Global and Local Horizon Quantum Mechanics

TL;DR

This paper introduces a quantum mechanical framework for describing horizons, both global and local, using a horizon wave-function derived from classical constraints, applicable to spherically symmetric quantum states.

Contribution

It extends horizon quantum mechanics to include local gravitational radii linked to the Misner-Sharp mass, using a minisuperspace-like formalism.

Findings

Consistent description of local gravitational radius in quantum states.

Extension of horizon wave-function formalism to local horizons.

Framework applicable to spatially localized quantum modes.

Abstract

Horizons are classical causal structures that arise in systems with sharply defined energy and corresponding gravitational radius. A global gravitational radius operator can be introduced for a static and spherically symmetric quantum mechanical matter state by lifting the classical "Hamiltonian" constraint that relates the gravitational radius to the ADM mass, thus giving rise to a "horizon wave-function". This minisuperspace-like formalism is shown here to be able to consistently describe also the local gravitational radius related to the Misner-Sharp mass function of the quantum source, provided its energy spectrum is determine by spatially localised modes.