Working Paper Article Version 2 This version is not peer-reviewed

Geometric Unification of Electromagnetism and Gravitation

Version 1 : Received: 2 November 2017 / Approved: 3 November 2017 / Online: 3 November 2017 (02:17:11 CET)
Version 2 : Received: 3 November 2019 / Approved: 4 November 2019 / Online: 4 November 2019 (04:04:58 CET)
Version 3 : Received: 8 August 2020 / Approved: 9 August 2020 / Online: 9 August 2020 (22:12:13 CEST)
Version 4 : Received: 24 July 2021 / Approved: 26 July 2021 / Online: 26 July 2021 (12:04:41 CEST)
Version 5 : Received: 5 December 2021 / Approved: 6 December 2021 / Online: 6 December 2021 (11:52:36 CET)
Version 6 : Received: 4 September 2022 / Approved: 6 September 2022 / Online: 6 September 2022 (04:24:39 CEST)
Version 7 : Received: 14 May 2023 / Approved: 15 May 2023 / Online: 15 May 2023 (14:37:07 CEST)
Version 8 : Received: 9 January 2024 / Approved: 11 January 2024 / Online: 12 January 2024 (09:54:40 CET)

How to cite: Beach, R. Geometric Unification of Electromagnetism and Gravitation. Preprints 2017, 2017110022 Beach, R. Geometric Unification of Electromagnetism and Gravitation. Preprints 2017, 2017110022


A recently proposed classical field theory comprised of four field equations that geometrically couple electromagnetism and gravitation in a fundamentally new way is reviewed. The cornerstone of the theory equates the derivatives of the Maxwell tensor to a vector field contracted with the Riemann-Christoffel curvature tensor. The new theory’s field equations show little resemblance to the field equations of classical physics, but both Maxwell’s equations of electromagnetism and Einstein’s equation of General Relativity augmented by a term that can mimic the properties of dark matter and dark energy are shown to be a consequence. Emphasized is the unification brought to electromagnetic and gravitational phenomena as well as the consistency of solutions of the new theory with those of the classical Maxwell and Einstein field equations. Unique to the four field equations reviewed here and based on specific solutions to them are: the emergence of antimatter and its behavior in gravitational fields, the emergence of dark matter and dark energy mimicking terms in the context of General Relativity, an underlying relationship between electromagnetic and gravitational radiation, the impossibility of negative mass solutions that would generate repulsive gravitational fields or antigravity, and a method for quantizing the charge and mass of particle-like solutions.


unified field theory; electromagnetism; Maxwell’s equations; gravitation; General Relativity; Einstein’s field equation; gravitational radiation; dark matter; dark energy; antigravity


Physical Sciences, Particle and Field Physics

Comments (1)

Comment 1
Received: 4 November 2019
Commenter: Raymond Beach
Commenter's Conflict of Interests: Author
Comment: Updated and corrected throughout.
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