Thermodynamics of Kerr black hole: Tsallis-Cirto composition law and entropy quantization

The processes of splitting and merging of black holes obey the composition law generated by the Tsallis-Cirto $δ=2$ statistics. The same composition law expresses the full entropy of the Reissner-Nordström black hole via the entropies of its outer and inner horizons. He we apply this composition law to the entropy of the Kerr black hole. As distinct from Reissner-Nordström black hole, where the full entropy depends only on mass M and does not depend on its charge Q, the entropy of Kerr black hole is the sum of contributions from its mass M and angular momentum J, i.e. S(M,J)=S(M,0) + 4π√J(J+1). Here $S(M,0)$ is the entropy of the Schwarzschild black hole. This demonstrates that when the Kerr black hole with J 1 absorbs or emits a massless particle with spin sz=± 1/2, its entropy changes by $|ΔS| = 2π$. We also considered the quantization of entropy suggested by the toy model, in which the black hole thermodynamics is represented by the ensemble of the Planck-scale black holes -- Planckons.