KIDs are non-generic

Details KIDs are non-generic KIDs are non-generic

2004-03-10

arxiv.org/abs/gr-qc/0403042v2

Annales Henri Poincare 6 (2005) 155-194

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

latex2e, 38 pages in A4 now, minor corrections throughout

Scientific paper

10.1007/s00023-005-0202-3

We prove that generic solutions of the vacuum constraint Einstein equations do not possess any global or local space-time Killing vectors, 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 non-existence 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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