1997/03/31 by V. C. de Andrade, J. G. Pereira · 1 voice · 292 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Classical field theory #Classical mechanics #Cosmology and Gravitation Theories #Gauge theory #General relativity #Geodesic #Geometry #Gravitation #Gravitational acceleration #Gravitational field #Gravitoelectromagnetism #Introduction to gauge theory #Linearized gravity #Lorentz force #Lorentz transformation #Lorenz gauge condition #Magnetic field #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Relativity and Gravitational Theory #Scalar (mathematics) #Spacetime #Speed of gravity #Test particle #Torsion (gastropod) #gr-qc
paper · pdf · doi:10.1103/physrevd.56.4689
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 56(8), 4689-4695 (American Physical Society) · Equations (44)-(47) corrected
arxiv created 1997/06/23 · openalex publication_date 1997/10/15 · arxiv updated 2011/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In the context of a gauge theory for the translation group, we have obtained, for a spinless particle, a gravitational analogue of the Lorentz force. Then, we have shown that this force equation can be rewritten in terms of magnitudes related to either the teleparallel or the Riemannian structures induced in spacetime by the presence of the gravitational field. In the first case, it gives a force equation, with torsion playing the role of force. In the second, it gives the usual geodesic equation of general relativity. The main conclusion is that scalar matter is able to feel any one of the above spacetime geometries, the teleparallel and the metric ones. Furthermore, both descriptions are found to be completely equivalent in the sense that they give the same physical trajectory for a spinless particle in a gravitational field.