Dynamics of empty homogeneous isotropic three-dimensional spaces

TL;DR

This paper classifies seven distinct solution types within general relativity that describe the possible dynamics of empty, homogeneous, isotropic three-dimensional spaces, highlighting their relevance in the limit of negligible matter influence.

Contribution

It identifies and characterizes seven solution types of the Einstein equations for empty homogeneous isotropic spaces, clarifying their behavior when matter effects are minimal.

Findings

Seven types of solutions for empty homogeneous isotropic spaces are identified.

Solutions converge to specific types as matter influence diminishes.

Provides a comprehensive classification within general relativity theory.

Abstract

It is shown that there are seven types of solutions described in the framework of general relativity theory (GRT), the dynamics of empty homogeneous isotropic three-dimensional spaces. Solution of the equations of GRT, which describes the dynamics of a homogeneous isotropic universe, in the limiting case of vanishingly small effect of matter on the metric properties of space must go to one of them.