Model of a solar system in the conservative geometry

TL;DR

This paper explores a conservative geometry-based model of the solar system, proposing solutions that align with general relativity parameters but differ in Einstein tensor properties, suggesting potential for experimental validation.

Contribution

It introduces a new geometric framework extending general relativity with solutions compatible with solar system observations and predicts small deviations in Einstein tensor components.

Findings

Models with free-field solutions are inadequate for the Solar System.

Standard Schwarzschild metric is incompatible with the new theory.

Solutions with sources match PPN parameters, approximating Schwarzschild.

Abstract

Pandres has shown that an enlargement of the covariance group to the group of conservative transformations leads to a richer geometry than that of general relativity. Using orthonormal tetrads as field variables, the fundamental geometric object is the curvature vector denoted by $C_\mu$. From an appropriate scalar Lagrangian field equations for both free-field and the field with sources have been developed. We first review models which use a free-field solution to model the Solar System and why these results are unacceptable. We also show that the standard Schwarzschild metric is also unacceptable in our theory. Finally we show that there are solutions which involve sources which agree with general relativity PPN parameters and thus approximate the Schwarzschild solution. The main difference is that the Einstein tensor is not identically zero but includes small values for the density, radial pressure and tangential pressure. Higher precision experiments should be able to determine the validity of these models. These results add further confirmation that the theory developed by Pandres is the fundamental theory of physics.