Non-Rotating BTZ Black Hole Area Spectrum from Quasi-normal Modes

TL;DR

This paper derives an equally spaced mass spectrum for non-rotating BTZ black holes using quasi-normal modes and Bohr-Sommerfeld quantization, revealing a non-equally spaced horizon area spectrum unlike higher-dimensional black holes.

Contribution

It introduces a novel method combining quasi-normal mode frequencies and adiabatic invariants to determine the black hole's mass and area spectra.

Findings

Mass spectrum is equally spaced.

Horizon area spectrum is not equally spaced.

Method links vibrational frequencies to quantum spectra.

Abstract

In this paper, by using the quasi-normal frequencies for non-rotating BTZ black hole derived by Cardos and Lemos, also via Bohr-Sommerfeld quantization for an adiabatic invariant, $I=\int {dE\over \omega(E)}$, which $E$ is the energy of system and $\omega(E)$ is vibrational frequency, we leads to an equally spaced mass spectrum. The result for the area of event horizon is $A_{n}=2\pi \sqrt{\frac{nm \hbar}{\Lambda}}$ which is not equally spaced, in contrast with area spectrum of black hole in higher dimension.