Lorentz Invariant Vacuum Solutions in General Relativity

TL;DR

This paper classifies all Lorentz invariant vacuum solutions in general relativity, demonstrating that they correspond to space-times of constant curvature, thus providing a complete characterization of such solutions.

Contribution

It explicitly finds and proves that all Lorentz invariant vacuum solutions are space-times of constant curvature, filling a gap in the classification of Einstein's solutions.

Findings

All Lorentz invariant vacuum solutions are space-times of constant curvature.

The solutions include Minkowski, de Sitter, and anti-de Sitter spaces.

The classification is complete for Lorentz invariant vacuum solutions.

Abstract

All Lorentz invariant solutions of vacuum Einstein's equations are found. It is proved that these solutions describe space-times of constant curvature.