Annales Henri Poincaré

, Volume 6, Issue 1, pp 155–194

KIDs are Non-Generic

  • Robert Beig
  • Piotr T. Chruściel
  • Richard Schoen
Original Paper

DOI: 10.1007/s00023-005-0202-3

Cite this article as:
Beig, R., Chruściel, P.T. & Schoen, R. Ann. Henri Poincaré (2005) 6: 155. doi:10.1007/s00023-005-0202-3


We prove that the space-time developments of generic solutions of the vacuum constraint Einstein equations do not possess any global or local Killing vectors, when Cauchy data are prescribed on an asymptotically flat Cauchy surface, or on a compact Cauchy surface with mean curvature close to a constant, or for CMC asymptotically hyperbolic initial data sets. More generally, we show that nonexistence of global symmetries implies, generically, non-existence of local ones. As part of the argument, we prove that generic metrics do not possess any local or global conformal Killing vectors.

Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  • Robert Beig
    • 1
  • Piotr T. Chruściel
    • 2
  • Richard Schoen
    • 3
  1. 1.Institut für Theoretische PhysikUniversität WienViennaAustria
  2. 2.Département de Mathématiques, Faculté des Sciences ToursFrance
  3. 3.Department of MathematicsStanford UniversityPalo AltoUSA

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