Spectroscopy of the rotating BTZ black hole via adiabatic invariance

TL;DR

This paper extends the adiabatic invariance method to derive an equally spaced, rotation-independent horizon area spectrum for the rotating BTZ black hole, supporting Bekenstein's conjecture without requiring quasinormal modes.

Contribution

It applies the adiabatic invariance approach to the rotating BTZ black hole to derive a quantized, rotation-independent horizon area spectrum, avoiding the need for quasinormal frequencies.

Findings

The horizon area spectrum is equally spaced.

The spectrum is independent of the black hole's rotation parameter.

The method does not require quasinormal mode analysis.

Abstract

According to Bohr-Sommerfeld quantization rule, an equally spaced horizon area spectrum of a static, spherically symmetric black hole was obtained under an adiabatic invariant action. This method can be extended to the rotating black holes. As an example, we apply this method to the rotating BTZ black hole and obtain the quantized spectrum of the horizon area. It is shown that the area spectrum of the rotating BTZ black hole is equally spaced and irrelevant to the rotating parameter, which is consistent with the Bekenstein conjecture. Specifically, the derivation do not need the quasinormal frequencies and the small angular momentum limit.