Noncommutative Solitons of Gravity

TL;DR

This paper explores noncommutative three-dimensional gravity, discovering various non-perturbative solutions such as spacetime bubbles and dimensional reductions, which could provide insights into quantum gravity.

Contribution

It introduces new non-perturbative solutions in noncommutative gravity, including spacetime bubbles and interpolating metrics, expanding understanding of noncommutative gravitational models.

Findings

Found nontrivial noncommutative gravity solutions

Identified solutions as spacetime bubbles and dimensional reductions

Solutions are non-perturbative in the noncommutative parameter 

Abstract

We investigate a three-dimensional gravitational theory on a noncommutative space which has a cosmological constant term only. We found various kinds of nontrivial solutions, by applying a similar technique which was used to seek noncommutative solitons in noncommutative scalar field theories. Some of those solutions correspond to bubbles of spacetimes, or represent dimensional reduction. The solution which interpolates $G_{\mu\nu}=0$ and Minkowski metric is also found. All solutions we obtained are non-perturbative in the noncommutative parameter $\theta$, therefore they are different from solutions found in other contexts of noncommutative theory of gravity and would have a close relation to quantum gravity.