Covariant theory of gravitation in the framework of special relativity

TL;DR

This paper develops a covariant, special relativity-based theory of gravity that predicts gravitomagnetic effects, analogous to electromagnetism, and aligns with recent gravitational wave observations, without replacing Einstein's theory.

Contribution

It derives a gravitomagnetic force from special relativity, showing its similarity to Maxwell's equations and providing a first approximation for gravitational phenomena in flat spacetime.

Findings

Gravitomagnetic fields satisfy Maxwell-like equations.

Gravitational waves propagate at the speed of light.

Gravity shares properties with electromagnetism under special relativity.

Abstract

In this work, we study the magnetic effects of gravity in the framework of special relativity. Imposing covariance of the gravitational force with respect to the Lorentz transformations, we show from a thought experiment that a magnetic-like force must be present whenever two or more bodies are in motion. The exact expression for this gravitomagnetic force is then derived purely from special relativity and the consequences of such a covariant theory are developed. For instance, we show that the gravitomagnetic fields satisfy a system of differential equations similar to the Maxwell equations of electrodynamics. This implies that the gravitational waves spread out with the speed of light in a flat spacetime, which is in agreement with the recent results concerning the gravitational waves detection. We also propose that the vector potential can be associated with the interaction momentum in the same way as the scalar potential is usually associated with the interaction energy. Other topics are also discussed, for example, the transformation laws for the fields, the energy and momentum stored in the gravitomagnetic fields, the invariance of the gravitational mass and so on. We remark that is not our intention here to propose an alternative theory of gravitation but, rather, only a first approximation for the gravitational phenomena, so that it can be applied whenever the gravitational force can be regarded as an ordinary effective force field and special relativity can be used with safety. To make this point clear we present briefly a comparison between our approach and that based on the (linearized) Einstein's theory. Finally, we remark that although we have assumed nothing from the electromagnetic theory, we found that gravity and electricity share many properties in common - these similarities, in fact, are just a requirement of special relativity that must apply to any physically (...)