English

Weyl gravity as general relativity

General Relativity and Quantum Cosmology 2014-07-30 v3 High Energy Physics - Theory

Abstract

When the full connection of Weyl conformal gravity is varied instead of just the metric, the resulting vacuum field equations reduce to the vacuum Einstein equation, up to the choice of local units, if and only if the torsion vanishes. This result differs strongly from the usual fourth-order formulation of Weyl gravity.

Keywords

Cite

@article{arxiv.1310.0526,
  title  = {Weyl gravity as general relativity},
  author = {James T. Wheeler},
  journal= {arXiv preprint arXiv:1310.0526},
  year   = {2014}
}

Comments

Final version, 11 pages. The role of torsion is clarified, two appendices - on structure equations and Bianchi identities and on the basis equation - have been added

R2 v1 2026-06-22T01:38:37.802Z