Quasinormal modes of the near extremal Schwarzschild-de Sitter black hole

TL;DR

This work derives exact quasinormal mode frequencies for scalar, electromagnetic, and gravitational perturbations of a near-extremal Schwarzschild–de Sitter black hole. By exploiting the near-extremal geometry, the effective potential reduces to the Pöschl–Teller form, allowing closed-form solutions for the QNM spectrum via hypergeometric methods and yielding ω = κ_b[ -(n+1/2)i + sqrt(V0/κ_b^2 − 1/4) ]. The results provide analytic, highly damped QNM frequencies with a real part independent of the overtone number n, matching Moss–Norman fits and clarifying the exactness of the Pöschl–Teller approximation in this regime. The findings have implications for the Barbero–Immirzi parameter discussion and suggest extensions to higher-dimensional and AdS contexts, where AdS/CFT may further illuminate the role of QNMs in holography.

Abstract

We present an exact expression for the quasinormal modes of scalar, electromagnetic and gravitational perturbations of a near extremal Scwarzschild-de Sitter black hole and we show why a previous approximation holds exactly in this near extremal regime. In particular, our results give the asymptotic behavior of the quasinormal frequencies for highly damped modes, which as recently attracted much attention due to the proposed identification of its real part with the Barbero-Immirzi parameter.