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The Einstein-scalar field constraints on asymptotically Euclidean manifolds

Yvonne Choquet-Bruhat·James Isenberg·Daniel Pollack
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Abstract

We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills fields, because the scalar field introduces three extra terms into the Lichnerowicz equation, rather than just one. Our proofs are constructive and allow for arbitrary dimension (>2) as well as low regularity initial data.

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Yvonne Choquet-Bruhat, James Isenberg, Daniel Pollack. 2005-06-20. The Einstein-scalar field constraints on asymptotically Euclidean manifolds. https://arxiv.org/abs/gr-qc/0506101

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