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 $\Psi_2^T$, $\Psi_0^T$ and $\Psi_4^T$ associated with these transverse frames. In both cases it is only necessary to choose a particular root of a cubic expression.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 $Z$, 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 $Z$ remain small.Comment: 4 pages, accepted in PR