Proof of Bekenstein-Mukhanov ansatz in loop quantum gravity

TL;DR

This paper provides a straightforward proof within loop quantum gravity that black hole horizon areas are discretized linearly, giving physical meaning to the quantum numbers involved, thus supporting the Bekenstein-Mukhanov ansatz.

Contribution

It offers the first clear proof of the Bekenstein-Mukhanov ansatz in LQG, linking macroscopic black hole area quantization to physical quantum numbers.

Findings

Black hole horizon area is linearly quantized in LQG.

Quantum numbers have a physical interpretation in the LQG framework.

Supports the Bekenstein-Mukhanov ansatz with a rigorous proof.

Abstract

A simple proof of Bekenstein-Mukhanov(BM) ansatz is given within the loop quantum gravity(LQG) framework. The macroscopic area of an equilibrium black hole horizon indeed manifests a linear quantization. The quantum number responsible for this discreteness of the macroscopic area has a physical meaning in the LQG framework, unlike the ad hoc one that remained unexplained in BM ansatz.