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

TL;DR

This paper analytically refines the calculation of superradiant instabilities in Kerr-Newman black holes, correcting previous errors and extending accuracy to next-to-leading order, with results aligning well with numerical data.

Contribution

It provides the first next-to-leading order analytical solution for Kerr-Newman black hole superradiance, correcting a key factor in prior models and improving accuracy.

Findings

Corrects a missing factor in previous leading-order results.

Achieves good agreement with numerical calculations.

Shows the error increases with the parameter $\alpha$.

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.