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KIDs are non-generic

R. Beig·P. T. Chrusciel·R. Schoen
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Abstract

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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R. Beig, P. T. Chrusciel, R. Schoen. 2004-10-06. KIDs are non-generic. https://doi.org/10.1007/s00023-005-0202-3

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