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 have obtained the perturbative black-hole solution up to the order $\O(\alpha a^3)$ for any $D$, where $\alpha$ is the Gauss-Bonnet coupling, while the $D=5$ solution which is non-perturbative in mass has been found in analytic form up to the order $\O(\alpha a^7)$. 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.

中文翻译：

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简单地旋转爱因斯坦-高斯-邦尼理论中的高维黑洞

根据旋转参数的幂使用摄动展开 $\mathrm{一种}$ 我们构造了轴对称且渐近平坦的黑洞度量 $d$维爱因斯坦-高斯-引擎盖理论。在五维时空中，我们找到了场方程的两个解，描述了渐近平坦的黑洞，尽管其中只有一个在质量上是微扰的，也就是说，当黑洞质量变为零时，它会进入Minkowski时空。我们已经获得了任意阶的扰动黑洞解，直到$ \ O（\ alpha a ^ 3）$$d$，在哪里 $\alpha$ 是高斯-邦纳特耦合，而 $d=5$在分析形式中找到了质量为非摄动的解，直到$ \ O（\ alpha a ^ 7）$为止。为了检查扩展中的收敛性$\mathrm{一种}$ 我们分析了该时空中的光子轨道的特征，并计算了光子轨道的频率和光子球体的半径。