Thurston Geometries in Three-Dimensional New Massive Gravity

TL;DR

This paper demonstrates that all Thurston geometries in three dimensions are solutions to the equations of motion in 3D new massive gravity, including their Lorentzian versions.

Contribution

It establishes a connection between Thurston geometries and solutions in 3D new massive gravity, expanding understanding of possible vacuum solutions.

Findings

Thurston geometries are vacuum solutions in 3D new massive gravity.

Lorentzian counterparts of these geometries are also solutions.

Provides a classification of geometries within this gravity theory.

Abstract

We show that the three-dimensional Thurston geometries are vacuum solutions to the 3D new massive gravity equations of motion. We analyze their Lorentzian counterparts as well.