Localised particles and fuzzy horizons: A tool for probing Quantum Black Holes

The horizon is a classical concept that arises in general relativity, and is therefore not clearly defined when the source cannot be reliably described by classical physics. To any (sufficiently) localised quantum mechanical wave-function, one can associate a horizon wave-function which yields the probability of finding a horizon of given radius centred around the source. We can then associate to each quantum particle a probability that it is a black hole, and the existence of a minimum black hole mass follows naturally, which agrees with the one obtained from the hoop conjecture and the Heisenberg uncertainty principle.