The G Gravitational Parameter and the Concepts of Mass and Dark Matter

TL;DR

This paper proposes a geometric unified theory where the gravitational constant G is derived from a non-Riemannian curvature scalar of a background substratum, linking mass, dark matter effects, and gravitational interactions.

Contribution

It introduces a new geometric framework where G varies with matter-energy content, providing a novel explanation for dark matter effects and connecting macroscopic and microscopic mass scales.

Findings

The gravitational constant G is derived from a curvature scalar of a background substratum.

The theory suggests G can vary depending on matter-energy distribution, affecting gravitational interactions.

Dark matter effects are interpreted as geometric consequences of the substratum structure.

Abstract

The gravitational coupling parameter G is determined by a non riemannian curvature scalar of a background substratum. This substratum represents an inertial solution to the nonlinear equations of a geometric unified theory and provides a limit solution to general solutions in the theory. When a solution approaches the substratum solution as a limit we physically obtain a newtonian limit of the gravitational sector of the unified theory. The curvature scalar is determined by the interaction mass-energy content of the solution. In the limit the equation reduces to Poisson equation and the curvature scalar reduces to the constant substratum curvature scalar which determines Newton gravitational constant G. Outside the limit the curvature parameter replaces the newtonian constant G as the coupling parameter of Einstein equation of gravitation. This new parameter may be approximately constant in certain physical conditions but, in general should be considered a variable which depends on the matter and energy on space-time. This effect and the geometric structure of matter and fields may be interpreted as dark matter effects. The substratum also determines a constant mass parameter for field excitations which obey the Dirac equation and behave as particles. Physically we consider that the substratum provides two related mass scales: the gravitational constant G characterizes a macroscopic mass scale and a fundamental particle mass m characterizes a microscopic mass scale. The substratum geometrically represents the physical concept of inertial system.