Quasinormal modes of extremal black holes

TL;DR

This paper extends a modified continued fraction method to compute quasinormal modes of extremal black holes, including charged Reissner-Nordstrom and neutral Kerr black holes, addressing previous methodological limitations.

Contribution

It generalizes Onozawa et al.'s method to new extremal black hole cases, enabling accurate quasinormal mode calculations where traditional methods fail.

Findings

Successfully applied the generalized method to extremal Reissner-Nordstrom black holes.

Compared results with near extremal cases to highlight differences and similarities.

Provided a framework for future studies of extremal black hole perturbations.

Abstract

The continued fraction method (also known as Leaver's method) is one of the most effective techniques used to determine the quasinormal modes of a black hole. For extremal black holes, however, the method does not work (since, in such a case, the event horizon is an irregular singular point of the associated wave equation). Fortunately, there exists a modified version of the method, devised by Onozawa et al. [Phys. Rev. D 53, 7033 (1996)], which works for neutral massless fields around an extremal Reissner-Nordstrom black hole. In this paper, we generalize the ideas of Onozawa et al. to charged massless perturbations around an extremal Reissner-Nordstrom black hole and to neutral massless perturbations around an extremal Kerr black hole. Similarities and differences between the results of the original continued fraction method for near extremal black holes and the results of the new continued fraction method for extremal black holes are discussed.