关于5维Birkhoff定理的有效性：一个例外情况的故事
On the validity of the 5-dimensional Birkhoff theorem: The tale of an exceptional case
摘要：
5维Birkhoff定理给出了包含具有宇宙对称性的空间超曲面的5维真空时空类。这个定理被5d真空Gergely-Maartens（GM）时空所违背，它不是上述类型的代表，但包含静态爱因斯坦膜作为嵌入超曲面。我们证明了5d Birkhoff定理在较弱的意义下仍然成立：GM时空与某些允许类黑洞时空的退化视界度规有关。这一结果类似于广义相对论中极端Reissner-Nordstrom时空的视界区域与Bertotti-Robinson时空之间的联系。
英文摘要：
The 5-dimensional (5d) Birkhoff theorem gives the class of 5d vacuum space-times containing spatial hypersurfaces with cosmological symmetries. This theorem is violated by the 5d vacuum Gergely-Maartens (GM) space-time, which is not a representant of the above class, but contains the static Einstein brane as embedded hypersurface. We prove that the 5d Birkhoff theorem is still satisfied in a weaker sense: the GM space-time is related to the degenerated horizon metric of certain black-hole space-times of the allowed class. This result resembles the connection between the Bertotti-Robinson space-time and the horizon region of the extremal Reissner-Nordstrom space-time in general relativity.
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