Proposed Method of Combining Continuum Mechanics With Einstein Field Equations

Piotr Ogonowski

doi:10.20944/preprints202206.0221.v7

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preprints.org > physical sciences > particle and field physics > doi: 10.20944/preprints202206.0221.v7

Preprint Article Version 7 Preserved in Portico This version is not peer-reviewed

Proposed Method of Combining Continuum Mechanics With Einstein Field Equations

Piotr Ogonowski

Version 1 : Received: 14 June 2022 / Approved: 15 June 2022 / Online: 15 June 2022 (10:16:18 CEST)
Version 2 : Received: 27 June 2022 / Approved: 27 June 2022 / Online: 27 June 2022 (14:30:11 CEST)
Version 3 : Received: 30 June 2022 / Approved: 1 July 2022 / Online: 1 July 2022 (12:37:08 CEST)
Version 4 : Received: 11 July 2022 / Approved: 11 July 2022 / Online: 11 July 2022 (09:41:10 CEST)
Version 5 : Received: 17 July 2022 / Approved: 18 July 2022 / Online: 18 July 2022 (10:56:25 CEST)
Version 6 : Received: 14 August 2022 / Approved: 16 August 2022 / Online: 16 August 2022 (05:24:45 CEST)
Version 7 : Received: 15 September 2022 / Approved: 16 September 2022 / Online: 16 September 2022 (07:11:49 CEST)
Version 8 : Received: 3 November 2022 / Approved: 3 November 2022 / Online: 3 November 2022 (07:03:12 CET)
Version 9 : Received: 28 November 2022 / Approved: 29 November 2022 / Online: 29 November 2022 (03:59:30 CET)
Version 10 : Received: 15 December 2022 / Approved: 16 December 2022 / Online: 16 December 2022 (04:30:07 CET)

A peer-reviewed article of this Preprint also exists.

Ogonowski, P. Proposed Method of Combining Continuum Mechanics with Einstein Field Equations. International Journal of Modern Physics D 2023, doi:10.1142/s0218271823500104. Ogonowski, P. Proposed Method of Combining Continuum Mechanics with Einstein Field Equations. International Journal of Modern Physics D 2023, doi:10.1142/s0218271823500104.

Abstract

The article proposes an amendment to the relativistic continuum mechanics which introduce the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress-energy tensor for a system with an electromagnetic field, leads to the solution of Einstein Field Equations indicating a relationship between the electromagnetic field tensor and the metric tensor. In this EFE solution, the cosmological constant is related to the invariant of the electromagnetic field tensor, and an additional gravitational pull appears, dependent on the velocity of orbiting bodies and the vacuum energy contained in the system. In flat Minkowski spacetime, the vanishing four-divergence of this stress-energy tensor expresses relativistic Cauchy's momentum equation, leading to the emergence of force densities which can be developed and parameterized to obtain known interactions. Transformation equations were also obtained between spacetime with fields and forces, and a curved spacetime reproducing the motion resulting from the fields under consideration, which allows for the extension of the solution with new fields.

Keywords

general relativity; cosmology; continuum mechanics; fluid dynamics; field theory; electrodynamics; Hamiltonian mechanics

Subject

Physical Sciences, Particle and Field Physics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Comments (1)

Comment 1

Received: 16 September 2022
Commenter: Piotr Ogonowski
Commenter's Conflict of Interests: Author

Comment: Article after revision in the journal. Editorial changes have been added and a proof that h is a metric tensor has been supplemented.

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