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arXiv · 2511.19129

The Einstein constraints and differential forms

Andrzej Okolow·Jakub Szymankiewicz
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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.

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Andrzej Okolow, Jakub Szymankiewicz. 2025-11-24. The Einstein constraints and differential forms. https://doi.org/10.1007/s10714-026-03527-0

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