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

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.