论文标题
Horndeski重力为$ d \ rightArrow4 $高斯 - 邦网的极限
Horndeski Gravity as $D\rightarrow4$ Limit of Gauss-Bonnet
论文作者
论文摘要
我们提出了一个$ d \ rightarrow 4 $限制的Einstein-Gauss-Bonnet（EGB）重力的程序，该程序在四个维度中导致了一个定义明确的动作原理。我们的构造基于压实$ d $二维的EGB重力，$（d-4）$ - 尺寸最大对称空间，然后重新定义高斯 - 骨网耦合$α\ rightarrow \ rightarrow \fracα{d-4} $。最终的模型是属于Horndeski重力家族的特殊标量调整理论。研究标量理论中的静态黑洞溶液。有趣的是，度量配置文件独立于内部空间的曲率，与$ d \ rightarrow 4 $限制了通常的EGB黑洞，具有不寻常的高斯 - bonnet耦合$ \fracα{d-4} $。内部空间的曲率信息代替在额外标量字段的轮廓中编码。我们的过程也可以推广，以通过压实$（D-P）$ - 尺寸最大对称空间的$ d $维理论来定义高斯组合的进一步限制。这些导致不同的$ d \ rightarrow 4 $ egb重力限制以及其$ d \ rightarrow 2,3 $限制。
We propose a procedure for the $D\rightarrow 4$ limit of Einstein-Gauss-Bonnet (EGB) gravity that leads to a well defined action principle in four dimensions. Our construction is based on compactifying $D$-dimensional EGB gravity on a $(D-4)$-dimensional maximally symmetric space followed by redefining the Gauss-Bonnet coupling $α\rightarrow \fracα{D-4}$. The resulting model is a special scalar-tensor theory that belongs to the family of Horndeski gravity. Static black hole solutions in the scalar-tensor theory are investigated. Interestingly, the metric profile is independent of the curvature of the internal space and coincides with the $D\rightarrow 4$ limit of the usual EGB black hole with the unusual Gauss-Bonnet coupling $\fracα{D-4}$. The curvature information of the internal space is instead encoded in the profile of the extra scalar field. Our procedure can also be generalized to define further limits of the Gauss-Bonnet combination by compactifying the $D$-dimensional theory on a $(D-p)$-dimensional maximally symmetric space with $p\leq 3$. These lead to different $D\rightarrow 4$ limits of EGB gravity as well as its $D\rightarrow 2,3$ limits.
