On completeness of orbits of Killing vector fields
General Relativity and Quantum Cosmology
2010-04-06 v1
Abstract
A Theorem is proved which reduces the problem of completeness of orbits of Killing vector fields in maximal globally hyperbolic, say vacuum, space--times to some properties of the orbits near the Cauchy surface. In particular it is shown that all Killing orbits are complete in maximal developements of asymptotically flat Cauchy data, or of Cauchy data prescribed on a compact manifold. This result gives a significant strengthening of the uniqueness theorems for black holes.
Keywords
Cite
@article{arxiv.gr-qc/9304029,
title = {On completeness of orbits of Killing vector fields},
author = {Piotr T. Chrusciel},
journal= {arXiv preprint arXiv:gr-qc/9304029},
year = {2010}
}
Comments
16 pages, Latex, preprint NSF-ITP-93-44