Black hole remnants due to GUP or quantum gravity?

Abstract

Based on the micro-black hole gedanken experiment as well as on general considerations of quantum mechanics and gravity the generalized uncertainty principle (GUP) is analyzed by using the running Newton constant. The result is used to decide between the GUP and quantum gravitational effects as a possible mechanism leading to the black hole remnants of about Planck mass.PACS numbers: 04.70.Dy The cogent argument for the black hole to evaporate entirely is that there are no evident symmetry or quantum number preventing it. Nevertheless, the heuristic derivation of the Hawking temperature with the use of GUP prevents a black hole from complete evaporation, just like the prevention of hydrogen atom from collapse by the uncertainty principle [1]. The generalized uncertainty relation takes into account the gravitational interaction of the photon and the particle being observed. This consideration relies on classical gravitational theory [2,3]. The quantum corrected Schwarzschild space-time obtained with the use of running Newton constant also indicates that the black hole evaporation stops when its mass approaches the critical value of the order of Planck mass [6]. On the other hand the quantum corrected gravity modifies this GUP as well. It is fair to ask whether the halt of black hole radiation is provided by GUP or it is due to quantum gravitational effects. Let us give a critical view of this problem.Let us briefly discuss the modification of Heisenberg uncertainty principle due to gravitational interaction. The main conceptual point concerning GUP is that there is an additional uncertainty in quantum measurement due to gravitational interaction. We focus on consideration of this problem presented in [2], (h = c = 1 is assumed in what follows). The approach proposed in this paper relying on classical gravity is to calculate the displacement of electron caused by the gravitational interaction with the photon and add it to the position uncertainty. The photon due to gravitational interaction imparts to electron the acceleration given by a = G 0 ∆E/r 2 (G 0 is experimentally observed value of Newton's constant for macroscopic values of distances). Assuming r 0 is the size of the interaction region the variation of the velocity of the electron is given by ∆v ∼ G 0 ∆E/r 0 and correspondingly ∆x g ∼ G 0 ∆E. Therefore the total uncertainty in the position is given bywhere α is the factor of order unity in respect with the stringy induced GUP [4]. The Eq.(1) exhibits the * Electronic address: maziashvili@hepi.edu.ge minimal observable distance. However, the minimal observable distance is determined rather due to collapse of ∆E than merely by the Eq. (1), because it puts simply the bound on the measurement procedure. In this way one gets that for α ≥ 2 the ∆x min = √ 2αG 0 while for α < 2 the minimal observable distance is given by ∆x min = 8G 0 /(4 − α). In the framework of this discussion one can obtain the GUP in higher dimensional case as well as on the brane [5].The heuristic derivation of black hole evaporation ...

Modified clock inequalities and modified black hole lifetime

“…Introduction of the GUP has drawn considerable attention and many authors considered various problems in the framework of GUP, such as Refs. [28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60]. Note, however, it should be kept in mind that this GUP is derived based upon only heuristic arguments, and is thus far from proven.…”

Black hole remnants and the information loss paradox

“…At the Planck scale, it is no longer clear that the concept of a horizon, or even the metric itself still makes sense 4 . Over the years, progresses have been made in both understanding GUP as well as applying GUP to various black holes [which consistently yield remnant pictures] [59][60][61][62][63][64][65][66][67][68][69][70][71]. Note that, the form of GUP could vary depending on the models considered, and as such the black holes of various GUP models could have different thermodynamical properties.…”

Self-completeness and the generalized uncertainty principle

“…GUP approaches have found a myriad of applications in high energy physics and quantum systems, including quantum field theory [35,36], gauge theories [37], cosmology [38,39] and particle physics [40]. Applications to black hole thermodynamics are of particular interest in the present context, and the interested reader is referred to [8,10,41,42,43,44,45,46,47,48] and references therein.…”