Spinning Kerr black holes with stationary massive scalar clouds: The large-coupling regime

TL;DR

This paper analytically derives the spectrum of stationary massive scalar fields around spinning Kerr black holes in the large-coupling regime, confirming results with numerical data and providing insights into black hole scalar field configurations.

Contribution

The paper introduces a compact analytical formula for the scalar field mass spectrum around Kerr black holes in the large-coupling regime, validated by numerical data.

Findings

Derived a formula for the scalar field mass spectrum in the large-coupling regime

Confirmed analytical results with existing numerical data

Enhanced understanding of stationary scalar clouds around Kerr black holes

Abstract

We study analytically the Klein-Gordon wave equation for stationary massive scalar fields linearly coupled to spinning Kerr black holes. In particular, using the WKB approximation, we derive a compact formula for the discrete spectrum of scalar field masses which characterize the stationary composed Kerr-black-hole-massive-scalar-field configurations in the large-coupling regime $M\mu\gg1$ (here $M$ and $\mu$ are respectively the mass of the central black hole and the proper mass of the scalar field). We confirm our analytically derived formula for the Kerr-scalar-field mass spectrum with numerical data that recently appeared in the literature.