On stationary vacuum solutions to the Einstein equations
General Relativity and Quantum Cosmology
2009-10-31 v3 Differential Geometry
Abstract
It is proved that the only geodesically complete stationary vacuum solution of the Einstein equations is the empty Minkowski space, or a quotient of it by a discrete group of isometries, generalizing a classical result of Lichnerowicz. In addition, we obtain an apriori bound on the curvature of stationary vacuum solutions away from the boundary or horizon.
Keywords
Cite
@article{arxiv.gr-qc/0001091,
title = {On stationary vacuum solutions to the Einstein equations},
author = {Michael T. Anderson},
journal= {arXiv preprint arXiv:gr-qc/0001091},
year = {2009}
}
Comments
14 pages, Final version, to appear in Annales Henri Poincare