Quantum Horizons and Space-Time Non-Commutativity

TL;DR

This paper investigates the quantum dynamics of a scalar field near a black hole horizon, focusing on the construction and properties of a time operator within this region.

Contribution

It provides an explicit construction of a time operator near the horizon and analyzes its self-adjointness, advancing understanding of quantum space-time structure.

Findings

Constructed a time operator near the horizon.

Analyzed the self-adjointness of the time operator.

Enhanced understanding of quantum effects in black hole near-horizon regions.

Abstract

We study dynamics of a scalar field in the near-horizon region described by a static Klein-Gordon operator which is the Hamiltonian of the system. The explicite construction of a time operator near-horizon is given and its self-adjointness discussed.