title: Quantisation of Deformed Special Relativity

abstract:
  We consider deformed special relativity (DSR) theories on commutative
space-time, perhaps as an first approximation to a noncommutative space-time
formulation. The corresponding field theories in general possess derivatives of
all orders. From a quantisation procedure and the deformed Dirac equation in
momentum space we obtain for a specific DSR model enhanced expressions for
momentum and charge and finite vacuum contributions.


title: Coleman - de Luccia instanton of the second order in a brane world

abstract:
  The second order Coleman - de Luccia instanton and its action in the Randall
- Sundrum type II model are investigated and the comparison with the results in
Einstein's general relativity is done in the present paper.


title:
On boosted space-times with cosmological constant and their
  ultrarelativistic limit

abstract:
  The problem of deriving a shock-wave geometry with cosmological constant by
boosting a Schwarzschild-de Sitter (or anti-de Sitter) black hole is
re-examined. Unlike previous work in the literature, we deal with the exact
Schwarzschild-de Sitter (or anti-de Sitter) metric. By virtue of peculiar
cancellations in this exact calculation, where the metric does not depend
linearly on the mass parameter, we find a singularity of distributional nature
on a null hypersurface, which corresponds to a shock-wave geometry derived in a
fully non-perturbative way. The result agrees with previous calculations, where
the metric had been linearized in the mass parameter.


title: Spherical Harmonic Amplitudes From Grid Data

abstract:
  The problem of resolving spherical harmonic components from numerical data
defined on a rectangular grid has many applications, particularly for the
problem of gravitational radiation extraction. A novel method due to Misner
improves on traditional techniques by avoiding the need to cover the sphere
with a coordinate system appropriate to the grid geometry. This paper will
discuss Misner's method and suggest how it can be improved by exploiting local
regression techniques.


title: Post-Newtonian Theory and Dimensional Regularization

abstract:
  Inspiralling compact binaries are ideally suited for application of a
high-order post-Newtonian (PN) gravitational wave generation formalism. To be
observed by the LIGO and VIRGO detectors, these very relativistic systems (with
orbital velocities of the order of 0.5c in the last rotations) require
high-accuracy templates predicted by general relativity theory. Recent
calculations of the motion and gravitational radiation of compact binaries at
the 3PN approximation using the Hadamard self-field regularization have left
undetermined a few dimensionless coefficients called ambiguity parameters. In
this article we review the application of dimensional self-field
regularization, within Einstein's classical general relativity formulated in D
space-time dimensions, which finally succeeded in clearing up the problem, by
uniquely fixing the values of all the ambiguity parameters.


title: The structure of cosmic time

abstract:
  Following the approach of Julien Lesgourgues [astro-ph/0409426], we analyze
the mathematical structure of the time co-ordinate of present day cosmological
models, where these models include a cosmological constant term to account for
the observed acceleration of the universe: we find that in all cases, except
for a set of measure zero in the parameter space, the time is given by an
(abelian) integral on a torus; the imaginary period of this integral then gives
a natural periodicity in imaginary time for the universe; following Stephen
Hawking, this periodicity may be interpreted either as giving a fundamental
mass scale for the universe, or (using Planck's constant) a fundamental
temperature, or both. The precise structure that emerges suggests that the
structure of time can be regarded as an order parameter arising perhaps in a
phase transition in the early universe; one might hope that this structure
would be predictable in any fundamental theory.


title:
Energy of general 4-dimensional stationary axisymmetric spacetime in the
  teleparallel geometry

abstract:
  The field equation with the cosmological constant term is derived and the
energy of the general 4-dimensional stationary axisymmetric spacetime is
studied in the context of the hamiltonian formulation of the teleparallel
equivalent of general relativity (TEGR). We find that, by means of the integral
form of the constraints equations of the formalism naturally without any
restriction on the metric parameters, the energy for the asymptotically flat/de
Sitter/Anti-de Sitter stationary spacetimes in the Boyer-Lindquist coordinate
can be expressed as $E=\frac{1}{8\pi}\int_S d\theta d\phi(sin\theta
\sqrt{g_{\theta\theta}}+\sqrt{g_{\phi\phi}}-(1/\sqrt{g_{rr}})(\partial{\sqrt{g_
{\theta\theta} g_{\phi\phi}}}/\partial r))$. It is surprised to learn that the
energy expression is relevant to the metric components $g_{rr}$,
$g_{\theta\theta}$ and $g_{\phi\phi}$ only. As examples, by using this formula
we calculate the energies of the Kerr-Newman (KN), Kerr-Newman Anti-de Sitter
(KN-AdS), Kaluza-Klein, and Cveti\v{c}-Youm spacetimes.


title: Berry Phase in the Gravitational Quantum Well and the Seiberg-Witten map

abstract:
  We explicitly compute the geometrical Berry phase for the noncommutative
gravitational quantum well for different SW maps. We find that they lead to
different partial contributions to the Berry phase. For the most general map we
obtain that $\Delta\gamma(S)\sim{\eta}^3$, in a segment S of the path in the
configuration space where $\sqrt{\eta}$ is the fundamental momentum scale for
the noncommutative gravitational quantum well. For the full closed path, we
find, through an explicit computation, that $\gamma(C)=0$. This result is
consistent with the fact that physical properties are independent of the SW map
and shows that these maps do not introduce degeneracies or level crossing in
the noncommutative extensions of the gravitational quantum well.


title:
The polygon model for 2+1D gravity: the constraint algebra and problems
  of quantization

abstract:
  In this Master thesis we consider 't Hooft's polygon model for 2+1D gravity.
After a detailed review of the polygon model in the classical context, we
discuss problems associated with its quantization and calculate the explicitly
the full Poisson structure of the constraints.
  The calculation of the Poisson structure in chapter 6 introduces corrections
and generalizations to earlier published results. We show that the full Poisson
structure closes on shell, but not off shell. An attempt is made to interpret
the gauge orbits generated by the constraints.


title:
Static vacuum solutions from convergent null data expansions at
  space-like infinity

abstract:
  We study formal expansions of asymptotically flat solutions to the static
vacuum field equations which are determined by minimal sets of freely
specifyable data referred to as `null data'. These are given by sequences of
symmetric trace free tensors at space-like infinity of increasing order. They
are 1:1 related to the sequences of Geroch multipoles. Necessary and sufficient
growth estimates on the null data are obtained for the formal expansions to be
absolutely convergent. This provides a complete characterization of all
asymptotically flat solutions to the static vacuum field equations.


title:
The Distinction Between Dirac and Majorana Neutrino Wave Packets Due to
  Gravity and Its Impact on Neutrino Oscillations

abstract:
  We present the possibility that Dirac and Majorana neutrino wave packets can
be distinguished when subject to spin-gravity interaction while propagating
through vacuum described by the Lense-Thirring metric. By adopting the
techniques of gravitational phase and time-independent perturbation theory
following the Brillouin-Wigner method, we generate spin-gravity matrix elements
from a perturbation Hamiltonian and show that this distinction is easily
reflected in well-defined gravitational corrections to the neutrino oscillation
length for a two-flavour system. Explicit examples are presented using the Sun
and SN1987A as the gravitational sources for the Lense-Thirring metric. This
approach offers the possibility to determine the absolute neutrino masses by
this method and identify a theoretical upper bound for the absolute neutrino
mass difference, where the distinctions between the Dirac and Majorana cases
are evident. We discuss the relevance of this analysis to the upcoming attempts
to measure the properties of low-energy neutrinos by SNO and other solar
neutrino observatories.


title: Boosted Kerr black hole

abstract:
  Initial data for boosted Kerr black hole are constructed in an axially
symmetric case. Momentum and hamiltonian constraints are solved numerically
using finite element method (FEM) algorithms. Both Bowen-York and puncture
boundary conditions are adopted and appropriate results are compared. Past and
future apparent horizons are also found numerically and the Penrose inequality
is tested in detail.


title: The Null Decomposition of Conformal Algebras

abstract:
  We analyze the decomposition of the enveloping algebra of the conformal
algebra in arbitrary dimension with respect to the mass-squared operator. It
emerges that the subalgebra that commutes with the mass-squared is generated by
its Poincare subalgebra together with a vector operator. The special cases of
the conformal algebras of two and three dimensions are described in detail,
including the construction of their Casimir operators.


title: Solution generating theorems for the TOV equation

abstract:
  The Tolman-Oppenheimer-Volkov [TOV] equation constrains the internal
structure of general relativistic static perfect fluid spheres. We develop
several "solution generating" theorems for the TOV, whereby any given solution
can be "deformed" to a new solution. Because the theorems we develop work
directly in terms of the physical observables -- pressure profile and density
profile -- it is relatively easy to check the density and pressure profiles for
physical reasonableness. This work complements our previous article [Phys. Rev.
D71 (2005) 124307; gr-qc/0503007] wherein a similar "algorithmic" analysis of
the general relativistic static perfect fluid sphere was presented in terms of
the spacetime geometry -- in the present analysis the pressure and density are
primary and the spacetime geometry is secondary. In particular, our "deformed"
solutions to the TOV equation are conveniently parameterized in terms of delta
rho_c and delta p_c, the finite shift in the central density and central
pressure. We conclude by presenting a new physical and mathematical
interpretation of the TOV equation -- as an integrability condition on the
density and pressure profiles.


title: Conceptual Unification of Gravity and Quanta

abstract:
  We present a model unifying general relativity and quantum mechanics. The
model is based on the (noncommutative) algebra \mbox{{\cal A}} on the groupoid
\Gamma = E \times G where E is the total space of the frame bundle over
spacetime, and G the Lorentz group. The differential geometry, based on
derivations of \mbox{{\cal A}}, is constructed. The eigenvalue equation for the
Einstein operator plays the role of the generalized Einstein's equation. The
algebra \mbox{{\cal A}}, when suitably represented in a bundle of Hilbert
spaces, is a von Neumann algebra \mathcal{M} of random operators representing
the quantum sector of the model. The Tomita-Takesaki theorem allows us to
define the dynamics of random operators which depends on the state \phi . The
same state defines the noncommutative probability measure (in the sense of
Voiculescu's free probability theory). Moreover, the state \phi satisfies the
Kubo-Martin-Schwinger (KMS) condition, and can be interpreted as describing a
generalized equilibrium state. By suitably averaging elements of the algebra
\mbox{{\cal A}}, one recovers the standard geometry of spacetime. We show that
any act of measurement, performed at a given spacetime point, makes the model
to collapse to the standard quantum mechanics (on the group G). As an example
we compute the noncommutative version of the closed Friedman world model.
Generalized eigenvalues of the Einstein operator produce the correct components
of the energy-momentum tensor. Dynamics of random operators does not ``feel''
singularities.


