Gauge symmetry and gravitoelectromagnetism
Abstract
A tensor description of perturbative Einsteinian gravity about an arbitrary background spacetime is developed. By analogy with the covariant laws of electromagnetism in spacetime, gravitoelectromagnetic 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 gravitoelectromagnetic 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.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 October 2000
 DOI:
 10.1088/02649381/17/19/311
 arXiv:
 arXiv:grqc/0003115
 Bibcode:
 2000CQGra..17.4125C
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics
 EPrint:
 29 pages nofigs