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arXiv · 1509.00793

Canonical variation of a Lorentzian metric

Benjamin Olea
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Abstract

Given a Lorentzian manifold $(M,g_L)$ and a timelike unitary vector field $E$, we can construct the Riemannian metric $g_R=g_L+2ω\otimesω$, being $ω$ 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 $(M,g_L)$.

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Benjamin Olea. 2015-09-02. Canonical variation of a Lorentzian metric. https://arxiv.org/abs/1509.00793

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