The Geometrization of Maxwell's Equations and the Emergence of Gravity and Antimatter

TL;DR

This paper develops a geometric framework for Maxwell's equations by coupling them to spacetime curvature, leading to a unified interpretation of electromagnetism, gravity, dark matter/energy, and antimatter within a single geometric theory.

Contribution

It introduces a geometricized electrodynamics theory coupling Maxwell's tensor to curvature, revealing new interpretations of charge, mass, and antimatter phenomena.

Findings

Derives Maxwell's equations from geometric coupling to curvature.

Shows solutions are consistent with Einstein's gravity including dark matter/energy effects.

Predicts properties and behaviors of antimatter from symmetries in the theory.

Abstract

Coupling the Maxwell tensor to the Riemann-Christoffel curvature tensor is shown to lead to a geometricized theory of electrodynamics. While this geometricized theory leads directly to the classical Maxwell equations, it also extends their physical interpretation by giving charge density, mass density and the four-velocity that describes their motions geometric definitions. Assuming the existence of a conserved energy-momentum tensor, all solutions to the geometricized theory of electrodynamics developed here are shown to be consistent with the emergence of gravity obeying the General Relativity field equation augmented by a term that mimics the properties of dark matter and/or dark energy. Finally, due to the symmetries of the theory, the properties and phenomenology of antimatter emerge in solutions.