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It is congruous with the quantum nature of the world to view the space-timegeometry as an emergent structure that shows classical features only at someobservational level. One can thus conceive the space-time manifold as a purelytheoretical arena, where quantum states are defined, with the additionalfreedom of changing coordinates like any other symmetry. Observables, includingpositions and distances, should then be described by suitable operators actingon such quantum states. In principle, the top-down (canonical) quantisation ofEinstein-Hilbert gravity falls right into this picture, but is notoriously veryinvolved. The complication stems from allowing all the classical canonicalvariables that appear in the (presumably) fundamental action to become quantumobservables acting on the "superspace" of all metrics, regardless of whetherthey play any role in the description of a specific physical system. On caninstead revisit the more humble "minisuperspace" approach and choose thegravitational observables not simply by imposing some symmetry, but motivatedby their proven relevance in the (classical) description of a given system. Inparticular, this review focuses on compact, spherically symmetric, quantummechanical sources, in order to determine the probability they are black holesrather than regular particles. The gravitational radius is therefore lifted tothe status of a quantum mechanical operator acting on the "horizonwave-function", the latter being determined by the quantum state of the source.This formalism is then applied to several sources with a mass around thefundamental scale, which are viewed as natural candidates of quantum blackholes.

Horizon Quantum Mechanics: a hitchhiker's guide to quantum black holes