title: Future Singularities of Isotropic Cosmologies

abstract:
  We show that globally and regularly hyperbolic future geodesically incomplete
isotropic universes, except for the standard all-encompassing `big crunch', can
accommodate singularities of only one kind, namely, those having a
non-integrable Hubble parameter, $H$. We analyze several examples from recent
literature which illustrate this result and show that such behaviour may arise
in a number of different ways. We also discuss the existence of new types of
lapse singularities in inhomogeneous models, impossible to meet in the
isotropic ones.


title: Can extra dimensional effects replace dark matter ?

abstract:
  In the braneworld scenario, the four dimensional effective Einstein equation
has extra terms which arise from the embedding of the 3-brane in the bulk. We
show that in this modified theory of gravity, it is possible to model
observations of galaxy rotation curves and the X-ray profiles of clusters of
galaxies, without the need for dark matter. In this scenario, a traceless
tensor field which arises from the projection of the bulk Weyl tensor on the
brane, provides the extra gravitational acceleration which is usually explained
through dark matter. We also predict that gravitational lensing observations
can possibly discriminate between the proposed higher dimensional effects and
dark matter, the deflection angles predicted in the proposed scenario being
around 75% to 80% of the usual predictions based on dark matter.


title: Curvature Coupling and Accelerated Expansion of the Universe

abstract:
  A new exactly solvable model for the evolution of relativistic kinetic system
interacting with an internal stochastic reservoir under the influence of a
gravitational background expansion is established. This model of
self-interaction is based on the relativistic kinetic equation for the
distribution function defined in the extended phase space. The supplementary
degree of freedom is described by the scalar stochastic variable (Langevin
source), which is considered to be the constructive element of the effective
one-particle force. The expansion of the Universe is shown to be accelerated
for the suitable choice of the non-minimal self-interaction force.


title: Minkowski electromagnetic analog for Kerr-Newman electrovac solution

abstract:
  An electromagnetic analog of the Kerr-Newman solution in general relativity
is derived, based on Minkowski's formulation for electromagnetic fields in
moving media. The equivalent system is a distribution of charges and currents
largely localized within a spinning disk of radius a. This occurs in a rotating
medium of inhomogeneous index of refraction and "frame dragging" at exactly
half the angular velocity of the electrical charge.


title: The Cosmological Origin of Inertia: Mach's Principle

abstract:
  The axes of gyroscopes experimentally define local non-rotating frames, i.e.
the time-evolution of axes of inertial frames. But what physical cause governs
the time-evolution of gyroscope axes? Starting from an unperturbed FRW
cosmology with k=0 we consider linear cosmological vorticity perturbations and
ask: Will cosmological vorticity perturbations exactly drag the axes of
gyroscopes relative to the directions of geodesics to galaxies in the
asymptotic FRW space? Using Cartan's formalism with local orthonormal bases we
cast the laws of gravitomagnetism into a form showing the close correspondence
with the laws of ordinary magnetism. Our results, valid for any equation of
state, are: 1) The dragging of a gyroscope axis by rotational perturbations
beyond the H-dot radius (H=Hubble constant) is exponentially suppressed. 2) If
the perturbation is a homogeneous rotation inside a perturbation radius, then
exact dragging of the gyroscope axis by the rotational perturbation is reached
exponentially fast, as the perturbation radius gets larger than the H-dot
radius. 3) The time-evolution of a gyroscope axis exactly follows a specific
average of the matter inside the H-dot radius. In this sense Mach's Principle
is a consequence of cosmology with Einstein gravity.


title:
A model problem for the initial-boundary value formulation of Einstein's
  field equations

abstract:
  In many numerical implementations of the Cauchy formulation of Einstein's
field equations one encounters artificial boundaries which raises the issue of
specifying boundary conditions. Such conditions have to be chosen carefully. In
particular, they should be compatible with the constraints, yield a well posed
initial-boundary value formulation and incorporate some physically desirable
properties like, for instance, minimizing reflections of gravitational
radiation.
  Motivated by the problem in General Relativity, we analyze a model problem,
consisting of a formulation of Maxwell's equations on a spatially compact
region of spacetime with timelike boundaries. The form in which the equations
are written is such that their structure is very similar to the
Einstein-Christoffel symmetric hyperbolic formulations of Einstein's field
equations. For this model problem, we specify a family of Sommerfeld-type
constraint-preserving boundary conditions and show that the resulting
initial-boundary value formulations are well posed. We expect that these
results can be generalized to the Einstein-Christoffel formulations of General
Relativity, at least in the case of linearizations about a stationary
background.


title:
Global characteristic problem for Einstein vacuum equations with small
  initial data: (I) The initial data constraints

abstract:
  We show how to prescribe the initial data of a characteristic problem
satisfying the costraints, the smallness, the regularity and the asymptotic
decay suitable to prove a global existence result. In this paper, the first of
two, we show in detail the construction of the initial data and give a sketch
of the existence result. This proof, which mimicks the analogous one for the
non characteristic problem in [Kl-Ni], will be the content of a subsequent
paper.


title: General Relativity with Torsion

abstract:
  General Relativity with nonvanishing torsion has been investigated in the
first order formalism of Poincare gauge field theory. In the presence of
torsion, either side of the Einstein equation has the nonvanishing covariant
divergence. This fact turned out to be self-consistent in the framework under
consideration. By using Noether's procedure with the definition of the Lie
derivative where the general coordinate transformation and the local Lorentz
rotation are combined, the revised covariant divergence of the energy momentum
is consistently obtained. Subsequently we have definitely derived the spin
correction to the energy momentum tensor for the Dirac field and the
Rarita-Schwinger field in the Einstein equation. We conjecture that the
accelerated expansion of the universe possibly arises due to the spin
correction in our framework.


title:
Static perfect fluid balls with given equation of state and cosmological
  constant

abstract:
  Static and spherically symmetric perfect fluid solutions of Einstein's field
equations with cosmological constant are analysed. After showing existence and
uniqueness of a regular solution at the centre the extension of this solution
is discussed. Then the existence of global solutions with given equation of
state and cosmological constant bounded by 4 pi rho_b, where rho_b is the
boundary density (given by the equation of state) of the perfect fluid ball, is
proved.


title: Quantized black holes, correspondence principle, and holographic bound

abstract:
  An equidistant spectrum of the horizon area of a quantized black hole does
not follow from the correspondence principle or from general statistical
arguments. Such a spectrum obtained earlier in loop quantum gravity (LQG) does
not comply with the holographic bound. This bound fixes the Barbero-Immirzi
parameter of LQG, and thus leads to the unique result for the spectrum of
horizon area.


title: On conformally flat initial data for Einstein equations

abstract:
  We describe conformally flat initial data, with explicitly given analytic
extrinsic curvature solving the vacuum momentum constraints. They follow from a
solution of Dain and Friedrich discovered in 2001. The cylindrically symmetric
subcase of the Bowen-York solution is a subclass of this general configuration.


title: Clock rate comparison in a uniform gravitational field

abstract:
  A partially alternative derivation of the expression for the time dilation
effect in a uniform static gravitational field is obtained by means of a
thought experiment in which rates of clocks at rest at different heights are
compared using as reference a clock bound to a free falling reference system
(FFRS). Derivations along these lines have already been proposed, but generally
introducing some shortcut in order to make the presentation elementary. The
treatment is here exact: the clocks whose rates one wishes to compare are let
to describe their world lines (Rindler's hyperbolae) with respect to the FFRS,
and the result is obtained by comparing their lengths in space-time. Only at
the end of the paper the corresponding GR metric is derived, to the purpose of
making a comparison to the solutions of Einstein field equation. The exercise
may nonetheless prove pedagogically instructive insofar as it shows that the
exact result of General Relativity (GR) can be obtained in terms of physical
and geometrical reasoning without having recourse to the general formalism. It
also compels to deal with a few subtle points inherent in the very foundations
of GR.


title: Time-Delay Interferometry

abstract:
  Equal-arm interferometric detectors of gravitational radiation allow phase
measurements many orders of magnitude below the intrinsic phase stability of
the laser injecting light into their arms. This is because the noise in the
laser light is common to both arms, experiencing exactly the same delay, and
thus cancels when it is differenced at the photo detector. In this situation,
much lower level secondary noises then set overall performance. If, however,
the two arms have different lengths (as will necessarily be the case with
space-borne interferometers), the laser noise experiences different delays in
the two arms and will hence not directly cancel at the detector. In order to
solve this problem, a technique involving heterodyne interferometry with
unequal arm lengths and independent phase-difference readouts has been
proposed. It relies on properly time-shifting and linearly combining
independent Doppler measurements, and for this reason it has been called
Time-Delay Interferometry (or TDI). This article provides an overview of the
theory and mathematical foundations of TDI as it will be implemented by the
forthcoming space-based interferometers such as the Laser Interferometer Space
Antenna (LISA) mission. We have purposely left out from this first version of
our ``Living Review'' article on TDI all the results of more practical and
experimental nature, as well as all the aspects of TDI that the data analysts
will need to account for when analyzing the LISA TDI data combinations. Our
forthcoming ``second edition'' of this review paper will include these topics.


title: Constraint Algebra in Causal Loop Quantum Gravity

abstract:
  de-Broglie--Bohm causal interpretation of canonical quantum gravity in terms
of Ashtekar new variables is built. The Poisson brackets of (deBroglie--Bohm)
constraints are derived and it is shown that the Poisson bracket of Hamiltonian
with itself would change with respect to its classical counterpart.


title: Free vacuum for loop quantum gravity

abstract:
  We linearize extended ADM-gravity around the flat torus, and use the
associated Fock vacuum to construct a state that could play the role of a free
vacuum in loop quantum gravity. The state we obtain is an element of the
gauge-invariant kinematic Hilbert space and restricted to a cutoff graph, as a
natural consequence of the momentum cutoff of the original Fock state. It has
the form of a Gaussian superposition of spin networks. We show that the peak of
the Gaussian lies at weave-like states and derive a relation between the
coloring of the weaves and the cutoff scale. Our analysis indicates that the
peak weaves become independent of the cutoff length when the latter is much
smaller than the Planck length. By the same method, we also construct
multiple-graviton states. We discuss the possible use of these states for
deriving a perturbation series in loop quantum gravity.


