FORMAL ANALOGIES BETWEEN GRAVITATION AND ELECTRODYNAMICS

Abstract

We develop a theoretical framework that allows us to compare electromagnetism with 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 is sometimes done in the literature. We construct the electromagnetic analogue to 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 geometrical 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.