The Geometrization of Maxwell’s Homogenous Equation and the Emergence of Gravity

A recently proposed classical field theory in which the Maxwell tensor is coupled to the Riemann-Christoffel curvature tensor in a fundamentally new way is reviewed and extended. This proposed geometrization of the Maxwell tensor leaves the classical equations of electromagnetism unchanged, but also leads to the emergence of gravity as all solutions of the proposed field equations are shown to be solutions of Einstein’s equation of General Relativity augmented by a term that can mimic the properties of dark matter and/or dark energy. Using specific solutions to the proposed theory, the unification brought to electromagnetic and gravitational phenomena as well as the consistency of those solutions with those of the classical Maxwell and Einstein field equations are emphasized throughout. Unique to the four fundamental field equations that comprise the proposed theory, and based on specific solutions to them are: the emergence of antimatter and its behavior in gravitational fields, the emergence of dark matter and dark energy mimicking terms in the context of General Relativity, an underlying relationship between electromagnetic and gravitational radiation, the impossibility of negative mass solutions that would generate repulsive gravitational fields or antigravity, and a method for quantizing the charge and mass of particle-like solutions.