The effects of a minimal length on the Kerr metric

The effects of a minimal length on the Kerr metric are studied within the pseudo-complex General Relativity (pcGR), which has a minimal length parameter and also depends on a $r$-dependent metric, allowing for the accumulation of dark energy around a star. The relevant parameters are the rotational Kerr parameter $a$, the mass of a black hole, and a parameter measuring the amount of dark energy accumulated. It is found that the metric is modified by a factor, depending on $r$, resulting in a maximal acceleration. This factor shows several singularities. For small black holes, the corresponding effective potentials exhibit potential barriers, avoiding the increase of the black hole's mass. It is found that the effects of a minimal length are only of importance for very small mass black holes and vanish for macroscopic black holes.