About Gravitomagnetism

TL;DR

This paper explores the theoretical foundations of gravitomagnetism, comparing different approaches within special and general relativity, and discusses their implications on the equations governing gravitational motion.

Contribution

It clarifies the relationships between various definitions of gravitomagnetic fields and demonstrates their effects on the geodesic equation in linearized general relativity.

Findings

The gravitomagnetic field strength differs by a factor of two between approaches.

Full linearized general relativity predicts the same gravitomagnetic strength as the second approach.

Different definitions significantly impact the geodesic equation and second-order effects.

Abstract

The gravitomagnetic field is the force exerted by a moving body on the basis of the intriguing interplay between geometry and dynamics which is the analog to the magnetic field of a moving charged body in electromagnetism. The existence of such a field has been demonstrated based on special relativity approach and also by special relativity plus the gravitational time dilation for two different cases, a moving infinite line and a uniformly moving point mass, respectively. We treat these two approaches when the applied cases are switched while appropriate key points are employed. Thus, we demonstrate that the strength of the resulted gravitomagnetic field in the latter approach is twice the former. Then, we also discuss the full linearized general relativity and show that it should give the same strength for gravitomagnetic field as the latter approach. Hence, through an exact analogy with the electrodynamic equations, we present an argument in order to indicate the best definition amongst those considered in this issue in the literature. Finally, we investigate the gravitomagnetic effects and consequences of different definitions on the geodesic equation including the second order approximation terms.