On a field tensor for gravity and electromagnetism

TL;DR

This paper proposes a unified tensor framework using a rank-three Lanczos tensor to describe both gravitational and electromagnetic phenomena in relativity, identifying their field components and proposing divergence-based field equations.

Contribution

It introduces a novel tensor field approach that unifies gravity and electromagnetism within a single mathematical framework, with specific field decompositions and divergence equations.

Findings

Identifies a rank-three Lanczos tensor as suitable for unifying gravity and electromagnetism.

Decomposes the tensor into gravitational and electromagnetic components.

Proposes divergence equations as field equations for the unified theory.

Abstract

We show that a three rank Lanczos type tensor field is an appropriate choice to describe relativistic electromagnetic and gravitational effects. More precisely, we identify the irreducible field-decompositions of this tensor as gravitational and electromagnetic fields. A set of divergence equations are proposed as field equations.