Tsallis–Cirto entropy of black hole and black hole atom

The quantum tunneling processes related to the black hole determine the black hole thermodynamics. The Hawking temperature is determined by the quantum tunneling processes of radiation of particles from the black hole. On the other hand, the Bekenstein-Hawking entropy of the black hole is obtained by consideration of the macroscopic quantum tunneling processes of splitting of black hole to the smaller black holes. These tunneling processes also determine the composition rule for the black hole entropy, which coincides with the composition rule for the non-extensive Tsallis–Cirto $\delta=2$ entropy. This composition rule suggests that the mass spectrum of the black hole is equidistant, $M=NM_0$. Here $N$ is an integer number and $M_0=\sqrt{2}m_{\rm P}$ is the mass quantum expressed via the reduced Planck mass $m_{\rm P}$. The Bekenstein–Hawking entropy of the black hole with mass $M=NM_0$ is $S_{\rm BH}(N)=N^2$.