Area spectra of the rotating BTZ black hole from quasinormal modes

TL;DR

This paper derives an equally spaced, cosmological constant-independent quantized horizon area spectrum for rotating BTZ black holes using quasinormal modes and Bohr-Sommerfeld quantization, extending previous methods to rotating cases.

Contribution

It applies quasinormal mode analysis and Bohr-Sommerfeld quantization to derive the horizon area spectrum of rotating BTZ black holes, including the rotating case.

Findings

Horizon area spectrum is equally spaced.

Spectrum is independent of the cosmological constant.

Method applicable to black holes with discrete quasinormal modes.

Abstract

Following Bekenstein's suggestion that the horizon area of a black hole should be quantized, the discrete spectrum of the horizon area has been investigated in various ways. By considering the quasinormal mode of a black hole, we obtain the transition frequency of the black hole, analogous to the case of a hydrogen atom, in the semiclassical limit. According to Bohr's correspondence principle, this transition frequency at large quantum number is equal to classical oscillation frequency. For the corresponding classical system of periodic motion with this oscillation frequency, an action variable is identified and quantized via Bohr-Sommerfeld quantization, from which the quantized spectrum of the horizon area is obtained. This method can be applied for black holes with discrete quasinormal modes. As an example, we apply the method for the both non-rotating and rotating BTZ black holes and obtain that the spectrum of the horizon area is equally spaced and independent of the cosmological constant for both cases.