Quasinormal modes of the BTZ black hole under scalar perturbations with a non-minimal coupling: Exact spectrum

TL;DR

This paper derives exact quasinormal mode spectra for a non-rotating BTZ black hole perturbed by a non-minimally coupled scalar field, highlighting the effects of coupling and cosmological constant.

Contribution

It provides an analytical solution for the quasinormal frequencies of the BTZ black hole with non-minimal scalar coupling, validated against semi-analytical methods.

Findings

Exact quasinormal frequencies obtained using hypergeometric functions.

Excellent agreement with 6th order WKB semi-analytical results.

Nonminimal coupling and cosmological constant influence the spectrum.

Abstract

We perturb the non-rotating BTZ black hole with a non-minimally coupled massless scalar field, and we compute the quasinormal spectrum exactly. We solve the radial equation in terms of hypergeometric functions, and we obtain an analytical expression for the quasinormal frequencies. In addition, we compare our analytical results with the 6th order semi-analytical WKB method, and we find an excellent agreement. The impact of the nonminimal coupling as well as of the cosmological constant on the quasinormal spectrum is briefly discussed.