Killing Initial Data
General Relativity and Quantum Cosmology
2010-04-06 v1
Abstract
We study space-time Killing vectors in terms of their "lapse and shift" relative to some spacelike slice. We give a necessary and sufficient condition in order for these lapse-shift pairs, which we call Killing initial data (KID'S), to form a Lie algebra under the bracket operation induced by the Lie commutator of vector fields on space-time. This result is applied to obtain a theorem on the periodicity of orbits for a class of Killing vector fields in asymptotically flat space-times.
Keywords
Cite
@article{arxiv.gr-qc/9604040,
title = {Killing Initial Data},
author = {R. Beig and Piotr T. Chrusciel},
journal= {arXiv preprint arXiv:gr-qc/9604040},
year = {2010}
}
Comments
17 pages