Preprint Article Version 6 Preserved in Portico This version is not peer-reviewed

Proposed Method of Combining Continuum Mechanics With Einstein Field Equations

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)

How to cite: Ogonowski, P. Proposed Method of Combining Continuum Mechanics With Einstein Field Equations. Preprints 2022, 2022060221 (doi: 10.20944/preprints202206.0221.v6). Ogonowski, P. Proposed Method of Combining Continuum Mechanics With Einstein Field Equations. Preprints 2022, 2022060221 (doi: 10.20944/preprints202206.0221.v6).

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, General & Theoretical Physics

Comments (1)

Comment 1
Received: 16 August 2022
Commenter: Piotr Ogonowski
Commenter's Conflict of Interests: Author
Comment: Corrected equation (3.23) added. The equations in section "4. Conclusions" have been corrected to include this amendment.
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