Abstract We consider the D → 3 limit of Gauss–Bonnet gravity. We find two distinct but similar versions of the theory and obtain black hole solutions for each. For one theory the solution is an interesting generalization of the BTZ black hole that does not have constant curvature but whose thermodynamics is identical. The other theory admits a solution that is asymptotically AdS but does not approach the BTZ black hole in the limit of small Gauss–Bonnet coupling. We also discuss the distinction between our solutions and those obtained by taking a D → 3 limit of solutions to D-dimensional Einstein Gauss–Bonnet gravity. We find that these latter metrics are not solutions of the theories we consider except for particular constraints on the parameters.

中文翻译：

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低维 Gauss-Bonnet 引力和 BTZ 黑洞

摘要 我们考虑 Gauss-Bonnet 引力的 D → 3 极限。我们找到了该理论的两个不同但相似的版本，并为每个版本获得了黑洞解。对于一个理论，解决方案是 BTZ 黑洞的一个有趣的概括，它没有恒定的曲率，但其热力学是相同的。另一种理论承认渐近 AdS 的解决方案，但在小高斯 - 博内耦合的极限内不接近 BTZ 黑洞。我们还讨论了我们的解与通过对 D 维爱因斯坦高斯-博内引力取解的 D → 3 极限获得的解之间的区别。我们发现，除了对参数的特定限制外，这些后面的指标不是我们考虑的理论的解决方案。