title:
Nonlinear r-modes in neutron stars: A hydrodynamical limitation on
  r-mode amplitudes

abstract:
  Previously we found that large amplitude $r$-modes could decay
catastrophically due to nonlinear hydrodynamic effects. In this paper we found
the particular coupling mechanism responsible for this catastrophic decay, and
identified the fluid modes involved. We find that for a neutron star described
by a polytropic equation of state with polytropic index $\Gamma=2$, the
coupling strength of the particular three-mode interaction causing the decay is
strong enough that the usual picture of the $r$-mode instability with a flow
pattern dominated by that of an $r$-mode can only be valid for the
dimensionless $r$-mode amplitude less than $O(10^{-2})$.


title: Energy flux through the horizon in the black hole-domain wall systems

abstract:
  We study various configurations in which a domain wall (or cosmic string),
described by the Nambu-Goto action, is embedded in a background space-time of a
black hole in $(3+1)$ and higher dimensional models. We calculate energy fluxes
through the black hole horizon. In the simplest case, when a static domain wall
enters the horizon of a static black hole perperdicularly, the energy flux is
zero. In more complicated situations, where parameters which describe the
domain wall surface are time and position dependent, the flux is non-vanishing
is principle. These results are of importance in various conventional
cosmological models which accommodate the existence of domain walls and strings
and also in brane world scenarios.


title: Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe

abstract:
  In three spacetime dimensions, general relativity drastically simplifies,
becoming a ``topological'' theory with no propagating local degrees of freedom.
Nevertheless, many of the difficult conceptual problems of quantizing gravity
are still present. In this review, I summarize the rather large body of work
that has gone towards quantizing (2+1)-dimensional vacuum gravity in the
setting of a spatially closed universe.


title: Non-asymptotically flat black holes/branes

abstract:
  In the framework of string-inspired dilatonic gravity theories (from 4 to $D$
space-time dimensions), we construct new non-asymptotically flat black hole or
black brane solutions. For particular values of the dilatonic coupling
constant, we generalize static solutions to rotating ones, using the target
space isometry group. We compute their masses and their angular momentum using
the modern approach to the computation of energy in General Relativity, the
quasilocal formalism, and we check the agreement of these solutions with the
first law of black hole thermodynamics. Finally, we study a new black hole
family in the 2+1 dimensional theory of Topologically Massive Gravity.


title: Polarization states of gravitational waves with a massive graviton

abstract:
  Using the Newman-Penrose formalism, we obtain the explicit expressions for
the polarization modes of weak, plane gravitational waves with a massive
graviton. Our analysis is restricted for a specific bimetric theory whose term
of mass, for the graviton, appears as an effective extra contribution to the
stress-energy tensor. We obtain for such kind of theory that the extra states
of polarization have amplitude several orders of magnitude smaller than the
polarizations purely general relativity (GR), h_(+) and h_(x), in the
VIRGO-LIGO frequency band. This result appears using the best limit to the
graviton mass inferred from solar system observations and if we consider that
all the components of the metric perturbation have the same amplitude h.
However, if we consider low frequency gravitational waves (e.g., f_(GW) ~
10^(-7) Hz), the extra polarization states produce similar Newman-Penrose
amplitudes that the polarization states purely GR. This particular
characteristic of the bimetric theory studied here could be used, for example,
to directly impose limits on the mass of the graviton from future experiments
that study the cosmic microwave background (CMB).


title: High-Speed Cylindrical Collapse of Perfect Fluid

abstract:
  The gravitational collapse of cylindrically distributed perfect fluid is
studied. We assume the collapsing speed of fluid is very large and investigate
such a situation by recently proposed high-speed approximation scheme. We show
that if the value of the pressure divided by the energy density is bounded
below by some positive value, the high-speed collapse is necessarily halted.
This suggests that the collapsing perfect fluid of realistic ideal gas
experiences the pressure bounce. However even in the case of mono-atomic ideal
gas, arbitrarily large tidal force for freely falling observers are realizable
by setting the initial collapsing velocity exceedingly large. In order that the
high-speed collapse of cylindrical perfect fluid forms spacetime singularity,
the equation of state should be very soft.


title: Comments on "Counter example to the quantum inequality"

abstract:
  In a recent preprint, Krasnikov has claimed that to show that quantum energy
inequalities (QEIs) are violated in curved spacetime situations, by considering
the example of a free massless scalar field in two-dimensional de Sitter space.
We show that this claim is incorrect, and based on misunderstandings of the
nature of QEIs. We also prove, in general two-dimensional spacetimes, that flat
spacetime QEIs give a good approximation to the curved spacetime results on
sampling timescales short in comparison with natural geometric scales.


title:
Constraint on the Squeeze Parameter of Inflaton from Cosmological
  Constant

abstract:
  The inflaton is highly likely to settle in a squeezed vacuum state after
inflation. The relic inflaton after inflation and reheating undergoes a damped
oscillatory motion and contributes to the effective cosmological constant. We
interpret the renormalized energy density from the squeezed vacuum state as an
effective cosmological constant. Using the recent observational data on the
cosmological constant, we find the constraint on the squeeze parameter of the
inflaton in the early universe.


title: Unified model of loop quantum gravity and matter

abstract:
  We reconsider the unified model of gravitation and Yang--Mills interactions
proposed by Chakraborty and Peld\'an, in the light of recent formal
developments in loop quantum gravity. In particular, we show that one can
promote the Hamiltonian constraint of the unified model to a well defined
anomaly-free quantum operator using the techniques introduced by Thiemann, at
least for the Euclidean theory. The Lorentzian version of the model can be
consistently constructed, but at the moment appears to yield a correct weak
field theory only under restrictive assumptions, and its quantization appears
problematic.


title:
Matters of Gravity, the newsletter of the Topical Group in Gravitation
  of the American Physical Society

abstract:
  Contents:
  Community news:
  Message from the Chair, by Jim Isenberg
  We hear that..., by Jorge Pullin
  THE TGG WYP Speakers Program, by Richard Price
  Research Briefs:
  Gravity Probe B is launched, by Bill Hamilton
  Questions and progress in mathematical general relativity, by Jim Isenberg
  Summary of recent preliminary LIGO results, by Alan Wiseman for the LSC
  100 Years ago, by Jorge Pullin
  Conference reports:
  Einstein 125, by Abhay Ashtekar
  The 7th Eastern Gravity Meeting, by Deirdre Shoemaker
  2004 Aspen GWADW, by Syd Meshkov
  Fifth LISA Symposium, by Curt Cutler
  GR17, by Brien Nolan
  Loops and Spinfoams, by Carlo Rovelli
  20th Pacific coast gravity meeting, by Michele Vallisneri


title: Gluing Initial Data Sets for General Relativity

abstract:
  We establish an optimal gluing construction for general relativistic initial
data sets. The construction is optimal in two distinct ways. First, it applies
to generic initial data sets and the required (generically satisfied)
hypotheses are geometrically and physically natural. Secondly, the construction
is completely local in the sense that the initial data is left unaltered on the
complement of arbitrarily small neighborhoods of the points about which the
gluing takes place. Using this construction we establish the existence of
cosmological, maximal globally hyperbolic, vacuum space-times with no constant
mean curvature spacelike Cauchy surfaces.


title:
A Nonlinear Coupling Network to Simulate the Development of the r-mode
  Instablility in Neutron Stars I. Construction

abstract:
  R-modes of a rotating neutron star are unstable because of the emission of
gravitational radiation. We explore the saturation amplitudes of these modes
determined by nonlinear mode-mode coupling. Modelling the star as
incompressible allows the analytic computation of the coupling coefficients.
All couplings up to n=30 are obtained, and analytic values for the shear
damping and mode normalization are presented. In a subsequent paper we perform
numerical simulations of a large set of coupled modes.


title: Stability of a vacuum nonsingular black hole

abstract:
  This is the first of series of papers in which we investigate stability of
the spherically symmetric space-time with de Sitter center. Geometry,
asymptotically Schwarzschild for large $r$ and asymptotically de Sitter as
$r\to 0$, describes a vacuum nonsingular black hole for $m\geq m_{cr}$ and
particle-like self-gravitating structure for $m < m_{cr}$ where a critical
value $m_{cr}$ depends on the scale of the symmetry restoration to de Sitter
group in the origin. In this paper we address the question of stability of a
vacuum non-singular black hole with de Sitter center to external perturbations.
We specify first two types of geometries with and without changes of topology.
Then we derive the general equations for an arbitrary density profile and show
that in the whole range of the mass parameter $m$ objects described by
geometries with de Sitter center remain stable under axial perturbations. In
the case of the polar perturbations we find criteria of stability and study in
detail the case of the density profile $\rho(r)=\rho_0 e^{-r^3/r_0^2 r_g}$
where $\rho_0$ is the density of de Sitter vacuum at the center, $r_0$ is de
Sitter radius and $r_g$ is the Schwarzschild radius.


title:
The implications of Mexican-hat mirrors: calculations of thermoelastic
  noise and interferometer sensitivity to perturbation for the
  Mexican-hat-mirror proposal for advanced LIGO

abstract:
  Thermoelastic noise will be the most significant noise source in
advanced-LIGO interferometers with sapphire test masses. The standard plan for
advanced-LIGO has optimized the optics, within the framework of conventional
mirrors, to reduce thermoelastic noise. Recently, we and our collaborators have
proposed going beyond the bounds of traditional optics to increase the
effective beam spot size and thus lower thermoelastic noise. One particular
proposal for mirror shapes (``Mexican-hat mirrors'') yields the class of
``mesa'' beams.
  In this paper, we outline a general procedure for analyzing light propagating
in individual arm cavities, and the associated thermoelastic noise, in the
presence of arbitrary optics. We apply these procedures to study the
Mexican-hat proposal. Results obtained by the techniques of this paper were
presented elsewhere, to demonstrate that the Mexican-hat proposal for
advanced-LIGO both significantly lowers thermoelastic noise and does not
significantly complicate the function of the interferometer.


title: Acausality in Gowdy spacetimes

abstract:
  We present a parametrization of $T^3$ and $S^1\times S^2$ Gowdy cosmological
models which allows us to study both types of topologies simultaneously. We
show that there exists a coordinate system in which the general solution of the
linear polarized special case (with both topologies) has exactly the same
functional dependence. This unified parametrization is used to investigate the
existence of Cauchy horizons at the cosmological singularities, leading to a
violation of the strong cosmic censorship conjecture. Our results indicate that
the only acausal spacetimes are described by the Kantowski-Sachs and the
Kerr-Gowdy metrics.


