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arXiv 0908.0661gr-qchep-th
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（n+1）维Einstein-Yang-Mills引力的拓扑黑洞

Topological Black Holes of (n+1)-dimensional Einstein-Yang-Mills Gravity

N. Bostani, M. H. Dehghani

备注：
14 pages, 2 figures, accepted by Mod. Phys. Lett. A
发表信息：
Mod.Phys.Lett.A25:1507-1519,2010
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摘要：

本文给出了非阿贝尔杨-米尔斯场存在时爱因斯坦引力的拓扑解。在（$n+1$）维中，我们把$So(n(n-1)/2-1,1)$半单群看作Yang-Mills规范群，引入了具有双曲视界的黑洞解.我们认为四维解与爱因斯坦-麦克斯韦引力的四维解完全相同，而高维解是新的。我们研究了高维解的性质，发现尽管5维中的度量函数不同，但5维中的解与Einstein-Maxwell（EM）理论的拓扑5维解具有相同的性质.但在6维及更高维，具有非负质量的EYM和EM引力的拓扑解具有不同的性质。首先，EYM解的奇点不存在裸奇点，是类空的，而拓扑Reissner-Nordstrom解的奇点是类时的。第二，在EYM引力中不存在具有非负质量的极端6维或更高维的黑洞，而在EM引力中存在这类解。此外，EYM理论不存在具有非负质量的静态渐近de Sitter解，而EM引力存在。

英文摘要：

We present the topological solutions of Einstein gravity in the presence of a non-Abelian Yang-Mills field. In ($n+1$) dimensions, we consider the $So(n(n-1)/2-1,1)$ semisimple group as the Yang-Mills gauge group, and introduce the black hole solutions with hyperbolic horizon. We argue that the 4-dimensional solution is exactly the same as the 4-dimensional solution of Einstein-Maxwell gravity, while the higher-dimensional solutions are new. We investigate the properties of the higher-dimensional solutions and find that these solutions in 5 dimensions have the same properties as the topological 5-dimensional solution of Einstein-Maxwell (EM) theory although the metric function in 5 dimensions is different. But in 6 and higher dimensions, the topological solutions of EYM and EM gravities with non-negative mass have different properties. First, the singularity of EYM solution does not present a naked singularity and is spacelike, while the singularity of topological Reissner-Nordstrom solution is timelike. Second, there are no extreme 6 or higher-dimensional black holes in EYM gravity with non-negative mass, while these kinds of solutions exist in EM gravity. Furthermore, EYM theory has no static asymptotically de Sitter solution with non-negative mass, while EM gravity has.

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