论文标题
在罗宾边界中的小带电反DE保姆黑洞的稳定性
Stability of small charged anti-de Sitter black holes in the Robin boundary
论文作者
论文摘要
我们通过分析和数值研究了带电的抗DE保姆（ADS）黑洞中中性和带电标量场的准频率（QNF），并讨论了QNF的黑洞的稳定性。我们专注于标量场的质量平方$μ^2 $的范围，该量子场为$ζ$参数的罗宾边界条件适用于保形无穷大。我们发现，如果半径$ r _ {+} $的黑洞和充电$ q $比广告长度$ \ ell $小得多，则可以根据反射边界条件在反射性边界条件下的超级拉力来理解带电的标量字段的不稳定性。 Noting that the s-wave normal frequency in the AdS spacetime is a decreasing function of $ζ$, we find that if $|eQ|\ell/r_{+}$ is greater than $(3+\sqrt{9+4μ^2\ell^2})/2$, where $e$ is the charge of the scalar field, the black hole is superradiantly unstable irrespectively of $ζ$.另一方面，如果$ | eq | \ ell/r _ {+} $等于或小于此临界值，则稳定性至关重要地取决于$ζ$，并且在不稳定性开始时似乎纯粹是振荡的模式。我们认为，由于超级不稳定性的结果，标量场从黑洞和能量从其环境电场中获得了电荷，而黑洞则为标量场提供了电荷，并从标量场获得了能量，但减少了其渐近质量参数。
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 parametrised 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 $\ell$, 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 $|eQ|\ell/r_{+}$ is greater than $(3+\sqrt{9+4μ^2\ell^2})/2$, where $e$ is the charge of the scalar field, the black hole is superradiantly unstable irrespectively of $ζ$. On the other hand, if $|eQ|\ell/r_{+}$ 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.
