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).
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