Final state of instabilities in Born-Infeld black holes
arXiv:2001.05177 · doi:10.1016/j.physletb.2020.135842
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 and a BI black hole for . 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.
arXiv comment15 pages, 8 figures, to appear in PLB
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