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We study a noncommutative (NC) deformation of a charged scalar field,minimally coupled to a classical (commutative) Reissner Nordstrom likebackground. The deformation is performed via a particularly chosen Killingtwist to ensure that the geometry remains undeformed (commutative). An actiondescribing a NC scalar field minimally coupled to the RN geometry is manifestlyinvariant under the deformed U(1) gauge symmetry. We find the equation ofmotion and conclude that the same equation is obtained from the commutativetheory in a modified geometrical background described by an effective metric.This correspondence we call duality between formal and effective approach. Wealso show that a NC deformation via semi Killing twist operator cannot berewriten in terms of an effective metric. There is a dual description for thoseparticular deformations.

Noncommutative scalar field theory in a curved background: duality between noncommutative and effective commutative description