Radial geodesics as a microscopic origin of black hole entropy . II : Exercise with the Kerr - Newman black hole

We specify an angular motion on geodesics to reduce the problem to the case of radial motion elaborated in previous chapters. An appropriate value of entropy for a charged and rotating black hole is obtained by calculating the partition function on thermal geodesics confined under horizons. The quantum aggregation is classified in a similar way to the Reissner–Nordstrøm black hole. A rotation of Kerr–Newman black hole involves a new feature in the description of geodesics responsible for the entropy of black hole: a nonzero projection of angular momentum on the axis of rotation is permitted by the symmetry of the problem. Therefore, we start with a specification of angular motion on geodesics of conserved orbital momentum in Section 2. Then, the procedure has a little to differ from the Reissner–Nordstrøm black hole. The difference is reduced to a particular dependence of mass sum on the polar angle, that allows us to evaluate the partition function and entropy for a cool state of aggregation in agreement with the Bekenstein–Hawking formula [1–3] in Section 3. A short summary is situated in Section 4.