Aretakis hair for extreme Kerr black holes with axisymmetric scalar perturbations
Aretakis hair for extreme Kerr black holes with axisymmetric scalar perturbations
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DOI：
10.1103/physrevd.107.124023
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发表时间：
2023-04
影响因子：
5
通讯作者：
L. Burko;G. Khanna;S. Sabharwal
中科院分区：
文献类型：
--
作者：
L. Burko;G. Khanna;S. Sabharwal
我们研究的演化轴对称标量场扰动的极端克尔时空的多极矩$\ell^{\prime}$高于最低辐射模式的初始数据，我们测量模式$\ell$ -和第一次也视界电荷-激发模式耦合相互作用。然后，我们找到了Ori-Sela前因子，一个可以在有限距离处进行评估的特定量，以及沿着极端克尔黑洞事件视界的阿雷塔基斯常数沿着，这些初始数据准备的序列仅与事件视界的距离不同。我们发现，在近场的初始数据有一个线性关系的Aretakis常数和Ori-Sela前因子。对于初始数据比这些更远的线性关系是不普遍的，我们建议，更强的数值模拟将需要恢复线性。线性关系表明，阿雷塔基斯电荷沿着事件视界可以在有限的距离测量，从而扩展这种类型的违反无毛定理从最少的辐射轴对称模式也涉及模式耦合的情况。
We study the evolution of axially-symmetric scalar field perturbations on an extreme Kerr spacetime for initial data with multipole moments $\ell^{\prime}$ higher than the least radiative mode, and we measure modes $\ell$ -- and for the first time also horizon charges -- that are excited by mode coupling interactions. We then find the Ori-Sela prefactors, a certain quantity that can be evaluated at finite distances and the Aretakis constant along the event horizon of the extreme Kerr black hole for a sequence of initial data preparations that differ only by their distance from the event horizon. We find that for initial data in the near field there is a linear relationship of the Aretakis constant and the Ori-Sela prefactor. For initial data farther than these the linear relationship is not universal, and we propose that stronger numerical simulations would be needed to regain linearity. The linear relationship suggests that the Aretakis charge along the event horizon can be measured at a finite distance, thereby extending this type of violation of the no-hair theorems from the least radiative axisymmetric mode also to situations that involve mode coupling.