Quantum statistics and noncommutative black holes

TL;DR

This paper investigates the behavior of scalar fields near noncommutative black holes modeled by a $$-cylinder Hopf algebra, revealing new realizations and properties of the algebra that influence quantum field dynamics at the Planck scale.

Contribution

Introduces a new class of realizations of the $$-cylinder Hopf algebra with a smooth deformation limit and analyzes the properties of the $R$-matrix and twisted flip operator.

Findings

The new realizations have a smooth limit as deformation vanishes.

The twisted flip operator is realization-independent within this class.

The $R$-matrix is quasi-triangular up to first order in deformation.

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.