Derivation of generalized Einstein's equations of gravitation in inertial systems based on a sink flow model of particles

TL;DR

This paper generalizes Einstein's equations using a sink flow model of particles within a relativistic fluidic aether, deriving equations that reduce to Einstein's in weak fields, thus proposing a novel physical foundation for gravitation.

Contribution

It introduces a new derivation of Einstein's equations based on a mechanical model of vacuum and sink flow particles within special relativistic continuum mechanics.

Findings

Derived generalized Einstein's equations in inertial systems.

Showed reduction to Einstein's equations in weak field limits.

Established a tensorial potential satisfying wave equations.

Abstract

J. C. Maxwell, B. Riemann and H. Poincar$\acute{e}$ have proposed the idea that all microscopic particles are sink flows in a fluidic aether. Following this research program, a previous theory of gravitation based on a mechanical model of vacuum and a sink flow model of particles is generalized by methods of special relativistic continuum mechanics. In inertial coordinate systems, we construct a tensorial potential which satisfies the wave equations. Inspired by the equations of motion of a test particle, a definition of a metric tensor of a Riemannian spacetime is introduced. Applying Fock's theorem, generalized Einstein's equations in inertial systems are derived based on some assumptions. These equations reduce to Einstein's equations in case of weak field in harmonic coordinate systems.