Comments on area spectra in Loop Quantum Gravity

TL;DR

This paper critically analyzes various area spectra in Loop Quantum Gravity, focusing on the Equally Spaced spectrum, and discusses their mathematical consistency and relation to quasinormal mode frequencies.

Contribution

It demonstrates that the Equally Spaced spectrum operator is not well-defined in LQG and clarifies issues related to area spectra and QNM frequencies.

Findings

ES spectrum operator is not well-defined in LQG

Highlights issues with area spectra and QNM frequency relations

Provides critical comparison of recent spectrum proposals

Abstract

We examine and compare different area spectra that have been recently considered in Loop Quantum Gravity (LQG). In particular we focus our attention on a Equally Spaced (ES) spectrum operator introduced by Alekseev et. al. that has gained recent attention. We show that such operator is not well defined within the LQG framework, and comment on the issue regarding area spectra and QNM frequencies.