Quantization of the black hole area as quantization of the angular momentum component

Abstract

In transforming from Schwarzschild to Euclidean Rindler coordinates the Schwarzschild time transforms to a periodic angle. As is well-known, this allows one to introduce the Hawking temperature and is an origin of black hole thermodynamics. On the other hand, according to quantum mechanics this angle is conjugate to the $z$ component of the angular momentum. From the commutation relation and quantization condition for the angular momentum component it is found that the area of the horizon of a Schwarzschild black hole is quantized with the quantum $\Delta A = 8\pi l_P^{2}$. It is shown that this conclusion is also valid for a generic Kerr-Newman black hole.