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

TL;DR

This paper proves the existence and stability of zero-damped quasinormal modes near extremal horizons in certain black hole spacetimes, revealing their universal presence and robustness under perturbations.

Contribution

It establishes the presence of zero-damped modes for the conformal Klein-Gordon equation on Reissner-Nordström-de Sitter backgrounds and demonstrates their stability under potential perturbations.

Findings

Zero-damped modes exist for conformal Klein-Gordon on Reissner-Nordström-de Sitter backgrounds.

Zero-damped modes are stable under potential perturbations.

The phenomenon is shown to be present in a broad class of spherically symmetric black holes.

Abstract

It 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 $i\alpha$ in the extremal limit and cluster in a neighbourhood of the line $\Im s=\alpha$. In this paper, we establish that this property is present for the conformal Klein-Gordon equation on a Reissner-Nordstr\"om-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.