Working Paper Article Version 4 This version is not peer-reviewed

The Geometrization of Maxwell’s Homogenous Equation and the Emergence of Gravity

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. The Geometrization of Maxwell’s Homogenous Equation and the Emergence of Gravity. Preprints 2017, 2017110022 Beach, R. The Geometrization of Maxwell’s Homogenous Equation and the Emergence of Gravity. Preprints 2017, 2017110022


A recently proposed classical field theory in which the Maxwell tensor is coupled to the Riemann-Christoffel curvature tensor in a fundamentally new way is reviewed and extended. This proposed geometrization of the Maxwell tensor leaves the classical equations of electromagnetism unchanged, but also leads to the emergence of gravity as all solutions of the proposed field equations are shown to be solutions of Einstein’s equation of General Relativity augmented by a term that can mimic the properties of dark matter and/or dark energy. Using specific solutions to the proposed theory, the unification brought to electromagnetic and gravitational phenomena as well as the consistency of those solutions with those of the classical Maxwell and Einstein field equations are emphasized throughout. Unique to the four fundamental field equations that comprise the proposed theory, 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.


Maxwell’s equations; General Relativity; unification of electromagnetism and gravitation; dark matter and dark energy; electromagnetic and gravitational radiation; antimatter; antigravity; quantization


Physical Sciences, Space Science

Comments (1)

Comment 1
Received: 26 July 2021
Commenter: Raymond Beach
Commenter's Conflict of Interests: Author
Comment: I've recast the description of the fundamental field equations (1) - (4) as a geometricized version of classical electromagnetism and updated the manuscript thoughout accordingly.  Also, note that I have updated the tile from, "Geometric Unification of Electromagnetism and Gravitation" to "The Geometrization of Maxwell’s Homogenous Equation and the Emergence of Gravity".
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