Multimomentum Maps on Null Hypersurfaces
Giampiero Esposito, Cosimo Stornaiolo

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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Spacecraft Dynamics and Control
