Next-to-leading-order solution to Kerr-Newman black hole superradiance

Abstract

The superradiant instabilities of Kerr-Newman black holes with charged or uncharged massive spin-0 fields are calculated analytically to the next-to-leading order in the limit of $\alpha \sim r_g\mu \ll 1$. A missing factor of $1/2$ in the previous leading-order result is identified. The next-to-leading order result has a compact form and is in good agreement with existing numerical calculations. The percentage error increases with $\alpha$, from a few percent for $\alpha \sim 0.1$ to about $50\%$ for $\alpha \sim 0.4$. Massive neutral scalars too heavy to be produced with Kerr black hole superradiance may exist in the superradiant region of Kerr-Newman black holes.

11 pages, 5 figures, 2 tables. Correction: The third paragraph of Sec. III A contained errors and has been replaced, along with Eq. (27). Matches Physical Review D version

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