Lie algebraic Noncommutative Gravity

TL;DR

This paper develops a formulation of gravity on Lie algebraic noncommutative spacetime using the Seiberg--Witten map, revealing no first-order corrections despite the generalized noncommutative structure.

Contribution

It provides explicit Seiberg--Witten maps for gauge parameters, potentials, and field strengths in Lie algebraic noncommutative gravity, extending previous canonical models.

Findings

No first-order correction in noncommutative gravity with Lie algebraic structure

Explicit expressions for Seiberg--Witten maps derived

Generalized noncommutative structure does not alter first-order classical results

Abstract

We exploit the Seiberg -- Witten map technique to formulate the theory of gravity defined on a Lie algebraic noncommutative space time. Detailed expressions of the Seiberg -- Witten maps for the gauge parameters, gauge potentials and the field strengths have been worked out. Our results demonstrate that notwithstanding the introduction of more general noncommutative structure there is no first order correction, exactly as happens for a canonical (i.e. constant) noncommutativity.