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. 
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