arXiv 2103.091102021-03hep-thgr-qc

从爱因斯坦-高斯-博内引力论看广义相对论

General Relativity from Einstein-Gauss-Bonnet gravity

Fabrizio Canfora, Adolfo Cisterna, Sebastian Fuenzalida, Carla Henriquez-Baez, Julio Oliva

备注：: 20 pages, 3 figures. v2: 20 pages, 2 figures, references added and typos fixed. To appear in Physical Review D
发表信息：: Phys. Rev. D 104, 044026 (2021)
DOI：: 10.1103/PhysRevD.104.044026

摘要：

在这项工作中，我们表明，在四维爱因斯坦引力可以一致地从一个通用的高曲率Lovelock理论在$D=4+p$维紧化，是$p\geq1$。紧化是在直积空间$\mathcal{M}_D=\mathcal{M}_4\times\mathcal{K}^p$上进行的，其中$\mathcal{K}^p$是常曲率的欧氏内部流形。该过程以这样的方式进行，即不需要在耦合常数之间进行微调。紧化要求用合适的$p$ -形式的通量来修饰内部流形，这些形式的场强与内部空间的体积形式成比例。我们明确地将爱因斯坦-高斯-邦纳理论从六维紧化为四维爱因斯坦理论，并从五维开始勾画出类似的紧化过程。我们构造了几个黑弦/p-膜解，其中一个由膜上的Schwarzschild黑洞构成的五维渐近平坦黑弦是特别有趣的.最后，热力学的解决方案进行了描述，我们发现，一致的紧化修改熵包括一个常数项，这可能会导致偏离通常的行为的霍金-佩奇相变。新的情况是可能的，其中大黑洞占主导地位的规范ensample的所有温度以上的最低值。

英文摘要：

In this work we show that Einstein gravity in four dimensions can be consistently obtained from the compactification of a generic higher curvature Lovelock theory in dimension $D=4+p$, being $p\geq1$. The compactification is performed on a direct product space $\mathcal{M}_D=\mathcal{M}_4\times\mathcal{K}^p$, where $\mathcal{K}^p$ is a Euclidean internal manifold of constant curvature. The process is carried out in such a way that no fine tuning between the coupling constants is needed. The compactification requires to dress the internal manifold with the flux of suitable $p$-forms whose field strengths are proportional to the volume form of the internal space. We explicitly compactify Einstein-Gauss-Bonnet theory from dimension six to Einstein theory in dimension four and sketch out a similar procedure for this compactification to take place starting from dimension five. Several black string/p-branes solutions are constructed, among which, a five dimensional asymptotically flat black string composed of a Schwarzschild black hole on the brane is particularly interesting. Finally, the thermodynamic of the solutions is described and we find that the consistent compactification modifies the entropy by including a constant term, which may induce a departure from the usual behavior of the Hawking-Page phase transition. New scenarios are possible in which large black holes dominate the canonical ensamble for all temperatures above the minimal value.

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