The Einstein constraints and differential forms
General Relativity and Quantum Cosmology
2026-04-01 v1
Abstract
We express the vacuum Einstein constraints in terms of differential forms - the forms include one-forms constituting an orthonormal coframe of the spatial metric. We show that if the metric is real-analytic, then the constraints can be always expressed locally as a system of first order PDE's - this system is obtained by a special choice of the coframe, which reduces to zero all second order terms in the scalar constraint.
Cite
@article{arxiv.2511.19129,
title = {The Einstein constraints and differential forms},
author = {Andrzej Okolow and Jakub Szymankiewicz},
journal= {arXiv preprint arXiv:2511.19129},
year = {2026}
}
Comments
18 pages, no figure, LaTeX