Formal analogies between gravitation and electrodynamics

TL;DR

This paper establishes a fully covariant theoretical framework comparing electromagnetism and gravitation, enabling direct analogies and transfer of geometrical tools between the two theories without approximations.

Contribution

It introduces a novel covariant approach to compare gravity and electromagnetism, including electromagnetic analogues of Riemann and Weyl tensors, and clarifies conditions for their mapping.

Findings

Identified conditions under which gravity maps to electrodynamics

Constructed electromagnetic analogues of Riemann and Weyl tensors

Demonstrated applicability of geometrical tools across theories

Abstract

We develop a theoretical framework that allows us to compare electromagnetism and gravitation in a fully covariant way. This new scenario does not rely on any kind of approximation nor associate objects with different operational meaning as it's sometime done in the literature. We construct the electromagnetic analogue to the Riemann and Weyl tensors and develop the equations of motion for these objects. In particular, we are able to identify precisely how and in what conditions gravity can be mapped to electrodynamics. As a consequence, many of the gemometrical tools of General Relativity can be applied to Electromagnetism and vice-versa. We hope our results would shed new light in the nature of electromagnetic and gravitational theories.