STAG Research Centre and Mathematical Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom.
DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
Phys Rev Lett. 2015 Apr 17;114(15):151101. doi: 10.1103/PhysRevLett.114.151101. Epub 2015 Apr 13.
We provide strong evidence that, up to 99.999% of extremality, Kerr-Newman black holes (KNBHs) are linear mode stable within Einstein-Maxwell theory. We derive and solve, numerically, a coupled system of two partial differential equations for two gauge invariant fields that describe the most general linear perturbations of a KNBH. We determine the quasinormal mode (QNM) spectrum of the KNBH as a function of its three parameters and find no unstable modes. In addition, we find that the lowest radial overtone QNMs that are connected continuously to the gravitational ℓ=m=2 Schwarzschild QNM dominate the spectrum for all values of the parameter space (m is the azimuthal number of the wave function and ℓ measures the number of nodes along the polar direction). Furthermore, the (lowest radial overtone) QNMs with ℓ=m approach Reω=mΩH(ext) and Imω=0 at extremality; this is a universal property for any field of arbitrary spin |s|≤2 propagating on a KNBH background (ω is the wave frequency and ΩH(ext) the black hole angular velocity at extremality). We compare our results with available perturbative results in the small charge or small rotation regimes and find good agreement.
我们提供了强有力的证据表明，在爱因斯坦-麦克斯韦理论中， Kerr-Newman 黑洞（KNBH）在高达 99.999%的极端情况下是线性模式稳定的。我们推导出并数值求解了一个描述 KNBH 最一般线性扰动的两个规范不变场的两个偏微分方程的耦合系统。我们确定了 KNBH 的准正则模式（QNM）谱作为其三个参数的函数，并发现没有不稳定模式。此外，我们发现，与引力 ℓ=m=2 Schwarzschild QNM 连续连接的最低径向泛频 QNMs 主导了所有参数空间值的谱（m 是波函数的角数，ℓ 沿极向测量节点数）。此外，在极端情况下，具有 ℓ=m 的（最低径向泛频）QNMs 具有 Reω=mΩH(ext) 和 Imω=0；这是在 KNBH 背景上传播的任意自旋|s|≤2 的任何场的普遍性质（ω 是波频率，ΩH(ext) 是极端情况下的黑洞角速度）。我们将我们的结果与小电荷或小转动情况下的可用微扰结果进行了比较，并发现了很好的一致性。
