Strong breaking of black-hole uniqueness from coexisting scalarization mechanisms

TL;DR

This paper demonstrates a theory where multiple black-hole solution branches coexist, leading to a strong violation of the traditional Kerr black-hole uniqueness, driven by scalarization mechanisms triggered by a scalar field coupling.

Contribution

The study introduces a theory with coexisting scalarization mechanisms causing multiple black-hole solutions and strong violation of Kerr uniqueness.

Findings

Multiple black-hole solution branches coexist.

Transitions between different black-hole solutions are both continuous and discontinuous.

Scalarization mechanisms are triggered by a scalar field coupling to the Gauss-Bonnet invariant.

Abstract

Black-hole uniqueness, i.e., the statement that all stationary vacuum black holes in the universe are described by the Kerr solution, is expected to break in theories beyond General Relativity. This breaking can take a particularly strong form, if several branches of black-hole solutions beyond the Kerr solution coexist. We find an example of a theory that exhibits such strong breaking. In this theory, a cubic coupling of a scalar field to the Gauss-Bonnet invariant triggers black-hole scalarization through a non-linear instability of the Kerr solution. At large spin, curvature-induced and spin-induced scalarization mechanisms compete at fixed sign of the coupling. This results in a rich phase structure of black-hole solutions and continuous as well as discontinuous transitions between the different branches of black holes.