Charged scalar field perturbations in Ernst black holes

TL;DR

This paper investigates the stability and quasinormal modes of charged massive scalar fields in Ernst black hole backgrounds, revealing critical magnetic and scalar charge values affecting decay rates and spectrum splitting.

Contribution

It provides a semi-analytical and numerical analysis of scalar field perturbations in Ernst black holes, identifying critical parameters and their effects on stability and spectrum.

Findings

Decay rate behavior depends on scalar mass relative to a critical value.

Identification of critical magnetic and scalar charge values affecting mode stability.

Observation of spectrum splitting due to the Zeeman effect.

Abstract

We consider the propagation of a charged massive scalar field in the background of a four-dimensional Ernst black hole and study its stability analyzing the quasinormal modes (QNMs), which are calculated using the semi-analytical Wentzel-Kramers-Brillouin method and numerically using the continued fraction method. Mainly, we find that for a scalar field mass less than a critical mass, the decay rate of the QNMs decreases when the harmonic angular number $\ell$ increases; and for a scalar field mass greater than the critical mass the behaviour is inverted, i.e, the longest-lived modes are always the ones with the lowest angular number recovering the standard behaviour. Also, we find a critical value of the external magnetic field, as well as, a critical value of the scalar field charge that exhibit the same behaviour with respect to the angular harmonic numbers. In addition, we show that the spacetime allows stable quasibound states and we observe a splitting of the spectrum due to the Zeeman effect. Finally, we show that the unstable null geodesic in the equatorial plane is connected with the QNMs when the azimuthal quantum number satisfy $m= \pm \ell$ in the eikonal limit.