A possible Reinterpretation of Einstein's Equations

TL;DR

This paper revisits Einstein's equations, reformulating them to resemble Maxwell's equations and proposing a new interpretation that links gravity and electromagnetism through an extended equivalence principle.

Contribution

It introduces a modified formulation of Einstein's equations that aligns with Maxwell's equations and proposes a novel interpretation connecting gravity and electromagnetism.

Findings

Reformulation of Einstein's equations akin to Maxwell's equations

Elimination of scalar potential and Lorentz force restrictions

Derivation of Maxwell equations from Einstein's equations

Abstract

In this paper, we first review Huei's formulation in which it is shown that the linearized Einstein equations can be written in the same form as the Maxwell equations. We eliminate some imperfections like the scalar potential which is ill linked to the electric-type field, the Lorentz-type force which is obtained with a time independence restriction and the undesired factor 4 which appears in the magnetic-type part. Second, from these results and in the light of a recent work by C.C. Barros, we propose an extension of the equivalence principle and we suggest a new interpretation for Einstein's equations by showing that the electromagnetic Maxwell equations can be derived from a new version of Einstein's ones.