Thermodynamics of Kerr black hole: Tsallis-Cirto composition law and entropy quantization
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915819415404544 |
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| author | Volovik, G. E. |
| author_facet | Volovik, G. E. |
| contents | 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. 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. $S(M,J)=S(M,0) + 4π\sqrt{J(J+1)}$. 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 $s_z=\pm 1/2$, 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. The Tsallis-Cirto composition law is also extended to the thermodynamics of Kerr-Newman black hole. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_00748 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Thermodynamics of Kerr black hole: Tsallis-Cirto composition law and entropy quantization Volovik, G. E. General Relativity and Quantum Cosmology High Energy Physics - Phenomenology 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. 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. $S(M,J)=S(M,0) + 4π\sqrt{J(J+1)}$. 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 $s_z=\pm 1/2$, 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. The Tsallis-Cirto composition law is also extended to the thermodynamics of Kerr-Newman black hole. |
| title | Thermodynamics of Kerr black hole: Tsallis-Cirto composition law and entropy quantization |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2509.00748 |