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Reissner-Nordström 黑洞对电磁波与引力波的散射和转换：Regge 极点描述

Scattering and conversion of electromagnetic and gravitational waves by Reissner-Nordström black holes: The Regge pole description

Mohamed Ould El Hadj

备注：
v2: minor changes and a few typos corrected in the text to match the published version
发表信息：
Phys. Rev. D 107, 104051 (2023)
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AI总结：

本文用 Regge 极点（复角动量）方法研究 Reissner-Nordström 黑洞对电磁波和引力波的散射与转换，通过数值计算极点谱、推导渐近表达式和解析近似截面，半经典地统一解释了黑洞辉光与轨道振荡现象。

摘要：

我们利用 Regge 极点描述，即复角动量方法，研究了单色平面引力波和电磁波入射到 Reissner-Nordström 黑洞时的散射与转换问题。为此，我们首先数值计算了不同荷质比构型下的 Regge 极点谱。随后，我们推导了最低 Regge 极点的渐近表达式，并通过考虑 Bohr-Sommerfeld 型量子化条件，从 Regge 轨迹得到了弱阻尼准正规频率谱。接着，我们利用复角动量表示和分波展开方法，构造了不同过程的散射振幅、转换振幅以及总微分截面。最后，我们基于最低 Regge 极点的渐近表达式及其相应留数，并依据 Regge 极点与在光子（引力子）球附近传播的“表面波”之间的对应关系，给出了不同过程散射截面和转换截面的解析近似。这使我们能够提取高频区域（即短波长区域）分波展开中所编码的物理解释，并以非常好的符合度半经典地描述黑洞辉光和大部分轨道振荡，从而从纯波动的观点统一了这两种现象。

英文摘要：

We investigate the problem of scattering and conversion of monochromatic planar gravitational and electromagnetic waves impinging upon a Reissner-Nordström black hole using a Regge pole description, i.e., a complex angular momentum approach. For this purpose, we first compute numerically the Regge pole spectrum for various charge-to-mass ratio configurations. We then derive an asymptotic expressions for the lowest Regge poles, and by considering Bohr-Sommerfeld-type quantization conditions, obtain the spectrum of weakly damped quasinormal frequencies from the Regge trajectories. Next, we construct the scattering and conversion amplitudes as well as the total differential cross sections for different processes using both a complex angular momentum representation and a partial wave expansion method. Finally, we provide an analytical approximation of the scattering and conversion cross sections of different processes from asymptotic expressions for the lowest Regge poles and the associated residues based on the correspondence Regge poles, "surface waves" propagating close to the photon (graviton) sphere. This allows us to extract the physical interpretation encoded in the partial wave expansions in the high-frequency regime (i.e., in the short-wavelength regime), and to describe semiclassically with very good agreement both black hole glory and a large part of the orbiting oscillations, thus unifying these two phenomena from a purely wave point of view.

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