indicate some important limits of any
linearized averaging procedure with respect to cosmological perturbations which
are the result of averages over large amplitude small and intermediate scale
inhomogeneities, and show our averaging procedure can be approximately
implemented by that of Zotov and Stoeger in these cases.


title: Stochastic semiclassical gravity

abstract:
  In the first part of this paper, we show that the semiclassical
Einstein-Langevin equation, introduced in the framework of a stochastic
generalization of semiclassical gravity to describe the back reaction of matter
stress-energy fluctuations, can be formally derived from a functional method
based on the influence functional of Feynman and Vernon. In the second part, we
derive a number of results for background solutions of semiclassical gravity
consisting of stationary and conformally stationary spacetimes and scalar
fields in thermal equilibrium states. For these cases, fluctuation-dissipation
relations are derived. We also show that particle creation is related to the
vacuum stress-energy fluctuations and that it is enhanced by the presence of
stochastic metric fluctuations.


title: Renormalized stress tensor in one-bubble spacetimes

abstract:
  We compute the two-point function and the renormalized expectation value of
the stress tensor of a quantum field interacting with a nucleating bubble. Two
simple models are considered. One is the massless field in the
Vilenkin-Ipser-Sikivie spacetime describing the gravitational field of a
reflection symmetric domain wall. The other is vacuum decay in flat spacetime
where the quantum field only interacts with the tunneling field on the bubble
wall. In both cases the stress tensor is of the perfect fluid form. The
assymptotic form of the equation of state are given for each model. In the VIS
case, we find that $p=-(1/3)\rho$, where the energy density $\rho$ is dominated
by the gradients of supercurvature modes.


title:
Gupta-Bleuler quantization for minimally coupled scalar fields in de
  Sitter space

abstract:
  We present in this paper a fully covariant quantization of the
minimally-coupled massless field on de Sitter space. We thus obtain a formalism
free of any infrared (e.g logarithmic) divergence. Our method is based on a
rigorous group theoretical approach combined with a suitable adaptation (Krein
spaces) of the Wightman-G\"{a}rding axiomatic for massless fields
(Gupta-Bleuler scheme). We make explicit the correspondence between unitary
irreducible representations of the de Sitter group and the field theory on de
Sitter space-time. The minimally-coupled massless field is associated with a
representation which is the lowest term of the discrete series of unitary
representations of the de Sitter group. In spite of the presence of negative
norm modes in the theory, no negative energy can be measured: expressions as
$\le n_{k_1}n_{k_2}...|T_{00}|n_{k_1}n_{k_2}...\re$ are always positive.


title: Hawking Radiation from Feynman Diagrams

abstract:
  The aim of this letter is to clarify the relationships between Hawking
radiation and the scattering of light by matter falling into a black hole. To
this end we analyze the S-matrix elements of a model composed of a massive
infalling particle (described by a quantized field) and the radiation field.
These fields are coupled by current-current interactions and propagate in the
Schwarzschild geometry. As long as the photons energy is much smaller than the
mass of the infalling particle, one recovers Hawking radiation since our
S-matrix elements identically reproduce the Bogoliubov coefficients obtained by
treating the trajectory of the infalling particle classically. But after a
brief period, the energy of the `partners' of Hawking photons reaches this mass
and the production of thermal photons through these interactions stops. The
implications of this result are discussed.