查看更多>>摘要：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 GM(l)(2) = l = 1, 2,3, ..., 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_ = GM. The condition GM(l)(2) = 1 is tantamount to the mass-angular momentum relation M-l(2) =lM(p)(2), implying a mass-squared quantization in multiples of the Planck-mass-squared. Another important feature (also pointed out by Tanaka) is the holographic nature of these results that are based in recasting the Yang algebra associated with an 8D noncommuting phase space, involving, x(mu), 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, ..., 5. We finalize with a discussion of the noncommuting 3D isotropic and Born oscillators. Finding solutions to these oscillators merit investigation because they introduce explicit dynamics to the quantum black holes. We hope that the findings in this work, relating the Regge-like spectrum l = GM(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. (C) 2021 Elsevier B.V. All rights reserved.
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