Quantum properties of coherent black holes

The corpuscular model describes black holes as leaky bound states of gravitons.To account for the role of matter, an improved description of nonuniform geometries can be obtained by employing coherent states of gravitons, which recovers the Newtonian potential (with necessary departures) from a coherent state for a scalar field of gravitons in flat spacetime. Given that the majority of black holes in nature are very likely to spin, we study the quantum hair associated with coherent states describing slowly rotating black holes and show how it can be naturally related with the Bekenstein-Hawking entropy and with 1-loop quantum corrections of the metric for the (effectively) non-rotating case.We also estimate corrections induced by such quantum hair to the temperature of the Hawking radiation through the tunnelling method. We then provide a concise review of the key features of the horizon quantum mechanics formalism.This formalism is then applied to electrically neutral and spherically symmetric black hole geometries emerging from coherent quantum states of gravity to compute the probability that the matter source is inside the horizon.We find that quantum corrections to the classical horizon radius become significant if the matter core has a size comparable to the Compton length of the constituents and the system is indeed a black hole with probability very close to one unless the core radius is close to the (classical) gravitational radius.