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Sub-Planckian black holes and the Generalized Uncertainty Principle

  • Bernard Carr
  • Jonas MureikaEmail author
  • Piero Nicolini
Open Access
Regular Article - Theoretical Physics

Abstract

The Black Hole Uncertainty Principle correspondence suggests that there could exist black holes with mass beneath the Planck scale but radius of order the Compton scale rather than Schwarzschild scale. We present a modified, self-dual Schwarzschild-like metric that reproduces desirable aspects of a variety of disparate models in the sub-Planckian limit, while remaining Schwarzschild in the large mass limit. The self-dual nature of this solution under MM−1 naturally implies a Generalized Uncertainty Principle with the linear form \( \Delta x\sim \frac{1}{\Delta p}+\Delta p \). We also demonstrate a natural dimensional reduction feature, in that the gravitational radius and thermodynamics of sub-Planckian objects resemble that of (1 + 1)-D gravity. The temperature of sub-Planckian black holes scales as M rather than M−1 but the evaporation of those smaller than 10−36 g is suppressed by the cosmic background radiation. This suggests that relics of this mass could provide the dark matter.

Keywords

Models of Quantum Gravity Black Holes Cosmology of Theories beyond the SM 2D Gravity 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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© The Author(s) 2015

Authors and Affiliations

  1. 1.Astronomy Unit, Queen Mary University of LondonLondonUnited Kingdom
  2. 2.Department of PhysicsLoyola Marymount UniversityLos AngelesUnited States
  3. 3.Frankfurt Institute for Advandced Studies (FIAS)Frankfurt am MainGermany
  4. 4.Institut für Theoretische PhysikJohann Wolfgang Goethe-UniversitätFrankfurt am MainGermany

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