Article

Communications in Mathematical Physics

, Volume 49, Issue 2, pp 187-190

The existence of maximal slicings in asymptotically flat spacetimes

  • M. CantorAffiliated withDepartment of Physics and Astronomy, University of North Carolina
  • , A. FischerAffiliated withDepartment of Physics and Astronomy, University of North Carolina
  • , J. MarsdenAffiliated withDepartment of Physics and Astronomy, University of North Carolina
  • , N. Ō MurchadhaAffiliated withDepartment of Physics and Astronomy, University of North Carolina
  • , J. YorkAffiliated withDepartment of Physics and Astronomy, University of North Carolina

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Abstract

We consider Cauchy data (g, π) on IR3 that are asymptotically Euclidean and that satisfy the vacuum constraint equations of general relativity. Only those (g, π) are treated that can be joined by a curve of “sufficiently bounded” initial data to the trivial data (δ, 0). It is shown that in the Cauchy developments of such data, the maximal slicing condition tr π=0 can always be satisfied. The proof uses the recently introduced “weighted Sobolev spaces” of Nirenberg, Walker, and Cantor.