Generic master equations for quasi-normal frequencies

TL;DR

This paper derives general master equations for highly-damped quasi-normal frequencies in multi-horizon spacetimes using semi-analytic and monodromy methods, revealing how parameter ratios influence the structure of QNFs.

Contribution

It provides a unified derivation of generic master equations for QNFs across different horizon configurations and links the existence of frequency families to parameter ratios.

Findings

Master equations are consistent across different methods.

Existence of QNF families depends on rationality of parameter ratios.

General results relate QNF structures to spacetime parameters.

Abstract

Generic master equations governing the highly-damped quasi-normal frequencies [QNFs] of one-horizon, two-horizon, and even three-horizon spacetimes can be obtained through either semi-analytic or monodromy techniques. While many technical details differ, both between the semi-analytic and monodromy approaches, and quite often among various authors seeking to apply the monodromy technique, there is nevertheless widespread agreement regarding the the general form of the QNF master equations. Within this class of generic master equations we can establish some rather general results, relating the existence of "families" of QNFs of the form omega_{a,n} = (offset)_a + i n (gap) to the question of whether or not certain ratios of parameters are rational or irrational.