The Geometric Gravitational Internal Problem

TL;DR

This paper presents a geometric unified theory that derives Einstein's equations with a cosmological constant and a generalized form for non-empty space, aligning with standard tests and Newtonian limits.

Contribution

It introduces a geometric energy momentum equation that extends Einstein's equations to non-empty space within a unified framework.

Findings

Matching exterior solution agrees with standard relativity tests

Derives Einstein's equations with cosmological constant from geometric principles

Obtains Newtonian limit consistent with Poisson's equation

Abstract

In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for empty space. For non empty space we obtain a generalized Einstein equation, relating the Einstein tensor to a geometric stress energy tensor. The matching exterior solution is in agreement with the standard relativity tests. Furthermore, there is a Newtonian limit where we obtain Poisson's equation.