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arXiv 1712.03398gr-qchep-th
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Robin边界条件下Kerr-mirror和Kerr-AdS黑洞的超辐射不稳定性

Superradiant instabilities in the Kerr-mirror and Kerr-AdS black holes with Robin boundary conditions

Hugo R. C. Ferreira, Carlos A. R. Herdeiro

摘要:

最近的研究发现,具有Robin边界条件的标量场可以同时触发BTZ黑洞的超辐射不稳定性和体不稳定性。为了理解这种行为的普遍性和仔细研究这种行为的起源,我们考虑在这里的克尔BH的超辐射不稳定性限制在镜状腔或在AdS空间,也触发了一个标量场与红细胞。这些边界条件是确保空腔/AdS空间是一个孤立系的最一般的边界条件,并且作为一种特殊情况,包括通常考虑的Dirichlet边界条件(DBC)。尽管某些红细胞的超辐射模式与DBCs的超辐射模式只有轻微的不同,但在这两种情况下,我们发现,当我们改变红细胞时,频率的虚部可以达到任意大的正值。我们将这种增长解释为当某些RBC被施加到镜状腔或AdS边界时,由两种受限几何形状的体积不稳定性引起的,而不是由BH的能量提取引起的,与BTZ行为类似。

英文摘要:

It has been recently observed that a scalar field with Robin boundary conditions (RBCs) can trigger both a superradiant and a bulk instability for a BTZ black hole (BH). To understand the generality and scrutinize the origin of this behavior, we consider here the superradiant instability of a Kerr BH confined either in a mirror-like cavity or in AdS space, triggered also by a scalar field with RBCs. These boundary conditions are the most general ones that ensure the cavity/AdS space is an isolated system, and include, as a particular case, the commonly considered Dirichlet boundary conditions (DBCs). Whereas the superradiant modes for some RBCs differ only mildly from the ones with DBCs, in both cases we find that as we vary the RBCs, the imaginary part of the frequency may attain arbitrarily large positive values. We interpret this growth as being sourced by a bulk instability of both confined geometries when certain RBCs are imposed to either the mirror-like cavity or the AdS boundary, rather than by energy extraction from the BH, in analogy with the BTZ behavior.

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