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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.
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.
Received:
11 July 2022
Commenter:
Piotr Ogonowski
Commenter's Conflict of Interests:
Author
Comment:
The explicit calculation of the gravitational force was supplemented and bibliographic entries were added. The "4. Conclusions" section was also expanded, demonstrating the possibility of using the obtained equations to analyze such phenomena as Dark Matter, Dark Energy, Inflation phase, Hubble constant tension and others.
Commenter: Piotr Ogonowski
Commenter's Conflict of Interests: Author