This work explores a heuristic connection between modified black holes and the generalized uncertainty principle (GUP). Revisiting Bekenstein's analysis of a particle governed by the GUP and captured by a black hole with undetermined parameters, we find a class of modified Schwarzschild black holes that saturate the Bekenstein-Hawking entropy to the maximum extent. Although curvature singularities cannot yet be definitely ruled out, the modified black holes avoid complete evaporation and end up as zero-temperature remnants. The Hayward black hole is the simplest case, even though it is not the only choice.
Li et al. (Thu,) studied this question.