Communications in Mathematical Physics

, Volume 130, Issue 1, pp 95–109 | Cite as

On maximal surfaces in asymptotically flat space-times

  • R. Bartnik
  • P. T. Chruściel
  • N. Ō Murchadha
Article

Abstract

Existenc of maximal and “almost maximal” hypersurfaces in asymptotically flat space-times is established under boundary conditions weaker than those considered previously. We show in particular that every vacuum evolution of asymptotically flat data for the Einstein equations can be foliated by slices maximal outside a spatially compact set and that every (strictly) stationary asymptotically flat space-time can be foliated by maximal hypersurfaces. Amongst other uniqueness results, we show that maximal hypersurfaces can be used to “partially fix” an asymptotic Poincaré group.

Keywords

Boundary Condition Neural Network Statistical Physic Complex System Nonlinear Dynamics 

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • R. Bartnik
    • 1
  • P. T. Chruściel
    • 2
  • N. Ō Murchadha
    • 3
  1. 1.Centre for Mathematical AnalysisAustralian National UniversityCanberraAustralia
  2. 2.Department of PhysicsYale UniversityNew HavenUSA
  3. 3.Physics DepartmentUniversity CollegeCorkIreland

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