Minimum Length Effects in Black Hole Physics

Abstract

We review the main consequences of the possible existence of a minimum measurable length, of the order of the Planck scale, on quantum effects occurring in black hole physics. In particular, we focus on the ensuing minimum mass for black holes and how modified dispersion relations affect the Hawking decay, both in four space-time dimensions and in models with extra spatial dimensions. In the latter case, we briefly discuss possible phenomenological signatures. Gravity and minimum lengthPhysics is characterized by a variety of research fields and diversified tools of investigation that strongly depend on the length scales under consideration. As a result, one finds an array of sub-disciplines, spanning from cosmology, to astrophysics, geophysics, molecular and atomic physics, nuclear and particle physics. In a nutshell, we can say that Physics concerns events occurring at scales between the radius of the Universe and the typical size of observed elementary particles. It is not hard to understand that such a rich array of physical phenomena requires specific formalisms. For instance, at macroscopic scales, models of the Universe are obtained in terms of general relativity, while at microscopic scales quantum physics has been proven to be the adequate theory for the miniaturised world.

Horizon quantum fuzziness for non-singular black holes

“…as in Refs. [9,10]. Unfortunately, it is indeed impossible to replicate this machinery in any multi-particle model without requiring a fully dynamical approach, which extends the idea of Ref.…”

“…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.…”

“…If we now connect the quantum uplifting of the ADM mass with the spectral decomposition (18), it is easy to see that not all the vectors belonging to H are physical states. In fact, they are the ones that allow us to gain a horizon-law relation, intended as a constraint "à la Gupta-Bleuler", between the spectrum of H and the one of R…”

“…[9]. The fact that the vast majority of the toy gravitons is sharply distributed, at least from a macroscopic perspective, has a simple consequence on the expectation value of the horizon operators (23) and (24).…”

“…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].…”