The Generalized Uncertainty Principle and Black Hole Remnants

Adler, Ronald J.; Chen, Pisin; Santiago, David I.

doi:10.1023/a:1015281430411

Cited by 749 publications

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“…In a recent paper [12], a generalized uncertainty principle (GUP) [15,16,17,18] was invoked to argue that the total evaporation of a black hole may be prevented, and as a result there should exist a black hole remnant with Planck mass and size. Here we speculate that the stability of such BHR may be further protected by supersymmetry, in the form of the extremal black hole [13].…”

Section: Introductionmentioning

confidence: 99%

Inflation induced Planck-size black hole remnants as dark matter

Chen

2005

New Astronomy Reviews

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While there exist various candidates, the identification of dark matter remains unresolved. Recently it was argued that the generalized uncertainty principle (GUP) may prevent a black hole from evaporating completely, and as a result there should exist a Planck-size BHR at the end of its evaporation. We speculate that the stability of BHR may be further protected by supersymmetry in the form of extremal black hole. If this is indeed the case and if a sufficient amount of small black holes can be produced in the early universe, then the resultant BHRs can be an interesting candidate for DM. We demonstrate that this is the case in the hybrid inflation model. By assuming BHR as DM, our notion imposes a constraint on the hybrid inflation potential. We show that such a constraint is not fine-tuned. Possible observational signatures are briefly discussed.

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Section: Introductionmentioning

confidence: 99%

Inflation induced Planck-size black hole remnants as dark matter

Chen

2005

New Astronomy Reviews

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“…To avoid this problem, Zel'dovich has proposed that black holes with masses below Planck mass should be associated with stable elementary particles [37]. Also, the occurrence of black hole remnants within the framework of a generalized uncertainty principle has been investigated in [38,39].…”

Section: Black Hole Remnantsmentioning

confidence: 99%

Black hole remnants at the LHC

Koch

Bleicher

Hossenfelder

2005

J. High Energy Phys.

103

110

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Within the scenario of large extra dimensions, the Planck scale is lowered to values soon accessible. Among the predicted effects, the production of TeV mass black holes at the LHC is one of the most exciting possibilities. Though the final phases of the black hole's evaporation are still unknown, the formation of a black hole remnant is a theoretically well motivated expectation. We analyze the observables emerging from a black hole evaporation with a remnant instead of a final decay. We show that the formation of a black hole remnant yields a signature which differs substantially from a final decay. We find the total transverse momentum of the black hole event to be significantly dominated by the presence of a remnant mass providing a strong experimental signature for black hole remnant formation.

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“…As one sees from Eq. (2) the GUP amended Hawking temperature becomes complex if the mass of the black hole is less than 1/2G 1/2 0 , leading thereby to the nonzero minimal black hole mass [1].As it is evident the GUP assumes two ∆E values for a given ∆x. But the choice of the lower value is well motivated physically because for relatively small values of ∆E the gravitational uncertainty becomes negligible in comparison with the standard term and therefore in the limit ∆x ≫ √ G 0 one has to recover the standard uncertainty relation.…”

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“…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 proceeds as follows [1]. (In paper [1] α = 1 is assumed).…”

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Black hole remnants due to GUP or quantum gravity?

Maziashvili

2006

Physics Letters B

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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 ...

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The Generalized Uncertainty Principle and Black Hole Remnants

Cited by 749 publications

References 6 publications

Inflation induced Planck-size black hole remnants as dark matter

Inflation induced Planck-size black hole remnants as dark matter

Black hole remnants at the LHC

Black hole remnants due to GUP or quantum gravity?

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