Lovelock's theorem revisited

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Lovelock's theorem revisited

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Title: Lovelock's theorem revisited
Author: Navarro Garmendia, Alberto; Navarro Garmendia, José
Abstract: Sea (X, g) una variedad pseudo-riemanniana arbitraria. Un resultado célebre por Lovelock ([4], [5], [6]) da una descripción explícita de todos los de segundo orden natural (0,2) -tensors en X, que satisface las condiciones de ser simétrica y divergencia libre. Aparte de la doble métrica, el tensor de Einstein de g es el ejemplo más sencillo. En este trabajo, ofrecemos una prueba corta y autónoma de este teorema, es la simplificación de la existente mediante la formalización de la noción de derivada de un tensor natural.Let (X, g) be an arbitrary pseudo-riemannian manifold. A celebrated result by Lovelock ([4], [5], [6]) gives an explicit description of all second-order natural (0,2)-tensors on X, that satisfy the conditions of being symmetric and divergence-free. Apart from the dual metric, the Einstein tensor of g is the simplest example. In this paper, we give a short and self-contained proof of this theorem, simplifying the existing one by formalizing the notion of derivative of a natural tensor.
Description: Publicado en: J.Geom.Phys.61:1950-1956,2011 DOI: 10.1016/j.geomphys.2011.05.004
URI: http://hdl.handle.net/10662/2553
Date: 2010-12


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