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Sub-Planckian Black Holes And The Generalized Uncertainty Principle, Bernard Carr, Jonas R. Mureika, Piero Nicolini

Jonas Mureika

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 …