Noncommutative QFT and Relative Entropy on Axisymmetric Bifurcate Killing Horizons

We construct a deformed algebraic quantum field theory on bifurcate Killing horizons in stationary axisymmetric spacetimes. The deformation is generated by the commuting actions of affine dilations along the null generators of the horizon and rotations about the axis of symmetry, analogously to the Moyal-Rieffel deformation. Physically, this effectively implements a noncommutative geometric structure of the horizon. Moreover, we compute the relative entropy between coherent states in the deformed horizon theory, which remains strictly positive and exhibits a novel second-order correction in the deformation parameter, which becomes particularly significant for black holes whose horizon area is sufficiently small for Planck-scale effects to become non-negligible.