Canepa G, Cattaneo A S, Tecchiolli M
Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland.
Ann Henri Poincare. 2021;22(9):3149-3198. doi: 10.1007/s00023-021-01038-z. Epub 2021 Mar 17.
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.
我们在共架形式体系下分析广义相对论在类光边界情形下的边界结构，即当诱导的洛伦兹度规在边界上的限制是退化的时候。我们根据对边界场辛空间的约束来描述相关的约化相空间。我们明确计算约束的泊松括号并识别出第一类和第二类约束。特别地，在3 + 1维情形下，我们表明约化相空间有两个局部自由度，而非非退化情形下通常的四个。
