Abstract
A classical field theory of gravity and electromagnetism is developed. The starting point of the theory is the Maxwell equations which are directly tied to the Riemann-Christoffel curvature tensor. This is done through the derivatives of the Maxwell tensor which are equated to a vector field contracted with the curvature tensor, i.e., . The electromagnetic portion of the theory is shown to be equivalent to the classical Maxwell equations with the addition of a hidden variable. Because the proposed equations describing electromagnetism and gravity differ from the classical Maxwell-Einstein equations, their ability to describe classical physics is shown for several situations by direct calculation. The inclusion of antimatter and its behavior in a gravitational field, and the possibility of particle-like solutions exhibiting quantized charge, mass and angular momentum are discussed.
Highlights
Since the introduction of General Relativity, numerous classical field theories have been proposed which attempt to explain electromagnetism and gravitation in a unified and geometric framework [1] [2]
A continuous field theory is proposed with dynamical variables represented by two 2nd-order tensor fields, two vector fields, and two scalar fields. All of these fields are familiar to classical physics with the exception of the vector field aλ, which is used to couple the derivatives of the Maxwell tensor to the Riemann-Christoffel curvature tensor
Ν c of the theory, are in the weak field limit exactly those of classical electromagnetism on Minkowski spacetime and so in the weak field limit the proposed theory corresponds to the classical Maxwell theory as already demonstrated for several physical situations
Summary
Since the introduction of General Relativity, numerous classical field theories have been proposed which attempt to explain electromagnetism and gravitation in a unified and geometric framework [1] [2]. Instead of starting with that weak field analysis, the algebraic properties of the Riemann-Christoffel tensor are exploited to relate the Maxwell tensor and its derivatives to the curvature tensor This leads naturally to a set of field equations that reduces in their weak field limit to the classical Maxwell equations and provides an underlying geometric basis for electromagnetism. A continuous field theory is proposed with dynamical variables represented by two 2nd-order tensor fields, two vector fields, and two scalar fields All of these fields are familiar to classical physics with the exception of the vector field aλ , which is used to couple the derivatives of the Maxwell tensor to the Riemann-Christoffel curvature tensor. For the definitions of the Riemann-Christoffel curvature tensor and the Ricci tensor, the conventions used by Weinberg are followed [6].1
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