2000/03/31 by Stewart J. Clark, Simon J. Clark, Robin W. Tucker +1 · 4 citations
Mathematics · Physics and Astronomy · #Analogy #Classical electromagnetism #Classical mechanics #Cosmology and Gravitation Theories #Covariant transformation #Electromagnetic field #Electromagnetic tensor #Electromagnetism #Gauge anomaly #Gauge theory #Geodesic #Geometry #Gravitation #Gravitational field #Introduction to gauge theory #Lorenz gauge condition #Mathematical descriptions of the electromagnetic field #Mathematical physics #Mathematics #Mathematics of general relativity #Maxwell's equations #Maxwell's equations in curved spacetime #Metric tensor #Numerical relativity #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Relativity and Gravitational Theory #Spacetime #Symmetry (geometry) #Tensor (intrinsic definition) #Test particle #astro-ph #gr-qc
paper · pdf · doi:10.1088/0264-9381/17/19/311
published as Class.Quant.Grav.17:4125-4158,2000 · 29 pages no-figs
openalex publication_date 2000/09/19 · arxiv created 2000/09/22 · arxiv updated 2014/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
A tensor description of perturbative Einsteinian gravity about an arbitrary background spacetime is developed. By analogy with the covariant laws of electromagnetism in spacetime, gravito-electromagnetic potentials and fields are defined to emulate electromagnetic gauge transformations under substitutions belonging to the gauge symmetry group of perturbative gravitation. These definitions have the advantage that on a flat background, with the aid of a covariantly constant timelike vector field, a subset of the linearized gravitational field equations can be written in a form that is fully analogous to Maxwell's equations (without awkward factors of four and extraneous tensor fields). It is shown how the remaining equations in the perturbed gravitational system restrict the time dependence of solutions to these equations and thereby prohibit the existence of propagating vector fields. The induced gravito-electromagnetic Lorentz force on a test particle is evaluated in terms of these fields together with the torque on a small gyroscope. It is concluded that the analogy of perturbative gravity to Maxwell's description of electromagnetism can be valuable for (quasi-)stationary gravitational phenomena but that the analogy has its limitations.