Improved Analytic Solution of Black Hole Superradiance

The approximate solution of the Klein-Gordon equation for a real scalar field of mass \(\mu\) 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,...

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Bibliographic Details
Published in:arXiv.org 2022-08
Main Authors: Shou-Shan Bao, Qi-Xuan, Xu, Zhang, Hong
Format: Article
Language:English
Subjects:
Exact solutions
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Summary:The approximate solution of the Klein-Gordon equation for a real scalar field of mass \(\mu\) 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 \(r_g \mu\). Especially the percentage error is \(\lesssim 10\%\) in the region of \(r_g\mu \lesssim 0.35\). The NLO solution also has a compact form and could be used straightforwardly.
ISSN:2331-8422
DOI:10.48550/arxiv.2201.10941