Improved Analytic Solution of Black Hole Superradiance

Abstract

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.

5 pages, 3 figures, Accepted by PRD

References in corpus (14)

• Discovering the QCD Axion with Black Holes and Gravitational Waves
• Instability of the massive Klein-Gordon field on the Kerr spacetime
• Gravitational wave searches for ultralight bosons with LIGO and LISA
• Stochastic and resolvable gravitational waves from ultralight bosons
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• Superradiance evolution of black hole shadows revisited
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• Searching for ultralight bosons with supermassive black hole ringdown
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• Gravitational waves from superradiant instabilities of rotating black holes

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• Subdominant Modes of Scalar Superradiant Instability and Gravitational Wave Beats
• Constrains of the axion-like particle from black hole spin superradiance
• Superradiant instabilities of massive bosons around exotic compact objects
• Next-to-leading-order solution to Kerr-Newman black hole superradiance
• Evolution and detection of vector superradiant instabilities
• Superradiant instability of area quantized Kerr black hole with discrete reflectivity
• ALP production from light primordial black holes: The role of superradiance
• Superradiant dark matter production from primordial black holes: Impact of multiple modes and gravitational wave emission
• Boson Cloud Atlas: Direct mass measurements of superradiance clouds near black holes
• The Stochastic Gravitational Wave Background from Primordial Gravitational Atoms
• Local Group Velocity Distribution inside Superradiant Condensates
• Superradiance and Quasinormal Modes of Massive Scalar Fields around Kerr Black Holes in Einstein-Maxwell-Dilaton-Axion Theory with Perfect Fluid Dark Matter
• Effect of accretion on scalar superradiant instability