High frequency quasi-normal modes for black holes with generic singularities II: Asymptotically non-flat spacetimes

TL;DR

This paper extends the analysis of high frequency quasi-normal modes to asymptotically non-flat black hole spacetimes, revealing that Hod's conjecture may not hold universally across different asymptotic geometries.

Contribution

The authors derive master equations for asymptotic QNM frequencies in non-flat spacetimes, unifying flat and de Sitter cases and separately analyzing anti-de Sitter cases.

Findings

Real part of QNM frequencies is generally not proportional to ln(3).

Hod's conjecture may be restrictive and not universally applicable.

Unified treatment of flat and de Sitter spacetimes with separate analysis for anti-de Sitter.

Abstract

The possibility that the asymptotic quasi-normal mode (QNM) frequencies can be used to obtain the Bekenstein-Hawking entropy for the Schwarzschild black hole -- commonly referred to as Hod's conjecture -- has received considerable attention. To test this conjecture, using monodromy technique, attempts have been made to analytically compute the asymptotic frequencies for a large class of black hole spacetimes. In an earlier work, two of the current authors computed the high frequency QNMs for scalar perturbations of $(D+2)$ dimensional spherically symmetric, asymptotically flat, single horizon spacetimes with generic power-law singularities. In this work, we extend these results to asymptotically non-flat spacetimes. Unlike the earlier analyses, we treat asymptotically flat and de Sitter spacetimes in a unified manner, while the asymptotic anti-de Sitter spacetimes is considered separately. We obtain master equations for the asymptotic QNM frequency for all the three cases. We show that for all the three cases, the real part of the asymptotic QNM frequency -- in general -- is not proportional to ln(3) thus indicating that the Hod's conjecture may be restrictive.