The fuzzy BTZ

Abstract

Abstract We introduce a model of a noncommutative BTZ black hole, obtained by quantisation of Poincaré coordinates together with a moving frame. The fuzzy BTZ black hole carries a covariant differential calculus, satisfies Einstein’s equations and has a constant negative curvature. The construction passes through a larger space, the fuzzy anti-de Sitter, and implements discrete BTZ identifications as conjugations by a unitary operator. We derive the spectrum of the suitably regularised radial coordinate: it consists of a continuum of scattering states outside the horizon r + and an infinite discrete set of bound states inside.

Keywords

• Black Holes
• Models of Quantum Gravity
• Non-Commutative Geometry
• Space-Time Symmetries