title:
On the spectral shift and the time delay of light in a Rindler
  accelerated frame

abstract:
  We discuss two effects predicted by the general theory of relativity in the
context of Rindler accelerated observers: the gravitational spectral shift and
the time delay of light. We show that these effects also appear in a Rindler
frame in the absence of gravitational field, in accordance with the Einstein's
equivalence principle.


title: Gravitoelectromagnetism and Dark Energy in Superconductors

abstract:
  A gravitomagnetic analogue of the London moment in superconductors can
explain the anomalous Cooper pair mass excess reported by Janet Tate.
Ultimately the gravitomagnetic London moment is attributed to the breaking of
the principle of general covariance in superconductors. This naturally implies
non-conservation of classical energy-momentum. Possible relation with the
manifestation of dark energy in superconductors is questioned.


title:
Black hole solutions of dimensionally reduced Einstein-Gauss-Bonnet
  gravity

abstract:
  We study the phase space of the spherically symmetric solutions of the system
obtained from the dimensional reduction of the six-dimensional Einstein-Gauss-
Bonnet action. We show the existence of solutions with nonflat asymptotic
behavior.


title: The adventures of Spacetime

abstract:
  We discuss how developments in physics often imply in the need that spacetime
acquires an increasingly richer and complex structure. General Relativity was
the first theory to show us the way to connect space and time with the physical
world. Since then, scrutinizing the ways spacetime might exist is, in a way,
the very essence of physics. Physics has thus given substance to the pioneering
work of scores of brilliant mathematicians who speculated on the geometry and
topology of spaces.


title:
"Kludge" gravitational waveforms for a test-body orbiting a Kerr black
  hole

abstract:
  One of the most exciting potential sources of gravitational waves for
low-frequency, space-based gravitational wave (GW) detectors such as the
proposed Laser Interferometer Space Antenna (LISA) is the inspiral of compact
objects into massive black holes in the centers of galaxies. The detection of
waves from such "extreme mass ratio inspiral" systems (EMRIs) and extraction of
information from those waves require template waveforms. The systems' extreme
mass ratio means that their waveforms can be determined accurately using black
hole perturbation theory. Such calculations are computationally very expensive.
There is a pressing need for families of approximate waveforms that may be
generated cheaply and quickly but which still capture the main features of true
waveforms. In this paper, we introduce a family of such "kludge" waveforms and
describe ways to generate them. We assess performance of the introduced
approximations by comparing "kludge" waveforms to accurate waveforms obtained
by solving the Teukolsky equation in the adiabatic limit (neglecting GW
backreaction). We find that the kludge waveforms do extremely well at
approximating the true gravitational waveform, having overlaps with the
Teukolsky waveforms of 95% or higher over most of the parameter space for which
comparisons can currently be made. Indeed, we find these kludges to be of such
high quality (despite their ease of calculation) that it is possible they may
play some role in the final search of LISA data for EMRIs.


title: Hawking-like radiation does not require a trapped region

abstract:
  We discuss the issue of quasi-particle production by ``analogue black holes''
with particular attention to the possibility of reproducing Hawking radiation
in a laboratory. By constructing simple geometric acoustic models, we obtain a
somewhat unexpected result: We show that in order to obtain a stationary and
Planckian emission of quasi-particles, it is not necessary to create a trapped
region in the acoustic spacetime (corresponding to a supersonic regime in the
fluid flow). It is sufficient to set up a dynamically changing flow
asymptotically approaching a sonic regime with sufficient rapidity in
laboratory time.


title: Classical and quantum behavior of the generic cosmological solution

abstract:
  In the present paper we generalize the original work of C.W. Misner
\cite{M69q} about the quantum dynamics of the Bianchi type IX geometry near the
cosmological singularity. We extend the analysis to the generic inhomogeneous
universe by solving the super-momentum constraint and outlining the dynamical
decoupling of spatial points. Firstly, we discuss the classical evolution of
the model in terms of the Hamilton-Jacobi approach as applied to the
super-momentum and super-Hamiltonian constraints; then we quantize it in the
approximation of a square potential well after an ADM reduction of the dynamics
with respect to the super-momentum constraint only. Such a reduction relies on
a suitable form for the generic three-metric tensor which allows the use of its
three functions as the new spatial coordinates. We get a functional
representation of the quantum dynamics which is equivalent to the Misner-like
one when extended point by point, since the Hilbert space factorizes into
$\infty^3$ independent components due to the parametric role that the
three-coordinates assume in the asymptotic potential term. Finally, we discuss
the conditions for having a semiclassical behavior of the dynamics and we
recognize that this already corresponds to having mean occupation numbers of
order $\mathcal{O}(10^2)$.


title:
Hawking temperature for various kinds of black holes from Heisenberg
  uncertainty principle

abstract:
  Hawking temperature is computed for a large class of black holes (with
spherical, toroidal and hyperboloidal topologies) using only laws of classical
physics plus the "classical" Heisenberg Uncertainty Principle. This principle
is shown to be fully sufficient to get the result, and there is no need to this
scope of a Generalized Uncertainty Principle.


title: Energy of a Stringy Charged Black Hole in the Teleparallel Gravity

abstract:
  This paper has been removed by arXiv administrators because it plagiarizes
gr-qc/0212018, gr-qc/0501002, and gr-qc/9601044.
  This paper has excessive overlap with the following papers also written by
the authors or their collaborators: gr-qc/0603108, gr-qc/0606022,
gr-qc/0603027, gr-qc/0603063, gr-qc/0607083, gr-qc/0607095, gr-qc/0511030,
gr-qc/0512080, gr-qc/0601141, gr-qc/0608050, gr-qc/0607082, gr-qc/0511095,
gr-qc/0612016, and others.


title: The Causet Mechanism for the Creation of Energy

abstract:
  Sorkin's causet mechanism is generalized to include energy exchange between
causet elements and conventional vacuum fluctuations to the inflationary epoch.
In this, the dark energy of the adiabatic era is the fluctuating remnant of
inflation. The mechanism is also applicable to black hole evaporation.


title: The emergence of background geometry from quantum fluctuations

abstract:
  We show how the quantization of two-dimensional gravity leads to an
(Euclidean) quantum space-time where the average geometry is that of constant
negative curvature and where the Hartle-Hawking boundary condition arises
naturally.


title: Particles as Wilson lines of gravitational field

abstract:
  Since the work of Mac-Dowell-Mansouri it is well known that gravity can be
written as a gauge theory for the de Sitter group. In this paper we consider
the coupling of this theory to the simplest gauge invariant observables that
is, Wilson lines. The dynamics of these Wilson lines is shown to reproduce
exactly the dynamics of relativistic particles coupled to gravity, the gauge
charges carried by Wilson lines being the mass and spin of the particles.
Insertion of Wilson lines breaks in a controlled manner the diffeomorphism
symmetry of the theory and the gauge degree of freedom are transmuted to
particles degree of freedom.


title:
Detecting a stochastic background of gravitational waves in the presence
  of non-Gaussian noise: A performance of generalized cross-correlation
  statistic

abstract:
  We discuss a robust data analysis method to detect a stochastic background of
gravitational waves in the presence of non-Gaussian noise. In contrast to the
standard cross-correlation (SCC) statistic frequently used in the stochastic
background searches, we consider a {\it generalized cross-correlation} (GCC)
statistic, which is nearly optimal even in the presence of non-Gaussian noise.
The detection efficiency of the GCC statistic is investigated analytically,
particularly focusing on the statistical relation between the false-alarm and
the false-dismissal probabilities, and the minimum detectable amplitude of
gravitational-wave signals. We derive simple analytic formulae for these
statistical quantities. The robustness of the GCC statistic is clarified based
on these formulae, and one finds that the detection efficiency of the GCC
statistic roughly corresponds to the one of the SCC statistic neglecting the
contribution of non-Gaussian tails. This remarkable property is checked by
performing the Monte Carlo simulations and successful agreement between
analytic and simulation results was found.


title: Solar System experiments do not yet veto modified gravity models

abstract:
  The dynamical equivalence between modified and scalar-tensor gravity theories
is revisited and it is concluded that it breaks down in the limit to general
relativity. A gauge-independent analysis of cosmological perturbations in both
classes of theories lends independent support to this conclusion. As a
consequence, the PPN formalism of scalar-tensor gravity and Solar System
experiments do not veto modified gravity, as previously thought.


title: The generalized Heun equation in QFT in curved space-times

abstract:
  In this article we give a brief outline of the applications of the
generalized Heun equation (GHE) in the context of Quantum Field Theory in
curved space-times. In particular, we relate the separated radial part of a
massive Dirac equation in the Kerr-Newman metric and the static perturbations
for the non-extremal Reissner-Nordstr\"{o}m solution to a GHE.


title: Theorems on Null-Paths and Red-Shift

abstract:
  In the present work, we prove the validity of two theorems on null-paths in a
version of absolute parallelism geometry. A version of these theorems has been
originally established and proved by Kermak, McCrea and Whittaker (KMW) in the
context of Riemannian geometry. The importance of such theorems is their use,
in applications, to derive a general formula for the red-shift of spectral
lines coming from distant objects. The formula derived in the present work, can
be applied for both cosmological and astrophysical red-shifts. It takes into
account the shifts resulting from gravitation, different motions of the source
of photons, spin of the moving particle (photons) and the direction of the line
of sight. It is shown that this formula cannot be derived in the context of
Riemannian geometry, but it can be reduced to a formula given by KMW under
certain conditions.


title: The strong equivalence principle from gravitational gauge structure

abstract:
  Gravitational self-interactions are assumed to be determined by the covariant
derivative acting on the Riemann-Christoffel field strength. Once imposed on a
metric theory, this Yang-Mills gauge constraint extends the equality of
gravitational mass and inertial mass to compact bodies with non-negligible
gravitational binding energy. Applied to generalized Brans-Dicke theories, it
singles out one tensor theory and one scalar theory for gravity but also
suggests a way to implement a minimal violation of the strong equivalence
principle.


