Proposed method of combining continuum mechanics with Einstein Field Equations

TL;DR

This paper introduces a novel approach combining continuum mechanics with Einstein's equations, linking electromagnetic fields, spacetime curvature, and vacuum energy to derive new solutions and force interactions.

Contribution

It proposes an amended relativistic continuum mechanics framework that relates density tensors to spacetime curvature, leading to new solutions of Einstein's Field Equations involving electromagnetic fields.

Findings

Derived a symmetric stress-energy tensor incorporating electromagnetic fields.

Established a relationship between the cosmological constant and electromagnetic invariants.

Developed transformation equations connecting curved and flat spacetimes with fields.

Abstract

The article proposes an amendment to the relativistic continuum mechanics which introduces 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 additional pulls appear, dependent on the vacuum energy contained in the system. In flat Minkowski spacetime, the vanishing four-divergence of the proposed 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.