title: Limitations of Radar Coordinates

abstract:
  The construction of a radar coordinate system about the world line of an
observer is discussed. Radar coordinates for a hyperbolic observer as well as a
uniformly rotating observer are described in detail. The utility of the notion
of radar distance and the admissibility of radar coordinates are investigated.
Our results provide a critical assessment of the physical significance of radar
coordinates.


title:
A Semiclassical ANEC Constraint On Classical Traversable Lorentzian
  Wormholes

abstract:
  The present article lies at the interface between gravity, a highly nonlinear
phenomenon, and quantum field theory. The nonlinear field equations of Einstein
permit the theoretical existence of classical wormholes. One of the fundamental
questions relates to the practical viability of such wormholes. One way to
answer this question is to assess if the total \emph{volume} of exotic matter
needed to maintain the wormhole is finite. Using this value as the lower bound,
we propose a modified semiclassical volume Averaged Null Energy Condition
(ANEC) constraint as a method of discarding many solutions as being possible
self-consistent wormhole solutions of semiclassical gravity. The proposed
constraint is consistent with known results. It turns out that a class of
Morris-Thorne wormholes can be ruled out on the basis of this constraint.


title: What is a particle?

abstract:
  Theoretical developments related to the gravitational interaction have
questioned the notion of particle in quantum field theory (QFT). For instance,
uniquely-defined particle states do not exist in general, in QFT on a curved
spacetime. More in general, particle states are difficult to define in a
background-independent quantum theory of gravity. These difficulties have lead
some to suggest that in general QFT should not be interpreted in terms of
particle states, but rather in terms of eigenstates of local operators. Still,
it is not obvious how to reconcile this view with the empirically-observed
ubiquitous particle-like behavior of quantum fields, apparent for instance in
experimental high-energy physics, or "particle"-physics. Here we offer an
element of clarification by observing that already in flat space there exist
--strictly speaking-- two distinct notions of particles: globally defined
$n$-particle Fock-states and *local particle states*. The last describe the
physical objects detected by finite-size particle detectors and are eigenstates
of local field operators. In the limit in which the particle detectors are
appropriately large, global and local particle states converge in a weak
topology (but not in norm). This observation has little relevance for
flat-space theories --it amounts to a reminder that there are boundary effects
in realistic detectors--; but is relevant for gravity. It reconciles the two
points of view mentioned above. More importantly, it provides a definition of
local particle state that remains well-defined even when the conventional
global particle states are not defined. This definition plays an important role
in quantum gravity.


title: Eternal inflation and chaotic terminology

abstract:
  ``Eternal inflation'' is often confused with ``chaotic inflation''. Moreover,
the term ``chaotic inflation'' is being used in three different meanings (all
of them unrelated to eternal inflation). I make some suggestions in an effort
to untangle this terminological mess. I also give a brief review of the origins
of eternal inflation.


title:
Gravi-electromagnetism in five dimensions and moving bodies in Galaxy
  area

abstract:
  In Klein geometric model of space the mass is manifestation of the quantized
charges oscillations in additional compactified dimension. We analyze model in
which common in four-dimensional space-time for mass and electric charge of the
particle trajectory is disintegrated in five dimensions on movement of the mass
along null geodesic line and trajectory of the charge corresponding to the
time-like interval in 5D volume. We find relation between five-velocity vector
of electric charge and mass. This scheme is regarded to have concern with many
worlds theory. Considered approach is applied to the model of rotating space
having four-dimensional spherical symmetry. One proposed appearance additional
force in included 4D space-time, which may be explanation of the
Pioneer-effect. We analyze also possible part of this force in conservation of
the substance in Galaxy area.


title: Consistent discretization and loop quantum geometry

abstract:
  We apply the ``consistent discretization'' approach to general relativity
leaving the spatial slices continuous. The resulting theory is free of the
diffeomorphism and Hamiltonian constraints, but one can impose the
diffeomorphism constraint to reduce its space of solutions and the constraint
is preserved exactly under the discrete evolution. One ends up with a theory
that has as physical space what is usually considered the kinematical space of
loop quantum geometry, given by diffeomorphism invariant spin networks endowed
with appropriate rigorously defined diffeomorphism invariant measures and inner
products. The dynamics can be implemented as a unitary transformation and the
problem of time explicitly solved or at least reduced to as a numerical
problem. We exhibit the technique explicitly in 2+1 dimensional gravity.


title: Coupling of Gravity to Matter via SO(3,2) Gauge Fields

abstract:
  We consider gravity from the quantum field theory point of view and introduce
a natural way of coupling gravity to matter by following the gauge principle
for particle interactions. The energy-momentum tensor for the matter fields is
shown to be conserved and follows as a consequence of the dynamics in a
spontaneously broken SO(3,2) gauge theory of gravity. All known interactions
are described by the gauge principle at the microscopic level.


title: Rippled Cosmological Dark Matter from Damped Oscillating Newton Constant

abstract:
  Let the reciprocal Newton 'constant' be an apparently non-dynamical
Brans-Dicke scalar field damped oscillating towards its General Relativistic
VEV. We show, without introducing additional matter fields or dust, that the
corresponding cosmological evolution averagely resembles, in the Jordan frame,
the familiar dark radiation -> dark matter -> dark energy domination sequence.
The fingerprints of our theory are fine ripples, hopefully testable, in the FRW
scale factor; they die away at the General Relativity limit. The possibility
that the Brans-Dicke scalar also serves as the inflaton is favorably examined.


title: Pure quantum freezing of the 5$^{th}$ dimension

abstract:
  It is shown that superthin and superlong gravitational flux tube solutions in
the 5D Kaluza-Klein gravity have the region $(\approx l_{Pl})$ where the metric
signature changes from $\{+,-,-,-,- \}$ to $\{-,-,-,-,+ \}$. Such change is too
quickly from one of the paradigms of quantum gravity which tells that the
Planck length is the minimal length in the nature and consequently the physical
quantities can not change very quickly in the course of this length. For
avoiding such dynamic it is supposed that a pure quantum freezing of the
dynamic of the $5^{th}$ dimension takes place. As the continuation of the flux
tube metric in the longitudinal direction the Reissner-Nordstr\"om metric is
proposed. In the consequence of such construction one can avoid the appearance
of a point-like singularity in the extremal Reissner-Nordstr\"om solution.


title: Introduction to Loop Quantum Gravity and Spin Foams

abstract:
  These notes are a didactic overview of the non perturbative and background
independent approach to a quantum theory of gravity known as loop quantum
gravity. The definition of real connection variables for general relativity,
used as a starting point in the program, is described in a simple manner. The
main ideas leading to the definition of the quantum theory are naturally
introduced and the basic mathematics involved is described. The main
predictions of the theory such as the discovery of Planck scale discreteness of
geometry and the computation of black hole entropy are reviewed. The
quantization and solution of the constraints is explained by drawing analogies
with simpler systems. Difficulties associated with the quantization of the
scalar constraint are discussed.In a second part of the notes, the basic ideas
behind the spin foam approach are presented in detail for the simple solvable
case of 2+1 gravity. Some results and ideas for four dimensional spin foams are
reviewed.


title: More General Sudden Singularities

abstract:
  We present a general form for the solution of an expanding
general-relativistic Friedmann universe that encounters a singularity at finite
future time. The singularity occurs in the material pressure and acceleration
whilst the scale factor, expansion rate and material density remain finite and
the strong energy condition holds. We also show that the same phenomenon
occurs, but under different conditions, for Friedmann universes in gravity
theories arising from the variation of an action that is an arbitrary analytic
function of the scalar curvature.


title: Noncommutative Dynamics of Random Operators

abstract:
  We continue our program of unifying general relativity and quantum mechanics
in terms of a noncommutative algebra ${\cal A}$ on a transformation groupoid
$\Gamma = E \times G$ where $E$ is the total space of a principal fibre bundle
over spacetime, and $G$ a suitable group acting on $\Gamma $. We show that
every $a \in {\cal A}$ defines a random operator, and we study the dynamics of
such operators. In the noncommutative regime, there is no usual time but, on
the strength of the Tomita-Takesaki theorem, there exists a one-parameter group
of automorphisms of the algebra ${\cal A}$ which can be used to define a state
dependent dynamics; i.e., the pair $({\cal A}, \phi)$, where $\phi $ is a state
on ${\cal A}$, is a ``dynamic object''. Only if certain additional conditions
are satisfied, the Connes-Nikodym-Radon theorem can be applied and the
dependence on $\phi $ disappears. In these cases, the usual unitary quantum
mechanical evolution is recovered. We also notice that the same pair $({\cal
A}, \phi)$ defines the so-called free probability calculus, as developed by
Voiculescu and others, with the state $\phi $ playing the role of the
noncommutative probability measure. This shows that in the noncommutative
regime dynamics and probability are unified. This also explains probabilistic
properties of the usual quantum mechanics.


title: On the Weyl transverse frames in type I spacetimes

abstract:
  We apply a covariant and generic procedure to obtain explicit expressions of
the transverse frames that a type I spacetime admits in terms of an arbitrary
initial frame. We also present a simple and general algorithm to obtain the
Weyl scalars $\Psi_2^T$, $\Psi_0^T$ and $\Psi_4^T$ associated with these
transverse frames. In both cases it is only necessary to choose a particular
root of a cubic expression.


title: Numerical integration of the Teukolsky Equation in the time domain

abstract:
  We present a fourth order convergent (2+1) numerical code to solve the
Teukolsky equation in the time domain. Our approach is to rewrite the Teukolsky
equation as a system of first order differential equations. In this way we get
a system that has the form of an advection equation. This is used in
combination with a series expansion of the solution in powers of time. To
obtain a fourth order scheme we kept terms up to fourth derivative in time and
use the advection-like system of differential equations to substitute the
temporal derivatives by spatial derivatives. A local stability study leads to a
Courant factor of 1.5 for the nonrotating case. This scheme is used to evolve
gravitational perturbations in Schwarzschild and Kerr backgrounds. Our
numerical method proved to be fourth order convergent in r* and theta
directions. The correct power-law tail, ~1/t^{2\ell+3}, for general initial
data, and ~1/t^{2\ell+4}, for time symmetric data, was found in the simulations
where the duration in time of the tail phase was long enough. We verified that
it is crucial to resolve accurately the angular dependence of the mode at late
times in order to obtain these values of the exponents in the power-law decay.
In other cases, when the decay was too fast and round-off error was reached
before a tail was developed, the quasinormal modes frequencies provided a test
to determine the validity of our code.


