Kerr-Newman scalar clouds

TL;DR

This paper investigates scalar clouds around Kerr(-Newman) black holes, analyzing their existence conditions, spatial structures, and comparing numerical results with analytical approximations to deepen understanding of these bound states.

Contribution

It provides a comprehensive numerical analysis of scalar clouds, including their existence lines and spatial profiles, and compares these with existing analytical formulas.

Findings

Existence lines for various quantum numbers are mapped.

Numerical results show remarkable agreement with analytical approximations.

Scalar clouds are characterized by specific parameter conditions around Kerr(-Newman) black holes.

Abstract

Massive complex scalar fields can form bound states around Kerr black holes. These bound states -- dubbed scalar clouds -- are generically non-zero and finite on and outside the horizon; they decay exponentially at spatial infinity, have a real frequency and are specified by a set of integer "quantum" numbers (n,l,m). For a specific set of these numbers, the clouds are only possible along a 1-dimensional subset of the 2-dimensional parameter space of Kerr black holes, called an existence line. In this paper we make a thorough investigation of the scalar clouds due to neutral (charged) scalar fields around Kerr(-Newman) black holes. We present the location of the existence lines for a variety of quantum numbers, their spatial representation and compare analytic approximation formulas in the literature with our exact numerical results, exhibiting a sometimes remarkable agreement.