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PreprintCC BY-NC-ND 4.0arXiv

Komar superpotentials in extended theories of gravity

  • H. Arthur Weldon
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Abstract

This paper investigates Lagrangians with arbitrary dependence on the Riemann tensor and any number of derivatives. Noether's second theorem is applied separately to cal LG and cal LM, where the matter Lagrangian depends on a scalar field. For cal LG diffeomorphism invariance requires that the generalized Einstein tensor satisfy ∇αEαβ=0 and that there is a current satisfying 0=∂α(√g JαG2). The main result is an explicit formula for the superpotential Φ[αμ] that solves ∂μΦ[αμ]=√g JαG2. Some applications to f(R) gravity and various quadratic gravity theories are discussed. There are analogous results, including superpotentials, for the matter sector whenever the couplings to the matter fields contain derivatives of the metric.

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Cite

BibTeXRIS
BibTeX
@misc{weldon2026komar,
  title = {{Komar superpotentials in extended theories of gravity}},
  author = {H. Arthur Weldon},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12025},
  eprint = {2609.12025},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12025},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Komar superpotentials in extended theories of gravity
AU  - H. Arthur Weldon
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.12025
UR  - https://arxiv.org/abs/2609.12025
AB  - This paper investigates Lagrangians with arbitrary dependence on the Riemann tensor and any number of derivatives. Noether's second theorem is applied separately to cal L_G and cal L_M, where the matter Lagrangian depends on a scalar field. For cal L_G diffeomorphism invariance requires that the generalized Einstein tensor satisfy ∇_αE^αβ=0 and that there is a current satisfying 0=∂_α(√g J^α_G2). The main result is an explicit formula for the superpotential Φ^[αμ] that solves ∂_μΦ^[αμ]=√g J^α_G2. Some applications to f(R) gravity and various quadratic gravity theories are discussed. There are analogous results, including superpotentials, for the matter sector whenever the couplings to the matter fields contain derivatives of the metric.
ER  -