Affine metrics and algebroid structures: Application to general relativity and unification

TL;DR

This paper develops affine metrics and algebroid structures, applying them to general relativity to unify gravity and electromagnetism through a combined field equation that extends Einstein's theory.

Contribution

It introduces a novel framework using affine metrics and algebroid bundles for unifying gravity and electromagnetism in a single geometric structure.

Findings

Derived a unified field equation combining Einstein and Maxwell equations.

Proposed a new equation potentially leading to new physical insights.

Extended the geometric framework of general relativity.

Abstract

Affine metrics and its associated algebroid bundle are developed. Theses structures are applied to the general relativity and provide an structure for unification of gravity and electromagnetism. The final result is a field equation on the associated algebroid bundle that is similar to Einstein field equation but contain Einstein field equation and Maxwell equations simultaneously and contain a new equation that may have new results.