On the naturalness of Einstein’s equation

@article{Navarro2008OnTN,
  title={On the naturalness of Einstein’s equation},
  author={Jos'e Navarro and Juan Blanco Sancho},
  journal={Journal of Geometry and Physics},
  year={2008},
  volume={58},
  pages={1007-1014}
}
We compute all 2-covariant tensors naturally constructed from a semiriemannian metric g which are divergence-free and have weight greater than 2. As a consequence, it follows a characterization of the Einstein tensor as the only, up to a constant factor, 2-covariant tensor naturally constructed from a semiriemannian metric which is divergence-free and has weight 0 (i.e., is independent of the unit of scale). Since these two conditions are also satisfied by the energy-momentum tensor of a… 
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