On the Nature of Black Holes in Loop Quantum Gravity

TL;DR

This paper explores the quantum properties of black holes within loop quantum gravity, demonstrating bounds on black hole parameters, implications for extremal states, and insights into black hole thermodynamics at the Planck scale.

Contribution

It introduces a quantum operator algebra for black hole observables in loop quantum gravity and analyzes the spectra to reveal bounds and measurement limitations.

Findings

Bound on black hole parameters differs from classical relativity

Extremal black holes cannot be measured or proven to exist

Planck scale cutoff affects Hawking temperature and constrains the Immirzi parameter

Abstract

A genuine notion of black holes can only be obtained in the fundamental framework of quantum gravity resolving the curvature singularities and giving an account of the statistical mechanical, microscopic degrees of freedom able to explain the black hole thermodynamical properties. As for all quantum systems, a quantum realization of black holes requires an operator algebra of the fundamental observables of the theory which is introduced in this study based on aspects of loop quantum gravity. From the eigenvalue spectra of the quantum operators for the black hole area, charge and angular momentum, it is demonstrated that a strict bound on the extensive parameters, different from the relation arising in classical general relativity, holds, implying that the extremal black hole state can neither be measured nor can its existence be proven. This is, as turns out, a result of the specific form of the chosen angular momentum operator and the corresponding eigenvalue spectrum, or rather the quantum measurement process of angular momentum. Quantum mechanical considerations and the lowest, non-zero eigenvalue of the loop quantum gravity black hole mass spectrum indicate, on the one hand, a physical Planck scale cutoff of the Hawking temperature law and, on the other hand, give upper and lower bounds on the numerical value of the Immirzi parameter. This analysis provides an approximative description of the behavior and the nature of quantum black holes.