Noncommutative information is revealed from the static detector outside the black hole

Abstract

We investigate the transition behavior of the two-level atom as the Unruh-DeWitt detector outside a noncommutative black hole. When the mass of the black hole is small enough, the difference between the commutative and noncommutative black hole can be distinguished. In particular, an evident fluctuation appearing at a far distance from the horizon by calculating the quantum Fisher information of the transition rate with regard to the local Hawking temperature provides a novel and interesting result about the information extraction of the noncommutativity for a small-mass black hole.