Quasi-normal modes of the scalar hairy black hole

TL;DR

This paper computes the quasi-normal modes of scalar hairy black holes in AdS space using a numerical method, revealing the behavior of mode frequencies and the absence of infinitely long-lived modes.

Contribution

It introduces a numerical approach to calculate QNMs for potentials without analytical form and analyzes the impact of scalar field mass on mode stability.

Findings

Pure imaginary frequencies observed for some parameters.

Increasing scalar field mass does not produce infinitely long-lived modes.

Mode frequencies exhibit a minimum as scalar mass varies.

Abstract

We calculate QNMs of the scalar hairy black hole in the AdS background using Horowitz-Hubeny method for the potential that is not known in analytical form. For some black hole parameters we found pure imaginary frequencies. Increasing of the scalar field mass does not cause the imaginary part to vanish, it reaches some minimum and then increases, thus in the case under consideration the infinitely long living modes (quasi-resonances) do not appear.