High overtones of Dirac perturbations of a Schwarzschild black hole

TL;DR

This paper computes high overtone quasinormal modes of a Schwarzschild black hole for Dirac fields, revealing equidistant imaginary parts and a vanishing real part at high overtones, challenging their link to Loop Quantum Gravity.

Contribution

It provides the first detailed analysis of high overtone Dirac quasinormal modes, showing unique spectral properties distinct from integer-spin fields.

Findings

Imaginary parts are evenly spaced at high overtones.

Real parts tend to zero as overtone number increases.

Spacing is half of that for integer-spin fields.

Abstract

Using the Frobenius method, we find high overtones of the Dirac quasinormal spectrum for the Schwarzschild black hole. At high overtones, the spacing for imaginary part of $\omega_{n}$ is equidistant and equals to $\Im{\omega_{n+1}}-\Im{\omega_{n}} =i/8M$, ($M$ is the black hole mass), which is twice less than that for fields of integer spin. At high overtones, the real part of $\omega_{n}$ goes to zero. This supports the suggestion that the expected correspondence between quasinormal modes and Barbero-Immirzi parameter in Loop Quantum Gravity is just a numerical coincidence.