Quantum model for black holes and clocks

Abstract

We consider a stationary quantum system consisting of two non-interacting yet entangled subsystems, $\Xi$ and $\Gamma$. We identify a quantum theory characterizing $\Xi$ such that, in the quantum-to-classical crossover of the composite system, $\Gamma$ 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 $\Xi$ 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 $\Xi$. Finally, we recognize that the conditions used to characterize $\Gamma$ and $\Xi$ 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 $\Xi$ endows the SBH with all the characteristics of a "perfect" clock.