A detailed analytic study of the asymptotic quasinormal modes of Schwarzschild–anti de Sitter black holes

Abstract

We analyze analytically the asymptotic regions of the quasinormal mode frequency spectra with infinitely large overtone numbers for D-dimensional Schwarzschild black holes in anti de Sitter spacetimes. In this limit, we confirm the analytic results obtained previously in the literature using different methods. In addition, we show that in certain spacetime dimensions these techniques imply the existence of other regions of the asymptotic quasinormal mode frequency spectrum which have not previously appeared in the literature. For large black holes, some of these modes have a damping rate of 1.2T H , where T H is the Hawking temperature. This is less than the damping rate of the lowest overtone quasinormal mode calculated by other authors. It is not completely clear whether these modes actually exist or are an artifact of an unknown flaw in the analytic techniques being used. We discuss the possibility of the existence of these modes and explore some of the consequences. We also examine the possible connection between the asymptotic quasinormal modes of Schwarzschild-anti de Sitter black holes and the quantum level spacing of their horizon area spectrum.

Quantum tunneling, adiabatic invariance and black hole spectroscopy

“…Introducing a covariant form for the adiabatic invariant, Jiang and Han have combined the oscillating velocity of the black hole horizon to revisit the black hole spectroscopy of the Schwarzschild black hole in the tunneling picture [1]. It has been shown that the area spectrum of the Schwarzschild black hole is described with an equally spacing A = 8π 2 p , which is in agreement with Bekenstein's original proposal [7] and is fully in consistence with the previous findings by combining the black hole property of adiabaticity and the black hole quasinormal frequencies [24][25][26][27][28][29][30][31][32][33][34][35][49][50][51][52].…”

“…Following this new explanation and the black hole property of adiabaticity, it has been shown that the equally spaced area spectrum of a slowly rotating black hole can be expressed as the form A = 8π 2 p [25], which is exactly equal to the original result of Beken-stein [7]. Later, much further work has shown that the black hole spectroscopy in more general gravity frames can also be properly reproduced by combining the new explanation for quasinormal mode frequency and the black hole property of adiabaticity [24][25][26][27][28][29][30][31][32][33][34][35][49][50][51][52].…”

Quasinormal modes of black holes: From astrophysics to string theory

“…Using an analytic technique based on the complex coordinate WKB method, the so-called "highly real" quasinormal modes were reported to appear in the spectrum of Schwarzschild-anti de Sitter black holes. The real part of these quasinormal frequencies asymptotically approached infinity while the damping rate remained finite 169,170 . Since for large black holes the imaginary part of highly real quasinormal modes is less than those which are established as the fundamental modes, the highly real quasinormal modes must be dominant in the spectrum.…”

Area spectra of near extremal black holes

“…Applied this interpretation to the Schwarzschild spacetime, he concludes that the area spectrum of the horizon is equally spaced and is quantized in units ∆A = γl 2 p with γ = 8π, different from that obtained by Hod, Dreyer and Kunstatter. Based on this new interpretation, there are much work appeared [9,10,11,12,13,14,15,16,17,18,19,20,21]. For example, in the research on the area spectrum of slowly rotating Kerr black holes, Vagenas found the area spectrum is not equally spaced [9].…”