Multimomentum Maps on Null Hypersurfaces

TL;DR

This paper explores how multimomentum maps can be applied to the constraint analysis of general relativity on null hypersurfaces, revealing differences from spacelike cases and requiring combined approaches for complete constraint recovery.

Contribution

It demonstrates the application of multimomentum maps to null hypersurfaces in general relativity and identifies the need to incorporate Euler-Lagrange equations for full constraint analysis.

Findings

Some second class constraints contribute to the multimomentum map on null hypersurfaces

Combining multimomentum maps with non-evolutionary Euler-Lagrange equations recovers all secondary constraints

Analysis is specifically performed on the outgoing null cone

Abstract

This paper studies the application of multimomentum maps to the constraint analysis of general relativity on null hypersurfaces. It is shown that, unlike the case of spacelike hypersurfaces, some constraints which are second class in the Hamiltonian formalism turn out to contribute to the multimomentum map. To recover the whole set of secondary constraints found in the Hamiltonian formalism, it is necessary to combine the multimomentum map with those particular Euler-Lagrange equations which are not of evolutionary type. The analysis is performed on the outgoing null cone only.