Quantum black holes: The event horizon as a fuzzy sphere

Abstract

Modeling the event horizon of a black hole by a fuzzy sphere leads us to modify some suggestions in the literature concerning black hole mass spectra, We 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. Although the event horizon becomes a commutative sphere in the classical limit a vestige of the quantum theory still persists in that the event horizon stereographically projects onto the non-commutative plane. We also suggest how the classical bounds on extremal black holes might be modified in the quantum theory. © SISSA/ISAS 2005.