Expansion operators in spherically symmetric loop quantum gravity

TL;DR

This paper quantizes null expansion operators in spherically symmetric loop quantum gravity, revealing their spectral properties and implications for quantum horizons and singularity avoidance.

Contribution

It introduces a quantization of null expansions, analyzes their spectral features, and offers new insights into quantum horizons and singularity resolution.

Findings

Expansion operators are self-adjoint with generalized eigenstates.

Shared continuous spectra but different isolated eigenvalues.

Results inform quantum horizon concepts and singularity avoidance.

Abstract

The ingoing and outgoing null expansions associated to a spatial 2-sphere are quantized in the spherically symmetric model of loop quantum gravity. It is shown that the resulting expansion operators are self-adjoint in the kinematical Hilbert space with generalized eigenstates. It turns out that the outgoing and ingoing expansion operators share the common continuous part of their spectra but have different additional isolated eigenvalues. These results provide new insights on the avoidance of the singularities in classical general relativity and the establishment of certain notion of quantum horizons.