Gauge symmetryand gravito-electromagnetism

Abstract

A tensor description of perturbative Einsteinian gravity about anarbitrary background spacetime is developed. By analogy with thecovariant laws of electromagnetism in spacetime, gravito-electromagnetic potentials and fields are definedto emulate electromagnetic gauge transformations undersubstitutions belonging to the gauge symmetry group ofperturbative gravitation. These definitions have the advantagethat on a flat background, with the aid of a covariantly constanttimelike vector field, a subset of the linearized gravitationalfield equations can be written in a form that is fully analogousto Maxwell's equations (without awkward factors of four andextraneous tensor fields). It is shown how the remainingequations in the perturbed gravitational system restrict the timedependence of solutions to these equations and thereby prohibitthe existence of propagating vector fields. The induced gravito-electromagnetic Lorentz force on a test particle is evaluated interms ofthese fields together with the torque on a small gyroscope. It isconcluded that the analogy of perturbative gravity to Maxwell'sdescription of electromagnetism can be valuable for(quasi-)stationary gravitational phenomena but that the analogyhas its limitations.