Global and local horizon quantum mechanics

Abstract

Horizons are classical causal structures that arise in systems with sharply defined energy and corresponding gravitational radius. A global gravitational radius operator can be introduced for a static and spherically symmetric quantum mechanical matter state by lifting the classical "Hamiltonian" constraint that relates the gravitational radius to the ADM mass, thus giving rise to a "horizon wave-function". This minisuperspace-like formalism is shown here to be able to consistently describe also the local gravitational radius related to the Misner-Sharp mass function of the quantum source, provided its energy spectrum is determined by spatially localised modes.

Horizon quantum mechanics of rotating black holes

“…We start from reviewing the basics of the (global) HQM for static spherically symmetric sources [1][2][3][4][5][6][7][8], and then extend this formalism to rotating systems by means of the Kerr relation for the horizon radii in terms of the asymptotic mass and angular momentum of the space-time. In particular, we shall rely on the results for the "global" case of Ref.…”

“…The formalism dubbed horizon quantum mechanics (HQM) [1][2][3][4][5][6][7][8], was initially proposed with the purpose of describing the gravitational radius of spherically symmetric compact sources and determining the existence of a horizon in a quantum mechanical fashion. It therefore appears as a natural continuation in this research direction to extend the HQM to rotating sources.…”

“…The latter surfaces are proper horizons in a timeindependent configuration, which is the case we shall always a e-mail: casadio@bo.infn.it b e-mail: A.Giugno@physik.uni-muenchen.de c e-mail: andrea.giusti@bo.infn.it d e-mail: octavian.micu@spacescience.ro consider here. It is therefore rather straightforward to uplift this description of the causal structure of space-time to the quantum level by simply imposing the relation between the gravitational radius and the Misner-Sharp mass as an operatorial constraint to be satisfied by the physical states of the system [3].…”

Horizon quantum fuzziness for non-singular black holes

“…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.…”

“…The purpose of this paper is to analyse some semiclassical aspects of the Hayward spacetime by means of the horizon quantum mechanics formalism [9][10][11], while working within the framework of the corpuscular model for quantum black holes [12][13][14][15].…”