Comments on the Unification of Electromagnetism and Gravitation through "Generalized Einstein manifolds"

TL;DR

The paper critiques a recent geometric unification of electromagnetism and gravitation, clarifying that it only applies to source-free Maxwell equations and does not derive the full set of Maxwell equations.

Contribution

It provides a genuine derivation of source-free Maxwell equations within the generalized Einstein manifold framework, clarifying limitations of the previous unification scheme.

Findings

The proposed formulation only describes source-free Maxwell equations.

The original claim of unification with sources is not supported.

A correct derivation of source-free Maxwell equations is presented.

Abstract

H. Akbar-Zadeh has recently proposed (J Geom Phys 17 (1995) 342) a new geometric formulation of Einstein-Maxwell system with source in terms of what are called "Generalized Einstein manifolds". We show that, contrary to the claim, Maxwell equations have not been derived in this formulation and that, the assumed equations can be identified only as source-free Maxwell equations in the proposed geometric set up. A genuine derivation of source-free Maxwell equations is presented within the same framework. We draw a conclusion that the proposed unification scheme can pertain only to source-free situations.