Asymptotic Quasinormal Frequencies of Different Spin Fields in Spherically Symmetric Black Holes

TL;DR

This paper investigates the asymptotic quasinormal frequencies of various spin fields in Schwarzschild and Reissner-Nordström black holes, revealing universal patterns and differences based on black hole charge and extremality.

Contribution

It provides a comprehensive analysis of the asymptotic frequencies for different spin fields in spherically symmetric black holes, highlighting universal behaviors and distinctions.

Findings

Real part of frequency is ln3 for spin 0 and 2 in Schwarzschild.

All spin fields have zero real part in extremal Reissner-Nordström black holes.

Imaginary parts show a universal spacing of 1/4M in certain cases.

Abstract

We consider the asymptotic quasinormal frequencies of various spin fields in Schwarzschild and Reissner-Nordstr\"om black holes. In the Schwarzschild case, the real part of the asymptotic frequency is ln3 for the spin 0 and the spin 2 fields, while for the spin 1/2, the spin 1, and the spin 3/2 fields it is zero. For the non-extreme charged black holes, the spin 3/2 Rarita-Schwinger field has the same asymptotic frequency as that of the integral spin fields. However, the asymptotic frequency of the Dirac field is different, and its real part is zero. For the extremal case, which is relevant to the supersymmetric consideration, all the spin fields have the same asymptotic frequency, the real part of which is zero. For the imaginary parts of the asymptotic frequencies, it is interesting to see that it has a universal spacing of $1/4M$ for all the spin fields in the single-horizon cases of the Schwarzschild and the extreme Reissner-Nordstr\"om black holes. The implications of these results to the universality of the asymptotic quasinormal frequencies are discussed.