Influence of Lorentz violation on Dirac quasinormal modes in the Schwarzschild black hole spacetime

TL;DR

This study explores how Lorentz violation, introduced via a specific coefficient, affects Dirac quasinormal modes in Schwarzschild black holes, revealing that Lorentz violation alters damping rates and the asymptotic behavior of frequencies.

Contribution

It provides the first detailed analysis of Lorentz violation effects on Dirac quasinormal modes using third-order WKB and monodromy methods.

Findings

Real part decreases linearly with Lorentz violation parameter at fundamental overtone.

Imaginary part's variation with Lorentz violation becomes more complex for larger modes.

High overtones show non-zero real parts, differing from Lorentz-invariant cases.

Abstract

Using the third-order WKB approximation and monodromy methods, we investigate the influence of Lorentz violating coefficient $b$ (associated with a special axial-vector $b_{\mu}$ field) on Dirac quasinormal modes in the Schwarzschild black hole spacetime. At fundamental overtone, the real part decreases linearly as the parameter $b$ increases. But the variation of the imaginary part with $b$ becomes more complex. For the larger multiple moment $k$, the magnitude of imaginary part increases with the increase of $b$, which means that presence of Lorentz violation makes Dirac field damps more rapidly. At high overtones, it is found that the real part of high-damped quasinormal frequency does not tend to zero, which is quite a different from the symptotic Dirac quasinormal modes without Lorentz violation.