Analytical treatment of SUSY Quasi-normal modes in a non-rotating Schwarzschild black hole

TL;DR

This paper derives analytical solutions for the quasi-normal modes of a massless fermion around a Schwarzschild black hole using SUSY quantum mechanics, revealing purely imaginary frequencies linked to Hawking temperature.

Contribution

It provides the first analytical approximation of SUSY quasi-normal modes in a Schwarzschild black hole context, connecting them to Hawking temperature.

Findings

All excited states have purely imaginary frequencies.

The bottom state has a zero real energy eigenvalue.

Frequencies are expressed in terms of Hawking temperature.

Abstract

We use the Fock-Ivanenko formalism to obtain the Dirac equation which describes the interaction of a massless 1/2-spin neutral fermion with a gravitational field around a Schwarzschild black hole (BH). We obtain approximated analytical solutions for the eigenvalues of the energy (quasi-normal frequencies) and their corresponding eigenstates (quasi-normal states). The interesting result is that all the excited states [and their supersymmetric (SUSY) partners] have a purely imaginary frequency, which can be expressed in terms of the Hawking temperature. Furthermore, as one expects for SUSY Hamiltonians, the isolated bottom state has a real null energy eigenvalue.