title: Time (in)dependence in general relativity

abstract:
  We clarify the conditions for Birkhoff's theorem, that is, time-independence
in general relativity. We work primarily at the linearized level where guidance
from electrodynamics is particularly useful. As a bonus, we also derive the
equivalence principle. The basic time-independent solutions due to
Schwarzschild and Kerr provide concrete illustrations of the theorem. Only
familiarity with Maxwell's equations and tensor analysis is required.


title: The cosmic jerk parameter in f(R) gravity

abstract:
  We derive the expression for the jerk parameter in $f(R)$ gravity. We use the
Palatini variational principle and the field equations in the Einstein
conformal gauge. For the particular case $f(R)=R-\frac{\alpha^2}{3R}$, the
predicted value of the jerk parameter agrees with the SNLS SNIa and X-ray
galaxy cluster distance data but does not with the SNIa gold sample data.


title: Much ado about nothing: a treatise on empty and not-so-empty spacetimes

abstract:
  In this thesis three separate problems relevant to general relativity are
considered. Methods for algorithmically producing all the solutions of
isotropic fluid spheres have been developed over the last five years. A
different and somewhat simpler algorithm is discussed here, as well as
algorithms for anisotropic fluid spheres. The second and third problems are
somewhat more speculative in nature and address the nature of black hole
entropy. Specifically, the second problem looks at the genericity of the
so-called quasinormal mode conjecture introduced by Hod, while the third
problem looks at the near-horizon structure of a black hole in hope of gaining
an understanding of why so many different approaches yield the same entropy. A
method of finding the asymptotic QNM structure is found based on the Born
series, and serious problems for the QNM conjecture are discussed. The work in
this thesis does not completely discount the possibility that the QNM
conjecture is true. New results released weeks before this thesis was finished
showed that the QNM conjecture was flawed. Finally, the near-horizon structure
of a black hole is found to be very restricted, adding credence to the ideas
put forward by Carlip and Solodukhin that the black hole entropy is related to
an inherited symmetry from the classical theory.


title: Relativistic Kinetics of Phonon Gas in Superfluids

abstract:
  The relativistic kinetic theory of the phonon gas in superfluids is
developed. The technique of the derivation of macroscopic balance equations
from microscopic equations of motion for individual particles is applied to an
ensemble of quasi-particles. The necessary expressions are constructed in terms
of a Hamilton function of a (quasi-)particle. A phonon contribution into
superfluid dynamic parameters is obtained from energy-momentum balance
equations for the phonon gas together with the conservation law for superfluids
as a whole. Relations between dynamic flows being in agreement with results of
relativistic hydrodynamic consideration are found. Based on the kinetic
approach a problem of relativistic variation of the speed of sound under phonon
influence at low temperature is solved.


title: Modified Special Relativity on a fluctuating spacetime

abstract:
  It was recently proposed that deformations of the relativistic symmetry, as
those considered in Deformed Special Relativity (DSR), can be seen as the
outcome of a measurement theory in the presence of non-negligible (albeit
small) quantum gravitational fluctuations [1,2]. In this paper we explicitly
consider the case of a spacetime described by a flat metric endowed with
stochastic fluctuations and, for a free particle, we show that DSR-like
nonlinear relations between the spaces of the measured and classical momenta,
can result from the average of the stochastic fluctuations over a scale set be
the de Broglie wavelength of the particle. As illustrative examples we consider
explicitly the averaging procedure for some simple stochastic processes and
discuss the physical implications of our results.


title: Second and higher-order perturbations of a spherical spacetime

abstract:
  The Gerlach and Sengupta (GS) formalism of coordinate-invariant, first-order,
spherical and nonspherical perturbations around an arbitrary spherical
spacetime is generalized to higher orders, focusing on second-order
perturbation theory. The GS harmonics are generalized to an arbitrary number of
indices on the unit sphere and a formula is given for their products. The
formalism is optimized for its implementation in a computer algebra system,
something that becomes essential in practice given the size and complexity of
the equations. All evolution equations for the second-order perturbations, as
well as the conservation equations for the energy-momentum tensor at this
perturbation order, are given in covariant form, in Regge-Wheeler gauge.


title: Covariant description of the black hole entropy in 3D gravity

abstract:
  We study the entropy of the black hole with torsion using the covariant form
of the partition function. The regularization of infinities appearing in the
semiclassical calculation is shown to be consistent with the grand canonical
boundary conditions. The correct value for the black hole entropy is obtained
provided the black hole manifold has two boundaries, one at infinity and one at
the horizon. However, one can construct special coordinate systems, in which
the entropy is effectively associated with only one of these boundaries.


title: A Naturally Renormalized Quantum Field Theory

abstract:
  It was shown that quantum metric fluctuations smear out the singularities of
Green's functions on the light cone [1], but it does not remove other
ultraviolet divergences of quantum field theory. We have proved that the
quantum field theory in Krein space, {\it i.e.} indefinite metric quantization,
removes all divergences of quantum field theory with exception of the light
cone singularity [2,3]. In this paper, it is discussed that the combination of
quantum field theory in Krein space together with consideration of quantum
metric fluctuations, results in quantum field theory without any divergences.


title:
Quantum variational measurement and the "optical lever" intracavity
  topology of gravitational-wave detectors

abstract:
  The intracavity topologies of laser gravitational-wave detectors are the
promising way to obtain sensitivity of these devices significantly better than
the Standard Quantum Limit (SQL). The most challenging element of the
intracavity topologies is the \emph{local meter} which has to monitor position
of a small ($1\div10$ gram) local mirror and which precision defines the
sensitivity of the detector.
  To overcome the SQL, the quantum variational measurement can be used in the
local meter. In this method a frequency-dependent correlation between the meter
back-action noise and measurement noise is introduced, which allows to
eliminate the back-action noise component from the meter output signal. This
correlation is created by means of an additional filter cavity.
  In this article the sensitivity limitations of this scheme imposed by the
optical losses both in the local meter itself and in the filter cavity are
estimated. It is shown that the main sensitivity limitation stems from the
filter cavity losses. In order to overcome it, it is necessary to increase the
filter cavity length. In a preliminary prototype experiment about 10 meter long
filter cavity can be used to obtain sensitivity approximately $2\div3$ times
better than the SQL. For future QND gravitational-wave detectors with
sensitivity about ten times better than the SQL, the filter cavity length
should be within kilometer range.


title:
Galactic halos and gravastars: static spherically symmetric spacetimes
  in modern general relativity and astrophysics

abstract:
  The crucial role played by pressure in general relativity is explored in the
mathematically simple context of a static spherically symmetric geometry. By
keeping all pressure terms, the standard formalisms of rotation curve and
gravitational lensing observations are extended to a first post-Newtonian
order. It turns out that both post-Newtonian formalisms encode the
gravitational field differently. Therefore, combined observations of rotation
curves and gravitational lensing of the same galaxy can in principle be used to
infer both the density and pressure profile of the galactic fluid.
  The newly introduced post-Newtonian formalism might allow us to make
inferences about the equation of state of dark matter. While the Cold Dark
Matter paradigm is currently favoured in the astrophysics and cosmology
communities, the formalism presented herein offers an unprecedented way of
being able to directly observe the equation of state.
  In a logically distinct analysis, I investigate the effects of negative
pressure in compact objects, motivated by the recently introduced gravastar
model. I find that gravastar like objects can in principle mimic the external
gravitational field of a black hole. Unlike a black hole, however, gravastars
neither exhibit a pathological curvature singularity at the origin nor do they
posess an event horizon. Instead they are mathematically well defined
everywhere. Finally, another exotic option is considered as a mathematical
alternative to black holes: The anti-gravastar, which is characterized by a
core that has a negative mass-energy density.


title: Modified Dispersion Relations from the Renormalization Group of Gravity

abstract:
  We show that the running of gravitational couplings, together with a suitable
identification of the renormalization group scale can give rise to modified
dispersion relations for massive particles. This result seems to be compatible
with both the frameworks of effective field theory with Lorentz invariance
violation and deformed special relativity. The phenomenological consequences
depend on which of the frameworks is assumed. We discuss the nature and
strength of the available constraints for both cases and show that in the case
of Lorentz invariance violation, the theory would be strongly constrained.


title:
Constraining the relative inclinations of the planets B and C of the
  millisecond pulsar PSR B1257+12

abstract:
  We investigate on the relative inclination of the planets B and C orbiting
the pulsar PSR B1257+12 in connection with potential violations of the
equivalence principle (Abridged).


title: The group field theory approach to quantum gravity

abstract:
  We give a very concise review of the group field theory formalism for
non-perturbative quantum gravity, a higher dimensional generalisation of matrix
models. We motivate it as a simplicial and local realisation of the idea of 3rd
quantization of the gravitational field, equivalently of a quantum field theory
of simplicial geometry, in which also the topology of space is fully dynamical.
We highlight the basic structure of the formalism, and discuss briefly various
models that are being studied, some recent results and the many open issues
that future research should face. Finally, we point out the connections with
other approaches to quantum gravity, such as loop quantum gravity, quantum
Regge calculus and dynamical triangulations, and causal sets.


title: Variational Methods in Loop Quantum Cosmology

abstract:
  An action functional for the loop quantum cosmology difference equation is
presented. It is shown that by guessing the general form of the solution and
optimizing the action functional with respect to the parameters in the guessed
solution one can obtain approximate solutions which are reasonably good.


title:
On the Green's function and iterative solutions of Loop Quantum
  Cosmology

abstract:
  Here we shall find the green's function of the difference equation of loop
quantum cosmology. To illustrate how to use it, we shall obtain an iterative
solution for closed model and evaluate its corresponding Bohmian trajectory.


title: Coating thermal noise for arbitrary shaped beams

abstract:
  Advanced LIGO's sensitivity will be limited by coating noise. Though this
noise depends on beam shape, and though nongaussian beams are being seriously
considered for advanced LIGO, no published analysis exists to compare the
quantitative thermal noise improvement alternate beams offer. In this paper, we
derive and discuss a simple integral which completely characterizes the
dependence of coating thermal noise on shape. The derivation used applies
equally well, with minor modifications, to all other forms of thermal noise in
the low-frequency limit.


