Improved Analytic Solution of Black Hole Superradiance
arXiv:2201.10941 · doi:10.1103/PhysRevD.106.064016
Abstract
The approximate solution of the Klein-Gordon equation for a real scalar field of mass 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 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 . Especially the percentage error is in the region of . The NLO solution also has a compact form and could be used straightforwardly.
arXiv comment5 pages, 3 figures, Accepted by PRD
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