Boundary and corner terms in the action for general relativity
Boundary and corner terms in the action for general relativity
复制标题
广义相对论作用中的边界项和角项
DOI：
10.1088/1361-6382/aa6014
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发表时间：
2016
影响因子：
3.5
通讯作者：
S. Surya
中科院分区：
文献类型：
--
作者：
I. Jubb;J. Samuel;R. Sorkin;S. Surya
受量子引力的路径积分方法的启发，我们重温了广义相对论的作用原理。我们考虑一个时空区域，它的边界具有分段的C2分量，每个C2分量可以是类空的、类时的或零的，并考虑度规变化，其中只有度规到边界的拉回保持不变。考虑到所有这些度规变化，我们用Cartan的四分体形式统一地处理了类空、类时和零边界分量。除了计算简单之外，这种形式主义还为我们提供了一种识别角项的简单方法。我们还讨论了当边界是黑洞的事件视界时发生的“折痕”。我们的处理是几何的和内在的，我们用计算上更简单的四元组形式和更熟悉的度规形式给出了我们的结果。我们从更简单和更一般的角度恢复已知的结果，并找到一些新的结果。
We revisit the action principle for general relativity, motivated by the path integral approach to quantum gravity. We consider a spacetime region whose boundary has piecewise C2 components, each of which can be spacelike, timelike or null and consider metric variations in which only the pullback of the metric to the boundary is held fixed. Allowing all such metric variations we present a unified treatment of the spacelike, timelike and null boundary components using Cartan’s tetrad formalism. Apart from its computational simplicity, this formalism gives us a simple way of identifying corner terms. We also discuss ‘creases’ which occur when the boundary is the event horizon of a black hole. Our treatment is geometric and intrinsic and we present our results both in the computationally simpler tetrad formalism as well as the more familiar metric formalism. We recover known results from a simpler and more general point of view and find some new ones.