ON STATIONARY SOLUTIONS TO THE VACUUM EINSTEIN FIELD EQUATIONS

摘要

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 >= 0 is flat. When dim >= 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 R.