Quantum model for black holes and clocks

We consider a stationary quantum system consisting of two non-interacting yet entangled subsystems, Ξ and Γ. We identify a quantum theory characterizing Ξ such that, in the quantum-to-classical crossover of the composite system, Γ behaves as a test particle within the gravitational field of a Schwarzschild Black Hole (SBH) near its event horizon. We then show that this same quantum theory naturally provides a representation of Ξ in terms of bosonic modes, whose features match those of the Hawking radiation; this facilitates the establishment of precise relations between the phenomenological parameters of the SBH and the microscopic details of the quantum model for Ξ. Finally, we recognize that the conditions used to characterize Γ and Ξ coincide with those required by the Page and Wootters mechanism for identifying an evolving system and an associated clock. This leads us to discuss how the quantum model for Ξ endows the SBH with all the characteristics of a "perfect" clock.