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arXiv 1209.3308gr-qcmath.AP
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渐近反de Sitter黑洞上质量波动方程的有界性和增长性

Boundedness and growth for the massive wave equation on asymptotically anti-de Sitter black holes

Gustav H. Holzegel, Claude M. Warnick

摘要:

本文研究了在一般的、全局平稳的、渐近AdS黑洞背景上的自由质量标量场的全局动力学,并在无穷远处对$ψ$施加Dirichlet-、Neumann-或Robin-边界条件.这类黑洞包括满足Hawking Reall界$r_+^2 > |a|l$的规则Kerr-AdS黑洞。我们建立了一个合适的标准线性稳定性(在一致有界的意义上)的$ψ$和演示如何稳定的问题可以依赖于边界条件规定。特别是,在缓慢旋转的克尔AdS的情况下,我们得到的线性标量头发(即非平凡的固定解决方案)适当选择罗宾边界条件的存在性。

英文摘要:

We study the global dynamics of free massive scalar fields on general, globally stationary, asymptotically AdS black hole backgrounds with Dirichlet-, Neumann- or Robin- boundary conditions imposed on $ψ$ at infinity. This class includes the regular Kerr-AdS black holes satisfying the Hawking Reall bound $r_+^2 > |a|l$. We establish a suitable criterion for linear stability (in the sense of uniform boundedness) of $ψ$ and demonstrate how the issue of stability can depend on the boundary condition prescribed. In particular, in the slowly rotating Kerr-AdS case, we obtain the existence of linear scalar hair (i.e. non-trivial stationary solutions) for suitably chosen Robin boundary conditions.

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