A Detailed Analytic Study of the Asymptotic Quasinormal Modes of Schwarzschild-Anti De Sitter Black Holes

TL;DR

This paper analytically investigates the asymptotic quasinormal modes of Schwarzschild-AdS black holes across various dimensions, confirming previous results and discovering potential new modes with implications for black hole quantum properties.

Contribution

It provides a detailed analytical study of the asymptotic quasinormal modes, confirming prior findings and proposing the existence of new modes in certain spacetime dimensions.

Findings

Confirmed asymptotic quasinormal mode spectra for large overtone numbers.

Discovered potential new regions of the spectrum with modes having damping rates of 1.2T_H.

Discussed implications for black hole quantum area spectrum.

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.