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arXiv 1006.3604hep-thgr-qc
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偶数维中具有高阶曲率和规范修正的磁性黑洞

Magnetic black holes with higher-order curvature and gauge corrections in even dimensions

Hideki Maeda, Mokhtar Hassaine, Cristian Martinez

备注：
22 pages, 4 figures; v2, typos corrected, references added, style changed, published version in JHEP
发表信息：
JHEP 1008:123,2010
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摘要：

对于由Einstein-Gauss-Bonnet-Maxwell- $Λ$块给出的作用量，我们得到了具有$F^4$规范修正项的任意$n(\ge 4)$偶数维磁黑洞解.这种作用出现在具有常数介子和消失的高阶场的杂化弦论的低能极限中。假设时空是一个翘曲积${\ma M}^{2} \times {\ma K}^{n-2}$，其中${\ma K}^{n-2}$是一个$(n-2)$维爱因斯坦空间，它的外尔张量满足一个条件，这个条件最初由多蒂和格莱泽考虑。在几个合理的假设下，建立了${\ma K}^{n-2}$上翘曲因子轨道非零的情况下磁解的广义Jebsen-Birkhoff定理.我们证明了这样的磁解不存在于奇数维。相反，在偶数维，我们得到了显式的解决方案的情况下，${\ma K}^{n-2}$是$(n-2)/2$二维极大对称空间具有相同的常数翘曲因子的产品流形。在后一种情况下，我们表明，时空的整体结构急剧依赖于规范修正项的存在，以及时空维度的数量。

英文摘要：

We obtain magnetic black-hole solutions in arbitrary $n(\ge 4)$ even dimensions for an action given by the Einstein-Gauss-Bonnet-Maxwell-$Λ$ pieces with the $F^4$ gauge-correction terms. This action arises in the low energy limit of heterotic string theory with constant dilaton and vanishing higher form fields. The spacetime is assumed to be a warped product ${\ma M}^{2} \times {\ma K}^{n-2}$, where ${\ma K}^{n-2}$ is a $(n-2)$-dimensional Einstein space satisfying a condition on its Weyl tensor, originally considered by Dotti and Gleiser. Under a few reasonable assumptions, we establish the generalized Jebsen-Birkhoff theorem for the magnetic solution in the case where the orbit of the warp factor on ${\ma K}^{n-2}$ is non-null. We prove that such magnetic solutions do not exist in odd dimensions. In contrast, in even dimensions, we obtain an explicit solution in the case where ${\ma K}^{n-2}$ is a product manifold of $(n-2)/2$ two-dimensional maximally symmetric spaces with the same constant warp factors. In this latter case, we show that the global structure of the spacetime sharply depends on the existence of the gauge-correction terms as well as the number of spacetime dimensions.

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