Quasinormal modes of a charged scalar field in Ernst black holes

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. We mainly 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 behavior is inverted, i.e., the longest-lived modes are always the ones with the lowest angular number recovering the standard behavior. Also, we find a critical value of the external magnetic field, as well as a critical value of the scalar field charge that exhibits the same behavior 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 satisfies m = ±$\ell$ in the eikonal limit.