Area spectra versus entropy spectra in black holes in topologically massive gravity

TL;DR

This paper investigates the quantization of area and entropy spectra in black holes within topologically massive gravity, revealing that entropy spectra are universally equally spaced and independent of the Chern-Simons coupling, unlike area spectra.

Contribution

It demonstrates that entropy spectra in various black hole solutions of topologically massive gravity are universally equally spaced and unaffected by the Chern-Simons term, highlighting entropy's fundamental nature.

Findings

Entropy spectra are equally spaced and coupling-independent.

Area spectra depend on the coupling constant and are not equally spaced.

Entropy's universal behavior suggests it is more fundamental than horizon area.

Abstract

We consider the area and entropy spectra of black holes in topologically massive gravity with gravitational Chern-Simons term. The examples we consider are the BTZ black hole and the warped AdS black hole. For the non-rotating BTZ black hole, the area and entropy spectra are equally spaced and independent of the coupling constant $\v$ of the Chern-Simons term. For the rotating BTZ black hole case, the spectra of the inner and outer horizon areas are not equally spaced in general and dependent of the coupling constant $\v$. However the entropy spectrum is equally spaced and independent of the coupling constant $\v$. For the warped AdS black holes for $\v >1$ by using the quasinormal modes obtained without imposing the boundary condition at radial infinity we find again that the entropy spectrum is equally spaced and independent of the coupling constant $\v$, while the spectra of the inner and outer horizon areas are not equally spaced and dependent of the coupling constant $\v$. Our result implies that the entropy spectrum has a universal behavior regardless of the presence of the gravitational Chern-Simons term, and therefore it implies that the entropy is more `fundamental' than the horizon area.