Diffeomorphism covariant star products and noncommutative gravity

TL;DR

This paper develops a diffeomorphism covariant star product to create noncommutative gravity models on symplectic manifolds, successfully constructing deformations of 2D dilaton gravity and identifying an integrable model with known solutions.

Contribution

It introduces a covariant star product approach that preserves diffeomorphism invariance in noncommutative gravity, overcoming previous limitations and enabling explicit solutions.

Findings

Constructed noncommutative deformations of 2D dilaton gravity models.

Identified an integrable noncommutative gravity model.

Derived all classical solutions and analyzed their properties.

Abstract

The use of a diffeomorphism covariant star product enables us to construct diffeomorphism invariant gravities on noncommutative symplectic manifolds without twisting the symmetries. As an example, we construct noncommutative deformations of all two-dimensional dilaton gravity models thus overcoming some difficulties of earlier approaches. One of such models appears to be integrable. We find all classical solutions of this model and discuss their properties.