Preprint Article Version 5 Preserved in Portico This version is not peer-reviewed

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


A recently proposed classical field theory in which Maxwell’s equations are replaced by an equation that couples the Maxwell tensor to the Riemann-Christoffel curvature tensor in a fundamentally new way is reviewed and extended. This proposed geometrization of the Maxwell tensor provides a succinct framework for the classical Maxwell equations which are left intact as a derivable consequence. Beyond providing a basis for the classical Maxwell equations, the coupling of the Riemann-Christoffel curvature tensor to the Maxwell tensor leads to the emergence of gravity, with all solutions of the proposed theory also being solutions of Einstein’s equation of General Relativity augmented by a term that can mimic the properties of dark matter and/or dark energy. Both electromagnetic and gravitational phenomena are put an equal footing with both being tied to the curvature of space-time. Using specific solutions to the proposed theory, the unification brought to electromagnetic and gravitational phenomena as well as the consistency of solutions with those of the classical Maxwell and Einstein field equations is emphasized throughout. Unique to the proposed theory and based on specific solutions 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, and the impossibility of negative mass solutions that would generate repulsive gravitational fields or antigravity. Finally, a method for quantizing the charge, mass, and angular momentum of particle-like solutions as well as the possibility of superluminal transport of specific curvature related quantities is conjectured.


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


Physical Sciences, Space Science

Comments (1)

Comment 1
Received: 6 December 2021
Commenter: Raymond Beach
Commenter's Conflict of Interests: Author
Comment: The manuscript has been reorganized and the fundamental equations reduced by 1. Maxwell’s inhomogeneous equation that was previously listed as one of the fundamental equations is now shown to be a consequence of equation 1 under appropriate restrictions as discussed in section 2.1 of the reworked manuscript. The discussion given in section 5 has been expanded and reorganized with much of the discussion that was previously in the conclusion, now relocated to the discussion in section 5.  Finally, specific curvature dependent quantities are identified as being conserved and transported with superluminal velocities as detailed in section 5.7.  Note that the title of the manuscript has been shortened.
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