Neutrino quasinormal modes of the Reissner-Nordstr\"om black hole

TL;DR

This paper analyzes neutrino quasinormal modes of Reissner-Nordström black holes, revealing how frequencies depend on charge and quantum numbers, with modes forming spiral patterns and oscillatory behaviors.

Contribution

It provides a detailed analysis of neutrino quasinormal modes in charged black holes, highlighting their dependence on charge, angular momentum, and overtone number, including new spiral and oscillation phenomena.

Findings

Quasinormal frequencies become evenly spaced for large angular quantum number.

Frequencies in the complex plane form spiral patterns as charge increases.

Both real and imaginary parts oscillate with charge, with oscillation speed depending on overtone and angular quantum numbers.

Abstract

The neutrino quasinormal modes of the Reissner-Nordstr\"om (RN) black hole are investigated using continued fraction approach. We find, for large angular quantum number, that the quasinormal frequencies become evenly spaced and the spacing of the real part depends on the charge of the black hole and that of the imaginary part is zero. We then find that the quasinormal frequencies in the complex $\omega$ plane move counterclockwise as the charge increases. They get a spiral-like shape, moving out of their Schwarzschild value and ``looping in" towards some limiting frequency as the charge tends to the extremal value. The number of the spirals increases as the overtone number increases but it decreases as the angular quantum number increases. We also find that both the real and imaginary parts are oscillatory functions of the charge, and the oscillation becomes faster as the overtone number increases but it becomes slower as the angular quantum number increases.