KIDs are non-generic

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.

latex2e, 38 pages in A4 now, minor corrections throughout

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• Initial data engineering
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• On the Asymptotics for the Vacuum Einstein Constraint Equations
• Manifold structures for sets of solutions of the general relativistic constraint equations

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