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Title: Classical and quantum Lemaitre-Tolman-Bondi model for the nonmarginal case

Abstract

We extend the classical and quantum treatment of the Lemaitre-Tolman-Bondi (LTB) model to the nonmarginal case (defined by the fact that the shells of the dust cloud start with a nonvanishing velocity at infinity). We present the classical canonical formalism and address with particular care the boundary terms in the action. We give the general relation between dust time and Killing time. Employing a lattice regularization, we then derive and discuss for particular factor orderings exact solutions to all quantum constraints.

Authors:
; ;  [1];  [2];  [3]
  1. Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Strasse 77, 50937 Cologne (Germany) and Max-Planck-Institut fuer Gravitationsphysik, Am Muehlenberg 1, 14476 Golm (Germany)
  2. (Germany)
  3. (United States)
Publication Date:
OSTI Identifier:
20776763
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.73.044025; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COSMIC DUST; COSMOLOGY; EXACT SOLUTIONS; MATHEMATICAL MODELS; QUANTUM GRAVITY; VELOCITY

Citation Formats

Kiefer, Claus, Mueller-Hill, Jakob, Vaz, Cenalo, Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Strasse 77, 50937 Cologne, and Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221-0011. Classical and quantum Lemaitre-Tolman-Bondi model for the nonmarginal case. United States: N. p., 2006. Web. doi:10.1103/PhysRevD.73.044025.
Kiefer, Claus, Mueller-Hill, Jakob, Vaz, Cenalo, Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Strasse 77, 50937 Cologne, & Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221-0011. Classical and quantum Lemaitre-Tolman-Bondi model for the nonmarginal case. United States. doi:10.1103/PhysRevD.73.044025.
Kiefer, Claus, Mueller-Hill, Jakob, Vaz, Cenalo, Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Strasse 77, 50937 Cologne, and Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221-0011. Wed . "Classical and quantum Lemaitre-Tolman-Bondi model for the nonmarginal case". United States. doi:10.1103/PhysRevD.73.044025.
@article{osti_20776763,
title = {Classical and quantum Lemaitre-Tolman-Bondi model for the nonmarginal case},
author = {Kiefer, Claus and Mueller-Hill, Jakob and Vaz, Cenalo and Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Strasse 77, 50937 Cologne and Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221-0011},
abstractNote = {We extend the classical and quantum treatment of the Lemaitre-Tolman-Bondi (LTB) model to the nonmarginal case (defined by the fact that the shells of the dust cloud start with a nonvanishing velocity at infinity). We present the classical canonical formalism and address with particular care the boundary terms in the action. We give the general relation between dust time and Killing time. Employing a lattice regularization, we then derive and discuss for particular factor orderings exact solutions to all quantum constraints.},
doi = {10.1103/PhysRevD.73.044025},
journal = {Physical Review. D, Particles Fields},
number = 4,
volume = 73,
place = {United States},
year = {Wed Feb 15 00:00:00 EST 2006},
month = {Wed Feb 15 00:00:00 EST 2006}
}
  • In an earlier paper, we obtained exact solutions of the Wheeler-DeWitt equation for the Lemaitre-Tolman-Bondi model of gravitational collapse, employing a lattice regularization. In this paper, we derive Hawking radiation in nonmarginally bound models from our exact solutions. We show that a nonvanishing energy function does not spoil the (approximate) Planck spectrum near the horizon. We can also reliably compute corrections to the Bogoliubov coefficient because our solutions are exact. The corrections are obtained by going beyond the near-horizon region and are shown to introduce additional greybody factors, which modify the blackbody spectrum of radiation from the black hole.
  • We solve the quantum constraint equations of the Lemaitre-Tolman-Bondi model in a semiclassical approximation in which an expansion is performed with respect to the Planck length. We recover in this way the standard expression for the Hawking temperature as well as its first quantum gravitational correction. We then interpret this correction in terms of the one-loop trace anomaly of the energy-momentum tensor and thereby make contact with earlier work on quantum black holes.
  • We consider extensions of Lemaitre-Tolman-Bondi (LTB) spacetimes to the dissipative case. We have previously carried out a systematic study on LTB. This study is based on two different aspects of LTB. On the one hand, a symmetry property of LTB will be presented. On the other hand, the description of LTB in terms of some fundamental scalar functions (structure scalars) appearing in the orthogonal splitting of Riemann tensor will be provided. We shall consider as natural generalizations of LTB (hereafter referred to as GLTB) either those metrics admitting some similar kind of symmetry as LTB, or those sharing structure scalarsmore » with similar dependence on the metric.« less
  • Lemaitre-Tolman-Bondi models as specific spherically symmetric solutions of general relativity simplify in their reduced form some of the mathematical ingredients of black hole or cosmological applications. The conditions imposed in addition to spherical symmetry turn out to take a simple form at the kinematical level of loop quantum gravity, which allows a discussion of their implications at the quantum level. Moreover, the spherically symmetric setting of inhomogeneity illustrates several nontrivial properties of lattice refinements of discrete quantum gravity. Nevertheless, the situation at the dynamical level is quite nontrivial and thus provides insights to the anomaly problem. At an effective level,more » consistent versions of the dynamics are presented which implement the conditions together with the dynamical constraints of gravity in an anomaly-free manner. These are then used for analytical as well as numerical investigations of the fate of classical singularities, including nonspacelike ones, as they generically develop in these models. None of the corrections used here resolve those singularities by regular effective geometries. However, there are numerical indications that the collapse ends in a tamer shell-crossing singularity prior to the formation of central singularities for mass functions giving a regular conserved mass density. Moreover, we find quantum gravitational obstructions to the existence of exactly homogeneous solutions within this class of models. This indicates that homogeneous models must be seen in a wider context of inhomogeneous solutions and their reduction in order to provide reliable dynamical conclusions.« less
  • Marginal Lemaitre-Tolman-Bondi (LTB) models with corrections from loop quantum gravity have recently been studied with an emphasis on potential singularity resolution. This paper corroborates and extends the analysis in two regards: (i) the whole class of LTB models, including nonmarginal ones, is considered, and (ii) an alternative procedure to derive anomaly-free models is presented which first implements anomaly freedom in spherical symmetry and then the LTB conditions rather than the other way around. While the two methods give slightly different equations of motion, not altogether surprisingly given the ubiquitous sprawl of quantization ambiguities, final conclusions remain unchanged: compared to quantizationsmore » of homogeneous models, bounces seem to appear less easily in inhomogeneous situations, and even the existence of homogeneous solutions as special cases in inhomogeneous models may be precluded by quantum effects. However, compared to marginal models, bouncing solutions seem more likely with nonmarginal models.« less