title:
Probing Strong-Field Scalar-Tensor Gravity with Gravitational Wave
  Asteroseismology

abstract:
  We present an alternative way of tracing the existence of a scalar field
based on the analysis of the gravitational wave spectrum of a vibrating neutron
star. Scalar-tensor theories in strong-field gravity can potentially introduce
much greater differences in the parameters of a neutron star than the
uncertainties introduced by the various equations of state. The detection of
gravitational waves from neutron stars can set constraints on the existence and
the strength of scalar fields. We show that the oscillation spectrum is
dramatically affected by the presence of a scalar field, and can provide unique
confirmation of its existence.


title: Space-time revisited

abstract:
  The metric space-time is revised as a priori existing. It is substituted by
the world continuum endowed only with the affine connection. The metric,
accompanied by the tensor Goldstone boson, is to emerge during the spontaneous
breaking of the global affine symmetry. Implications for gravity and the
Universe are indicated.


title: On the Dirac field in the Palatini form of 1/R gravity

abstract:
  In recent papers (astro-ph/0306630, gr-qc/0312041) I have argued that the
observed cosmological acceleration can be accounted for by the inclusion of a
1/R term in the gravitational action in the Palatini formalism. Subsequently,
Flanagan (astro-ph/0308111, gr-qc/0403063) argued that this theory is
equivalent to a scalar-tensor theory which produces corrections to the standard
model that are ruled out experimentally.
  In this article I examine the Dirac field coupled to 1/R gravity. The Dirac
action contains the connection which was taken to be the Christoffel symbol,
not an independent quantity, in the papers by Flanagan. Since the metric and
connection are taken to be independent in the Palatini approach it is natural
to allow the connection that appears in the Dirac action to be an independent
quantity. This is the approach that is taken in this paper. The resulting
theory is very different and much more complicated than the one discussed in
Flanagan's papers.


title: A Minimal Model for Quantum Gravity

abstract:
  We argue that the model of a quantum computer with N qubits on a quantum
space background, which is a fuzzy sphere with n=2^N elementary cells, can be
viewed as the minimal model for Quantum Gravity. In fact, it is discrete, has
no free parameters, is Lorentz invariant, naturally realizes the Holographic
Principle, and defines a subset of punctures of spin networks' edges of Loop
Quantum Gravity labelled by spins j=2^(N-1)-1/2. In this model, the discrete
area spectrum of the cells, which is not equally spaced, is given in units of
the minimal area of Loop Quantum Gravity (for j=1/2), and provides a discrete
emission spectrum for quantum black holes. When the black hole emits one string
of N bits encoded in one of the n cells, its horizon area decreases of an
amount equal to the area of one cell.


title: On extra forces from large extra dimensions

abstract:
  The motion of a classical test particle moving on a 4-dimensional brane
embedded in an $n$-dimensional bulk is studied in which the brane is allowed to
fluctuate along the extra dimensions. It is shown that these fluctuations
produce three different forces acting on the particle, all stemming from the
effects of extra dimensions. Interpretations are then offered to describe the
origin of these forces and a relationship between the 4 and $n$-dimensional
mass of the particle is obtained by introducing charges associated with large
extra dimensions.


title: Does the coframe geometry can serve as a unification scheme?

abstract:
  The coframe field model is known as a viable model for gravity. The principle
problem is an interpretation of six additionaldegrees of freedom. We construct
a general family of connections which includes the connections of Levi-Civita
and Weitzenb\"{o}ck as the limiting cases. We show that for a special choice of
parameters, a subfamily of connections is invariant when the infinitesimal
field of transformations (antisymmetric tensor) satisfies the pair of vacuum
Maxwell equations -- one for torsion and one for non-metricity. Moreover, the
vacuum Maxwell equations turn to be the necessary and sufficient conditions for
invariance of the viable coframe action (alternative to GR). Consequently, for
the viable models, the coframe field is proved to have the Maxwell-type
behavior in addition to the known gravity sector.


title:
Riemannian light cone from vanishing birefringence in premetric vacuum
  electrodynamics

abstract:
  We consider premetric electrodynamics with a local and linear constitutive
law for the vacuum. Within this framework, we find quartic Fresnel wave
surfaces for the propagation of light. If we require vanishing birefringence in
vacuum, then a Riemannian light cone is implied. No proper Finslerian structure
can occur. This is generalized to dynamical equations of any order.


title: Hyperboloidal Slices and Artificial Cosmology for Numerical Relativity

abstract:
  This preliminary report proposes integrating the Maxwell equations in
Minkowski spacetime using coordinates where the spacelike surfaces are
hyperboloids asymptotic to null cones at spatial infinity. The space
coordinates are chosen so that Scri+ occurs at a finite coordinate and a smooth
extension beyond Scri+ is obtained. The question addressed is whether a Cauchy
evolution numerical integration program can be easily modified to compute this
evolution.
  In the spirit of the von Neumann and Richtmyer artificial viscosity which
thickens a shock by many orders of magnitude to facilitate numerical
simulation, I propose artificial cosmology to thicken null infinity Scri+ to
approximate it by a de Sitter cosmological horizon where, in conformally
compactified presentation, it provides a shell of purely outgoing null cones
where asymptotic waves can be read off as data on a spacelike pure outflow
outer boundary. This should be simpler than finding Scri+ as an isolated null
boundary or imposing outgoing wave conditions at a timelike boundary at finite
radius.


title: Tachyon as a Dark Energy Source

abstract:
  It is demonstrated that dark energy, driven by tachyons having non-minimal
coupling with curvature and self-interacting inverse cubic potential, decays to
cold dark matter in the late universe. It is found that this penomenon yields a
solution to `` cosmic coincidence problem''.


title:
Reducing Thermoelastic Noise in Gravitational-Wave Interferometers by
  Flattening the Light Beams

abstract:
  In the baseline design for advanced LIGO interferometers, the most serious
noise source is tiny, dynamically fluctuating bumps and valleys on the faces of
the arm-cavity mirrors, caused by random flow of heat in the mirrors' sapphire
substrates: so-called "thermoelastic noise". We propose replacing the
interferometers' baseline arm-cavity light beams, which have Gaussian-shaped
intensity profiles, by beams with mesa-shaped profiles that are flat in their
central ~7 cm of radius, and that then fall toward zero as quickly as is
allowed by diffraction in LIGO's 4 km arms. The mesa beams average the bumps
and valleys much more effectively than the Gaussian beams. As a result, if the
beam radii are adjusted so diffraction losses per bounce are about 10 ppm,
replacing Gaussian beams by mesa beams reduces the thermoelastic noise power by
about a factor 3. If other thermal noises are kept negligible, this will permit
advanced LIGO to beat the Standard Quantum Limit by about a factor 1.5 over a
bandwidth about equal to frequency, and the event rate for inspiraling neutron
star binaries will increase by about a factor 2.5. The desired mesa beams can
be produced from input, Gaussian-profile laser light, by changing the shapes of
the arm cavities' mirror faces from their baseline spherical shapes (with radii
of curvature of order 60 km) to Mexican-hat (MH) shapes that have a shallow
bump in the center but are otherwise much flatter in the central 10 cm than the
spherical mirrors, and then flare upward strongly in the outer 6 cm, like a
sombrero. We describe mesa beams and MH mirrors mathematically and we report
the results of extensive modeling calculations, which show that mesa-beam
interferometers are not much more sensitive than the Gaussian-beam
interferometers to errors in mirror figures, positions, and orientations.


title: Cosmology: Techniques and Observations

abstract:
  These lectures were addressed to nonspecialists willing to learn some basic
facts, approaches, tools and observational evidence which conform modern
cosmology. The aim is also to try to complement the many excellent treatises
that exists on the subject (an exhaustive treatment being in any case
impossible for lack of time, in the lectures, and of space here), instead of
trying to cover everything in a telegraphic way. We start by recalling in the
introduction a couple of philosophical questions that have always upset
inquiring minds. We then present some original mathematical approaches to
investigate a number of basic questions, as the comparison of two point
distributions (each point corresponding to a galaxy or galaxy cluster), the use
of non-standard statistics in the analysis of possible non-Gaussianities, and
the use of zeta regularization in the study of the contributions of vacuum
energy effects at the cosmological scale. And we also summarize a number of
important issues which are both undoubtedly beautiful (from the physical
viewpoint) and useful in present-day observational cosmology. To finish, the
reader should be warned that, for the reasons already given and lack of space,
some fundamental issues, as inflation, quantum gravity and string theoretical
fundamental approaches to cosmology will not be dealt with here. A minimal
treatment of any of them would consume more pages than the ones at disposal
and, again, a number of excellent treatments of these subjects are available.


title: Testing Quantum Gravity via Cosmogenic Neutrino Oscillations

abstract:
  Implications of some proposed theories of quantum gravity for neutrino flavor
oscillations are explored within the context of modified dispersion relations
of special relativity. In particular, approximate expressions for
Planck-scale-induced deviations from the standard oscillation length are
obtained as functions of neutrino mass, energy, and propagation distance.
Grounding on these expressions, it is pointed out that, in general, even those
deviations that are suppressed by the second power of the Planck energy may be
observable for ultra-high-energy neutrinos, provided they originate at
cosmological distances. In fact, for neutrinos in the highest energy range of
EeV to ZeV, deviations that are suppressed by as much as the seventh power of
the Planck energy may become observable. Accordingly, realistic possibilities
of experimentally verifying these deviations by means of the next generation
neutrino detectors--such as IceCube and ANITA--are investigated.


title: Analysis of Dynamic Axial-Symmetric Shells

abstract:
  The aim of this work is to analyze the dynamical behavior of relativistic
infinite axial-symmetric shells with flat interior and a radiation filled
curved exterior spacetimes. It will be proven, by the use of conservation
equations of Israel, that the given configuration does not let expansion or
collapse of the shell which was proposed before, but rather the shell stays at
constant radius. The case of null-collapse will also be considered in this work
and it will be shown that the shell collapses to zero radius, and moreover, if
cylindrical flatness is imposed a boundary layer is obtained still contrary to
previous works.


title: The finite mass beamsplitter in high power interferometers

abstract:
  The beamplitter in high-power interferometers is subject to significant
radiation-pressure fluctuations. As a consequence, the phase relations which
appear in the beamsplitter coupling equations oscillate and phase modulation
fields are generated which add to the reflected fields. In this paper, the
transfer function of the various input fields impinging on the beamsplitter
from all four ports onto the output field is presented including
radiation-pressure effects. We apply the general solution of the coupling
equations to evaluate the input-output relations of the dual-recycled
laser-interferometer topology of the gravitational-wave detector GEO600 and the
power-recycling, signal-extraction topology of advanced LIGO. We show that the
input-output relation exhibits a bright-port dark-port coupling. This mechanism
is responsible for bright-port contributions to the noise density of the output
field and technical laser noise is expected to decrease the interferometer's
sensitivity at low frequencies. It is shown quantitatively that the issue of
technical laser noise is unimportant in this context if the interferometer
contains arm cavities.


