A note on the quantization of a multi-horizon black hole

TL;DR

This paper explores the quantization of a multi-horizon Reissner-Nordstrom black hole by analyzing its quasinormal modes, linking specific resonances to fundamental area changes consistent with Bekenstein's scheme.

Contribution

It identifies two families of asymptotic resonances in the black hole spectrum and associates them with fundamental area quantizations, extending previous theoretical proposals.

Findings

Resonance linked to outer horizon area change of 4hbar ln2

Resonance associated with total area change of 4hbar ln3

Supports quantization schemes consistent with Bekenstein and Makela-Repo

Abstract

We consider the quasinormal spectrum of a charged scalar field in the (charged) Reissner-Nordstrom spacetime, which has two horizons. The spectrum is characterized by two distinct families of asymptotic resonances. We suggest and demonstrate the according to Bohr's correspondence principle and in agreement with the Bekenstein-Mukhanov quantization scheme, one of these resonances corresponds to a fundamental change of Delta A=4hbar ln2 in the surface area of the black-hole outer horizon. The second asymptotic resonance is associated with a fundamental change of Delta Atot=4hbar ln3 in the total area of the black hole (in the sum of the surface areas of the inner and outer horizons), in accordance with a suggestion of Makela and Repo.