Quantum of area $\Delta A=8\pi l_P^2$ and a statistical interpretation of black hole entropy

In contrast to alternative values, the quantum of area $\Delta A=8\pi l_P^2$ does not follow from the usual statistical interpretation of black hole entropy; on the contrary, a statistical interpretation follows from it. This interpretation is based on the two concepts: nonadditivity of black hole entropy and Landau quantization. Using nonadditivity a microcanonical distribution for a black hole is found and it is shown that the statistical weight of a black hole should be proportional to its area. By analogy with conventional Landau quantization, it is shown that quantization of a black hole is nothing but the Landau quantization. The Landau levels of a black hole and their degeneracy are found. The degree of degeneracy is equal to the number of ways to distribute a patch of area $8\pi l_P^2$ over the horizon. Taking into account these results, it is argued that the black hole entropy should be of the form $S_{\mathrm{bh}}=2\pi ·\Delta \Gamma$, where the number of microstates is $\Delta \Gamma =A/8\pi l_P^2$. The nature of the degrees of freedom responsible for black hole entropy is elucidated. The applications of the new interpretation are presented. The effect of noncommuting coordinates is discussed.