New solutions in pure gravity with degenerate tetrads

TL;DR

This paper introduces a new class of degenerate tetrad solutions in pure gravity, characterized by non-invertible tetrads with zero eigenvalues, expanding the landscape of possible geometries in first order gravity formulations.

Contribution

It discovers and classifies a novel set of degenerate solutions in pure gravity with non-zero torsion, characterized by specific eigenvalue degeneracies.

Findings

Identifies solutions with non-invertible tetrads and non-vanishing torsion.

Classifies solutions based on fundamental geometries E^2, S^2, and H^2.

Provides a geometric framework for degenerate four-geometries.

Abstract

In first order formulation of pure gravity, we find a new class of solutions to the equations of motion represented by degenerate four-geometries. These configurations are described by non- invertible tetrads with two zero eigenvalues and admit non-vanishing torsion. The homogeneous ones among these infinitely many degenerate solutions admit a geometric classification provided by the three fundamental geometries that a closed two-surface can accomodate, namely, E^2 , S^2 and H^2.