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arXiv 2007.10116gr-qchep-th
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Einstein-Gauss-Bonnet理论中简单旋转的高维黑洞

Simply rotating higher dimensional black holes in Einstein-Gauss-Bonnet theory

R. A. Konoplya, A. Zhidenko

备注：
12 pages, 1 figure
发表信息：
Phys. Rev. D 102, 084030 (2020)
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摘要：

在$D$维Einstein-Gauss-Bonnet理论中，利用旋转参数$a$的幂的微扰展开，构造了轴对称渐近平坦黑洞度规.在五维时空中，我们找到了描述渐近平坦黑洞的场方程的两个解，尽管其中只有一个是质量微扰的，也就是说，当黑洞质量为零时，它进入闵可夫斯基时空。对于任意的$D$，我们得到了$O(αa^3)$阶的微扰黑洞解，其中$α$是Gauss-Bonnet耦合，而质量上无微扰的$D=5$解的解析形式为$O(αa^7)$阶.为了检验$a$展开式的收敛性，我们分析了该时空中光子轨道的特征，计算了光子轨道的频率和光子球的半径。

英文摘要：

Using perturbative expansion in terms of powers of the rotation parameter $a$ we construct the axisymmetric and asymptotically flat black-hole metric in the $D$-dimensional Einstein-Gauss-Bonnet theory. In five-dimensional spacetime we find two solutions to the field equations, describing the asymptotically flat black holes, though only one of them is perturbative in mass, that is, goes over into the Minkowski spacetime when the black-hole mass goes to zero. We obtain the perturbative black-hole solution up to the order $O(αa^3)$ for any $D$, where $α$ is the Gauss-Bonnet coupling, while the $D=5$ solution which is nonperturbative in mass is found in analytic form up to the order $O(αa^7)$. In order to check the convergence of the expansion in $a$ we analyze characteristics of photon orbits in this spacetime and compute frequencies of the photon orbits and radius of the photon sphere.

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