Gravitational Constraints on a Lightlike boundary
Mathematical Physics
2021-08-24 v2 General Relativity and Quantum Cosmology
High Energy Physics - Theory
math.MP
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.
Cite
@article{arxiv.2010.14871,
title = {Gravitational Constraints on a Lightlike boundary},
author = {Giovanni Canepa and Alberto S. Cattaneo and Manuel Tecchiolli},
journal= {arXiv preprint arXiv:2010.14871},
year = {2021}
}
Comments
42 pages, accepted for publication in Ann. Henri Poincar\'e. Improved version, added section about independence of the structure from the choices