Gravitational Constraints on a Lightlike boundary

TL;DR

This paper investigates the boundary structure of General Relativity with lightlike boundaries, revealing a reduced phase space with fewer degrees of freedom due to degeneracy, and explicitly analyzing the associated constraints.

Contribution

It provides a detailed analysis of the boundary constraints and phase space structure for lightlike boundaries in GR, including explicit computations of Poisson brackets and degrees of freedom.

Findings

Reduced phase space has two local degrees of freedom in 3+1 dimensions

Explicit computation of Poisson brackets of boundary constraints

Identification of first- and second-class constraints

Abstract

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.