General Relativity, Maxwell's Electrodynamics, and the Foundations of the Quantum Theory of Gravitation and Matter

TL;DR

This paper extends General Relativity with electric-magnetic duality to include non-Abelian fields, develops new energy tensors from the field strength tensor, and proposes a framework to geometrize quantum physics through non-linear equations.

Contribution

It introduces novel energy tensors based on the field strength tensor and links classical gravity with quantum solutions via a unified geometric approach.

Findings

Development of energy tensors with non-vanishing trace from F^uv

Spacetime metric constrained by third-order equations involving Bianchi identity

Quantum solutions derived from the common appearance of F^uv in tensors

Abstract

The formalism of electric - magnetic duality, first pioneered by Reinich and Wheeler, extends General Relativity to encompass non-Abelian fields. Several energy Tensors T^uv with non-vanishing trace matter are developed solely as a function of the field strength tensor F^uv, including the Euler tensor, and tensors for matter in flux, pressure in flux, and stationary pressure. The spacetime metric g_uv is not only a solution to the second-order Einstein equation based on T^uv, but is also constrained by a third-order equation involving the Bianchi identity together with the gravitational energy components kappa_u for each T^uv. The common appearance of F^uv in all of the T^uv and kappa_v makes it possible to obtain quantum solutions for the spacetime metric, thereby geometrizing quantum physics as a non-linear theory.