2001/09/30 by James Isenberg, Rafe Mazzeo, Daniel Pollack · 1 citation
Mathematics · Physics and Astronomy · #gr-qc #math.AP #math.DG
paper · pdf · doi:10.1007/s00220-002-0722-3
published as Commun.Math.Phys.231:529-568,2002 · 42 pages, 4 figures, minor typos corrected, 1 reference added. To appear in Comm. Math. Phys. v3 (v2 had old Latex source file)
arxiv created 2002/07/26 · arxiv updated 2011/04/21
We establish a general gluing theorem for constant mean curvature solutions of the vacuum Einstein constraint equations. This allows one to take connected sums of solutions or to glue a handle (wormhole) onto any given solution. Away from this handle region, the initial data sets we produce can be made as close as desired to the original initial data sets. These constructions can be made either when the initial manifold is compact or asymptotically Euclidean or asymptotically hyperbolic, with suitable corresponding conditions on the extrinsic curvature. In the compact setting a mild nondegeneracy condition is required. In the final section of the paper, we list a number ways this construction may be used to produce new types of vacuum spacetimes.