Derivation of generalized Einstein's equations of gravitation in some non-inertial reference frames based on the theory of vacuum mechanics

TL;DR

This paper derives generalized Einstein's equations in certain non-inertial frames using vacuum mechanics, reducing to Einstein's equations under weak field and quasi-inertial conditions, and aligns with experimental results supporting general relativity.

Contribution

It introduces a novel derivation of Einstein's equations in non-inertial frames based on vacuum mechanics, expanding the theoretical framework beyond standard general relativity.

Findings

Generalized Einstein's equations are derived for specific non-inertial frames.

Under weak fields, these equations reduce to standard Einstein's equations.

The theory aligns with experiments supporting general relativity.

Abstract

When solving the Einstein's equations for an isolated system of masses, V. Fock introduces harmonic reference frame and obtains an unambiguous solution. Further, he concludes that there exists a harmonic reference frame which is determined uniquely apart from a Lorentz transformation if suitable supplementary conditions are imposed. It is known that wave equations keep the same form under Lorentz transformations. Thus, we speculate that Fock's special harmonic reference frames may have provided us a clue to derive the Einstein's equations in some special class of non-inertial reference frames. Following this clue, generalized Einstein's equations in some special non-inertial reference frames are derived based on the theory of vacuum mechanics. If the field is weak and the reference frame is quasi-inertial, these generalized Einstein's equations reduce to Einstein's equations. Thus, this theory may also explain all the experiments which support the theory of general relativity. There exist some differences between this theory and the theory of general relativity.