title: $\bar{SL}(4,R)$ Embedding for a 3D World Spinor Equation

abstract:
  A generic-curved spacetime Dirac-like equation in 3D is constructed. It has,
owing to the $\bar{SL}(n,R)$ group deunitarizing automorphism, a physically
correct unitarity and flat spacetime particle properties. The construction is
achieved by embedding $\bar{SL}(3,R)$ vector operator $X_{\mu}$, that plays a
role of Dirac's $\gamma_{\mu}$ matrices, into $\bar{SL}(4,R)$. Decomposition of
the unitary irreducible spinorial $\bar{SL}(4,R)$ representations gives rise to
an explicit form of the infinite $X_{\mu}$ matrices.


title: Tests of scalar-tensor gravity

abstract:
  The best motivated alternatives to general relativity are scalar-tensor
theories, in which the gravitational interaction is mediated by one or several
scalar fields together with the usual graviton. The analysis of their various
experimental constraints allows us to understand better which features of the
models have actually been tested, and to suggest new observations able to
discriminate between them. This talk reviews three classes of constraints on
such theories, which are qualitatively different from each other: (i)
solar-system experiments; (ii) binary-pulsar tests and future detections of
gravitational waves from inspiralling binaries; (iii) cosmological
observations. While classes (i) and (ii) impose precise bounds respectively on
the first and second derivatives of the matter-scalar coupling function, (iii)
a priori allows us to reconstruct the full shapes of the functions of the
scalar field defining the theory, but obviously with more uncertainties and/or
more theoretical hypotheses needed. Simple arguments such as the absence of
ghosts (to guarantee the stability of the field theory) nevertheless suffice to
rule out a wide class of scalar-tensor models. Some of them can be probed only
if one takes simultaneously into account solar-system and cosmological
observations.


title: Cosmological models from a dynamical systems perspective

abstract:
  It is useful to study the space of all cosmological models from a dynamical
systems perspective, that is, by formulating the Einstein field equations as a
dynamical system using appropriately normalized variables. We will discuss
various aspects of this work, the choices of normalization factor, multiple
representations of models, the past attractor, nonlinear dynamics in
close-to-Friedmann-Lemaitre models, Weyl curvature dominance, and numerical
simulations.


title:
A New Family of Light Beams and Mirror Shapes for Future LIGO
  Interferometers

abstract:
  Advanced LIGO's present baseline design uses arm cavities with Gaussian light
beams supported by spherical mirrors. Because Gaussian beams have large
intensity gradients in regions of high intensity, they average poorly over
fluctuating bumps and valleys on the mirror surfaces, caused by random thermal
fluctuations (thermoelastic noise). Flat-topped light beams (mesa beams) are
being considered as an alternative because they average over the thermoelastic
fluctuations much more effectively. However, the proposed mesa beams are
supported by nearly flat mirrors, which experience a very serious tilt
instability. In this paper we propose an alternative configuration in which
mesa-shaped beams are supported by nearly concentric spheres, which experience
only a weak tilt instability. The tilt instability is analyzed for these
mirrors in a companion paper by Savov and Vyatchanin. We also propose a
one-parameter family of light beams and mirrors in which, as the parameter
alpha varies continuously from 0 to pi, the beams and supporting mirrors get
deformed continuously from the nearly flat-mirrored mesa configuration ("FM")
at alpha=0, to the nearly concentric-mirrored mesa configuration ("CM") at
alpha=pi. The FM and CM configurations at the endpoints are close to optically
unstable, and as alpha moves away from 0 or pi, the optical stability improves.


title:
Estimate of Tilt Instability of Mesa-Beam and Gaussian-Beam Modes for
  Advanced LIGO

abstract:
  Sidles and Sigg have shown that advanced LIGO interferometers will encounter
a serious tilt instability, in which symmetric tilts of the mirrors of an arm
cavity cause the cavity's light beam to slide sideways, so its radiation
pressure exerts a torque that increases the tilt. Sidles and Sigg showed that
the strength T of this torque is 26.2 times greater for advanced LIGO's
baseline cavities -- nearly flat spherical mirrors which support Gaussian beams
(``FG'' cavities), than for nearly concentric spherical mirrors which support
Gaussian beams with the same diffraction losses as the baseline case -- ``CG''
cavities: T^{FG}/T^{CG} = 26.2. This has motivated a proposal to change the
baseline design to nearly concentric, spherical mirrors. In order to reduce
thermoelastic noise in advanced LIGO, O'Shaughnessy and Thorne have proposed
replacing the spherical mirrors and their Gaussian beams by ``Mexican-Hat''
(MH) shaped mirrors which support flat-topped, ``mesa'' shaped beams. In this
paper we compute the tilt-instability torque for advanced-LIGO cavities with
nearly flat MH mirrors and mesa beams (``FM'' cavities) and nearly concentric
MH mirrors and mesa beams (``CM'' cavities), with the same diffraction losses
as in the baseline FG case. We find that the relative sizes of the restoring
torques are T^{CM}/T^{CG} = 0.91, T^{FM}/T^{CG} = 96, T^{FM}/T^{FG} = 3.67.
Thus, the nearly concentric MH mirrors have a weaker tilt instability than any
other configuration. Their thermoelastic noise is the same as for nearly flat
MH mirrors, and is much lower than for spherical mirrors.


title: Acoustic Wormholes

abstract:
  Acoustic analogs of static, spherically symmetric massive traversable
Lorentzian wormholes are constructed as a {\em formal} extension of acoustic
black holes. The method is straightforward but the idea is interesting in
itself. The analysis leads to a new acoustic invariant for the massless
counterpart of the Einstein-Rosen model of an elementary particle. It is shown
that there is a marked, in a sense even counterintuitive, physical difference
between the acoustic analogs of black holes and wormholes. The analogy allows
us to also portray the nature of curvature singularity in the acoustic
language. It is demonstrated that the light ray trajectories in an optical
medium are the same as the sound trajectories in its acoustic analog. The
implications of these analogies in the laboratory set up and in the different
context of phantom energy accretion have been speculated.


title:
Non-violation of Energy Conditions in the future accelerated universe
  due to quantum effects

abstract:
  Here, an accelerated phantom model for the late universe is explored, which
is free from future singularity. It is interseting to see that this model
exhibits strong curvature for all time in future, unlike models with `big-rip
singularity' showing high curvature near singularity time only. So, quantum
gravity effects grow dominant as time increases in the late universe too. More
importantly, it is demonstrated that that quantum corrections to FRW equations
lead to non-violation of `cosmic energy conditions' of general relativity,
which are violated for accelerating universe without these corrections.


title: Canonical DSR

abstract:
  For a certain example of a "doubly special relativity theory" the modified
space-time Lorentz transformations are obtained from momentum space
transformations by using canonical methods. In the sequel an energy-momentum
dependent space-time metric is constructed, which is essentially invariant
under the modified Lorentz transformations. By associating such a metric to
every Planck cell in space and the energy-momentum contained in it, a solution
of the problem of macroscopic bodies in doubly special relativity is suggested.


title: Energy conditions and a bounce in FLRW cosmologies

abstract:
  Exploiting the existence of two "cosmological" constants, one associated with
the classical Lovelock theorem and one with the vacuum energy density, we
argue, in a model independent way, that in spatially closed FLRW cosmologies
with a positive definite effective cosmological constant there exists a range
in this constant that serves as a sufficient condition for the satisfaction of
the null, weak, strong and dominant energy conditions at a bounce. The
application of energy conditions is not unambiguous and we show how the bounce
can be considered classically and how, we believe more reasonably, it can be
considered a matter of quantum cosmology.


title: From Gravitons to Gravity: Myths and Reality

abstract:
  There is a general belief, reinforced by statements in standard textbooks,
that: (i) one can obtain the full non-linear Einstein's theory of gravity by
coupling a massless, spin-2 field $h_{ab}$ self-consistently to the total
energy momentum tensor, including its own; (ii) this procedure is unique and
leads to Einstein-Hilbert action and (iii) it only uses standard concepts in
Lorentz invariant field theory and does not involve any geometrical
assumptions. After providing several reasons why such beliefs are suspect --
and critically re-examining several previous attempts -- we provide a detailed
analysis aimed at clarifying the situation. First, we prove that it is
\textit{impossible} to obtain the Einstein-Hilbert (EH) action, starting from
the standard action for gravitons in linear theory and iterating repeatedly.
Second, we use the Taylor series expansion of the action for Einstein's theory,
to identify the tensor $\mathcal{S}^{ab}$, to which the graviton field $h_{ab}$
couples to the lowest order. We show that the second rank tensor
$\mathcal{S}^{ab}$ is {\it not} the conventional energy momentum tensor
$T^{ab}$ of the graviton and provide an explanation for this feature. Third, we
construct the full nonlinear Einstein's theory with the source being spin-0
field, spin-1 field or relativistic particles by explicitly coupling the spin-2
field to this second rank tensor $\mathcal{S}^{ab}$ order by order and summing
up the infinite series. Finally, we construct the theory obtained by self
consistently coupling $h_{ab}$ to the conventional energy momentum tensor
$T^{ab}$ order by order and show that this does {\it not} lead to Einstein's
theory. (condensed).


title: Some Thoughts on Energy Conditions and Wormholes

abstract:
  This essay reviews some of the recent progress in the area of energy
conditions and wormholes. Most of the discussion centers on the subject of
``quantum inequality'' restrictions on negative energy. These are bounds on the
magnitude and duration of negative energy which put rather severe constraints
on its possible macroscopic effects. Such effects might include the
construction of wormholes and warp drives for faster-than-light travel, and
violations of the second law of thermodynamics. Open problems and future
directions are also discussed.


title: omega dependence of the scalar field in Brans-Dicke theory

abstract:
  This article examines the claim that the Brans-Dicke scalar field \phi \to
\phi_{0} + O(1/\sqrt{\omega}) for large $\omega$ when the matter field is
traceless. It is argued that such a claim can not be true in general.


