We consider the action principles that are the lower dimensional limits of the Einstein–Gauss–Bonnet gravity via the Kaluza–Klein route. We study the vacua and obtain some exact solutions. We find that the reality condition of the theories may select one vacuum over the other from the two vacua that typically arise in Einstein–Gauss–Bonnet gravity. We obtain exact black hole and cosmological solutions carrying scalar hair, including scalar hairy BTZ black holes with both mass and angular momentum turned on. We also discuss the holographic central charges in the asymptotic AdS backgrounds.

A preprint version of the article is available at ArXiv.

中文翻译：

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真空度和精确解决方案，降低EGB的D限值

我们考虑的作用原理是通过Kaluza-Klein路线的爱因斯坦-高斯-引擎盖引力的下限尺寸。我们研究真空并获得一些精确的解决方案。我们发现，理论的现实条件可能会从爱因斯坦-高斯-帽子内引力中通常出现的两个真空中选择一个真空而不是另一个真空。我们获得携带标量头发的精确黑洞和宇宙学解决方案，包括同时打开质量和角动量的标量毛状BTZ黑洞。我们还将讨论渐近AdS背景下的全息中心电荷。

该文章的预印本可从ArXiv获得。