Fermionic Quasinormal Spectrum of the Kerr Black Hole

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 $Ω$, which is valid in the asymptotic limit $1 \ll ω_I \ll ω_R$. 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 $ΔA=4\hbar \ln 2$, while the emission of a Weyl neutrino field ($s=1/2$) corresponds to an adiabatic quantum transition with $ΔA=0$.