# On second-order, divergence-free tensors

@article{Navarro2013OnSD, title={On second-order, divergence-free tensors}, author={Jos'e Navarro}, journal={Journal of Mathematical Physics}, year={2013}, volume={55}, pages={062501} }

The aim of this paper is to describe the vector spaces of those second-order tensors on a pseudo-Riemannian manifold (i.e., tensors whose local expressions only involve second derivatives of the metric) that are divergence-free. The main result establishes isomorphisms between these spaces and certain spaces of tensors (at a point) that are invariant under the action of an orthogonal group. This result is valid for tensors with an arbitrary number of indices and symmetries among them and, in…

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