Quantum statistics and noncommutative black holes

Abstract

We study the behaviour of a scalar field coupled to a noncommutative black hole which is described by a $\kappa$-cylinder Hopf algebra. We introduce a new class of realizations of this algebra which has a smooth limit as the deformation parameter vanishes. The twisted flip operator is independent of the choice of realization within this class. We demonstrate that the $R$-matrix is quasi-triangular up to the first order in the deformation parameter. Our results indicate how a scalar field might behave in the vicinity of a black hole at the Planck scale.