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 T c and a BI black hole for T > T c . 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.

中文翻译：

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Born-Infeld 黑洞不稳定性的最终状态

摘要 我们研究了爱因斯坦-Born-Infeld 标量场理论中的两种线性不稳定性，并表明小Born-Infeld (BI) 黑洞在特定频率范围内具有超辐射不稳定性；BI耦合参数越大，不稳定的增长速度越慢。据预测，一个小的 BI 黑洞会衰变成一个小的毛茸茸的黑洞，它有一个带电的标量凝聚体漂浮在地平线附近。我们在数值上表明毛状黑洞和 BI 黑洞之间存在相变。度量解显示存在毛状黑洞对于 TT c 和 BI 黑洞对于 T > T c 。此外，BI 黑洞会受到快子质量的影响，导致近视界标量凝聚不稳定性，这与平面毛状黑洞有关。我们表明，BI 耦合参数与小毛状黑洞框架中的临界温度有直接关系。对于平面毛状黑洞而言，情况并非如此，其中较大的 BI 耦合参数会导致较小的临界温度。最后，表明一个小的毛状黑洞在临界温度下是稳定的，因此可以认为它是超辐射不稳定性的终点。