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Deformation and gluing for the Einstein constraints with the dominant energy condition

Banff International Research Station for Mathematical Innovation and Discovery

We discuss the extension of localized deformation results for the Einstein constraints map to the setting of the dominant energy condition. In the time-symmetric case, the analysis involves the scalar curvature map and the static vacuum equations. The case of the full constraints (joint work with Lan-Hsuan Huang) is more delicate where the dominant energy condition does not hold strictly, and a modified constraint operator is introduced in order to control the first-order change in the dominant energy inequality under perturbation. As time permits, we discuss applications to gluing and density results, and to the Bartnik mass.

Mathematics; Relativity and gravitational theory; Differential geometry

video/mp4

Author affiliation: Lafayette College

2017-02-04

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60361

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/