Noncommutative Gravity Solutions

TL;DR

This paper reviews noncommutative gravity formulated via Drinfeld twists, focusing on abelian twist geometries and presenting solutions to noncommutative Einstein equations compatible with curved spacetime.

Contribution

It provides a detailed study of abelian twist geometries and introduces solutions to noncommutative Einstein equations aligned with curved metrics.

Findings

Analysis of abelian twist geometry

Fundamental theorem of noncommutative Riemannian geometry

Explicit solutions to noncommutative Einstein equations

Abstract

We consider noncommutative geometries obtained from a triangular Drinfeld twist and review the formulation of noncommutative gravity. A detailed study of the abelian twist geometry is presented, including the fundamental theorem of noncommutative Riemannian geometry. Inspired by [1, 2], we obtain solutions of noncommutative Einstein equations by considering twists that are compatible with the curved spacetime metric.