A comparison of remnants in noncommutative Bardeen black holes

Abstract

We derive the mass term of the Bardeen metric in the presence of a noncommutative geometry induced minimal length. In this setup, the proposal of a stable black hole remnant as a candidate to store information is confirmed. We consider the possibility of having an extremal configuration with one degenerate event horizon and compare different sizes of black hole remnants. As a result, once the magnetic charge $g$ of the noncommutative Bardeen solution becomes larger, both the minimal nonzero mass $M_{0}$ and the minimal nonzero horizon radius $r_{0}$ get larger. This means, subsequently, under the condition of an adequate amount of $g$, the three parameters $g$, $M_{0}$, and $r_{0}$ are in a connection with each other linearly. According to our results, a noncommutative Bardeen black hole is colder than the noncommutative Schwarzschild black hole and its remnant is bigger, so the minimum required energy for the formation of such a black hole at particle colliders will be larger. We also find a closely similar result for the Hayward solution.