Quasinormal modes from potentials surrounding the charged dilaton black hole

TL;DR

This paper investigates the quasinormal modes of massless scalar perturbations around 3D charged-dilaton black holes, revealing how potential shapes influence purely imaginary versus complex frequencies.

Contribution

It clarifies the relationship between potential types and quasinormal mode characteristics in charged-dilaton black holes, highlighting the role of potential-step and barrier configurations.

Findings

Potential-step outside the horizon yields purely imaginary frequencies.

Potential-barrier results in complex quasinormal modes.

Distinct potential shapes determine the nature of quasinormal frequencies.

Abstract

We clarify the purely imaginary quasinormal frequencies of a massless scalar perturbation on the 3D charged-dilaton black holes. This case is quite interesting because the potential-step appears outside the event horizon similar to the case of the electromagnetic perturbations on the large Schwarzschild-AdS black holes. It turns out that the potential-step type provides the purely imaginary quasinormal frequencies, while the potential-barrier type gives the complex quasinormal modes.