Multimomentum Maps in General Relativity

TL;DR

This paper explores the properties of multimomentum maps on null hypersurfaces in General Relativity and their connection to the theory's constraint structure, revealing differences from spacelike hypersurfaces.

Contribution

It provides a detailed analysis of multimomentum maps on null hypersurfaces and their role in the constraint analysis of General Relativity, highlighting novel contributions to the understanding of second class constraints.

Findings

Constraints that are second class in Hamiltonian formalism contribute to the multimomentum map on null hypersurfaces.

Differences between null and spacelike hypersurfaces in the context of multimomentum maps are clarified.

The relation between multimomentum maps and the constraint structure in General Relativity is elucidated.

Abstract

The properties of multimomentum maps on null hypersurfaces, and their relation with the constraint analysis of General Relativity, are described. Unlike the case of spacelike hypersurfaces, some constraints which are second class in the Hamiltonian formalism turn out to contribute to the multimomentum map.