Annales Henri Poincaré

, Volume 6, Issue 1, pp 155–194

KIDs are Non-Generic


    • Institut für Theoretische PhysikUniversität Wien
  • Piotr T. Chruściel
    • Département de Mathématiques, Faculté des Sciences 
  • Richard Schoen
    • Department of MathematicsStanford University
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.

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© Birkhäuser Verlag, Basel 2005