AI 中文总结
本文研究极端克尔-纽曼黑洞，发现其视界附近共转度规扰动会被放大，采用近共转模式计算标度指数，揭示其与Aretakis效应的关联，为黑洞扰动研究提供新见解。
AI 中文摘要
通常情况下，坠入黑洞的观测者在穿越视界时不会感受到任何特殊现象。本文中我们发现一个有趣的例外：在极端克尔-纽曼（KN）时空的大部分参数范围内，与视界共转的扰动会在视界附近被放大，使得坠入黑洞的观测者在进入黑洞时经历异常巨大的潮汐形变。这类扰动产生的条件是黑洞外部存在一个持续的源，该源要么本身与视界共转，要么在关联频率ω=mΩ_H（其中m为方位角量子数，Ω_H为视界频率）处具有离散傅里叶支撑。在精确共转时，这种放大在形式上是无穷大的，我们采用近共转模式来保证微扰论的可控性。其 underlying 物理机制是极端极限下离散自相似性的出现，具有形式为-1/2±iα的复标度权重（α为实数）。这类似于黑洞迈斯纳效应，区别在于近视界场是被放大而非被屏蔽的。我们数值计算了极端KN黑洞耦合引力电磁（GEM）扰动的标度指数，表明这类复指数出现在Q<Q_*的参数范围内，其中Q_*≈0.93M。这些指数还能预测KN时空（无论是否在视界上）中一般GEM扰动的衰减和增长速率（Aretakis效应）。共转扰动的放大可被视为受驱动的Aretakis不稳定性。
英文摘要
Under normal circumstances, an observer falling into a black hole feels nothing special upon crossing the horizon. In this paper we find an intriguing exception: For most of the parameter range of the extremal Kerr-Newman (KN) spacetime, horizon co-rotating perturbations are enhanced near the horizon, such that an infalling observer experiences an anomalously large tidal deformation as they enter the black hole. Such perturbations arise when there is a persistent source outside the black hole that is either co-rotating itself or has discrete Fourier support at the associated frequencies $ω=mΩ_H$ (where $m$ is the azimuthal number and $Ω_H$ is the horizon frequency). The enhancement is formally infinite at precise co-rotation, and we work with a nearly co-rotating mode to keep perturbation theory under control. The underlying physics is the emergence of discrete self-similarity in the extremal limit, with complex scaling weights of the form $-1/2\pm iα$ for real $α$. It is analogous to the black hole Meissner effect, except that the near-horizon field is enhanced rather than screened. We numerically calculate the scaling exponents for coupled gravitoelectromagnetic (GEM) perturbations of extremal KN black holes and show that the complex exponents arise in the parameter range $Q < Q_*$ with $Q_*\approx.93M$. These exponents also predict the decay and growth rates (Aretakis effect) of generic GEM perturbations of the KN spacetime, both on and off the horizon. The enhancement of co-rotating perturbations can be viewed as a driven Aretakis instability.
Comments24 pages, 6 figures, 2 tables
