Canonical variation of a Lorentzian metric

Abstract

Given a Lorentzian manifold (M, gL) and a timelike unitary vector field E, we can construct the Riemannian metric gR=gL+2ω⊗ω, ω being the metrically equivalent one form to E. We relate the curvature of both metrics, especially in the case of E being Killing or closed, and we use the relations obtained to give some results about (M, gL). © 2014 Elsevier Inc.