A q-deformed Version of the Heavenly Equations

TL;DR

This paper introduces a $q$-deformed algebraic framework to extend the Heavenly equations and explores its implications for self-dual gravity in a deformed setting.

Contribution

It presents a novel $q$-deformed version of the Heavenly equations based on a $q$-deformed Moyal algebra linked to area-preserving diffeomorphisms.

Findings

Formulation of a $q$-deformed Heavenly equations

Discussion of the $q$-deformed self-dual gravity

Potential implications for quantum gravity models

Abstract

Using a $q$-deformed Moyal algebra associated with the group of area preserving diffeomorphisms of th two-dimensional torus $T^2$, sdiff$_q (T^2)$, a $q$-deformed version for the Heavenly equations is given. Finally, the two-dimensional chiral version of Self-dual gravity in this $q$-deformed context is briefly discussed.