We study the phenomena of superradiance for $F(R)$-Maxwell black holes in an AdS space-time. The AdS boundary plays the role of a mirror and provides a natural confining system that makes the superradiant waves bouncing back and forth between the region near the horizon and the reflective boundary, causing a possible superradiant instability. We obtain numerical solutions for static hairy black holes in this scenario and investigate their instability and explicitly address the stability of such solutions for spherical perturbations under specific conditions for the scalar charge and AdS radius. It is shown that for a small scalar charge or AdS radius the static hairy solution is stable under spherical perturbations. We conclude that under such conditions, new hairy black holes emerge as a possible endpoint of superradiant instability of the system.

中文翻译：

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F(R) 带电标量场理论中的超辐射不稳定性和渐近 AdS 毛状黑洞

我们研究了 AdS 时空中 $F(R)$-Maxwell 黑洞的超辐射现象。AdS 边界起到镜子的作用，并提供了一个自然的限制系统，使超辐射波在地平线附近的区域和反射边界之间来回反弹，导致可能的超辐射不稳定。我们在这种情况下获得了静态毛状黑洞的数值解，并研究了它们的不稳定性，并明确地解决了在标量电荷和 AdS 半径的特定条件下球形扰动的此类解的稳定性。结果表明，对于小的标量电荷或 AdS 半径，静态毛状解在球形扰动下是稳定的。我们得出的结论是，在这种情况下，新的毛状黑洞出现可能是系统超辐射不稳定性的终点。