title: Symmetries of the Energy-Momentum Tensor: Some Basic Facts

abstract:
  It has been pointed by Hall et al. [1] that matter collinations can be
defined by using three different methods. But there arises the question of
whether one studies matter collineations by using the ${\cal L}_\xi T_{ab}=0$,
or ${\cal L}_\xi T^{ab}=0$ or ${\cal L}_\xi T_a^b=0$. These alternative
conditions are, of course, not generally equivalent. This problem has been
explored by applying these three definitions to general static spherically
symmetric spacetimes. We compare the results with each definition.


title: Positioning with stationary emitters in a two-dimensional space-time

abstract:
  The basic elements of the relativistic positioning systems in a
two-dimensional space-time have been introduced in a previous work [Phys. Rev.
D {\bf 73}, 084017 (2006)] where geodesic positioning systems, constituted by
two geodesic emitters, have been considered in a flat space-time. Here, we want
to show in what precise senses positioning systems allow to make {\em
relativistic gravimetry}. For this purpose, we consider stationary positioning
systems, constituted by two uniformly accelerated emitters separated by a
constant distance, in two different situations: absence of gravitational field
(Minkowski plane) and presence of a gravitational mass (Schwarzschild plane).
The physical coordinate system constituted by the electromagnetic signals
broadcasting the proper time of the emitters are the so called {\em emission
coordinates}, and we show that, in such emission coordinates, the trajectories
of the emitters in both situations, absence and presence of a gravitational
field, are identical. The interesting point is that, in spite of this fact,
particular additional information on the system or on the user allows not only
to distinguish both space-times, but also to complete the dynamical description
of emitters and user and even to measure the mass of the gravitational field.
The precise information under which these dynamical and gravimetric results may
be obtained is carefully pointed out.


title:
A Dodecalogue of Basic Didactics from Applications of Abstract
  Differential Geometry to Quantum Gravity

abstract:
  We summarize the twelve most important in our view novel concepts that have
arisen, based on results that have been obtained, from various applications of
Abstract Differential Geometry (ADG) to Quantum Gravity (QG). The present
document may be used as a concise, yet informal, discursive and peripatetic
conceptual guide-cum-terminological glossary to the voluminous technical
research literature on the subject. In a bonus section at the end, we dwell on
the significance of introducing new conceptual terminology in future QG
research by means of `poetic language'


title: Quantum Nature of the Big Bang: Improved dynamics

abstract:
  An improved Hamiltonian constraint operator is introduced in loop quantum
cosmology. Quantum dynamics of the spatially flat, isotropic model with a
massless scalar field is then studied in detail using analytical and numerical
methods. The scalar field continues to serve as `emergent time', the big bang
is again replaced by a quantum bounce, and quantum evolution remains
deterministic across the deep Planck regime. However, while with the
Hamiltonian constraint used so far in loop quantum cosmology the quantum bounce
can occur even at low matter densities, with the new Hamiltonian constraint it
occurs only at a Planck-scale density. Thus, the new quantum dynamics retains
the attractive features of current evolutions in loop quantum cosmology but, at
the same time, cures their main weakness.


title: Cosmology in two-dimensional dilaton gravity theories

abstract:
  We study some aspects of classical & quantum cosmology in the context of
two-dimensionsal dilaton gravity theories with matter being described by a
perfect fluid. We derive the classical equations obeyed by the metric function
& the dilaton field. An impicit solution for the metric function is obtained &
used to discuss possible expansion & contraction scenarios for the universe.
Quantization is carried out & finite norm exact solutions of the Wheeler-DeWitt
equation are obtained.


title:
Covariant Counterterms and Conserved Charges in Asymptotically Flat
  Spacetimes

abstract:
  Recent work has shown that the addition of an appropriate covariant boundary
term to the gravitational action yields a well-defined variational principle
for asymptotically flat spacetimes and thus leads to a natural definition of
conserved quantities at spatial infinity. Here we connect such results to other
formalisms by showing explicitly i) that for spacetime dimension $d \ge 4$ the
canonical form of the above-mentioned covariant action is precisely the ADM
action, with the familiar ADM boundary terms and ii) that for $d=4$ the
conserved quantities defined by counter-term methods agree precisely with the
Ashtekar-Hansen conserved charges at spatial infinity.


title: Thermodynamics of horizons from a dual quantum system

abstract:
  It was shown recently that, in the case of Schwarschild black hole, one can
obtain the correct thermodynamic relations by studying a model quantum system
and using a particular duality transformation. We study this approach further
for the case a general spherically symmetric horizon. We show that the idea
works for a general case only if we define the entropy S as a congruence
("observer") dependent quantity and the energy E as the integral over the
source of the gravitational acceleration for the congruence. In fact, in this
case, one recovers the relation S=E/2T between entropy, energy and temperature
previously proposed by one of us in gr-qc/0308070. This approach also enables
us to calculate the quantum corrections of the Bekenstein-Hawking entropy
formula for all spherically symmetric horizons.


title: Lorentz Symmetry Derived from Lorentz Violation in the Bulk

abstract:
  We consider bulk fields coupled to the graviton in a Lorentz violating
fashion. We expect that the overly tested Lorentz symmetry might set
constraints on the induced Lorentz violation in the brane, and hence on the
dynamics of the interaction of bulk fields on the brane. We also use the
requirement for Lorentz symmetry to constrain the cosmological constant
observed on the brane.


title: Instabilities in numerical loop quantum cosmology

abstract:
  In this article we perform von Neumann analysis of the difference equations
that arise as a result of loop quantum gravity being applied to models of
cosmology and black holes. In particular, we study the numerical stability of
Bianchi I LRS (symmetric and non-symmetric constraint) and Schwarzschild
interior (symmetric constraint) models, and find that there exist domains over
which there are instabilities, generically. We also present explicit evolutions
of wave-packets in these models and clearly demonstrate the presence of these
instabilities.


title: Graviton Physics

abstract:
  The interactions of gravitons with matter are calculated in parallel with the
familiar photon case. It is shown that graviton scattering amplitudes can be
factorized into a product of familiar electromagnetic forms, and cross sections
for various reactions are straightforwardly evaluated using helicity methods.


title:
Decay of Solutions of the Teukolsky Equation for Higher Spin in the
  Schwarzschild Geometry

abstract:
  We prove that the Schwarzschild black hole is linearly stable under
electromagnetic and gravitational perturbations. Our method is to show that for
spin $s=1$ or $s=2$, solutions of the Teukolsky equation with smooth, compactly
supported initial data outside the event horizon, decay in $L^\infty_{loc}$.


title: Eccentricity content of binary black hole initial data

abstract:
  Using a post-Newtonian diagnostic tool developed by Mora and Will, we examine
numerically generated quasiequilibrium initial data sets that have been used in
recently successful numerical evolutions of binary black holes through plunge,
merger and ringdown. We show that a small but significant orbital eccentricity
is required to match post-Newtonian and quasiequilibrium calculations. If this
proves to be a real eccentricity, it could affect the fine details of the
subsequent numerical evolutions and the predicted gravitational waveforms.


title:
Quasi-Normal Modes of Brane-Localised Standard Model Fields II: Kerr
  Black Holes

abstract:
  This paper presents a comprehensive study of the fundamental quasinormal
modes of all Standard Model fields propagating on a brane embedded in a
higher-dimensional rotating black hole spacetime. The equations of motion for
fields with spin $s=0, 1/2$ and 1 propagating in the induced-on-the-brane
background are solved numerically, and the dependence of their QN spectra on
the black hole angular momentum and dimensionality of spacetime is
investigated. It is found that the brane-localised field perturbations are
longer-lived when the higher-dimensional black hole rotates faster, while an
increase in the number of transverse-to-the-brane dimensions reduces their
lifetime. Finally, the quality factor $Q$, that determines the best oscillator
among the different field perturbations, is investigated and found to depend on
properties of both the particular field studied (spin, multipole numbers) and
the gravitational background (dimensionality, black hole angular momentum
number).


title: Topology of the Causal Boundary for Standard Static Spacetimes

abstract:
  The topology of the causal boundary for standard static
spacetimes--spacetimes time-invariantly conformal to a metric product of the
Lorentz line and a Riemannian manifold--is studied in depth. As this is given
in terms of a set of real-valued functions on the Riemannian factor, one could
use a function-space topology, but physical reasons recommend a chronological
topology instead. The function-space topology has a simple product structure,
while the chronological topology might not. This paper examines when the
chronological topology coincides with the function-space topology and when it
has a simple product structure. A class of standard static spacetimes is
examined, all of which yield a simple product structure for the causal
boundary; the conformal class of these spacetimes includes classical spacetimes
such as external Schwarzschild or Reissner-Nordstrom.


title:
Area evolution, bulk viscosity and entropy principles for dynamical
  horizons

abstract:
  We derive from Einstein equation an evolution law for the area of a trapping
or dynamical horizon. The solutions to this differential equation show a causal
behavior. Moreover, in a viscous fluid analogy, the equation can be interpreted
as an energy balance law, yielding to a positive bulk viscosity. These two
features contrast with the event horizon case, where the non-causal evolution
of the area and the negative bulk viscosity require teleological boundary
conditions. This reflects the local character of trapping horizons as opposed
to event horizons. Interpreting the area as the entropy, we propose to use an
area/entropy evolution principle to select a unique dynamical horizon and time
slicing in the Cauchy evolution of an initial marginally trapped surface.


title:
Quantum Corrections to the Reissner-Nordstrom and Kerr-Newman Metrics:
  Spin 1

abstract:
  A previous evaluation of one-photon loop corrections to the energy-momentum
tensor has been extended to particles with unit spin and speculations are
presented concerning general properties of such forms.


title: Instability of charged and rotating naked singularities

abstract:
  We provide evidence that ``super-extremal'' black hole space-times (either
with charge larger than mass or angular momentum larger than mass), which
contain naked singularities, are unstable under linearized perturbations. This
is given by an infinite family of exact unstable solutions in the charged non
rotating case, and by a set of (unstable) numerical solutions in the rotating
case. These results may be relevant to the expectation that these space-times
cannot be the endpoint of physical gravitational collapse.


title: Probing Quantized Einstein-Rosen Waves with Massless Scalar Matter

abstract:
  The purpose of this paper is to discuss in detail the use of scalar matter
coupled to linearly polarized Einstein-Rosen waves as a probe to study quantum
gravity in the restricted setting provided by this symmetry reduction of
general relativity. We will obtain the relevant Hamiltonian and quantize it
with the techniques already used for the purely gravitational case. Finally we
will discuss the use of particle-like modes of the quantized fields to
operationally explore some of the features of quantum gravity within this
framework. Specifically we will study two-point functions, the Newton-Wigner
propagator, and radial wave functions for one-particle states.


