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arXiv · 0906.1949

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

Kostyantyn Ropotenko
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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 $ΔA = 8πl_P^{2}$. It is shown that this conclusion is also valid for a generic Kerr-Newman black hole.

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Kostyantyn Ropotenko. 2009-08-13. Quantization of the black hole area as quantization of the angular momentum component. https://doi.org/10.1103/physrevd.80.044022

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