2006/01/04 by Dan N. Vollick, Vollick, Dan N. · 1 citation
Earth and Planetary Sciences · Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geophysics and Gravity Measurements #High Energy Physics - Theory (hep-th) #Relativity and Gravitational Theory #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.gr-qc/0601016
9 pages
arxiv created 2006/01/04 · openalex publication_date 2006/01/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A modified gravitational action is considered which involves the quantity Fμν=∂μΓν-∂νΓμ, where Γμ=Γαμα. Since Γμ transforms like a U(1) gauge field under coordinate transformations terms such as FμνFμν are invariant under coordinate transformations. If such a term is added to the usual gravitational action the resulting field equations, obtained from a Palatini variation, are the Einstein-Proca equations. The vector field can be coupled to point charges or to a complex scalar density of weight ie, where e is the charge of the field. If this scalar density is taken to be g-ie/2 and the overall factor of the scalar density Lagrangian takes on a particular value the resulting field equations are the Einstein-Maxwell equations.