KIDs are non-generic
General Relativity and Quantum Cosmology
2009-11-10 v2
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.
Keywords
Cite
@article{arxiv.gr-qc/0403042,
title = {KIDs are non-generic},
author = {R. Beig and P. T. Chrusciel and R. Schoen},
journal= {arXiv preprint arXiv:gr-qc/0403042},
year = {2009}
}
Comments
latex2e, 38 pages in A4 now, minor corrections throughout