Degenerate spacetimes in first order gravity

TL;DR

This paper develops a systematic method to find all solutions in first order gravity with degenerate tetrads, revealing many solutions with inherent torsion and connections to Thurston's geometries.

Contribution

It introduces a comprehensive framework for solutions in first order gravity with degenerate tetrads, highlighting torsion and geometric classifications.

Findings

Many solutions exhibit non-zero torsion without matter.

Identifies eight special configurations linked to Thurston geometries.

Provides a systematic approach to classify solutions in degenerate cases.

Abstract

We present a systematic framework to obtain the most general solutions of the equations of motion in first order gravity theory with degenerate tetrads. There are many possible solutions. Generically, these exhibit non-vanishing torsion even in the absence of any matter coupling. These solutions are shown to contain a special set of eight configurations which are associated with the homogeneous model three-geometries of Thurston.