Horizons and the Wave Function of Planckian Quantum black holes

Abstract

At the Planck scale the distinction between elementary particles and black holes becomes fuzzy. The very definition of a "quantum black hole" (QBH) is an open issue. Starting from the idea that, at the Planck scale, the radius of the event horizon undergoes quantum oscillations, we introduce a black hole mass-radius Generalized Uncertainty Principle (GUP) and derive a corresponding gravitational wavelength. Next we recover a GUP encoding effective geometry. This semi-classical gravitational description admits black hole configurations only for masses higher than the Planck mass. Quantum corrections lead to a vanishing Hawking temperature when the Planck mass is approached from above. Finally we replace our semi-classical model by a relativistic wave equation for the " horizon wave function ". The solution admits a discrete mass spectrum which is bounded from below by a stable ground state with energy close to the Planck mass. Interestingly higher angular momentum states fit onto Regge trajectories indicating their stringy nature.

Bubbles Nucleation from a de Sitter-Planck background with Quantum Boltzmann Statistics

“…Carr's model suggests that a subtle and strict link exists between microphysics of elementary particles and macroscopic regime of black holes, in other words that all black holes are in some sense quantum and elementary particles can be seen as sub-Planckian black holes. Moreover, Carr's original idea has been developed by Spallucci and Smailagic [17], who have introduced a general, physically compelling criterion in order to distinguish between a quantum particle and a quantum black hole, in terms of the ratio of the Compton wavelength and the gravitational radius, in the sense that when their ratio is close to one we are in a genuine quantum gravity regime and the geometric, static Schwarzschild horizon does not provide a satisfactory description of a quantum black hole. These two authors have introduced a Generalized Uncertainty Principle between the mass of the quantum black hole and its horizon which leads to an "effective" Schwarzschild likegeometry with quantum gravity correction to the Newtonian potential, that nonetheless implies that a quantum black hole can exist only above the Planck mass.…”