An Analytical computation of asymptotic Schwarzschild quasinormal frequencies

By L. Motl. 2002

227 citations recorded by the source corpus.

Recently it has been proposed that a strange logarithmic expression for the so-called Barbero-Immirzi parameter, which is one of the ingredients that are necessary for Loop Quantum Gravity (LQG) to predict the correct black hole entropy, is not another sign of the inconsistency of this approach to quantization of General Relativity, but is rather a meaningful number that can be independently justified in classical GR. The alternative justification involves the knowledge of the real part of the frequencies of black hole quasinormal states whose imaginary part blows up. In this paper we present an analytical derivation of the states with frequencies approaching a large imaginary number plus ln 3 / 8 pi M; this constant has been only known numerically so far. We discuss the structure of the quasinormal states for perturbations of various spin. Possible implications of these states for thermal physics of black holes and quantum gravity are mentioned and interpreted in a new way. A general conjecture about the asymptotic states is stated. Although our main result lends some credibility to LQG, we also review some of its claims in a critical fashion and speculate about its possible future relevance for Quantum Gravity.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/978ba52dea0126ceafd068d14c30c69265412bc2

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Citations in the corpus

DE SITTER MUSINGS (2012, result): “This is in contrast to the quasinormal mode spectrum of the Schwarszchild black hole [54, 55, 56] or asymptotically AdS black holes [57, 58] which typically have a real part which is some function of the momenta.”
Gravity and the thermodynamics of horizons (2005, background): “l modes [see e.g.,[132,133,134,135]]. These modes have discrete frequencies which are complex, given by ωn = i n+(1/2) 4M + ln(3) 8πM +O(n−1/2) (116) The ln(3) in the above equation is not negotiable [136,137,138,139]. If one chooses SO(3) as the gauge group, then one can connect up the frequency of”
AdS / CFT correspondence, quasinormal modes, and thermal correlators in N=4 SYM (2003, methodology): “The approach used in [32] does not seem to work for the Heun equation, while the one employed in [33] is promising.”
Gravity and the Thermodynamics of Horizons (2003, background): “The ln(3) in the above equation is not negotiable [136,137,138,139].”
On the classification of asymptotic quasinormal frequencies for $d$-dimensional black holes and quantum gravity (2004, methodology): “Actually, an analytic calculation of the asymptotic quasinormal frequencies was first done in [13], in four dimensions, and then extended to d– dimensions in [14], at least for tensor type perturbations (and already using the monodromy method).”