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

TL;DR

This paper links black hole horizon area quantization to angular momentum quantization, deriving a universal quantum of area for Schwarzschild and Kerr-Newman black holes based on coordinate transformations and quantum mechanics principles.

Contribution

It introduces a novel approach connecting black hole horizon area quantization to the angular momentum component conjugate to Euclidean angle coordinates.

Findings

Horizon area is quantized with quantum ΔA = 8πl_P^2.

Quantization applies to both Schwarzschild and Kerr-Newman black holes.

The approach bridges black hole thermodynamics and quantum mechanics.

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.