Extremal Kerr-Newman black holes with extremely short charged scalar hair

TL;DR

This paper demonstrates that non-spherical hairy Kerr-Newman black holes can have external scalar fields that violate the 'no short hair' theorem, challenging previous assumptions about black hole hair extension.

Contribution

It provides analytical evidence that non-spherical charged scalar fields can exist close to rotating black holes, violating the previously established bound for hair extension.

Findings

Non-spherical hairy black holes can have scalar hair extending inside the photon sphere.

Charged scalar fields can form stationary configurations around Kerr-Newman black holes.

The 'no short hair' theorem does not hold for non-spherical configurations.

Abstract

The recently proved `no short hair' theorem asserts that, if a spherically-symmetric static black hole has hair, then this hair (the external fields) must extend beyond the null circular geodesic (the "photonsphere") of the corresponding black-hole spacetime: $r_{\text{field}}>r_{\text{null}}$. In this paper we provide compelling evidence that the bound can be {\it violated} by {\it non}-spherically symmetric hairy black-hole configurations. To that end, we analytically explore the physical properties of cloudy Kerr-Newman black-hole spacetimes -- charged rotating black holes which support linearized stationary charged scalar configurations in their exterior regions.