Approach to the extremal limit of the Schwarzschild-de Sitter black hole

TL;DR

This paper investigates the quasinormal modes of Schwarzschild-de Sitter black holes near the extremal limit, revealing improved agreement with the P"oschl-Teller approximation and establishing a perturbation framework for higher-order analysis.

Contribution

It demonstrates that quasinormal mode frequencies match the P"oschl-Teller approximation more closely than previously known and introduces a perturbation approach for higher-order studies.

Findings

Mode frequencies agree with P"oschl-Teller approximation to higher order.

The spectrum's approach to the limit depends on the units chosen.

A perturbation framework is established for future higher-order analysis.

Abstract

The quasinormal-mode spectrum of the Schwarzschild-de Sitter black hole is studied in the limit of near-equal black-hole and cosmological radii. It is found that the mode_frequencies_ agree with the P"oschl-Teller approximation to one more order than previously realized, even though the effective_potential_ does not. Whether the spectrum approaches the limiting one uniformly in the mode index is seen to depend on the chosen units (to the order investigated). A perturbation framework is set up, in which these issues can be studied to higher order in future.