arXiv 1306.57602013-06gr-qc

渐近反de Sitter黑洞的拟正规模

On quasinormal modes of asymptotically anti-de Sitter black holes

Claude M. Warnick

备注：: 81 pages, 6 figures. V3: To appear in Comm. Math. Phys
DOI：: 10.1007/s00220-014-2171-1

摘要：

本文研究了定常、渐近反德西特黑洞上强双曲系统的拟正规模问题，在无穷远处具有非常一般的边界条件。我们认为，对于一个在视界上的时间切片正则，QNM应该与解半群的无穷小生成元的某些H^k特征值相一致。使用这个定义，我们能够直接证明，拟正规频率形成一个离散的，可数的复平面的子集，在全球平稳的情况下，积累只有在无穷大。我们避免了任何亚纯扩张的需要，并且拟正规模是Hilbert空间上算子的诚实本征函数。我们的结果适用于任何线性领域通常考虑（克莱因-戈登，麦克斯韦，狄拉克等）。在一个静止的黑洞背景上，并且不依赖于度量的任何可分性或解析性。我们的方法和结果在很大程度上扩展到局部平稳的情况下。我们提供了一个反例的猜想，拟正规模式是完整的。我们将我们的方法直接通过亚纯延拓的方法。

英文摘要：

We consider the problem of quasinormal modes (QNM) for strongly hyperbolic systems on stationary, asymptotically anti-de Sitter black holes, with very general boundary conditions at infinity. We argue that for a time slicing regular at the horizon the QNM should be identified with certain H^k eigenvalues of the infinitesimal generator of the solution semigroup. Using this definition we are able to prove directly that the quasinormal frequencies form a discrete, countable subset of the complex plane, which in the globally stationary case accumulates only at infinity. We avoid any need for meromorphic extension, and the quasinormal modes are honest eigenfunctions of an operator on a Hilbert space. Our results apply to any of the linear fields usually considered (Klein-Gordon, Maxwell, Dirac etc.) on a stationary black hole background, and do not rely on any separability or analyticity properties of the metric. Our methods and results largely extend to the locally stationary case. We provide a counter-example to the conjecture that quasinormal modes are complete. We relate our approach directly to the approach via meromorphic continuation.

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