Gravitoelectromagnetic coupled perturbations and quasinormal modes of a charged black hole with scalar hair

TL;DR

This paper investigates the quasinormal modes of a novel four-dimensional charged black hole with scalar hair, revealing subtle differences from traditional black holes and uncovering new phenomena at higher angular numbers.

Contribution

It introduces a study of coupled gravitoelectromagnetic perturbations and computes QNM frequencies for a recently constructed scalar-hairy black hole.

Findings

Magnetic charge influences QNM frequencies.

Small differences in fundamental QNMs compared to Reissner-Nordström black holes.

New phenomena observed at higher angular numbers.

Abstract

From the quantum point of view, singularity should not exist. Recently, Bah and Heidmann constructed a five-dimensional singularity free topology star/black hole [Phys. Rev. Lett. 126, 151101 (2021)]. By integrating the extra dimension, a four-dimensional static spherical black hole with a magnetic charge and scalar hair can be obtained. In this paper, we study the quasinormal modes (QNMs) of the magnetic field and gravitational field on the background of this four-dimensional charged black hole with scalar hair. The odd parity of the gravitational perturbations couples with the even parity of the magnetic field perturbations. Two coupled second-order derivative equations are obtained. Using the matrix-valued direct integration method, we obtain the fundamental QNM frequencies numerically. The effect of the magnetic charge on the QNMs is studied. The differences of the frequencies of the fundamental QNMs between the charged black hole with scalar hair and the Reissner-Norstr\"{o}m black hole are very small for the angular number $l=2$. However, some new interesting results are found for higher angular number.