Tensor Potential Description of Matter and Space, III. Gravitation

TL;DR

This paper introduces a non-geometrical theory of gravitation based on a vector field and a tensor potential, proposing that space is materialized by matter and deriving new gravitational equations with solutions for spherical symmetry.

Contribution

It presents a novel non-geometrical gravitation theory using a tensor potential and vector field, differing from Einstein's equations and emphasizing matter's primacy.

Findings

Derived new gravitational equations from a matter-centric theory.

Obtained an exact Schwarzschild-like solution for spherical symmetry.

Discussed the existence of gravitational waves within linear approximation.

Abstract

A non-geometrical (but with curved space) theory of gravitation characterized by a vector field representing gravitational matter and a metric tensor presenting space is presented. It is derived from a more general theory of matter and space in which matter, described by a 3-index tensor potential, is the prime entity and space is deducible and cannot exist without matter. Philosophically, instead of geometrization of physics, the new theory advances an idea of materialization of space. The equations that govern the theory of gravitation are deduced from the equations of main theory and have a completely different form as compared to Einstein's equations of General Relativity. An exact solution for spherical symmetry of a point mass with a Schwarzschild type metric tensor is obtained. The subject of gravitational waves and cosmology is discussed. It is shown that gravitational waves can exist within linear approximation. In this case, the metrics tensor varies only in time domain while remaining Euclideanly flat in spatial components.