Quantization of the interior of the black hole

TL;DR

This paper applies canonical quantum gravity to the Schwarzschild black hole, quantizing the horizon and removing the classical singularity, leading to a finite, regular spacetime evolution near the black hole's core.

Contribution

It introduces a quantization of the Schwarzschild radius and horizon area, and demonstrates the removal of the singularity via Bohmian trajectories in quantum gravity.

Findings

Horizon is quantized in terms of Planck length and an integer n.

Black hole singularity is eliminated in the quantum model.

Bohm's trajectories near the singularity are finite and regular.

Abstract

In this work we study the Schwarzschild metric in the context of canonical quantum gravity inside the horizon, close of horizon and near the black hole singularity. Using this standard quantization procedure, we show that the horizon is quantized and the black hole singularity disappears. For the first case, quantization of the Schwarzschild radius was obtained in terms of the Planck length $l_{Pl}$, a positive integer $n$ and the ordering factor of the operator $p$. From the quantization of the Schwarzschild radius it was possible to determine the area of the black hole event horizon, its mass and the quantum energy of the Hawking radiation as well as its frequency. For the solution close to the interior black hole singularity, the wave function was determined and applied the DeBroglie-Bohm interpretation. The Bohm's trajectory was found near to the singularity. It which describes how the spacetime evolves over time and depends on the ordering factor of the operator $p$. Thus, for the case where $|1-p|\neq0,3$, the Bohm's trajectory is finite and regular, that is, the singularity is removed. For the case where $|1-p|=3$, the Bohm's trajectory assumes an exponential behavior, never going to zero, avoiding the singularity.That result allows that spacetime be extended beyond the classical singularity.