Quantum Black Holes: the Event Horizon as a Fuzzy Sphere

Abstract

Modeling the event horizon of a black hole by a fuzzy sphere it is shown that in the classical limit, for large astrophysical black-holes, the event horizon looks locally like a non-commutative plane with non-commutative parameter dictated by the Planck length. Some suggestions in the literature concerning black hole mass spectra are used to derive a formula for the mass spectrum of quantum black holes in terms of four integers which define the area, angular momentum, electric and magnetic charge of the black hole. We also suggest how the classical bounds on extremal black holes might be modified in the quantum theory.

14 pages, typeset in LaTeX; an error corrected, and abstract modified accordingly, some new references added

References in corpus (2)

• Black hole entropy in Loop Quantum Gravity
• Spectrum of rotating black holes and its implications for Hawking radiation

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• Extra dimensions in CERN LHC via mini-black holes: effective Kerr-Newman brane-world effects
• Entanglement Entropy on Fuzzy Spaces
• On Noncommutative Effects in Entropic Gravity
• Noncommutative Effects in the Black Hole Evaporation in Two Dimensions
• Thermofield dynamics and Gravity
• Fuzzy spaces topology change as a possible solution to the black hole information loss paradox
• Lifshitz field theories, Snyder noncomutative space-time and momentum dependent metric
• Black hole motion in Euclidean space as a diffusion process
• Fuzzy Schwarzschild (2+1)-spacetime
• A note on the fuzzy sphere area spectrum, black hole luminosity, and the quantum nature of spacetime