Pairing Correlations, Coherent States, and Black Holes

Doyeol Doyeol

Hawking radiation effects on an entangled pair near the event horizon of a Schwarzschild black hole are investigated. The Hawking radiation was found to degrade both the quantum coherence of the entangled state and the mutual correlations of the entangled pair. When the black hole evaporated completely, the measure of entanglement vanished, but the classical correlation between the entangled pair still remained.

V. V. Dodonov, E.V. Kurmyshev, Vladimir I. Man’ko

Mostafa Mansour, Zakaria Dahbi, M. Essakhi +1 more

Jérôme Turcotte

We study a stationary finite-dimensional bipartite quantum system composed of mass levels, labelled “black hole,” and energy levels, labelled “radiation.” Matched levels satisfy a fixed total-energy constraint. Analytically and across 128 paired numerical realizations, the diagonal part of the global state provides a perfect record between remaining mass and radiated energy, whereas off-diagonal coherence across energy branches supports Page–Wootters conditional evolution. Complete dephasing preserves stationarity, the energy shell, both imposed thermal local density matrices, and the classical energy record, while eliminating all nontrivial clock variation. Relational clocks are detected in 128/128 coherent states and 0/384 mixed controls. Within this finite family, diagonal correlations encode the record of change, whereas coherence supports relational change. This construction is a controlled toy model. It does not reproduce black-hole geometry, Hawking pair creation, backreaction, or the Page curve, and it does not claim to resolve the black-hole information paradox.

Matteo Fadel

Robert M. Wald

We attempt to gain some insight into the issue of whether pure states evolve to density matrices in the black hole evaporation process by examining the mode functions of the particles entering the black hole which are correlated with the particles which escape to infinity. We show that these particles enter the black hole singularity at relatively early times. This tends to support the view that pure states evolve to density matrices, i.e., that in this process quantum coherence is lost.