Expansion operators in spherically symmetric loop quantum gravity
Phys. Rev. D 113, 084037 – Published 15 April, 2026
DOI: https://doi.org/10.1103/c4j3-d8h2
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 have the same spectrum consisting of a continuous band and discrete points. In the subspaces with fixed quantum numbers on the edges of the graphs underlining the quantum states, the two operators still share the common continuous spectrum, while their discrete spectra can be different from each other. These results provide new insights on the avoidance of the singularities in classical general relativity and the establishment of a certain notion of quantum horizons.
