Generalized uncertainty principle and corpuscular gravity

Abstract

We show that the implications of the generalized uncertainty principle (GUP) in the black hole physics are consistent with the predictions of the corpuscular theory of gravity, in which a black hole is conceived as a Bose-Einstein condensate of weakly interacting gravitons stuck at the critical point of a quantum phase transition. In particular, we prove that the GUP-induced shift of the Hawking temperature can be reinterpreted in terms of non-thermal corrections to the spectrum of the black hole radiation, in accordance with the corpuscular gravity picture. By comparing the two scenarios, we are able to estimate the GUP deformation parameter β, which turns out to be of the order of unity, in agreement with the expectations of some models of string theory. We also comment on the sign of β, exploring the possibility of having a negative deformation parameter when a corpuscular quantum description of the gravitational interaction is assumed to be valid.

The deformation parameter of the generalized uncertainty principle

“…Incidentally, we note that the negative value of the β parameter predicted by Eq. (36), although it may appear surprising, has been already encountered in different scenarios: for an uncertainty relation formulated on a (crystal) lattice (see [20]); in the Magueijo and Smolin formulation of Doubly Special Relativity [35], where the fundamental commutator [X, P ] = ih(1−E/E p ) exhibits ah that can be interpreted as depending on the energy,h(E) → 0 when E → E P lanck ; in the analysis of the Chandrasekhar limit [36], where Y.C.Ong shows that β should be negative in order to have a match between GUP-predicted white dwarfs masses and the astrophysical measures; in the comparison between the modification of Hawking radiation predicted by GUP and that predicted by corpuscular models of Gravity [37,38,39]. All these hints point towards a negative β which would implies, immediately, [X,P ] = ih(1 + βP 2 /m 2 p c 2 ) → 0 for P → P P lanck .…”

Heuristic derivation of the Casimir effect from Generalized Uncertainty Principle

“…It is a direct manifestation of the non-trivial nature of quantum vacuum [20], which occurs whenever a quantum field is bounded in a finite region of space; such a confinement gives rise to a net attractive force between the confining plates, whose intensity has been successfully measured [21]. Since the foundational paper [22], the Casimir effect has been largely investigated in both flat [23] and curved [24] background, and in particular in quadratic theories of gravity [25], which have been studied also in other frameworks [26]. Further interesting applications have been addressed in the context of Lorentz symmetry breaking [27] and flavor mixing of fields [28].…”

Neutrino oscillations in extended theories of gravity

“…In passing, we point out that it is possible to infer a constraint on the free parameters of the quadratic action by virtue of the partitioning (37). Indeed, in light of several considerations already present in literature and applied to other physical frameworks [31,38], it is reasonable to assume that…”

“…For instance, a recent attempt to fulfill this aim has been made in the context of Casimir effect in Ref. [31], where non-trivial bounds on the free parameters appearing in such theories have been inferred by the evaluation of Casimir energy density and pressure. In the present paper, we will face this issue by analyzing neutrino flavor oscillations and computing the correction to the quantum mechanical phase arising from the extra terms in the gravitational action.…”