论文标题
$ d \ rightarrow 4 $ Einstein-Gauss-Bonnet重力的一致理论
A consistent theory of $D\rightarrow 4$ Einstein-Gauss-Bonnet gravity
论文作者
论文摘要
我们研究了$ d \ rightarrow 4 $限制的$ d $二维爱因斯坦 - 加斯 - 托内特重力，其中极限是用$ \tildeα=（d-4）\，α$保持固定的，而$α$是原始的高斯 - bonnet coupling。使用$ d $尺寸的ADM分解，我们澄清的是，极限是微妙和模棱两可的（如果不是不明显的话），并取决于如何使Hamiltonian或/和运动方程正规化的方式。为了在$ 4 $尺寸中找到与一般相对性不同的一致理论，正式化需要与lovelock定理一致，需要打破（一部分）差异不变性或导致额外的自由度。然后，我们提出了一个$ d \ rightarrow 4 $ Einstein-Gauss-Bonnet重力的一致理论，它通过破坏了时间差异不变性，具有两个动态的自由度，并认为，在许多合理的假设下，该理论是从时间表条件中选择的约束选择的独特之处。
We investigate the $D\rightarrow 4$ limit of the $D$-dimensional Einstein-Gauss-Bonnet gravity, where the limit is taken with $\tildeα=(D-4)\, α$ kept fixed and $α$ is the original Gauss-Bonnet coupling. Using the ADM decomposition in $D$ dimensions, we clarify that the limit is rather subtle and ambiguous (if not ill-defined) and depends on the way how to regularize the Hamiltonian or/and the equations of motion. To find a consistent theory in $4$ dimensions that is different from general relativity, the regularization needs to either break (a part of) the diffeomorphism invariance or lead to an extra degree of freedom, in agreement with the Lovelock theorem. We then propose a consistent theory of $D\rightarrow 4$ Einstein-Gauss-Bonnet gravity with two dynamical degrees of freedom by breaking the temporal diffeomorphism invariance and argue that, under a number of reasonable assumptions, the theory is unique up to a choice of a constraint that stems from a temporal gauge condition.
