It was suggested many years ago by Jacob Bekenstein that the rotation parameter of a black hole should be quantized as in usual quantum mechanics: J=n * hbar.
This would make sense only if this angular momentum, defined at the boundary, where the Kerr metric is asymptotically flat, can be identified with the angular momentum of a quantum system. This system, however, is a quantum system in flat spacetime, so the fact that its angular momentum is that of a Kerr black hole doesn't seem relevant. In fact it's the other way around, cf. http://arxiv.org/abs/gr-qc/9710076
Dear Dr. Nicolis, Thanks for your suggestions and useful reference.
Kerr metric, corresponding to the exterior metric of a rotating object, is a classical solution of general relativity, and therefore one cannot straight away apply the quantization of angular momentum that follow from the commutators of Lx, Ly, Lz and L^2 operators to the angular momentum parameter. An interesting question would be to obtain the metric outside a macroscopic quantum Bose-Einstein condensate that is rotating.
Dear Sir (Prof. Patrick Das Gupta ) thank you very much for your suggestions. But if we want to use the planck sized Kerr Rotating black hole then how can we quantise the rotation parameter.
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