Extreme Dilaton Black Holes in 2 +1 Dimensions: Quasinormal modes

TL;DR

This paper analytically computes the quasinormal modes of an extreme dilaton black hole in 2+1 dimensions, revealing purely imaginary frequencies and the stability characteristics of the modes, independent of black hole parameters.

Contribution

It provides exact solutions for quasinormal modes in a 2+1D dilaton black hole background and compares analytical results with numerical methods.

Findings

Quasinormal modes are purely imaginary.

Fundamental mode is always unstable.

Modes do not depend on black hole parameters.

Abstract

We study neutral massless scalar field perturbations around an extreme dilaton black hole in 2 +1 dimensions: the wave equations of the massless scalar field is shown to be exactly solvable in terms of Whittaker functions. Thus, the quasinormal modes are computed exactly and shown to be purely imaginary: we show the existence of stable and unstable modes. Interestingly, the quasinormal modes do not depend on the black holes parameters and the fundamental mode is always unstable and depends only on the parameters of the test field. Also, we determine the quasinormal frequencies via the improved asymptotic iteration method which shows a good agreement with the analytical results.