Charge, geometry, and effective mass

TL;DR

This paper explores the fundamental nature of charge in electromagnetic theory, comparing it to mass and analyzing its geometric representation in spacetime through the Reissner-Nordstrom solution.

Contribution

It demonstrates that charge, similar to mass, has a distinct spacetime signature, extending the understanding of charge's role in Einstein's theory of gravity.

Findings

Charge has a unique spacetime signature.

Reissner-Nordstrom solution links charge to spacetime geometry.

Charge's origin is not derived from the theory itself.

Abstract

Charge, like mass in Newtonian mechanics, is an irreducible element of electromagnetic theory that must be introduced ab initio. Its origin is not properly a part of the theory. Fields are then defined in terms of forces on either masses--in the case of Newtonian mechanics, or charges in the case of electromagnetism. General Relativity changed our way of thinking about the gravitational field by replacing the concept of a force field with the curvature of space-time. Mass, however, remained an irreducible element. It is shown here that the Reissner-Nordstrom solution to the Einstein field equations tells us that charge, like mass, has a unique space-time signature.