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PreprintarXiv licencearXiv

All theories of gravity with second-order traced field equations

  • Ángel J. Murcia
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Abstract

We classify all diffeomorphism-invariant theories of gravity which possess traced field equations of motion of second order in derivatives. We also prove in the affirmative a conjecture regarding the form of theories constructed algebraically from the Riemann tensor with second-order traced field equations and classify all polynomial quasi-topological gravities with second-order traced field equations.

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Cite

BibTeXRIS
BibTeX
@misc{murcia2026theories,
  title = {{All theories of gravity with second-order traced field equations}},
  author = {Ángel J. Murcia},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12097},
  eprint = {2610.12097},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12097},
}
RIS
TY  - UNPB
TI  - All theories of gravity with second-order traced field equations
AU  - Ángel J. Murcia
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.12097
UR  - https://arxiv.org/abs/2610.12097
AB  - We classify all diffeomorphism-invariant theories of gravity which possess traced field equations of motion of second order in derivatives. We also prove in the affirmative a conjecture regarding the form of theories constructed algebraically from the Riemann tensor with second-order traced field equations and classify all polynomial quasi-topological gravities with second-order traced field equations.
ER  -