Near Extremal Schwarzschild-de Sitter Black Hole Area Spectrum from Quasi-normal Modes

TL;DR

This paper derives the quantized area and entropy spectra of near extremal Schwarzschild-de Sitter black holes using quasi-normal mode frequencies and Bohr-Sommerfeld quantization, extending previous methods to asymptotically de Sitter spacetimes.

Contribution

It introduces a novel application of quasi-normal modes and Bohr-Sommerfeld quantization to determine the discrete spectra of near extremal Schwarzschild-de Sitter black holes, extending prior approaches to de Sitter backgrounds.

Findings

Derives equally spaced mass spectrum for near extremal Schwarzschild-de Sitter black holes.

Extends Kunstatter's method to asymptotically de Sitter black holes.

Provides a quantization framework for black hole horizon area and entropy.

Abstract

Using the quasi-normal modes frequency of near extremal Schwarzschild-de Sitter black holes, we obtain area and entropy spectrum for black hole horizon. By using Boher-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. In the other term we extend directly the Kunstatter's approach [7] to determine mass and entropy spectrum of near extremal Schwarzschild-de Sitter black holes which is asymptotically de Sitter rather than asymptotically flat.