Final state of instabilities in Born-Infeld black holes

Abstract

We study two types of linear instabilities in Einstein-Born-Infeld-scalar field theory and show that small Born-Infeld (BI) black holes suffer from superradiant instability within a particular range of frequencies; the larger the BI coupling parameter, the slower the growth rate of the instability. It is predicted that a small BI black hole decays into a small hairy black hole that has a charged scalar condensate floating near the horizon. We numerically show that there is a phase transition between hairy and BI black holes. The metric solution shows the existence of a hairy black hole for T < Tc and a BI black hole for T > Tc. In addition, the BI black hole will suffer from tachyonic mass, resulting in a near horizon scalar condensation instability, which is related to a planar hairy black hole. We show that the BI coupling parameter has a direct relation to the critical temperature in the small hairy black hole framework. This is not true for planar hairy black holes where a larger BI coupling parameter leads to a smaller critical temperature. Finally, it is shown that a small hairy black hole is stable at the critical temperature so it can be considered as the end point of superradiant instability.

Spherical black holes with minimally coupled scalar cloud/hair in Einstein-Born-Infeld gravity

“…We should emphasis that the cloud/hair considered here is secondary which is very different from the scalar condensation in holographic superconductor model in asymptotically AdS space. For the later case, the scalar hair results from near-horizon tachyonic instability and is primary [41,[46][47][48].…”

“…[26,27]. It should be noted that this is just the threshold condition for the occurrence of superradiance of Born-Infeld BH under charged scalar perturbations [41]. So up to first order expansions in (12), there are left only four free parameters, {σ h , V h , V 1 , ψ h }, characterizing the near-horizon behaviors of the solution.…”