All identically conserved gravitational tensors are metric variations of invariant actions

Creators: Deser, S.^{1, 2}

1. California Institute of Technology
2. Brandeis University

Abstract

I prove an old unsolved conjecture, the hard – necessary – part of its obvious sufficiency, namely that all identically conserved symmetric 2-tensors are necessarily metric variations of invariant actions, thus sparing the world more alternative gravity theories. The proof is reasonably simple, if perhaps a "physicist's".

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Acknowledgement

I thank my old collaborator, Y. Pang for useful correspondence, a referee for insisting on better details, and J. Franklin for tech help.

Funding

This work was supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics , Award Number de-sc0011632.

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Resource type: Journal Article
Publisher: Elsevier
Published in: Annals of Physics, 448, 169163, ISSN: 0003-4916.
Languages: English

Created:: September 17, 2025
Modified:: September 17, 2025