On an Expansion Method for Black Hole Quasinormal Modes and Regge Poles

TL;DR

This paper introduces a novel expansion method for calculating black hole quasinormal modes and Regge poles, relating wavefunctions to null geodesics and enabling high-order expansions validated across various spacetimes.

Contribution

The paper presents a new ansatz-based expansion technique for black hole QNMs and Regge poles, applicable to arbitrary static spherically-symmetric spacetimes, with validation and practical insights.

Findings

The method relates QNM frequencies to geodesic properties.

High-order expansions improve accuracy of QNM calculations.

Validation against existing methods confirms effectiveness.

Abstract

We present a new method for determining the frequencies and wavefunctions of black hole quasinormal modes (QNMs) and Regge poles. The key idea is a novel ansatz for the wavefunction, which relates the high-$l$ wavefunctions to null geodesics which start at infinity and end in perpetual orbit on the photon sphere. Our ansatz leads naturally to the expansion of QNMs in inverse powers of angular momentum $L = l + 1/2$ (in 4D), and to the expansion of Regge poles in inverse powers of frequency. The expansions can be taken to high orders. We begin by applying the method to the Schwarzschild spacetime, and validate our results against existing numerical and WKB methods. Next, we generalise the method to treat static spherically-symmetric spacetimes of arbitrary spatial dimension. We confirm that, at lowest order, the real and imaginary components of the QNM frequency are related to the orbital frequency and the Lyapunov exponent for geodesics at the unstable orbit. We apply the method to five spacetimes of current interest, and conclude with a discussion of the advantages and limitations of the new approach, and its practical applications.