An analytical computation of asymptotic Schwarzschild quasinormal frequencies

Abstract

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 a sign of an inconsistency of this approach to quantization of general relativity, but is 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 modes 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 3/8πGNM; this constant has been only known numerically so far. We discuss the structure of the quasinormal modes 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. © 2002 International Press.