On stationary solutions to the vacuum Einstein field equations

Abstract

We prove that any 4-dimensional geodesically complete spacetime with a timelike Killing field satisfying the vacuum Einstein field equation $Ric(g_M)=\lambda g_M$ with nonnegative cosmological constant $\lambda \ge 0$ is flat. When dim $\ge 5$, if the spacetime is assumed to be static additionally, we prove that its universal cover splits isometrically as a product of a Ricci flat Riemannian manifold and a real line.

24 pages

References in corpus (2)

• Conditions for nonexistence of static or stationary, Einstein-Maxwell, non-inheriting black-holes
• Local foliations and optimal regularity of Einstein spacetimes