Fermionic Quasinormal Spectrum of the Kerr Black Hole

TL;DR

This paper analytically derives the asymptotic fermionic quasinormal mode spectrum of Kerr black holes, linking it to black hole parameters and quantum transitions, revealing distinct area change signatures for different fermionic fields.

Contribution

It provides an analytic expression for fermionic quasinormal modes of Kerr black holes in the asymptotic limit, connecting them to quantum area changes and black hole parameters.

Findings

Rarita-Schwinger quantum emission relates to a fundamental area change of 4ħ ln 2.

Weyl neutrino emission corresponds to zero area change.

Analytic spectrum expression valid in the asymptotic regime.

Abstract

We study {\it analytically} the asymptotic quasinormal spectrum of fermionic fields in the Kerr spacetime. We find an analytic expression for these black-hole resonances in terms of the black-hole physical parameters: its Bekenstein-Hawking temperature $T_{BH}$, and its horizon's angular velocity $\Omega$, which is valid in the asymptotic limit $1 \ll \omega_I \ll \omega_R$. It is shown that according to Bohr's correspondence principle, the emission of a Rarita-Schwinger quantum ($s=3/2$) corresponds to a fundamental black-hole area change $\Delta A=4\hbar \ln 2$, while the emission of a Weyl neutrino field ($s=1/2$) corresponds to an adiabatic quantum transition with $\Delta A=0$.