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arXiv · 2201.10941

Improved Analytic Solution of Black Hole Superradiance

Shou-Shan Bao·Qi-Xuan Xu·Hong Zhang
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Abstract

The approximate solution of the Klein-Gordon equation for a real scalar field of mass $μ$ in the geometry of a Kerr black hole obtained by Detweiler \cite{Detweiler:1980uk} is widely used in the analysis of the stability of black holes as well as the search of axion-like particles. In this work, we confirm a missing factor $1/2$ in this solution, which was first identified in Ref.~\cite{Pani:2012bp}. The corrected result has strange features that put questions on the power-counting strategy. We solve this problem by adding the next-to-leading order (NLO) contribution. Compared to the numerical results, the NLO solution reduces the percentage error of the LO solution by a factor of 2 for all important values of $r_g μ$. Especially the percentage error is $\lesssim 10\%$ in the region of $r_gμ\lesssim 0.35$. The NLO solution also has a compact form and could be used straightforwardly.

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Shou-Shan Bao, Qi-Xuan Xu, Hong Zhang. 2022-08-23. Improved Analytic Solution of Black Hole Superradiance. https://doi.org/10.1103/physrevd.106.064016

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