Lovelock's theorem revisited

Details Lovelock's theorem revisited Lovelock's theorem revisited

2010-05-13

arxiv.org/abs/1005.2386v4

J.Geom.Phys.61:1950-1956,2011

Physics

Mathematical Physics

9 pages

Scientific paper

10.1016/j.geomphys.2011.05.004

Let (X, g) be an arbitrary pseudo-riemannian manifold. A celebrated result by Lovelock 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.

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