Horizon quantum mechanics of rotating black holes

Abstract

The horizon quantum mechanics is an approach that was previously introduced in order to analyze the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. In this work, we first extend the formalism to general spacetimes with asymptotic (ADM) mass and angular momentum. We then apply the extended horizon quantum mechanics to a harmonic model of rotating corpuscular black holes. We find that simple configurations of this model naturally suppress the appearance of the inner horizon and seem to disfavor extremal (macroscopic) geometries.

Orbits in a stochastic Schwarzschild geometry

“…In this work we started to consider in detail the effects of uncertainties in the determination of the black hole mass on geodesics, mainly motivated by studies of quantum aspects of black holes [23][24][25][26][27]. In particular, we analysed the consequences of a randomly distributed mass on qualitatively different orbits and we were interested in the possible differences between such effects and those simply stemming from the experimental uncertainties in the measurements of masses and positions.…”

“…For example, the Horizon Quantum Mechanics [23][24][25][26] offers an alternative perspective to the semiclassical approach to gravity, whose aim is to put under the spotlight the quantum features of a black hole's geometric structure inherited by a purely quantum mechanical description of its source. In this regard, the location of trapping surfaces becomes fuzzy because of the quantum mechanical nature of the source, thus providing a clear motivation for the study presented here.…”

Horizon quantum fuzziness for non-singular black holes

“…In this section, we shall introduce the reader to some general aspects of the horizon quantum mechanics (HQM), according to its most recent updates [16][17][18][19][20][21][22]. If one envisages the source of the gravitational field as a purely quantum object under this perspective, then one can faithfully picture both the ADM mass and the gravitational radius as quantum variables in return.…”

“…In this framework [11,21,22], we depict the wave-function of the whole system | ∈ H as an entangled state among |E α and the eigenstates of the gravitational radius operators acting on H G , i.e.…”

“…Although approximating the binding potential with a square well leads to interesting results [34], a more appropriate approximation for such a potential is provided by the harmonic black hole model [21,35], for which we have that V (r ) = V 0 (r ) (λ μ − r ), where…”