We analyse the boundary structure of general relativity in the coframe formalism in the case of a lightlike boundary, i.e. when the restriction of the induced Lorentzian metric to the boundary is degenerate. We describe the associated reduced phase space in terms of constraints on the symplectic space of boundary fields. We explicitly compute the Poisson brackets of the constraints and identify the first- and second-class ones. In particular, in the 3+1-dimensional case, we show that the reduced phase space has two local degrees of freedom, instead of the usual four in the non-degenerate case.

中文翻译：

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轻质边界上的引力约束

我们在类似光的边界的情况下，即当诱导洛伦兹度量对边界的限制退化时，在共框形式主义中分析广义相对论的边界结构。我们根据边界场辛空间的约束来描述相关联的缩减相空间。我们明确地计算约束的泊松括号并确定第一类和第二类。特别是，在 3+1 维的情况下，我们表明缩减的相空间具有两个局部自由度，而不是非退化情况下通常的四个。