title: Quantum Corrections to the Schwarzschild and Kerr Metrics: Spin 1

abstract:
  a previous evaluation of the one-graviton loop corrections to the
energy-momentum tensor has been extended to particles with unit spin and
speculations are presented concerning general properties of such forms.


title:
On causality and superluminal behavior in classical field theories.
  Applications to k-essence theories and MOND-like theories of gravity

abstract:
  Field theories whose full action is Lorentz invariant (or diffeomorphism
invariant) can exhibit superluminal behaviors through the breaking of local
Lorentz invariance. Quantum induced superluminal velocities are well-known
examples of this effect. The issue of the causal behavior of such propagations
is somewhat controversial in the literature and we intend to clarify it. We
provide a careful analysis of the meaning of causality in classical
relativistic field theories, and we stress the role played by the Cauchy
problem and the notions of chronology and time arrow. We show that superluminal
behavior threaten causality only if a prior chronology on spacetime is chosen.
In the case where superluminal propagations occur, however, there is at least
two non conformally related metrics on spacetime and thus two available notions
of chronology. These two chronologies are on equal footing and it would thus be
misleading to choose \textit{ab initio} one of them to define causality.
Rather, we provide a formulation of causality in which no prior chronology is
assumed. We argue this is the only way to deal with the issue of causality in
the case where some degrees of freedom propagate faster than others. We
actually show that superluminal propagations do not threaten causality. As an
illustration of these conceptual issues, we consider two field theories, namely
k-essences scalar fields and bimetric theories of gravity, and we derive the
conditions imposed by causality. We discuss various applications such as the
dark energy problem, MOND-like theories of gravity and varying speed of light
theories.


title: Solving Einstein's Equations With Dual Coordinate Frames

abstract:
  A method is introduced for solving Einstein's equations using two distinct
coordinate systems. The coordinate basis vectors associated with one system are
used to project out components of the metric and other fields, in analogy with
the way fields are projected onto an orthonormal tetrad basis. These field
components are then determined as functions of a second independent coordinate
system. The transformation to the second coordinate system can be thought of as
a mapping from the original ``inertial'' coordinate system to the computational
domain. This dual-coordinate method is used to perform stable numerical
evolutions of a black-hole spacetime using the generalized harmonic form of
Einstein's equations in coordinates that rotate with respect to the inertial
frame at infinity; such evolutions are found to be generically unstable using a
single rotating coordinate frame. The dual-coordinate method is also used here
to evolve binary black-hole spacetimes for several orbits. The great
flexibility of this method allows comoving coordinates to be adjusted with a
feedback control system that keeps the excision boundaries of the holes within
their respective apparent horizons.


title: Galactic Halos are Einstein Clusters of WIMPs

abstract:
  It is shown that an Einstein cluster of WIMPs, WIMPs on stable circular
geodesic orbits generating the static spherically symmetric gravitational field
of a galactic halo, can exactly reproduce the rotation curve of any galaxy
simply by adjusting the local angular momentum distribution and consequent
number distribution of the WIMPs. No new physics is involved (assuming the
forthcoming discovery of WIMPs). Further, stability of the orbits can require
an inner truncation of the halo and an explicit example of this is given. There
is no exact Newtonian counterpart to the model presented since pure Newtonian
gravity fails to account for the contribution made by the angular momentum
distribution of the particles in creating the gravitational field. In effect, a
galactic halo is supported by the hoop stresses created by the orbiting WIMPs.


title:
Factorization in Graviton Scattering and the "Natural" Value of the
  g-factor

abstract:
  The factorization property of graviton scattering amplitudes is reviewed and
show to be valid only if the "natural" value of the gyromagnetic ratio $g_S=2$
is employed -- independent of spin.


title: Inflationary scalar spectrum in loop quantum cosmology

abstract:
  In the context of loop quantum cosmology, we consider an inflationary era
driven by a canonical scalar field and occurring in the semiclassical regime,
where spacetime is a continuum but quantum gravitational effects are important.
The spectral amplitude and index of scalar perturbations on an unperturbed de
Sitter background are computed at lowest order in the slow-roll parameters. The
scalar spectrum can be blue-tilted and far from scale invariance, and tuning of
the quantization ambiguities is necessary for agreement with observations. The
results are extended to a generalized quantization scheme including those
proposed in the literature. Quantization of the matter field at sub-horizon
scales can provide a consistency check of such schemes.


title: Quantum Roots in Geometry: II

abstract:
  The present work is a review of a series of papers, published in the last ten
years, comprising an attempt to find a suitable avenue from geometry to
quantum. It shows clearly that, any non-symmetric geometry admits some built-in
quantum features. These features disappear completely once the geometry becomes
symmetric (torsion-less). It is shown that, torsion of space-time plays an
important role in both geometry and physics. It interacts with the spin of the
moving particle and with its charge. The first interaction, {\bf{Spin-Torsion
Interaction}}, has been used to overcome the discrepancy in the results of the
COW-experiment. The second interaction, {\bf{Charge-Torsion Interaction}}, is
similar to the Aharonov-Bohm effect.
  As a byproduct, a new version of Absolute Parallelism (AP) geometry, the
Parameterized Absolute Parallelism (PAP) geometry, has been established and
developed. This version can be used to construct field theories that admit some
quantum features. Riemannian geometry and conventional AP-geometry are special
cases of PAP-geometry.


title: Thin shell wormholes in higher dimensiaonal Einstein-Maxwell theory

abstract:
  We construct thin shell Lorentzian wormholes in higher dimensional
Einstein-Maxwell theory applying the ' Cut and Paste ' technique proposed by
Visser. The linearized stability is analyzed under radial perturbations around
some assumed higher dimensional spherically symmetric static solution of the
Einstein field equations in presence of Electromagnetic field. We determine the
total amount of exotic matter, which is concentrated at the wormhole throat.


title: Classical and Quantum Dilaton Gravity in Two Dimensions with Fermions

abstract:
  In this thesis the first order formulation of generalized dilaton gravities
in two dimensions coupled to a Dirac fermion is considered. After a Hamiltonian
analysis of the gauge symmetries and constraints of the theory and fixing
Eddington-Finkelstein gauge by use of the Batalin-Vilkovisky-Fradkin method,
the system is quantized in the Feynman path integral approach. It turns out
that the path integral over the dilaton gravity sector can be evaluated
exactly, while in the matter sector perturbative methods are applied. The
gravitationally induced four-fermi scattering vertices as well as asymptotic
states are calculated, and -- as for dilaton gravities coupled to scalar fields
-- a ``virtual black hole'' is found to form as an intermediary geometric state
in scattering processes. The results are compared to the well-known scalar case
and evidence for bosonization in this context is found.


title: The General Solution of Bianchi Type III Vacuum Cosmology

abstract:
  The second order Ordinary Differential Equation which describes the unknown
part of the solution space of some vacuum Bianchi Cosmologies is completely
integrated for Type III, thus obtaining the general solution to Einstein's
Field Equations for this case, with the aid of the sixth Painlev\'{e}
transcendent $P_{VI}$. For particular representations of $P_{VI}$ we obtain the
known Kinnersley two-parameter space-time and a solution of Euclidean
signature. The imposition of the space-time generalization of a "hidden"
symmetry of the generic Type III spatial slice, enables us to retrieve the
two-parameter subfamily without considering the Painlev\'{e} transcendent.


title: The Weyl curvature conjecture and black hole entropy

abstract:
  The universe today, with structure such as stars, galaxies and black holes,
seems to have evolved from a very homogeneous initial state. From this it
appears as if the entropy of the universe is decreasing, in violation of the
second law of thermodynamics. It has been suggested by Roger Penrose
\cite{grossmann:penrose:wcc} that this inconsistency can be solved if one
assigns an entropy to the spacetime geometry. He also pointed out that the Weyl
tensor has the properties one would expect to find in a description of a
gravitational entropy. In this article we make an attempt to use this so-called
Weyl curvature conjecture to describe the Hawking-Bekenstein entropy of black
holes and the entropy of horizons due to a cosmological constant.


title: On the relation between mathematical and numerical relativity

abstract:
  The large scale binary black hole effort in numerical relativity has led to
an increasing distinction between numerical and mathematical relativity. This
note discusses this situation and gives some examples of succesful interactions
between numerical and mathematical methods is general relativity.


title: Towards a novel wave-extraction method for numerical relativity

abstract:
  We present the recent results of a research project aimed at constructing a
robust wave extraction technique for numerical relativity. Our procedure makes
use of Weyl scalars to achieve wave extraction. It is well known that, with a
correct choice of null tetrad, Weyl scalars are directly associated to physical
properties of the space-time under analysis in some well understood way. In
particular it is possible to associate $\Psi_4$ with the outgoing gravitational
radiation degrees of freedom, thus making it a promising tool for numerical
wave--extraction. The right choice of the tetrad is, however, the problem to be
addressed. We have made progress towards identifying a general procedure for
choosing this tetrad, by looking at transverse tetrads where $\Psi_1=\Psi_3=0$.
  As a direct application of these concepts, we present a numerical study of
the evolution of a non-linearly disturbed black hole described by the
Bondi--Sachs metric. This particular scenario allows us to compare the results
coming from Weyl scalars with the results coming from the news function which,
in this particular case, is directly associated with the radiative degrees of
freedom. We show that, if we did not take particular care in choosing the right
tetrad, we would end up with incorrect results.


title: Accelerating universe in brane gravity with a confining potential

abstract:
  We construct the Einstein field equations on a 4-dimensional brane embedded
in an $m$-dimensional bulk where the matter fields are confined to the brane by
means of a confining potential. As a result, an extra term in the Friedmann
equation in a $m$-dimensional bulk appears that may be interpreted as the
X-matter, providing a possible phenomenological explanation for the
acceleration of the universe. The study of the relevant observational data
suggests good agreement with the predictions of this model.


