Sub-Planckian black holes and the Generalized Uncertainty Principle

Authors

Bernard Carr, Queen Mary University of London
Jonas R. Mureika, Loyola Marymount UniversityFollow
Piero Nicolini, Fachhochschule Frankfurt am Main

Document Type

Article

Publication Date

7-2015

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 M ↔ M⁻¹ naturally implies a Generalized Uncertainty Principle with the linear form Δx∼1/Δp+Δp. 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.

Publisher Statement

© The Author(s) 2015. JHEP is an open-access journal funded by SCOAP3 and licensed under CC BY 4.0

Repository Citation

Carr, B., Mureika, J. & Nicolini, P. J. High Energ. Phys. (2015) 2015: 52. doi:10.1007/JHEP07(2015)052