We analytically and numerically study quasinormal frequencies (QNFs) of neutral and charged scalar fields in the charged anti-de Sitter (AdS) black holes and discuss the stability of the black holes in terms of the QNFs. We focus on the range of the mass squared μ ² of the scalar fields for which the Robin boundary condition parametrized by ζ applies at the conformal infinity. We find that if the black hole of radius r ₊ and charge Q is much smaller than the AdS length ℓ, the instability of the charged scalar field can be understood in terms of superradiance in the reflective boundary condition. Noting that the s-wave normal frequency in the AdS spacetime is a decreasing function of ζ, we find that if |eQ|ℓ/r ₊ is greater than , where e is the charge of the scalar field, the black hole is superradiantly unstable irrespectively of ζ. On the other hand, if |eQ|ℓ/r ₊ is equal to or smaller than this critical value, the stability crucially depends on ζ and there appears a purely oscillating mode at the onset of the instability. We argue that as a result of the superradiant instability, the scalar field gains charge from the black hole and energy from its ambient electric field, while the black hole gives charge to the scalar field and gains energy from the scalar field but decreases its asymptotic mass parameter.

我们分析和数值研究了带电反德西特 (AdS) 黑洞中中性和带电标量场的准正规频率 (QNF)，并根据 QNF 讨论了黑洞的稳定性。我们关注标量场的质量平方μ ²的范围，由ζ参数化的 Robin 边界条件适用于共形无穷大。我们发现，如果半径为r ₊且电荷为Q 的黑洞远小于 AdS 长度ℓ，则带电标量场的不稳定性可以用反射边界条件中的超辐射来理解。注意到 AdS 时空中的 s 波法向频率是ζ，我们发现如果 | 情商| ℓ / r ₊大于，其中e是标量场的电荷，黑洞是超辐射不稳定的，与ζ无关。另一方面，如果 | 情商| ℓ / r ₊等于或小于该临界值，稳定性关键取决于ζ并且在不稳定开始时出现纯振荡模式。我们认为，由于超辐射不稳定性，标量场从黑洞获得电荷并从其周围电场获得能量，而黑洞给标量场充电并从标量场获得能量，但其渐近质量减少范围。