Noncommutative scalar quasinormal modes and quantization of entropy of a BTZ black hole

TL;DR

This paper derives exact quasinormal modes for a noncommutative scalar field around a BTZ black hole, revealing a duality with a commutative system and showing nonuniform, non-equispaced entropy and area spectra due to noncommutativity.

Contribution

It provides the first analytic expressions for noncommutative scalar quasinormal modes and explores their implications for black hole entropy and area quantization.

Findings

Quasinormal mode frequencies are obtained analytically.

Noncommutativity causes nonuniform spacing in entropy and area spectra.

A duality between noncommutative and commutative systems is suggested.

Abstract

We obtain an exact analytic expression for the quasinormal modes of a noncommutative massless scalar field in the background of a massive spinless BTZ black hole up to the first order in the deformation parameter. We also show that the equations of motion governing these quasinormal modes are identical in form to the equations of motion of a commutative massive scalar field in the background of a fictitious massive spinning BTZ black hole. This results hints at a duality between the commutative and noncommutative systems in the background of a BTZ black hole. Using the obtained results for quasinormal mode frequencies, the area and entropy spectra for the BTZ black hole in the presence of noncommutativity are calculated. In particular, the separations between the neighboring values of these spectra are determined and it is found that they are nonuniform. Therefore, it appears that the noncommutativity leads to a non-equispaced (discrete) area and entropy spectra.