title: Dirac Quantization of Parametrized Field Theory

abstract:
  Parametrized field theory (PFT) is free field theory on flat spacetime in a
diffeomorphism invariant disguise. It describes field evolution on arbitrary
foliations of the flat spacetime instead of only the usual flat ones, by
treating the `embedding variables' which describe the foliation as dynamical
variables to be varied in the action in addition to the scalar field. A formal
Dirac quantization turns the constraints of PFT into functional Schrodinger
equations which describe evolution of quantum states from an arbitrary Cauchy
slice to an infinitesimally nearby one.This formal Schrodinger picture- based
quantization is unitarily equivalent to the standard Heisenberg picture based
Fock quantization of the free scalar field if scalar field evolution along
arbitrary foliations is unitarily implemented on the Fock space. Torre and
Varadarajan (TV) showed that for generic foliations emanating from a flat
initial slice in spacetimes of dimension greater than 2, evolution is not
unitarily implemented, thus implying an obstruction to Dirac quantization.
  We construct a Dirac quantization of PFT,unitarily equivalent to the standard
Fock quantization, using techniques from Loop Quantum Gravity (LQG) which are
powerful enough to super-cede the no- go implications of the TV results. The
key features of our quantization include an LQG type representation for the
embedding variables, embedding dependent Fock spaces for the scalar field, an
anomaly free representation of (a generalization of) the finite transformations
generated by the constraints and group averaging techniques. The difference
between 2 and higher dimensions is that in the latter, only finite gauge
transformations are defined in the quantum theory, not the infinitesimal ones.


title:
Anomaly Induced Effective Action Combined with Generalized Brans-Dicke
  Theory

abstract:
  We consider the anomaly induced effective action in N=4 super Yang-Mills
theory in interaction with the Brans-Dicke (BD) field. The generalization of
the BD theory so as to permit an energy exchange between the scalar field and
ordinary matter fields, was recently worked out by T. Clifton and J. D. Barrow
[Phys. Rev. D 73, 104022 (2006)]. We derive the scalar field equations for the
dilaton field, and the BD field, and discuss the Friedmann equation in the
general case. The present paper is a continuation of an investigation some
years ago dealing with the case of conformal anomaly plus ordinary classical
gravity [I. Brevik and S. D. Odintsov, Phys. Lett. B 455, 104 (1999)].


title:
On a new symmetry of the solutions of the wave equation in the
  background of a Kerr black hole

abstract:
  This short paper derives the constant of motion of a scalar field in the
gravitational field of a Kerr black hole which is associated to a Killing
tensor of that space-time. In addition, there is found a related new symmetry
operator S for the solutions of the wave equation in that background. That
operator is a partial differential operator with a leading order time
derivative of the first order that commutes with a normal form of the wave
operator. That form is obtained by multiplication of the wave operator from the
left with the reciprocal of the coefficient function of its second order time
derivative. It is shown that S induces an operator that commutes with the
generator of time evolution in a formulation of the initial value problem for
the wave equation in the setting of strongly continuous semigroups.


title: A study of gravitational collapse with decaying of the vacuum energy

abstract:
  We study the gravitational collapse of a dust dark matter star in a
$\Lambda$-background. We consider two distinct cases: First we do not have a
dark matter and dark energy coupling; second, we consider that $\Lambda $ decay
in dark particles. The approach adopted assumes a modified matter expansion
rate and we have formation of a black hole, since that, we have the formation
of an apparent horizon. A brief comparison of the process of the matter
condensation using the gravitational collapse approach and the linear scalar
perturbation theory is considered.


title:
Spacetime Coarse Grainings in the Decoherent Histories Approach to
  Quantum Theory

abstract:
  We investigate the possibility of assigning consistent probabilities to sets
of histories characterized by whether they enter a particular subspace of the
Hilbert space of a closed system during a given time interval. In particular we
investigate the case that this subspace is a region of the configuration space.
This corresponds to a particular class of coarse grainings of spacetime
regions. We consider the arrival time problem and the problem of time in
reparametrization invariant theories as for example in canonical quantum
gravity. Decoherence conditions and probabilities for those application are
derived. The resulting decoherence condition does not depend on the explicit
form of the restricted propagator that was problematic for generalizations such
as application in quantum cosmology. Closely related is the problem of
tunnelling time as well as the quantum Zeno effect. Some interpretational
comments conclude, and we discuss the applicability of this formalism to deal
with the arrival time problem.


title: Classification of cosmological milestones

abstract:
  In this paper causal geodesic completeness of FLRW cosmological models is
analysed in terms of generalised power expansions of the scale factor in
coordinate time. The strength of the found singularities is discussed following
the usual definitions due to Tipler and Krolak. It is shown that while
classical cosmological models are both timelike and lightlike geodesically
incomplete, certain observationally alllowed models which have been proposed
recently are lightlike geodesically complete.


title: On the Physical Meaning of the Robinson-Trautman-Maxwell Fields

abstract:
  We study the Robinson-Trautman-Maxwell Fields in two closely related
coordinate systems, the original Robinson-Trautman (RT) coordinates (in a more
general context, often referred to as NU coordinates) and Bondi coordinates. In
particular, we identify one of the RT variables as a velocity and then from the
Bondi energy-momentum 4-vector, we find kinematic expressions for the mass and
momentum in terms of this velocity. From these kinematic expressions and the
energy-momentum loss equation we obtain surprising equations of motion for `the
center of mass' of the source where the motion takes place in the
four-dimensional Poincare translation sub-group of the BMS group.


title: Approximating the physical inner product of Loop Quantum Cosmology

abstract:
  In this article, we investigate the possibility of approximating the physical
inner product of constrained quantum theories. In particular, we calculate the
physical inner product of a simple cosmological model in two ways: Firstly, we
compute it analytically via a trick, secondly, we use the complexifier coherent
states to approximate the physical inner product defined by the master
constraint of the system. We will find that the approximation is able to
recover the analytic solution of the problem, which solidifies hopes that
coherent states will help to approximate solutions of more complicated
theories, like loop quantum gravity.


title: Higher Gauge Theory and Gravity in (2+1) Dimensions

abstract:
  Non-abelian higher gauge theory has recently emerged as a generalization of
standard gauge theory to higher dimensional (2-dimensional in the present
context) connection forms, and as such, it has been successfully applied to the
non-abelian generalizations of the Yang-Mills theory and 2-form
electrodynamics. (2+1)-dimensional gravity, on the other hand, has been a
fertile testing ground for many concepts related to classical and quantum
gravity, and it is therefore only natural to investigate whether we can find an
application of higher gauge theory in this latter context. In the present paper
we investigate the possibility of applying the formalism of higher gauge theory
to gravity in (2+1) dimensions, and we show that a nontrivial model of
(2+1)-dimensional gravity coupled to scalar and tensorial matter fields - the
$\Sigma\Phi EA$ model - can be formulated both as a standard gauge theory and
as a higher gauge theory. Since the model has a very rich structure - it admits
as solutions black-hole BTZ-like geometries, particle-like geometries as well
as Robertson-Friedman-Walker cosmological-like expanding geometries - this
opens a wide perspective for higher gauge theory to be tested and understood in
a relevant gravitational context. Additionally, it offers the possibility of
studying gravity in (2+1) dimensions coupled to matter in an entirely new
framework.


title: Teleparallel Energy-Momentum Distribution of Lewis-Papapetrou Spacetimes

abstract:
  In this paper, we find the energy-momentum distribution of stationary
axisymmetric spacetimes in the context of teleparallel theory by using
M$\ddot{o}$ller prescription. The metric under consideration is the
generalization of the Weyl metrics called the Lewis-Papapetrou metric. The
class of stationary axisymmetric solutions of the Einstein field equations has
been studied by Galtsov to include the gravitational effect of an {\it
external} source. Such spacetimes are also astrophysically important as they
describe the exterior of a body in equilibrium. The energy density turns out to
be non-vanishing and well-defined and the momentum becomes constant except
along $\theta$-direction. It is interesting to mention that the results reduce
to the already available results for the Weyl metrics when we take $\omega=0$.


title: Cosmological monopoles and non-abelian black holes

abstract:
  We discuss magnetic monopole solutions of the Einstein-Yang-Mills-Higgs
equations with a positive cosmological constant. These configurations approach
asymptotically the de Sitter spacetime background and exist only for a nonzero
Higgs potential. We find that the total mass of the solutions within the
cosmological horizon is finite. However, their mass evaluated by using the
surface counterterm method outside the cosmological horizon at early/late time
infinity generically diverges. Magnetic monopole solutions with finite mass and
noninteger charge are found however in a truncation of the theory with a
vanishing Higgs field. Both solutions with a regular origin and cosmological
black holes are studied, special attention being paid to the computation of the
global charges.


title: Averaging in Spherically Symmetric Cosmology

abstract:
  In the macroscopic gravity approach to the averaging problem in cosmology,
the Einstein field equations on cosmological scales are modified by appropriate
gravitational correlation terms. We study the averaging problem within the
class of spherically symmetric cosmological models. That is, we shall take the
microscopic equations and effect the averaging procedure to determine the
precise form of the correlation tensor in this case. In particular, by working
in volume preserving coordinates, we calculate the form of the correlation
tensor under some reasonable assumptions on the form for the inhomogeneous
gravitational field and matter distribution. We find that the correlation
tensor in a FLRW background must be of the form of a spatial curvature.
Inhomogeneities and spatial averaging, through this spatial curvature
correction term, can have a very significant dynamical effect on the dynamics
of the Universe and cosmological observations; in particular, we discuss
whether spatial averaging might lead to a more conservative explanation of the
observed acceleration of the Universe (without the introduction of exotic dark
matter fields). We also find that the correlation tensor for a non-FLRW
background can be interpreted as the sum of a spatial curvature and an
anisotropic fluid. This may lead to interesting effects of averaging on
astrophysical scales. We also discuss the results of averaging an inhomogeneous
Lemaitre-Tolman-Bondi solution as well as calculations of linear perturbations
(that is, the back-reaction) in an FLRW background, which support the main
conclusions of the analysis.


title:
Probing anisotropies of gravitational-wave backgrounds with a
  space-based interferometer III: Reconstruction of a high-frequency skymap

abstract:
  We develop a numerical scheme to make a high-frequency skymap of
gravitational-wave backgrounds (GWBs) observed via space-based interferometer.
Based on the cross-correlation technique, the intensity distribution of
anisotropic GWB can be directly reconstructed from the time-ordered data of
cross-correlation signals, with full knowledge of detector's antenna pattern
functions. We demonstrate how the planned space interferometer, LISA, can make
a skymap of GWB for a specific example of anisotropic signals. At the frequency
higher than the characteristic frequency $f_*=1/(2\pi L)$, where $L$ is the
arm-length of the detector, the reconstructed skymap free from the instrumental
noise potentially reaches the angular resolution up to the multipoles
$\ell\sim10$. The presence of instrumental noises degrades the angular
resolution. The resultant skymap has angular resolution with multipoles
$\ell\leq 6\sim7$ for the anisotropic signals with signal-to-noise ratio
S/N$>5$.


