A Noncommutative Spacetime Realization of Quantum Black Holes, Regge Trajectories and Holography

It is shown that the radial spectrum associated with a fuzzy sphere in a $noncommutative$ phase space characterized by the Yang algebra, leads $exactly$ to a Regge-like spectrum $G M^2_l = l = 1, 2,3, \ldots $, for $all$ positive values of $l$, and which is consistent with the extremal quantum Kerr black hole solution that occurs when the outer and inner horizon radius coincide $ r_+ = r_- = G M$. The condition $ G M_l^2 = l $ is tantamount to the mass-angular momentum relation $ M^2_l = l M_p^2 $ implying that the (extremal) horizon area is quantized in multiples of the minimal Planck area. Another important feature is the holographic nature of these results that are based in recasting the Yang algebra associated with an $8D$ noncommuting phase space, involving $ {\bf x}_\mu, {\bf p}_\nu, \mu, \nu = 0,1,2,3$, in terms of the $undeformed$ realizations of the Lorentz algebra generators $ J_{AB}$ corresponding to a $6D$-spacetime, and associated to a $12D$-phase-space with coordinates $ X_A, P_A; A = 0,1,2, \ldots, 5$. We hope that the findings in this work, relating the Regge-like spectrum $ l = G M^2 $ and the quantized area of black hole horizons in Planck bits, via the Yang algebra in Noncommutative phase spaces, will help us elucidate some of the impending issues pertaining the black hole information paradox and the role that string theory and quantum information will play in its resolution.