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arXiv 0906.4953hep-thgr-qc
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Einstein-Gauss-Bonnet度规：黑洞、黑弦和一个静态性定理

Einstein-Gauss-Bonnet metrics: black holes, black strings and a staticity theorem

C. Bogdanos, C. Charmousis, B. Gouteraux, R. Zegers

备注：
Minor changes and typos corrected, published version
发表信息：
JHEP 0910:037,2009
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摘要：

我们发现6维爱因斯坦-高斯-邦纳方程的一般解决方案中的一大类空间和时间相关的翘曲几何。几个不同的家庭的解决方案，其中一些包括黑弦度规，空间和时间依赖的解决方案和黑洞与异国情调的视野。其中，一些被证明是为了验证伯克霍夫型静力学定理，虽然在这里，通常假设的最大对称性的地平线上放松，允许异国情调的地平线几何形状。我们提供了明确的例子，这样的静态异国情调的黑洞，包括视界几何是伯格曼空间。我们发现，这种情况是非常不同的高维广义相对论，爱因斯坦空间是可接受的黑洞的视野和相关的黑洞潜力甚至不受影响。相反，在Einstein-Gauss-Bonnet理论中，这种奇异视界的非平凡Weyl张量通过高阶Gauss-Bonnet项暴露于体动力学，严重限制了允许的视界几何形状，并为黑洞势增加了一个新的类电荷参数。后者与四维视界的欧拉特征有关，并在某些情况下提供了额外的黑洞视界。

英文摘要：

We find the general solution of the 6-dimensional Einstein-Gauss-Bonnet equations in a large class of space and time-dependent warped geometries. Several distinct families of solutions are found, some of which include black string metrics, space and time-dependent solutions and black holes with exotic horizons. Among these, some are shown to verify a Birkhoff type staticity theorem, although here, the usual assumption of maximal symmetry on the horizon is relaxed, allowing exotic horizon geometries. We provide explicit examples of such static exotic black holes, including ones whose horizon geometry is that of a Bergman space. We find that the situation is very different from higher-dimensional general relativity, where Einstein spaces are admissible black hole horizons and the associated black hole potential is not even affected. In Einstein-Gauss-Bonnet theory, on the contrary, the non-trivial Weyl tensor of such exotic horizons is exposed to the bulk dynamics through the higher order Gauss-Bonnet term, severely constraining the allowed horizon geometries and adding a novel charge-like parameter to the black hole potential. The latter is related to the Euler characteristic of the four-dimensional horizon and provides, in some cases, additional black hole horizons.

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