The harmonic gauge condition in the gravitomagnetic equations

TL;DR

This paper clarifies that the analogy between gravitomagnetic equations and Maxwell's equations remains valid even with time-dependent potentials, correcting a misconception caused by an improper gauge limit.

Contribution

It demonstrates that the supposed breakdown of the analogy is due to an incorrect application of the harmonic gauge condition, reaffirming the analogy's validity.

Findings

The analogy holds for time-dependent potentials when the correct gauge limit is used.

Incorrect gauge assumptions led to the misconception of breakdown.

Proper gauge treatment preserves the physical content of gravitomagnetic equations.

Abstract

It has been asserted in the literature that the analogy between the linear and first order slow motion approximation of Einstein equations of General Relativity (gravitomagnetic equations) and the Maxwell-Lorentz equations of electrodynamics breaks down if the gravitational potentials are time dependent. In this work, we show that this assertion is not correct and it has arisen from an incorrect limit of the usual harmonic gauge condition, which drastically changes the physical content of the gravitomagnetic equations.