75 research outputs found
Entropy of generic quantum isolated horizons
We review our recent proposal of a method to extend the quantization of
spherically symmetric isolated horizons, a seminal result of loop quantum
gravity, to a phase space containing horizons of arbitrary geometry. Although
the details of the quantization remain formally unchanged, the physical
interpretation of the results can be quite different. We highlight several such
differences, with particular emphasis on the physical interpretation of black
hole entropy in loop quantum gravity.Comment: 4 pages, contribution to loops '11 conference proceedings; 2
references added, a sentence remove
Eigenspectral computtations for linear gravity and nonlinear toy models
Journal ArticleThe periodic standing-wave approach to binary inspiral assumes rigid rotation of gravitational fields and hence helically symmetric solutions. To exploit the symmetry, numerical computations must solve for "helical scalars," fields that are functions only of corotating coordinates, the labels on the helical Killing trajectories. Here we present the formalism for describing linearized general relativity in terms of helical scalars and we present solutions to the mixed partial differential equations of the linearized gravity problem (and to a toy nonlinear problem) using the adapted coordinates and numerical techniques previously developed for scalar periodic standing-wave computations. We argue that the formalism developed may suffice for periodic standing-wave computations for post-Minkowskian computations and for full general relativity
Towards wave extraction in numerical relativity: the quasi-Kinnersley frame
The Newman-Penrose formalism may be used in numerical relativity to extract
coordinate-invariant information about gravitational radiation emitted in
strong-field dynamical scenarios. The main challenge in doing so is to identify
a null tetrad appropriately adapted to the simulated geometry such that
Newman-Penrose quantities computed relative to it have an invariant physical
meaning. In black hole perturbation theory, the Teukolsky formalism uses such
adapted tetrads, those which differ only perturbatively from the background
Kinnersley tetrad. At late times, numerical simulations of astrophysical
processes producing isolated black holes ought to admit descriptions in the
Teukolsky formalism. However, adapted tetrads in this context must be
identified using only the numerically computed metric, since no background Kerr
geometry is known a priori. To do this, this paper introduces the notion of a
quasi-Kinnersley frame. This frame, when space-time is perturbatively close to
Kerr, approximates the background Kinnersley frame. However, it remains
calculable much more generally, in space-times non-perturbatively different
from Kerr. We give an explicit solution for the tetrad transformation which is
required in order to find this frame in a general space-time.Comment: 13 pages, 3 figure
Periodic standing-wave approzimation: post-Minkowski computations
Journal ArticleThe periodic standing-wave method studies circular orbits of compact objects coupled to helically symmetric standing-wave gravitational fields. From this solution an approximation is extracted for the strong field, slowly inspiralling motion of black holes and binary stars. Previous work on this model has dealt with nonlinear scalar models, and with linearized general relativity. Here we present the results of the method for the post-Minkowski (PM) approximation to general relativity, the first step beyond linearized gravity. We compute the PM approximation in two ways: first, via the standard approach of computing linearized gravitational fields and constructing from them quadratic driving sources for second-order fields, and second, by solving the second-order equations as an "exact" nonlinear system. The results of these computations have two distinct applications: (i) The computational infrastructure for the exact PM solution will be directly applicable to full general relativity. (ii) The results will allow us to begin supplying initial data to collaborators running general relativistic evolution codes
The periodic standing-wave approximation: eigenspectral computations for linear gravity and nonlinear toy models
The periodic standing wave approach to binary inspiral assumes rigid rotation
of gravitational fields and hence helically symmetric solutions. To exploit the
symmetry, numerical computations must solve for ``helical scalars,'' fields
that are functions only of corotating coordinates, the labels on the helical
Killing trajectories. Here we present the formalism for describing linearized
general relativity in terms of helical scalars and we present solutions to the
mixed partial differential equations of the linearized gravity problem (and to
a toy nonlinear problem) using the adapted coordinates and numerical techniques
previously developed for scalar periodic standing wave computations. We argue
that the formalism developed may suffice for periodic standing wave
computations for post-Minkowskian computations and for full general relativity.Comment: 21 pages, 10 figures, RevTe
The periodic standing-wave approximation: post-Minkowski computation
The periodic standing wave method studies circular orbits of compact objects
coupled to helically symmetric standing wave gravitational fields. From this
solution an approximation is extracted for the strong field, slowly
inspiralling motion of black holes and binary stars. Previous work on this
model has dealt with nonlinear scalar models, and with linearized general
relativity. Here we present the results of the method for the post-Minkowski
(PM) approximation to general relativity, the first step beyond linearized
gravity. We compute the PM approximation in two ways: first, via the standard
approach of computing linearized gravitational fields and constructing from
them quadratic driving sources for second-order fields, and second, by solving
the second-order equations as an ``exact'' nonlinear system. The results of
these computations have two distinct applications: (i) The computational
infrastructure for the ``exact'' PM solution will be directly applicable to
full general relativity. (ii) The results will allow us to begin supplying
initial data to collaborators running general relativistic evolution codes.Comment: 19 pages, 3 figures, 1 table, RevTe
Evolution Operators for Linearly Polarized Two-Killing Cosmological Models
We give a general procedure to obtain non perturbative evolution operators in
closed form for quantized linearly polarized two Killing vector reductions of
general relativity with a cosmological interpretation. We study the
representation of these operators in Fock spaces and discuss in detail the
conditions leading to unitary evolutions.Comment: Accepted for publication in Physical Review
The Speciality Index as invariant indicator in the BKL Mixmaster Dynamics
The speciality index, which has been mainly used in Numerical Relativity for
studying gravitational waves phenomena as an indicator of the special or
non-special Petrov type character of a spacetime, is applied here in the
context of Mixmaster cosmology, using the Belinski-Khalatnikov-Lifshitz map.
Possible applications for the associated chaotic dynamics are discussed
On the Weyl transverse frames in type I spacetimes
We apply a covariant and generic procedure to obtain explicit expressions of
the transverse frames that a type I spacetime admits in terms of an arbitrary
initial frame. We also present a simple and general algorithm to obtain the
Weyl scalars , and associated with these
transverse frames. In both cases it is only necessary to choose a particular
root of a cubic expression.Comment: 12 pages, submitted to Gen. Rel. Grav. (6-3-2004
Large quantum gravity effects and nonlocal variables
We reconsider here the model where large quantum gravity effects were first
found, but now in its Null Surface Formulation (NSF). We find that although the
set of coherent states for , the basic variable of NSF, is as restricted as
it is the one for the metric, while some type of small deviations from these
states may cause huge fluctuations on the metric, the corresponding
fluctuations on remain small.Comment: 4 pages, accepted in PR
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