Geodesics motion in fuzzy black hole space-times

Classical General Relativity predicts the existence of space-times with non-trivial casual structures known as Black Holes. A classical black hole could form by the gravitational collapse of a compact object, which should end into a singularity covered by a (sharply defined) horizon, with a size equal to the gravitational radius of the matter source. In a quantum theory, the matter source is described by a quantum state, and one can correspondingly describe its gravitational radius by means of a Horizon Wave-Function. The resulting space-time is therefore expected to be "fuzzy", and so will be the geodesic motion of test particles. Orbits of massive particles as well as trajectories of light rays around such fuzzy gravitational sources are here analysed in details using both analytical approximations and numerical calculations. The uncertainty in the time of radial free fall and the effects on the out-going radiation emitted by the collapsing matter will also be presented.