Densities of Electron's Continuum in Gravitational and Electromagnetic Fields

TL;DR

This paper explores the relativistic behavior of electron densities in gravitational and electromagnetic fields, deriving relations from tensor equations and highlighting limitations of electromagnetic intensities in describing matter motion.

Contribution

It introduces tensor-based relations for electron densities in combined gravitational and electromagnetic fields, connecting classical and quantum descriptions of matter.

Findings

Vector geodesic relations derived from tensor equations

Classical four-flows depend on local four-potentials

Potential electromagnetic intensities suffice for simple matter motion

Abstract

Relativistic dynamics of distributed mass and charge densities of the extended classical particle is discussed for arbitrary gravitational and electromagnetic fields. Vector geodesic relations for material space densities are consequences of tensor gravitational equations for continuous sources and their fields. Classical four-flows of elementary material space depend on local four-potentials for charged densities, like in quantum theory. Six electromagnetic intensities can describe satisfactorily only the simplest, potential kind of continuous matter motion.