Sub-Planckian black holes and the Generalized Uncertainty Principle

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.

A preprint version of the article is available at ArXiv.

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Carr, B., Mureika, J. & Nicolini, P. Sub-Planckian black holes and the Generalized Uncertainty Principle. J. High Energ. Phys. 2015, 52 (2015). https://doi.org/10.1007/JHEP07(2015)052

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Keywords

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