Dirac Quasi-Normal Modes in Schwarzschild Black Hole Spacetimes

TL;DR

This paper calculates the quasi-normal mode frequencies of Dirac fields, both massless and massive, around Schwarzschild black holes, revealing how these frequencies depend on parameters like angular momentum and mass.

Contribution

It provides the first detailed analysis of Dirac quasi-normal modes in Schwarzschild spacetime using the WKB approximation, highlighting how mass and angular momentum influence decay rates and oscillation frequencies.

Findings

Real parts of frequencies increase with angular momentum $$.

Imaginary parts increase with mode number $n$ for fixed $$.

Massive fields oscillate faster and decay more slowly as mass increases.

Abstract

We evaluate both the massless and the massive Dirac quasi-normal mode frequencies in the Schwarzschild black hole spacetime using the WKB approximation. For the massless case, we find that, similar to those for the integral spin fields, the real parts of the frequencies increase with the angular momentum number $\kappa$, while the imaginary parts or the dampings increase with the mode number $n$ for fixed $\kappa$. For the massive case, the oscillation frequencies increase with the mass $m$ of the field, while the dampings decrease. Fields with higher masses will therefore decay more slowly.