标题： 带电标量场扰动在恩斯特黑洞中 显示英文标题

标题： Charged scalar field perturbations in Ernst black holes

摘要： 我们考虑带电大质量标量场在四维厄恩斯特黑洞背景中的传播，并通过准正则模（QNMs）分析其稳定性，这些QNMs使用半解析的Wentzel-Kramers-Brillouin方法计算，并数值上使用连续分数方法计算。 主要地，我们发现当标量场质量小于临界质量时，QNMs的衰减率随着角谐波数$\ell$的增加而减小；而对于标量场质量大于临界质量的情况，行为相反，即最长寿的模总是具有最低的角数，恢复了标准行为。 此外，我们发现外部磁场的一个临界值以及标量场电荷的一个临界值，它们相对于角谐波数表现出相同的行为。 另外，我们表明时空允许稳定的准束缚态，并观察到由于塞曼效应导致的谱线分裂。 最后，我们表明当方位量子数满足$m= \pm \ell$时，赤道平面中的不稳定零测地线与QNMs相关，在几何光学极限下。 显示英文摘要

摘要： 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.