Some exact quasi-normal frequencies of a massless scalar field in the Schwarzschild space-time

TL;DR

This paper identifies previously unrecognized quasinormal modes of a massless scalar field in Schwarzschild spacetime, providing an analytical formula and a generalized convergence criterion to account for these modes.

Contribution

It introduces an analytical formula for missing quasinormal modes and generalizes the Gauss convergence criterion for Schwarzschild spacetime.

Findings

Not all quasinormal modes are captured by the characteristic continued fraction.

New analytical formula for previously missing modes.

Generalized convergence criterion for better mode detection.

Abstract

We show that not all quasinormal modes of a massless scalar field in the Schwarzschild metric are encoded in the corresponding characteristic equation expressed by means of a continued fraction. We provide an analytical formula for these new hitherto missing quasinormal modes, and in doing that we also construct a generalization of the Gauss convergence criterion.