Gauge and Einstein gravity from non-abelian gauge models on noncommutative spaces

Following the formalism of enveloping algebras and star product calculus we formulate and analyze a model of gauge gravity on noncommutative spaces and examine the conditions of its equivalence to the general relativity theory. The corresponding Seiberg–Witten maps are established which allow the definition of respective dynamics for a finite number of gravitational gauge field components on noncommutative spaces.