English

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

R2 v1 2026-07-22T12:31:04.494Z