A note on quasinormal modes: A tale of two treatments

TL;DR

This paper investigates conflicting predictions about quasinormal mode frequencies of Schwarzschild-de Sitter black holes, resolving discrepancies between two analytical methods by critically examining their limiting procedures.

Contribution

It offers a critical reassessment of the monodromy analysis's limiting procedure, clarifying the dependence of quasinormal mode frequencies on angular momentum.

Findings

Revealed the importance of the limiting procedure in monodromy calculations.

Resolved the discrepancy between P"oschl-Teller and monodromy predictions.

Provided insights into the behavior of quasinormal modes in degenerate-horizon limits.

Abstract

There is an apparent discrepancy in the literature with regard to the quasinormal mode frequencies of Schwarzschild-de Sitter black holes in the degenerate-horizon limit. On the one hand, a Poschl-Teller-inspired method predicts that the real part of the frequencies will depend strongly on the orbital angular momentum of the perturbation field whereas, on the other hand, the degenerate limit of a monodromy-based calculation suggests there should be no such dependence (at least, for the highly damped modes). In the current paper, we provide a possible resolution by critically re-assessing the limiting procedure used in the monodromy analysis.