title:
Scalar gravity with preferred frame: asymptotic post-Newtonian scheme
  and the weak equivalence principle

abstract:
  A scalar theory of gravity with a preferred reference frame is presented. It
is insisted on the dynamics, which involves a (non-trivial) extension of
Newton's second law, and on the new version (v2) with isotropic space metric.
We display the energy conservation equation obtained with v2. Then the
principles of the asymptotic post-Newtonian approximation are discussed in some
detail. The results of its application to the motion of a small extended body
in a weakly-gravitating system are given and discussed: the weak equivalence
principle was violated in v1, due to its anisotropic space metric (as the
standard Schwarzschild metric), but is valid with v2.


title: Energy Flux Correlations and Moving Mirrors

abstract:
  We study the quantum stress tensor correlation function for a massless scalar
field in a flat two-dimensional spacetime containing a moving mirror. We
construct the correlation functions for right-moving and left-moving fluxes for
an arbitrary trajectory, and then specialize them to the case of a mirror
trajectory for which the expectation value of the stress tensor describes a
pair of delta-function pulses, one of negative energy and one of positive
energy. The flux correlation function describes the fluctuations around this
mean stress tensor, and reveals subtle changes in the correlations between
regions where the mean flux vanishes.


title:
Hadamard regularization of the third post-Newtonian gravitational wave
  generation of two point masses

abstract:
  Continuing previous work on the 3PN-accurate gravitational wave generation
from point particle binaries, we obtain the binary's 3PN mass-type quadrupole
and dipole moments for general (not necessarily circular) orbits in harmonic
coordinates. The final expressions are given in terms of their ``core'' parts,
resulting from the application of the pure Hadamard-Schwartz (pHS) self-field
regularization scheme, and augmented by an ``ambiguous'' part. In the case of
the 3PN quadrupole we find three ambiguity parameters, xi, kappa and zeta, but
only one for the 3PN dipole, in the form of the particular combination
xi+kappa. Requiring that the dipole moment agree with the center-of-mass
position deduced from the 3PN equations of motion in harmonic coordinates
yields the relation xi+kappa=-9871/9240. Our results will form the basis of the
complete calculation of the 3PN radiation field of compact binaries by means of
dimensional regularization.


title: Physical Vacuum Properties and Internal Space Dimension

abstract:
  The paper addresses matrix spaces, whose properties and dynamics are
determined by Dirac matrices in Riemannian spaces of different dimension and
signature. Among all Dirac matrix systems there are such ones, which nontrivial
scalar, vector or other tensors cannot be made up from. These Dirac matrix
systems are associated with the vacuum state of the matrix space. The simplest
vacuum system realization can be ensured using the orthonormal basis in the
internal matrix space. This vacuum system realization is not however unique.
The case of 7-dimensional Riemannian space of signature 7(-) is considered in
detail. In this case two basically different vacuum system realizations are
possible: (1) with using the orthonormal basis; (2) with using the
oblique-angled basis, whose base vectors coincide with the simple roots of
algebra E_{8}.
  Considerations are presented, from which it follows that the least-dimension
space bearing on physics is the Riemannian 11-dimensional space of signature
1(-)& 10(+). The considerations consist in the condition of maximum vacuum
energy density and vacuum fluctuation energy density.


title: An analytic cylindrically symmetric solution for collapsing dust

abstract:
  Dust configurations are the simplest models for astrophysical objects. Here
we examine the gravitational collapse of an infinite cylinder of dust and give
an analytic interior solution. Surprisingly, starting with a cylindrically
symmetric ansatz one arrives at a 3-space with constant curvature, i.e. the
resulting metric describes a piece of the Friedman interior of the
Oppenheimer-Snyder collapse. Indeed, by introducing double polar coordinates, a
3-space of constant curvature can be interpreted as a cylindrically symmetric
space as well. This result shows afresh that topology is not fixed by the
Einstein equations.


title: Mass and charge fluctuations and black hole entropy

abstract:
  The effects of thermal fluctuations of the mass (horizon area) and electric
charge, on the entropy of non-rotating charged {\it macroscopic} black holes,
are analyzed using a grand canonical ensemble. Restricting to Gaussian
fluctuations around equilibrium, and assuming a power law type of relation
between the black hole mass, charge and horizon area, characterized by two real
positive indices, the grand canonical entropy is shown to acquire a logarithmic
correction with a positive coefficient proportional to the sum of the indices.
However, the root mean squared fluctuations of mass and charge relative to the
mean values of these quantities turn out to be independent of the details of
the assumed mass-area relation. We also comment on possible cancellation
between log (area) corrections arising due to {\it fixed area} quantum
spacetime fluctuations and that due to thermal fluctuations of the area and
other quantities.


title: Formation of Wakes by Chiral, Conducting Cosmic Strings

abstract:
  Chiral cosmic strings are naturally produced at the end of D-term inflation
and they present very interesting cosmological consequences. In this work, we
investigate the formation and evolution of wakes by a chiral string. We show
that, for cold dark matter, the mechanism of forming wakes by a chiral string
is similar to the mechanism by an ordinary string.


title: The gravitational phase shift in a matter-wave interferometer (MIGO)

abstract:
  The original computation did not take into account the initial phase shift. A
corrected computation, included as section II in the revised version of
gr-qc/0407039, still gives a term proportional to the derivative of the signal,
qualitatively confirming the original result.


title:
A dynamical systems approach to the tilted Bianchi models of solvable
  type

abstract:
  We use a dynamical systems approach to analyse the tilting spatially
homogeneous Bianchi models of solvable type (e.g., types VI$_h$ and VII$_h$)
with a perfect fluid and a linear barotropic $\gamma$-law equation of state. In
particular, we study the late-time behaviour of tilted Bianchi models, with an
emphasis on the existence of equilibrium points and their stability properties.
We briefly discuss the tilting Bianchi type V models and the late-time
asymptotic behaviour of irrotational Bianchi VII$_0$ models. We prove the
important result that for non-inflationary Bianchi type VII$_h$ models vacuum
plane-wave solutions are the only future attracting equilibrium points in the
Bianchi type VII$_h$ invariant set. We then investigate the dynamics close to
the plane-wave solutions in more detail, and discover some new features that
arise in the dynamical behaviour of Bianchi cosmologies with the inclusion of
tilt. We point out that in a tiny open set of parameter space in the type IV
model (the loophole) there exists closed curves which act as attracting limit
cycles. More interestingly, in the Bianchi type VII$_h$ models there is a
bifurcation in which a set of equilibrium points turn into closed orbits. There
is a region in which both sets of closed curves coexist, and it appears that
for the type VII$_h$ models in this region the solution curves approach a
compact surface which is topologically a torus.


title: Proposed New Test of Spin Effects in General Relativity

abstract:
  The recent discovery of a double-pulsar PSR J0737-3039A/B provides an
opportunity of unequivocally observing, for the first time, spin effects in
general relativity. Existing efforts involve detection of the precession of the
spinning body itself. However, for a close binary system, spin effects on the
orbit may also be discernable. Not only do they add to the advance of the
periastron (by an amount which is small compared to the conventional
contribution) but they also give rise to a precession of the orbit about the
spin direction. The measurement of such an effect would also give information
on the moment of inertia of pulsars.


title:
Velocities and Momenta in an Extended Elliptic Form of the Initial Value
  Conditions

abstract:
  The complete form of the constraints following from their conformal structure
is extended so as to include constant mean curvature and other mean curvature
foliations. This step is demonstrated using the momentum phase space approach.
This approach yields equations of exactly the same form as the extended
conformal thin sandwich approach. In solving the equations, it is never
necessary actually to perform a tensor decomposition.


title:
Regular and quasi black hole solutions for spherically symmetric charged
  dust distributions in the Einstein-Maxwell theory

abstract:
  Static spherically symmetric distributions of electrically counterpoised dust
(ECD) are used to construct solutions to Einstein-Maxwell equations in
Majumdar--Papapetrou formalism. Unexpected bifurcating behaviour of solutions
with regard to source strength is found for localized, as well as for the
delta-function ECD distributions. Unified treatment of general ECD
distributions is accomplished and it is shown that for certain source strengths
one class of regular solutions approaches Minkowski spacetime, while the other
comes arbitrarily close to black hole solutions.


title: Bianchi type I universe with viscous fluid

abstract:
  We study the evolution of a homogeneous, anisotropic Universe given by a
Bianchi type-I cosmological model filled with viscous fluid, in the presence of
a cosmological constant $\Lambda$. The role of viscous fluid and $\Lambda$ term
in the evolution the BI space-time is studied. Though the viscosity cannot
remove the cosmological singularity, it plays a crucial part in the formation
of a qualitatively new behavior of the solutions near singularity. It is shown
that the introduction of the $\Lambda$ term can be handy in the elimination of
the cosmological singularity. In particular, in case of a bulk viscosity, it
provides an everlasting process of evolution ($\Lambda < 0$), whereas, for some
positive values of $\Lambda$ and the bulk viscosity being inverse proportional
to the expansion, the BI Universe admits a singularity-free oscillatory mode of
expansion. In case of a constant bulk viscosity and share viscosity being
proportional to expansion, the model allows oscillatory mode accompanied by an
exponential growth even with a negative $\Lambda$. Space-time singularity in
this case occurs at $t \to -\infty$.


title: Synchronization Gauges and the Principles of Special Relativity

abstract:
  The axiomatic bases of Special Relativity Theory (SRT) are thoroughly
re-examined from an operational point of view, with particular emphasis on the
status of Einstein synchronization in the light of the possibility of arbitrary
synchronization procedures in inertial reference frames. Once correctly and
explicitly phrased, the principles of SRT allow for a wide range of `theories'
that differ from the standard SRT only for the difference in the chosen
synchronization procedures, but are wholly equivalent to SRT in predicting
empirical facts. This results in the introduction, in the full background of
SRT, of a suitable synchronization gauge. A complete hierarchy of
synchronization gauges is introduced and elucidated, ranging from the useful
Selleri synchronization gauge (which should lead, according to Selleri, to a
multiplicity of theories alternative to SRT) to the more general Mansouri-Sexl
synchronization gauge and, finally, to the even more general
Anderson-Vetharaniam-Stedman's synchronization gauge. It is showed that all
these gauges do not challenge the SRT, as claimed by Selleri, but simply lead
to a number of formalisms which leave the geometrical structure of Minkowski
spacetime unchanged. Several aspects of fundamental and applied interest
related to the conventional aspect of the synchronization choice are discussed,
encompassing the issue of the one-way velocity of light on inertial and
rotating reference frames, the GPS's working, and the recasting of Maxwell
equations in generic synchronizations. Finally, it is showed how the gauge
freedom introduced in SRT can be exploited in order to give a clear explanation
of the Sagnac effect for counter-propagating matter beams.