title: Conservation laws for dynamical black holes

abstract:
  An essentially complete new paradigm for dynamical black holes in terms of
trapping horizons is presented, including dynamical versions of the physical
quantities and laws which were considered important in the classical paradigm
for black holes in terms of Killing or event horizons. Three state functions
are identified as surface integrals over marginal surfaces: irreducible mass,
angular momentum and charge. There are three corresponding conservation laws,
expressing the rate of change of the state function in terms of flux integrals,
or equivalently as divergence laws for associated conserved currents. The
currents of energy and angular momentum include the matter energy tensor in a
physically appropriate way, plus terms attributable to an effective energy
tensor for gravitational radiation. Four other state functions are derived: an
effective energy, surface gravity, angular speed and electric potential. There
follows a dynamical version of the so-called first law of black-hole mechanics.
A corresponding zeroth law holds for null trapping horizons.


title: The Momentum Four-Vector in Brans-Dicke Wormholes

abstract:
  This paper has been removed by arXiv administrators because it plagiarizes
K.K. Nandi and Y.Z. Zhang, "An algorithm for generating rotating Brans-Dicke
wormhole solutions," gr-qc/0606012; and Ragab M. Gad, "Energy and Momentum
Densities Associated with Solutions Exhibiting Directional Type Singularities,"
gr-qc/0404108.


title: Relative Energy Associated with a White Hole Model of the Big Bang

abstract:
  This paper has been removed by arXiv administrators because it plagiarizes
gr-qc/9803014, "A White Hole Model of the Big Bang," by Philip Gibbs.


title: Schrodinger representation for the polarized Gowdy model

abstract:
  The polarized ${\bf T}^3$ Gowdy model is, in a standard gauge, characterized
by a point particle degree of freedom and a scalar field degree of freedom
obeying a linear field equation on ${\bf R}\times{\bf S}^1$. The Fock
representation of the scalar field has been well-studied. Here we construct the
Schrodinger representation for the scalar field at a fixed value of the Gowdy
time in terms of square-integrable functions on a space of distributional
fields with a Gaussian probability measure. We show that ``typical'' field
configurations are slightly more singular than square-integrable functions on
the circle. For each time the corresponding Schrodinger representation is
unitarily equivalent to the Fock representation, and hence all the Schrodinger
representations are equivalent. However, the failure of unitary
implementability of time evolution in this model manifests itself in the mutual
singularity of the Gaussian measures at different times.


title:
A Note on the Local Cosmological Constant and the Dark Energy
  Coincidence Problem

abstract:
  It has been suggested that the Dark Energy Coincidence Problem could be
interpreted as a possible link between the cosmological constant and a massive
graviton. We show that by using that link and models for the graviton mass a
dark energy density can be obtained that is indeed very close to measurements
by WMAP. As a consequence of the models, the cosmological constant was found to
depend on the density of matter. A brief outline of the cosmological
consequences such as the effect on the black hole solution is given.


title:
Gravitomagnetic Fields in Rotating Superconductors to Solve Tate's
  Cooper Pair Mass Anomaly

abstract:
  Superconductors have often been used to claim gravitational anomalies in the
context of breakthrough propulsion. The experiments could not be reproduced by
others up to now, and the theories were either shown to be wrong or are often
based on difficult to prove assumptions. We will show that superconductors
indeed could be used to produce non-classical gravitational fields, based on
the established disagreement between theoretical prediction and measured
Cooper-pair mass in Niobium. Tate et al failed to measure the Cooper-pair mass
in Niobium as predicted by quantum theory. This has been discussed in the
literature without any apparent solution. Based on the work from DeWitt to
include gravitomagnetism in the canonical momentum of Cooper-pairs, the authors
published a number of papers discussing a possibly involved gravitomagnetic
field in rotating superconductors to solve Tate's measured anomaly. Although
one possibility to match Tate's measurement, a number of reasons were developed
by the authors over the last years to show that the gravitomagnetic field in a
rotating quantum material must be different from its classical value and that
Tate's result is actually the first experimental sign for it. This paper
reviews the latest theoretical approaches to solve the Tate Cooper-pair anomaly
based on gravitomagnetic fields in rotating superconductors.


title: Does Pressure Increase or Decrease Active Gravitational Mass Density?

abstract:
  It is known that, for a static fluid sphere, the GeneralRelativistic (GR)
Effective Mass Energy Density (EMD) appears to be (rho + 3 p), where rho is the
bare mass density, p is the isotropic pressure, from a purely localized view
point. But since there is no truly local definition of ``gravitational field'',
such a notion could actually be misleading. On the other hand, by using the
Tolman mass formula, we point out that, from a global perspective, the Active
Gravitational Mass Energy Density (AGMD) is sqrt{g_{00}} (rho + 3 p) and which
is obviously smaller than (rho + 3p) because g_{00} < 1. Then we show that the
AGMD eventually is (rho - 3p), i.e., exactly opposite to what is generally
believed. We further identify the AGMD to be proportional to the Ricci Scalar.
By using this fundamental and intersting property, we obtain the GR virial
theorem in terms of appropriate ``proper energies''.


title: The Einstein-Cartan-Elko system

abstract:
  The present paper analyses the Einstein-Cartan theory of gravitation with
Elko spinors as sources of curvature and torsion. After minimally coupling the
Elko spinors to torsion, the spin angular momentum tensor is derived and its
structure is discussed. It shows a much richer structure than the Dirac
analogue and hence it is demonstrated that spin one half particles do not
necessarily yield only an axial vector torsion component. Moreover, it is
argued that the presence of Elko spinors partially solves the problem of
minimally coupling Maxwell fields to Einstein-Cartan theory.


title: Energy and Momentum of The Szekeres Universes in Tele-parallel Gravity

abstract:
  This paper has been removed by arXiv administrators because it plagiarizes
gr-qc/0603075 and others.
  This paper has excessive overlap with the following papers also written by
the authors or their collaborators: gr-qc/0606080, gr-qc/0607126,
gr-qc/0607109, gr-qc/0607110, and others.


title: $\Lambda$ effect in the cosmological expansion of voids

abstract:
  The dynamical effect of the cosmological constant $\Lambda$ on a single
spherical void evolving in a the universe is investigated within a non linear
perturbation of Newton-Friedmann models. The void expands with a huge initial
burst which freezes asymptotically with time up to matching Hubble flow. For
$\Omega_{\circ}\sim 0.3$, $\Lambda$-effect on the kinematics intervenes
significantly by amplifying the expansion rate at redshift $z\sim 1.7$. As a
result, the size increases with the background density and with $\Lambda$, what
interprets by the gravitational attraction of borders from outside regions and
the gravitational repulsion of borders. The velocity flow within the void
region depends solely on $\Lambda$, it reads $\vec{v}=\sqrt{\Lambda/3}\vec{r}$.
Hence, the empty regions are swept out for spatially closed Friedmann models
what provides us with a stability criterion.


title:
Negative Komar Mass of Single Objects in Regular, Asymptotically Flat
  Spacetimes

abstract:
  We study two types of axially symmetric, stationary and asymptotically flat
spacetimes using highly accurate numerical methods. The one type contains a
black hole surrounded by a perfect fluid ring and the other a rigidly rotating
disc of dust surrounded by such a ring. Both types of spacetime are regular
everywhere (outside of the horizon in the case of the black hole) and fulfil
the requirements of the positive energy theorem. However, it is shown that both
the black hole and the disc can have negative Komar mass. Furthermore, there
exists a continuous transition from discs to black holes even when their Komar
masses are negative.


title:
Phenomenology of amplitude-corrected post-Newtonian gravitational
  waveforms for compact binary inspiral. I. Signal-to-noise ratios

abstract:
  We study the phenomenological consequences of amplitude-corrected
post-Newtonian (PN) gravitational waveforms, as opposed to the more commonly
used restricted PN waveforms, for the quasi-circular, adiabatic inspiral of
compact binary objects. In the case of initial detectors it has been shown that
the use of amplitude-corrected waveforms for detection templates would lead to
significantly lower signal-to-noise ratios (SNRs) than those suggested by
simulations based exclusively on restricted waveforms. We further elucidate the
origin of the effect by an in-depth analytic treatment. The discussion is
extended to advanced detectors, where new features emerge. Non-restricted
waveforms are linear combinations of harmonics in the orbital phase, and in the
frequency domain the $k$th harmonic is cut off at $k f_{LSO}$, with $f_{LSO}$
the orbital frequency at the last stable orbit. As a result, with
non-restricted templates it is possible to achieve sizeable signal-to-noise
ratios in cases where the dominant harmonic (which is the one at twice the
orbital phase) does not enter the detector's bandwidth. This will have
important repercussions on the detection of binary inspirals involving
intermediate-mass black holes. For sources at a distance of 100 Mpc, taking
into account the higher harmonics will double the mass reach of Advanced LIGO,
and that of EGO gets tripled. Conservative estimates indicate that the
restricted waveforms underestimate detection rates for intermediate mass binary
inspirals by at least a factor of twenty.


title: Solar System planetary orbital motions and f(R) Theories of Gravity

abstract:
  In this paper we study the effects of $f(R)$ Theories of Gravity on Solar
System gravitational tests. In particular, starting from an exact solution of
the field equation in vacuum, in the Palatini formalism, we work out the
effects that the modifications to the Newtonian potential would induce on the
Keplerian orbital elements of the Solar System planets, and compare them with
the latest results in planetary orbit determination from the EPM2004
ephemerides. It turns out that the longitudes of perihelia and the mean
longitudes are affected by secular precessions. We obtain the resulting best
estimate of the parameter $k$ which, being simply related to the scalar
curvature, measures the non linearity of the gravitational theory. We use our
results to constrain the cosmological constant and show how $f(R)$ functions
can be constrained, in principle. What we obtain suggests that, in agreement
with other recent papers, the Solar System experiments are not effective to set
such constraints, if compared to the cosmologically relevant values.


