Electromagnetic radiation generated by a charged particle falling radially into a Schwarzschild black hole: A complex angular momentum description
Antoine Folacci, Mohamed Ould El Hadj
备注：
arXiv admin note: substantial text overlap with arXiv:1807.09056, v2 : A few typos corrected and minor changes in the text to match the published version
By using complex angular momentum techniques, we study the electromagnetic radiation generated by a charged particle falling radially from infinity into a Schwarzschild black hole. We consider both the case of a particle initially at rest and that of a particle projected with a relativistic velocity and we construct complex angular momentum representations and Regge pole approximations of the partial wave expansions defining the Maxwell scalar $ϕ_2$ and the energy spectrum $dE/dω$ observed at spatial infinity. We show, in particular, that Regge pole approximations involving only one Regge pole provide effective resummations of these partial wave expansions permitting us (i) to reproduce with very good agreement the black hole ringdown without requiring a starting time, (ii) to describe with rather good agreement the tail of the signal and sometimes the pre-ringdown phase, and (iii) to explain the oscillations in the electromagnetic energy spectrum radiated by the charged particle. The present work as well as a previous one concerning the gravitational radiation generated by a massive particle falling into a Schwarzschild black hole [A. Folacci and M. Ould El Hadj, Phys. Rev. D$\textbf{98}$, 064052 (2018), arXiv:1807.09056 [gr-qc]] highlight the benefits of studying radiation from black holes in the complex angular momentum framework (they obviously appear when the approximations obtained involve a small number of Regge poles and have a clear physical interpretation) but also to exhibit the limits of this approach (this is the case when it is necessary to take into account background integral contributions).
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Stochastic motion of massless particles near event horizons in Schwarzschild and Reissner-Nordström spacetimes
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）；School of Mathematics, Guangxi University（广西大学数学学院）；Guangxi Center for Mathematical Research, Guangxi University（广西大学广西数学研究中心）；Ningde No.5 Middle School of Fujian（福建省宁德第五中学）
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Istituto per le Applicazioni del Calcolo “M. Picone,” CNR（意大利国家研究委员会计算应用研究所）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院基础物理与数学科学学院，中国科学院大学）
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