Buraco negro BTZ em teoria de campos não-comutativa.

Abstract

In this work we use the Langragian of the Higgs Abelian model in terms of the noncommutative fields and through the Seiberg-Witten map we expand the fields in terms of the commutative ones, we derive the equations of motion referring to this model operating through a variational method. We work with this model using the non-commutative BTZ black hole and thus obtain the equations of motion, where a coordinate substitution was made in order to simplify the equation. We study the scattering process working with a Schr¨odinger-type equation, in which we take a specific case, we chose to work here using the BTZ metric of the non-commutative and non-rotating case. We calculate the gray body factor for this case where we obtain a dependence with the angular frequency ω.