title: Two Loop Scalar Bilinears for Inflationary SQED

abstract:
  We evaluate the one and two loop contributions to the expectation values of
two coincident and gauge invariant scalar bilinears in the theory of massless,
minimally coupled scalar quantum electrodynamics on a locally de Sitter
background. One of these bilinears is the product of two covariantly
differentiated scalars, the other is the product of two undifferentiated
scalars. The computations are done using dimensional regularization and the
Schwinger-Keldysh formalism. Our results are in perfect agreement with the
stochastic predictions at this order.


title: Electric and Magnetic Black Hole Solutions of Moller's Four-Momentum

abstract:
  This paper has been removed by arXiv administrators because it plagiarizes
hep-th/0311050, gr-qc/0306101, gr-qc/9601044, gr-qc/0412111, hep-th/9604047,
and gr-qc/0212018.


title: Spherically Symmetric Solutions to Fourth-Order Theories of Gravity

abstract:
  Gravitational theories generated from Lagrangians of the form f(R) are
considered. The spherically symmetric solutions to these equations are
discussed, paying particular attention to features that differ from the
standard Schwarzschild solution. The asymptotic form of solutions is described,
as is the lack of validity of Birkhoff's theorem. Exact solutions are presented
which illustrate these points and their stability and geodesics are
investigated.


title: Semiclassical states for quantum cosmology

abstract:
  In a metric variable based Hamiltonian quantization, we give a prescription
for constructing semiclassical matter-geometry states for homogeneous and
isotropic cosmological models. These "collective" states arise as infinite
linear combinations of fundamental excitations in an unconventional "polymer"
quantization. They satisfy a number of properties characteristic of
semiclassicality, such as peaking on classical phase space configurations. We
describe how these states can be used to determine quantum corrections to the
classical evolution equations, and to compute the initial state of the universe
by a backward time evolution.


title: Thick Domain Walls in AdS Black Hole Spacetimes

abstract:
  Equations of motion for a real self-gravitating scalar field in the
background of a black hole with negative cosmological constant were solved
numerically. We obtain a sequence of static axisymmetric solutions representing
thick domain wall cosmological black hole systems, depending on the mass of
black hole, cosmological parameter and the parameter binding black hole mass
with the width of the domain wall. For the case of extremal cosmological black
hole the expulsion of scalar field from the black hole strongly depends on it.


title: Algebraic Quantum Gravity (AQG) I. Conceptual Setup

abstract:
  We introduce a new top down approach to canonical quantum gravity, called
Algebraic Quantum Gravity (AQG):The quantum kinematics of AQG is determined by
an abstract $*-$algebra generated by a countable set of elementary operators
labelled by an algebraic graph. The quantum dynamics of AQG is governed by a
single Master Constraint operator. While AQG is inspired by Loop Quantum
Gravity (LQG), it differs drastically from it because in AQG there is
fundamentally no topology or differential structure. A natural Hilbert space
representation acquires the structure of an infinite tensor product (ITP) whose
separable strong equivalence class Hilbert subspaces (sectors) are left
invariant by the quantum dynamics. The missing information about the topology
and differential structure of the spacetime manifold as well as about the
background metric to be approximated is supplied by coherent states. Given such
data, the corresponding coherent state defines a sector in the ITP which can be
identified with a usual QFT on the given manifold and background. Thus, AQG
contains QFT on all curved spacetimes at once, possibly has something to say
about topology change and provides the contact with the familiar low energy
physics. In particular, in two companion papers we develop semiclassical
perturbation theory for AQG and LQG and thereby show that the theory admits a
semiclassical limit whose infinitesimal gauge symmetry agrees with that of
General Relativity. In AQG everything is computable with sufficient precision
and no UV divergences arise due to the background independence of the
undamental combinatorial structure. Hence, in contrast to lattice gauge theory
on a background metric, no continuum limit has to be taken, there simply is no
lattice regulator that must be sent to zero.


title: Algebraic Quantum Gravity (AQG) II. Semiclassical Analysis

abstract:
  In the previous article a new combinatorial and thus purely algebraical
approach to quantum gravity, called Algebraic Quantum Gravity (AQG), was
introduced. In the framework of AQG existing semiclassical tools can be applied
to operators that encode the dynamics of AQG such as the Master constraint
operator. In this article we will analyse the semiclassical limit of the
(extended) algebraic Master constraint operator and show that it reproduces the
correct infinitesimal generators of General Relativity. Therefore the question
whether General Relativity is included in the semiclassical sector of the
theory, which is still an open problem in LQG, can be significantly improved in
the framework of AQG. For the calculations we will substitute SU(2) by U(1)^3.
That this substitution is justified will be demonstrated in the third article
of this series


title: Algebraic Quantum Gravity (AQG) III. Semiclassical Perturbation Theory

abstract:
  In the two previous papers of this series we defined a new combinatorical
approach to quantum gravity, Algebraic Quantum Gravity (AQG). We showed that
AQG reproduces the correct infinitesimal dynamics in the semiclassical limit,
provided one incorrectly substitutes the non -- Abelean group SU(2) by the
Abelean group $U(1)^3$ in the calculations. The mere reason why that
substitution was performed at all is that in the non -- Abelean case the volume
operator, pivotal for the definition of the dynamics, is not diagonisable by
analytical methods. This, in contrast to the Abelean case, so far prohibited
semiclassical computations. In this paper we show why this unjustified
substitution nevertheless reproduces the correct physical result: Namely, we
introduce for the first time semiclassical perturbation theory within AQG (and
LQG) which allows to compute expectation values of interesting operators such
as the master constraint as a power series in $\hbar$ with error control. That
is, in particular matrix elements of fractional powers of the volume operator
can be computed with extremely high precision for sufficiently large power of
$\hbar$ in the $\hbar$ expansion. With this new tool, the non -- Abelean
calculation, although technically more involved, is then exactly analogous to
the Abelean calculation, thus justifying the Abelean analysis in retrospect.
The results of this paper turn AQG into a calculational discipline.


title: Energy Momentum Localization in Marder Space-Time

abstract:
  This paper has been removed by arXiv administrators because it plagiarizes
hep-th/0308070, gr-qc/9910015, and others.
  This paper has excessive overlap with the following papers also written by
the authors or their collaborators: gr-qc/0607103, gr-qc/0606080,
gr-qc/0607119, gr-qc/0502043, gr-qc/0505079, gr-qc/0607115, gr-qc/0506061,
gr-qc/0607109, and others.


title: On the Energy Momentum in Bianchi Type I-III-V-VI0 Space-Time

abstract:
  This paper has been removed by arXiv administrators because it plagiarizes
gr-qc/0303009, hep-th/0405047, gr-qc/0602107, hep-th/0311050, gr-qc/0412120,
gr-qc/0508005, and others.
  This paper has excessive overlap with the following papers also written by
the authors or their collaborators: gr-qc/0607119, gr-qc/0607115,
gr-qc/0606080, gr-qc/0607110, gr-qc/0607102, gr-qc/0510123, gr-qc/0607126,
gr-qc/0602012, and others.


title:
Topological defect solutions in the spherically symmetric space-time
  admitting conformal motion

abstract:
  This paper has excessive overlap with the following papers also written by
the authors or their collaborators: hep-th/0505013 and 0705.2930.


title: Cosmological model with Born-Infeld type scalar field

abstract:
  The non-abelian generalization of the Born-Infeld non-linear lagrangian is
extended to the non-commutative geometry of matrices on a manifold. In this
case not only the usual SU(n) gauge fields appear, but also a natural
generalization of the multiplet of scalar Higgs fields, with the double-well
potential as a first approximation. The matrix realization of non-commutative
geometry provides a natural framework in which the notion of a determinant can
be easily generalized and used as the lowest-order term in a gravitational
lagrangian of a new kind. As a result, we obtain a Born-Infeld-like lagrangian
as a root of sufficiently high order of a combination of metric, gauge
potentials and the scalar field interactions. We then analyze the behavior of
cosmological models based on this lagrangian. It leads to primordial inflation
with varying speed, with possibility of early deceleration ruled by the
relative strength of the Higgs field.


title:
Fatal Missing Link from Classical Brane Dynamics to Einstein Gravity and
  a Quantum Theoretical Solution

abstract:
  It is argued that the Einstein equation on a braneworld at low curvature
cannot be derived from its classical brane dynamics (i. e. dynamics of the
brane as a classical object in the higher dimensional spacetime) as far as the
action of the system has smooth low-curvature limit. We discuss possible
solutions to the problem.


title:
Motion of a vector particle in a curved space-time. III. Development of
  techniques of calculation

abstract:
  The studies of influence of spin on a photon's motion in a Schwartzschild
spacetime is continued. In the previous paper [13] the first order correction
to the geodesic motion is found for the first half of the photon world line.
The system of equations for the first order correction to the geodesic motion
is reduced to a non-uniform linear ordinary differential equation. The equation
obtained is solved by the standard method of integration of the Green function.


title:
Examples of Heun and Mathieu functions as solutions of wave equations in
  curved spaces

abstract:
  We give examples where the Heun function exists in general relativity. It
turns out that while a wave equation written in the background of certain
metric yields Mathieu functions as its solutions in four space-time dimensions,
the trivial generalization to five dimensions results in the double confluent
Heun function. We reduce this solution to the Mathieu function with some
transformations.


title: Energy Momentum of Marder Universe in Teleparallel gravity

abstract:
  This paper has been removed by arXiv administrators because of overlap with
gr-qc/0408043 and 0706.3245.
  This paper has excessive overlap with the following papers also written by
the authors or their collaborators: gr-qc/0607110, gr-qc/0607126,
gr-qc/0608024, gr-qc/0603044, gr-qc/0505078, gr-qc/0502042, gr-qc/0502031,
gr-qc/0606028, gr-qc/0508018, gr-qc/0511095, and others.


title:
Energy Momentum Localization for Bianchi I-III-V-VI0 Universe in
  Teleparallel Gravity

abstract:
  This paper has been removed by arXiv administrators because it plagiarizes
gr-qc/0010068.
  This paper has excessive overlap with the following papers also written by
the authors or their collaborators: gr-qc/0607109, gr-qc/0607126,
gr-qc/0607103, gr-qc/0607115, gr-qc/0607119, gr-qc/0608024, gr-qc/0601133,
gr-qc/0603044, gr-qc/0607089, gr-qc/0505078, and others.