Dirac Quasinormal modes of Schwarzschild black hole

TL;DR

This paper investigates the quasinormal modes of Dirac fields around Schwarzschild black holes, revealing evenly spaced frequencies at high quantum numbers and comparing them to other perturbations.

Contribution

It provides a detailed analysis of Dirac quasinormal modes using continued fraction and Hill-determinant methods, highlighting their spacing and dependence on quantum numbers.

Findings

Fundamental frequencies are evenly spaced for large angular quantum number.

Spacing of frequencies is approximately 0.38490-0.00000i.

Imaginary part spacing is about -i/4M, similar to other perturbations.

Abstract

The quasinormal modes (QNMs) associated with the decay of Dirac field perturbation around a Schwarzschild black hole is investigated by using continued fraction and Hill-determinant approaches. It is shown that the fundamental quasinormal frequencies become evenly spaced for large angular quantum number and the spacing is given by $\omega_{\lambda+1}- \omega_{\lambda}=0.38490-0.00000i$. The angular quantum number has the surprising effect of increasing real part of the quasinormal frequencies, but it almost does not affect imaginary part, especially for low overtones. In addition, the quasinormal frequencies also become evenly spaced for large overtone number and the spacing for imaginary part is $Im(\omega_{n+1})-Im(\omega_n)\approx -i/4M$ which is same as that of the scalar, electromagnetic, and gravitational perturbations.