Communications in Mathematical Physics

, Volume 49, Issue 2, pp 187–190

The existence of maximal slicings in asymptotically flat spacetimes

  • M. Cantor
  • A. Fischer
  • J. Marsden
  • N. Ō Murchadha
  • J. York
Article

DOI: 10.1007/BF01608741

Cite this article as:
Cantor, M., Fischer, A., Marsden, J. et al. Commun.Math. Phys. (1976) 49: 187. doi:10.1007/BF01608741

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.

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • M. Cantor
    • 1
  • A. Fischer
    • 1
  • J. Marsden
    • 1
  • N. Ō Murchadha
    • 1
  • J. York
    • 1
  1. 1.Department of Physics and AstronomyUniversity of North CarolinaChapel HillUSA
  2. 2.Department of MathematicsDuke UniversityDurhamUSA
  3. 3.Department of MathematicsUniversity of CaliforniaSanta CruzUSA
  4. 4.Department of MathematicsUniversity of CaliforniaBerkeleyUSA