Affine Metrics: An Structure for Unification of Gravitation and Electromagnetism

This paper is mainly intended to define a mathematical framework for unification of gravity and electromagnetism. The main idea is that affine concepts replace linear concepts in the context of general relativity. First, we introduce affine metrics on affine spaces,and then generalize semi-Riemannian manifolds to affine semi-Riemannian manifolds and investigate their associated connections and geodesics and curvatures. Then we apply these concepts to space-times in order to combine Maxwell’s and Einstein’s field equations into one equation.