title: Future Asymptotic Behaviour of Tilted Bianchi models of type IV and VIIh

abstract:
  Using dynamical systems theory and a detailed numerical analysis, the
late-time behaviour of tilting perfect fluid Bianchi models of types IV and
VII$_h$ are investigated. In particular, vacuum plane-wave spacetimes are
studied and the important result that the only future attracting equilibrium
points for non-inflationary fluids are the plane-wave solutions in Bianchi type
VII$_h$ models is discussed. A tiny region of parameter space (the loophole) in
the Bianchi type IV model is shown to contain a closed orbit which is found to
act as an attractor (the Mussel attractor). From an extensive numerical
analysis it is found that at late times the normalised energy-density tends to
zero and the normalised variables 'freeze' into their asymptotic values. A
detailed numerical analysis of the type VII$_h$ models then shows that there is
an open set of parameter space in which solution curves approach a compact
surface that is topologically a torus.


title:
The GEMS Approach to Stationary Motions in the Spherically Symmetric
  Spacetimes

abstract:
  We generalize the work of Deser and Levin on the unified description of
Hawking radiation and Unruh effect to general stationary motions in spherically
symmetric black holes. We have also matched the chemical potential term of the
thermal spectrum of the two sides for uncharged black holes.


title: Exact Relativistic Static Charged Perfect Fluid Disks

abstract:
  Using the well-known ``displace, cut and reflect'' method used to generate
disks from given solutions of Einstein field equations, we construct static
charged disks made of perfect fluid based on the Reissner-Nordstr\"{o}m
solution in isotropic coordinates. We also derive a simple stability condition
for charged and non charged perfect fluid disks. As expected, we find that the
presence of charge increases the regions of instability of the disks.


title:
A General Relativistic Model for the Gravitational Field of Active
  Galactic Nuclei Surrounded by a Disk

abstract:
  An exact but simple general relativistic model for the gravitational field of
active galactic nuclei is constructed, based on the superposition in Weyl
coordinates of a black hole, a Chazy-Curzon disk and two rods, which represent
matter jets. The influence of the rods on the matter properties of the disk and
on its stability is examined. We find that in general they contribute to
destabilize the disk. Also the oscillation frequencies for perturbed circular
geodesics on the disk are computed, and some geodesic orbits for the superposed
metric are numerically calculated.


title: On the stability of general relativistic geometric thin disks

abstract:
  The stability of general relativistic thin disks is investigated under a
general first order perturbation of the energy momentum tensor. In particular,
we consider temporal, radial and azimuthal "test matter" perturbations of the
quantities involved on the plane $z=0$. We study the thin disks generated by
applying the "displace, cut and reflect" method, usually known as the image
method, to the Schwarzschild metric in isotropic coordinates and to the
Chazy-Curzon metric and the Zipoy-Voorhees metric ($\gamma$-metric) in Weyl
coordinates. In the case of the isotropic Schwarzschild thin disk, where a
radial pressure is present to support the gravitational attraction, the disk is
stable and the perturbation favors the formation of rings. Also, we found the
expected result that the thin disk models generated by the Chazy-Curzon and
Zipoy-Voorhees metric with only azimuthal pressure are not stable under a
general first order perturbation


title: Mission Design for the Laser Astrometric Test Of Relativity

abstract:
  This paper focuses on the mission design for the Laser Astrometric Test Of
Relativity (LATOR). This mission uses laser interferometry between two
micro-spacecraft whose lines of sight pass close by the Sun to accurately
measure deflection of light in the solar gravity. The key element of the
experimental design is a redundant geometry optical truss provided by a
long-baseline (100 m) multi-channel stellar optical interferometer placed on
the International Space Station (ISS). The spatial interferometer is used for
measuring the angles between the two spacecraft and for orbit determination
purposes. The geometric redundancy enables LATOR to measure the departure from
Euclidean geometry caused by the solar gravity field to a very high accuracy.
Such a design enables LATOR to improve the value of the parameterized
post-Newtonian (PPN) parameter $\gamma$ to unprecedented levels of accuracy of
1 part in 10$^{8}$; the misison will also measure effects of the next
post-Newtonian order ($\propto G^2$) of light deflection resulting from
gravity's intrinsic non-linearity. The solar quadrupole moment parameter,
$J_2$, will be measured with high precision, as well as a variety of other
relativistic effects including Lense-Thirring precession. LATOR will lead to
very robust advances in the tests of Fundamental physics: this mission could
discover a violation or extension of general relativity, or reveal the presence
of an additional long range interaction in the physical law.


title: Signaling, Entanglement, and Quantum Evolution Beyond Cauchy Horizons

abstract:
  Consider a bipartite entangled system half of which falls through the event
horizon of an evaporating black hole, while the other half remains coherently
accessible to experiments in the exterior region. Beyond complete evaporation,
the evolution of the quantum state past the Cauchy horizon cannot remain
unitary, raising the questions: How can this evolution be described as a
quantum map, and how is causality preserved? What are the possible effects of
such nonstandard quantum evolution maps on the behavior of the entangled
laboratory partner? More generally, the laws of quantum evolution under extreme
conditions in remote regions (not just in evaporating black-hole interiors, but
possibly near other naked singularities and regions of extreme spacetime
structure) remain untested by observation, and might conceivably be non-unitary
or even nonlinear, raising the same questions about the evolution of entangled
states. The answers to these questions are subtle, and are linked in unexpected
ways to the fundamental laws of quantum mechanics. We show that terrestrial
experiments can be designed to probe and constrain exactly how the laws of
quantum evolution might be altered, either by black-hole evaporation, or by
other extreme processes in remote regions possibly governed by unknown physics.


title: Comments on the Quantum Vacuum and the Light Acceleration

abstract:
  The recent observations on the far quasars absorption lines spectra and
comparison of these lines with laboratory ones provide a framework for
explantation of these observations by considering a varying fine structure
constant, over the cosmological time-scale. Also, there seems to be an
anomalous acceleration in the Pioneer spacecraft 10/11 about $ 10^{-10} {\rm
m}/{\rm s^2}$. These matters lead Ranada to study the quantum vacuum to explain
these problems by introducing a phenomenological model for the variation of
$\alpha$. In this manuscript we want to show that this model is not a quantum
model; it is a classical model that is only in accordance with mentioned
observations by adjusting some parameters and is not based on a fundamental
physical intuition.


title:
The problem of time and gauge invariance in the quantization of
  cosmological models. I. Canonical quantization methods

abstract:
  The paper is the first of two parts of a work reviewing some approaches to
the problem of time in quantum cosmology, which were put forward last decade,
and which demonstrated their relation to the problems of reparametrization and
gauge invariance of quantum gravity. In the present part we remind basic
features of quantum geometrodynamics and minisuperspace cosmological models,
and discuss fundamental problems of the Wheeler - DeWitt theory. Various
attempts to find a solution to the problem of time are considered in the
framework of the canonical approach. Possible solutions to the problem are
investigated making use of minisuperspace models, that is, systems with a
finite number of degrees of freedom. At the same time, in the last section of
the paper we expand our consideration beyond the minisuperspace approximation
and briefly review promising ideas by Brown and Kuchar, who propose that dust
interacting only gravitationally can be used for time measuring, and the
unitary approach by Barvinsky and collaborators. The latter approach admits
both the canonical and path integral formulations and anticipates the
consideration of recent developments in the path integral approach in the
second part of our work.


title: Irrotational vortex geometry of torsion loops

abstract:
  The irrotational vortex geometry carachter of torsion loops is displayed by
showing that torsion loops and nonradial flow acoustic metrics are conformally
equivalent in $(1+1)$ dimensions while radial flow acoustic spacetime are
conformally related in $(2+1)$ dimensional spacetime. The analysis of
2-dimensional space allows us to express the fluid density in terms of the
parameters of torsion loop metric. These results lead us to conclude that the
acoustic metric of vortex flows is the gravitational analog of torsion loop
spacetime. Since no vorticity in the fluids is considered we do not make
explicit use of non-Riemannian geometry of vortex acoustics in classical
fluids. Acoustic nonradial flows are shown to exihibit a full analogy with
torsion loop metric.


title:
Non-Riemannian vortex geometry of rotational viscous fluids and breaking
  of the acoustic Lorentz invariance

abstract:
  Acoustic torsion recently introduced in the literature (Garcia de
Andrade,PRD(2004),7,64004) is extended to rotational incompressible viscous
fluids represented by the generalised Navier-Stokes equation. The fluid
background is compared with the Riemann-Cartan massless scalar wave equation,
allowing for the generalization of Unruh acoustic metric in the form of
acoustic torsion, expressed in terms of viscosity, velocity and vorticity of
the fluid. In this work the background vorticity is nonvanishing but the
perturbation of the flow is also rotational which avoids the problem of
contamination of the irrotational perturbation by the background vorticity. The
acoustic Lorentz invariance is shown to be broken due to the presence of
acoustic torsion in strong analogy with the Riemann-Cartan gravitational case
presented recently by Kostelecky (PRD 69,2004,105009). An example of analog
gravity describing acoustic metric is given based on the teleparallel loop
where the acoustic torsion is given by the Lense-Thirring rotation and the
acoustic line element corresponds to the Lense-Thirring metric.


title:
Lessons Learned from the Pioneers 10/11 for a Mission to Test the
  Pioneer Anomaly

abstract:
  Analysis of the radio-metric tracking data from the Pioneer 10/11 spacecraft
at distances between 20--70 astronomical units (AU) from the Sun has
consistently indicated the presence of an anomalous, small, constant Doppler
frequency drift. The drift is a blue-shift, uniformly changing with rate a_t =
(2.92 +/- 0.44) x 10^(-18) s/s^2. It can also be interpreted as a constant
acceleration of a_P = (8.74 +/- 1.33) x 10^(-8) cm/s^2 directed towards the
Sun. Although it is suspected that there is a systematic origin to the effect,
none has been found. As a result, the nature of this anomaly has become of
growing interest. Here we discuss the details of our recent investigation
focusing on the effects both external to and internal to the spacecraft, as
well as those due to modeling and computational techniques. We review some of
the mechanisms proposed to explain the anomaly and show their inability to
account for the observed behavior of the anomaly. We also present lessons
learned from this investigation for a potential deep-space experiment that will
reveal the origin of the discovered anomaly and also will characterize its
properties with an accuracy of at least two orders of magnitude below the
anomaly's size. A number of critical requirements and design considerations for
such a mission are outlined and addressed.


