Selection Rules for Black-Hole Quantum Transitions

TL;DR

This paper proposes that black hole quantum transitions follow specific selection rules similar to atomic spectroscopy, using quasinormal modes to identify forbidden and allowed transitions based on their frequencies.

Contribution

It introduces a novel approach applying Bohr's correspondence principle to black hole quasinormal modes to derive quantum transition rules.

Findings

Frequencies with vanishing real part correspond to forbidden transitions.

Neutrino field spectra show comega_Re approaches zero, indicating forbidden fermionic transitions.

The method links classical black hole oscillations to quantum transition rules.

Abstract

We suggest that quantum transitions of black holes comply with selection rules, analogous to those of atomic spectroscopy. In order to identify such rules, we apply Bohr's correspondence principle to the quasinormal ringing frequencies of black holes. In this context, classical ringing frequencies with an asymptotically vanishing real part \omega_R correspond to virtual quanta, and may thus be interpreted as forbidden quantum transitions. With this motivation, we calculate the quasinormal spectrum of neutrino fields in spherically symmetric black-hole spacetimes. It is shown that \omega_R->0 for these resonances, suggesting that the corresponding fermionic transitions are quantum mechanically forbidden.