# Lovelock's theorem revisited

@article{Navarro2011LovelocksTR, title={Lovelock's theorem revisited}, author={Alberto Navarro and Jos'e Navarro}, journal={Journal of Geometry and Physics}, year={2011}, volume={61}, pages={1950-1956} }

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.

## 18 Citations

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