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<p>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 coframe, which reduces to zero all second order terms in the scalar constraint. We also present a general formula for coframes, which allow for this simplification of the constraint and give it additionally a certain symmetric form.</p>

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The Einstein constraints and differential forms

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • Andrzej Okołów,
  • Jakub Szymankiewicz

摘要

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 coframe, which reduces to zero all second order terms in the scalar constraint. We also present a general formula for coframes, which allow for this simplification of the constraint and give it additionally a certain symmetric form.