title: Thermodynamics of a collapsing shell in an expanding Universe

abstract:
  We describe the quasi-static collapse of a radiating, spherical shell of
matter in de Sitter space-time using a thermodynamical formalism. It is found
that the specific heat at constant area and other thermodynamical quantities
exhibit singularities related to phase transitions during the collapse.


title:
The problem of time and gauge invariance in the quantization of
  cosmological models. II. Recent developments in the path integral approach

abstract:
  The paper is the second part of the work devoted to the problem of time in
quantum cosmology. Here we consider in detail two approaches within the scope
of Feynman path integration scheme: The first, by Simeone and collaborators, is
gauge-invariant and lies within the unitary approach to a consistent
quantization of gravity. It is essentially based on the idea of
deparametrization (reduction to physical degrees of freedom) as a first step
before quantization. The other approach by Savchenko, Shestakova and Vereshkov
is rather radical. It is an attempt to take into account peculiarities of the
Universe as a system without asymptotic states that leads to the conclusion
that quantum geometrodynamics constructed for such a system is, in general, a
gauge-noninvariant theory. However, this theory is shown to be mathematically
consistent and the problem of time is solved in this theory in a natural way.


title: Tree-level Scattering Amplitude in de Sitter Space

abstract:
  In previous papers [1,2], it was proved that a covariant quantization of the
minimally coupled scalar field in de Sitter space is achieved through addition
of the negative norm states. This causal approach which eliminates the infrared
divergence, was generalized further to the calculation of the graviton
propagator in de Sitter space [3] and one-loop effective action for scalar
field in a general curved space-time [4]. This method gives a natural
renormalization of the above problems. Pursuing this approach, in the present
paper the tree-level scattering amplitudes of the scalar field, with one
graviton exchange, has been calculated in de Sitter space. It is shown that the
infrared divergence disappears and the theory automatically reaches a
renormalized solution of the problem.


title: Energy conservation and equivalence principle in General Relativity

abstract:
  The generalized Stokes theorem (connecting integrals of dimensions 3 and 4)
is formulated in a curved space-time in terms of paths in Minkowski space
(forming Path Group). A covariant integral form of the conservation law for the
energy-momentum of matter is then derived in General Relativity. It extends
Einstein's equivalence principle on the energy conservation, since it
formulates the conservation law for the energy-momentum of matter without
explicit including the gravitational field in the formulation.


title:
The Campbell--Magaard Theorem is inadequate and inappropriate as a
  protective theorem for relativistic field equations

abstract:
  Given a particular prescription for the Einstein field equations (EFE's), it
is important to have general protective theorems that lend support to it. The
prescription of data on a timelike hypersurface for the (n + 1)-d EFE's arises
in `noncompact Kaluza--Klein theory', and in certain kinds of braneworlds and
low-energy string theory. The Campbell--Magaard (CM) theorem, which asserts
local existence (and, with extra conditions, uniqueness) of analytic embeddings
of completely general n-d manifolds into vacuum (n + 1)-d manifolds, has often
recently been invoked as a protective theorem for such prescriptions. But in
this paper I argue that there are problems with loosening the CM thoerem of
restrictive meanings in its statement, which is worthwhile thing to do in
pursuit of the proposed applications. While I remedy some problems by
identifying the required topology, delineating what `local' can be taken to
mean, and offering a new, more robust and covariant proof, other problems
remain unsurmountable. The theorem lends only inadequate support, both because
it offers no guarantee of continuous dependence on the data and because it
disregards causality. Furthermore, the theorem is only for the analytic
functions which renders it inappropriate for the study of the relativistic
equations of modern physics. Unfortunately, there are no known general theorems
that offer adequate protection to the proposed applications' prescription. I
conclude by making some suggestions for more modest progress.


title: Geometrodynamics: Spacetime or Space ?

abstract:
  This thesis concerns the split of Einstein's field equations (EFE's) with
respect to nowhere null hypersurfaces. Areas covered include A) the foundations
of relativity, deriving geometrodynamics from relational first principles and
showing that this form accommodates a sufficient set of fundamental matter
fields to be classically realistic, alternative theories of gravity that arise
from similar use of conformal mathematics. B) GR Initial value problem (IVP)
methods, the badness of timelike splits of the EFE's and studying braneworlds
under guidance from GR IVP and Cauchy problem methods.


title: Einstein-Aether Theory

abstract:
  We review the status of "Einstein-Aether theory", a generally covariant
theory of gravity coupled to a dynamical, unit timelike vector field that
breaks local Lorentz symmetry. Aspects of waves, stars, black holes, and
cosmology are discussed, together with theoretical and observational
constraints. Open questions are stressed.


title: A new form of the rotating C-metric

abstract:
  In a previous paper, we showed that the traditional form of the charged
C-metric can be transformed, by a change of coordinates, into one with an
explicitly factorizable structure function. This new form of the C-metric has
the advantage that its properties become much simpler to analyze. In this
paper, we propose an analogous new form for the rotating charged C-metric, with
structure function G(\xi)=(1-\xi^2)(1+r_{+}A\xi)(1+r_{-}A\xi), where r_\pm are
the usual locations of the horizons in the Kerr-Newman black hole. Unlike the
non-rotating case, this new form is not related to the traditional one by a
coordinate transformation. We show that the physical distinction between these
two forms of the rotating C-metric lies in the nature of the conical
singularities causing the black holes to accelerate apart: the new form is free
of torsion singularities and therefore does not contain any closed timelike
curves. We claim that this new form should be considered the natural
generalization of the C-metric with rotation.


title: An interior solution of constant density to Gurses metric

abstract:
  We give here an interior metric which matches Gurses metric. The metric given
here is a sphere of electrically counterpoised dust (ECD) of constant density.
We use Lane Emden equation for obtaining the interior solution.


title: Energy-Momentum Distribution: A Crucial Problem in General Relativity

abstract:
  This paper is aimed to elaborate the problem of energy-momentum in General
Relativity. In this connection, we use the prescriptions of Einstein,
Landau-Lifshitz, Papapetrou and M\"{o}ller to compute the energy-momentum
densities for two exact solutions of Einstein field equations. The spacetimes
under consideration are the non-null Einstein-Maxwell solutions and the
singularity-free cosmological model. The electromagnetic generalization of the
G\"{o}del solution and the G\"{o}del metric become special cases of the
non-null Einstein-Maxwell solutions. It turns out that these prescriptions do
not provide consistent results for any of these spacetimes. These inconsistence
results verify the well-known proposal that the idea of localization does not
follow the lines of pseudo-tensorial construction but instead follows from the
energy-momentum tensor itself. These differences can also be understood with
the help of the Hamiltonian approach.


title: Photon-graviton pair conversion

abstract:
  We consider the conversion of gravitons and photons as a four-wave mixing
process. A nonlinear coupled systems of equations involving two gravitons and
two photons is obtained, and the energy exchange between the different degrees
of freedom is found. The scattering amplitudes are obtained, from which a
crossection for incoherent processes can be found. An analytical example is
given, and applications to the early Universe are discussed.


title: On the geometry of pp-wave type spacetimes

abstract:
  Global geometric properties of product manifolds ${\cal M}= M \times \R^2$,
endowed with a metric type $<\cdot, \cdot > = < \cdot, \cdot >_R + 2 dudv +
H(x,u) du^2$ (where $<\cdot, \cdot >_R$ is a Riemannian metric on $M$ and $H:M
\times \R \to \R$ a function), which generalize classical plane waves, are
revisited. Our study covers causality (causal ladder, inexistence of horizons),
geodesic completeness, geodesic connectedness and existence of conjugate
points. Appropiate mathematical tools for each problem are emphasized and the
necessity to improve several Riemannian (positive definite) results is claimed.


title:
Limits on gravitational wave emission from selected pulsars using LIGO
  data

abstract:
  We place direct upper limits on the amplitude of gravitational waves from 28
isolated radio pulsars by a coherent multi-detector analysis of the data
collected during the second science run of the LIGO interferometric detectors.
These are the first direct upper limits for 26 of the 28 pulsars. We use
coordinated radio observations for the first time to build radio-guided phase
templates for the expected gravitational wave signals. The unprecedented
sensitivity of the detectors allow us to set strain upper limits as low as a
few times $10^{-24}$. These strain limits translate into limits on the
equatorial ellipticities of the pulsars, which are smaller than $10^{-5}$ for
the four closest pulsars.


title: Gravitational entropy in cosmological models

abstract:
  We discuss whether an appropriately defined dimensionless scalar function
might be an acceptable candidate for the gravitational entropy, by explicitly
considering Szekeres and Bianchi type VI$_{h}$ models that admit an isotropic
singularity. We also briefly discuss other possible gravitational entropy
functions, including an appropriate measure of the velocity dependent
Bel-Robinson tensor.


title: Semiclassical back reaction around a cosmic dislocation

abstract:
  The energy-momentum vacuum average of a conformally coupled massless scalar
field vibrating around a cosmic dislocation (a cosmic string with a dislocation
along its axis) is taken as source of the linearized semiclassical Einstein
equations. The solution up to first order in the Planck constant is derived.
Motion of a test particle is then discussed, showing that under certain
circumstances a helical-like dragging effect, with no classical analogue around
the cosmic dislocation, is induced by back reaction.


title:
Observables in a Noncommutative Unification of Quanta and Gravity. A
  Final Model

abstract:
  We further develop a noncommutative model unifying quantum mechanics and
general relativity proposed in {\it Gen. Rel. Grav.} (2004) {\bf 36}, 111-126.
Generalized symmetries of the model are defined by a groupoid $\Gamma $ given
by the action of a finite group on a space $E$. The geometry of the model is
constructed in terms of suitable (noncommutative) algebras on $\Gamma $. We
investigate observables of the model, especially its position and momentum
observables. This is not a trivial thing since the model is based on a
noncommutative geometry and has strong nonlocal properties. We show that, in
the position representation of the model, the position observable is a
coderivation of a corresponding coalgebra, "coparallelly" to the well known
fact that the momentum observable is a derivation of the algebra. We also study
the momentum representation of the model. It turns out that, in the case of the
algebra of smooth, quickly decreasing functions on $\Gamma $, the model in its
"quantum sector" is nonlocal, i.e., there are no nontrivial coderivations of
the corresponding coalgebra, whereas in its "gravity sector" such coderivations
do exist. They are investigated.