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arXiv 2208.02497hep-thgr-qc
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爱因斯坦-高斯-博内黑弦的大图$α$

Einstein-Gauss-Bonnet black strings at large $α$

Ryotaku Suzuki, Shinya Tomizawa

备注：
24 pages, 17 figures; v2: minor modifications, references added, 25 pages
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摘要：

在高维广义相对论（GR）中，最简单的黑弦可能是史瓦西时空和平坦空间方向的直接产物。然而，众所周知，爱因斯坦-高斯-邦纳理论不允许这样一个琐碎而简单的解决方案。我们提出了一种新的分析技术，它假设高斯-博内（GB）项成为主导的爱因斯坦-希尔伯特（EH）项。假设用视界尺度归一化的无量纲耦合常数$α$足够大，我们发现时空被分成GB区和GR区，它们通过GB项和EH项可比的过渡区相匹配。利用这个大$α$近似，我们确实构造了新的黑弦解析解，并由此解析计算了大$α$下黑弦的各种物理量。此外，我们证实，所有这些解析结果与数值计算是一致的。我们还讨论了一般Einstein-Lovelock黑洞的可能推广。

英文摘要：

The simplest black string in higher-dimensional general relativity (GR) is perhaps the direct product of a Schwarzschild spacetime and a flat spatial direction. However, it is known that the Einstein-Gauss-Bonnet theory does not allow such a trivial and simple solution. We propose a novel analytic technique, which assumes that the Gauss-Bonnet (GB) term becomes dominant over the Einstein-Hilbert (EH) term. Assuming the dimensionless coupling constant $α$ normalized by the horizon scale is large enough, we find that the spacetime is separated into the GB region and GR region, which are matched via the transition region where the GB and EH terms are comparable. Using this large $α$ approximation, we indeed construct new analytic solutions of black strings, from which we analytically compute various physical quantities of black strings at large $α$. Moreover, we confirm that all these analytic results are consistent with the numerical calculation. We also discuss the possible extension to general Einstein-Lovelock black holes.

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