The Einstein-Scalar Field Constraints on Asymptotically Euclidean Manifolds*
Yvonne Choquet-Bruhat , James Isenberg , Daniel Pollack
Chinese Annals of Mathematics, Series B ›› 2006, Vol. 27 ›› Issue (1) : 31 -52.
The Einstein-Scalar Field Constraints on Asymptotically Euclidean Manifolds*
By using the conformal method, solutions of the Einstein-scalar field gravitational constraint equations are obtained. 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. The proofs are constructive and allow for arbitrary dimension (> 2) as well as low regularity initial data.
Einstein-scalar field / Constraints / Asymptotically Euclidian / 83C05
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