Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds

TL;DR

This paper proves a universal lower bound on the proper lengths of stationary charged scalar clouds around Kerr-Newman black holes, showing these configurations cannot be arbitrarily short and are supported across a wide parameter space.

Contribution

It establishes a no-short hair theorem for charged scalar clouds around Kerr-Newman black holes, providing a universal lower bound on their proper lengths.

Findings

Proper lengths are bounded from below by 34343434

The bound 34343434 is valid for all Kerr-Newman spacetimes and scalar field parameters

The lower bound is a universal relation valid across the entire parameter regime

Abstract

It has recently been revealed that charged scalar clouds, spatially regular matter configurations which are made of linearized charged massive scalar fields, can be supported by spinning and charged Kerr-Newman black holes. Using analytical techniques, we establish a no-short hair theorem for these stationary bound-state field configurations. In particular, we prove that the effective proper lengths of the supported charged massive scalar clouds are bounded from below by the remarkably compact dimensionless relation $\ell/M>\ln(3+\sqrt{8})$, where $M$ is the mass of the central supporting black hole. Intriguingly, this lower bound is universal in the sense that it is valid for all Kerr-Newman black-hole spacetimes [that is, in the entire regime $\{a/M\in(0,1],Q/M\in[0,1)\}$ of the dimensionless spin and charge parameters that characterize the central supporting black holes] and for all values of the physical parameters (electric charge $q$, proper mass $\mu$, and angular harmonic indexes $\{l,m\}$) that characterize the supported stationary bound-state scalar fields.