Existence of Zero-Damped Quasinormal Frequencies for Nearly Extremal Black Holes

Abstract

AbstractIt has been observed that many spacetimes which feature a near-extremal horizon exhibit the phenomenon of zero-damped modes. This is characterised by the existence of a sequence of quasinormal frequencies which all converge to some purely imaginary number $$i\alpha $$ i α in the extremal limit and cluster in a neighbourhood of the line $${{\,\mathrm{Im}\,}}s=\alpha $$ Im s = α . In this paper, we establish that this property is present for the conformal Klein–Gordon equation on a Reissner–Nordström–de Sitter background. This follows from a similar result that we prove for a class of spherically symmetric black hole spacetimes with a cosmological horizon. We also show that the phenomenon of zero-damped modes is stable to perturbations that arise through adding a potential.