Communications in Mathematical Physics

, Volume 231, Issue 3, pp 529–568 | Cite as

Gluing and Wormholes for the Einstein Constraint Equations

  • James Isenberg
  • Rafe Mazzeo
  • Daniel Pollack

Abstract:

 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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • James Isenberg
    • 1
  • Rafe Mazzeo
    • 2
  • Daniel Pollack
    • 3
  1. 1.University of Oregon, Eugene, OR 97403, USA. E-mail: jim@newton.uoregon.eduUS
  2. 2.Stanford University, Stanford, CA 92740, USA. E-mail: mazzeo@math.stanford.eduUS
  3. 3.University of Washington, Seattle, WA 98195-4350, USA. E-mail: pollack@math.washington.eduUS

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