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 $$\delta = 2$$ statistics. The same composition law expresses the full entropy of the Reissner–Nordström black hole via the entropies of its outer and inner horizons. Here we apply this composition law to the thermodynamics 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., $$S(M,J) = S(M,0) + 4\pi \sqrt {J(J + 1)} $$ . Here $$S(M,0)$$ is the entropy of the Schwarzschild black hole. This demonstrates that when the Kerr black hole with $$J \gg 1$$ absorbs or emits a massless particle with spin $${{s}_{z}} = \pm 1{\text{/}}2$$ , its entropy changes by $${\text{|}}\Delta S{\text{|}} = 2\pi $$ . 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. The Tsallis–Cirto composition law is also extended to the thermodynamics of Kerr–Newman black hole and Schwarzschild–de Sitter black hole.