Dynamical formation of a hairy black hole in a cavity from the decay of unstable solitons

TL;DR

This paper demonstrates through numerical relativity that unstable solitons in the Einstein-Maxwell-charged-Klein-Gordon system can evolve into hairy black holes or bald Reissner-Nordström black holes, revealing two formation channels for scalar hair.

Contribution

It provides the first numerical evidence that unstable charged scalar solitons can evolve into hairy black holes, expanding understanding of superradiant instability endpoints.

Findings

Unstable solitons can evolve into hairy black holes.

Unstable solitons can also evolve into bald Reissner-Nordström black holes.

Two distinct pathways to form hairy black holes are identified.

Abstract

Recent numerical relativity simulations within the Einstein--Maxwell--(charged-)Klein-Gordon (EMcKG) system have shown that the non-linear evolution of a superradiantly unstable Reissner-Nordstr\"om black hole (BH) enclosed in a cavity, leads to the formation of a BH with scalar hair. Perturbative evidence for the stability of such hairy BHs has been independently established, confirming they are the true endpoints of the superradiant instability. The same EMcKG system admits also charged scalar soliton-type solutions, which can be either stable or unstable. Using numerical relativity techniques, we provide evidence that the time evolution of some of these $\textit{unstable}$ solitons leads, again, to the formation of a hairy BH. In some other cases, unstable solitons evolve into a (bald) Reissner-Nordstr\"om BH. These results establish that the system admits two distinct channels to form hairy BHs at the threshold of superradiance: growing hair from an unstable (bald) BH, or growing a horizon from an unstable (horizonless) soliton. Some parallelism with the case of asymptotically flat boson stars and Kerr BHs with scalar hair is drawn.