Quantum black holes as solvents

TL;DR

This paper proposes a new perspective on black hole entropy, viewing it as a thermodynamic quantity related to the accessible phase space, and draws an analogy to solvation processes to explain the black hole information paradox.

Contribution

It introduces a novel analogy between black hole entropy and solvation, suggesting quantum gravitational degrees of freedom activate near the singularity, offering insights into the information paradox.

Findings

Black hole entropy is better understood as thermodynamic, not informational.

The phase volume associated with black holes cannot arise from matter entanglement alone.

Quantum gravitational degrees of freedom are activated near the singularity, affecting the final state.

Abstract

Almost all of the entropy in the universe is in the form of Bekenstein--Hawking (BH) entropy of super-massive black holes. This entropy, if it satisfies Boltzmann's equation $S=\log{\cal N}$, hence represents almost all the accessible phase space of the Universe, somehow associated to objects which themselves fill out a very small fraction of ordinary three-dimensional space. Although time scales are very long, it is believed that black holes will eventually evaporate by emitting Hawking radiation, which is thermal when counted mode by mode. A pure quantum state collapsing to a black hole will hence eventually re-emerge as a state with strictly positive entropy, which constitutes the famous black hole information paradox. Expanding on a remark by Hawking we posit that BH entropy is a thermodynamic entropy, which must be distinguished from information-theoretic entropy. The paradox can then be explained by information return in Hawking radiation. The novel perspective advanced here is that if BH entropy counts the number of accessible physical states in a quantum black hole, then the paradox can be seen as an instance of the fundamental problem of statistical mechanics. We suggest a specific analogy to the increase of the entropy in a solvation process. We further show that the huge phase volume (${\cal N}$), which must be made available to the universe in a gravitational collapse, cannot originate from the entanglement between ordinary matter and/or radiation inside and outside the black hole. We argue that, instead, the quantum degrees of freedom of the gravitational field must get activated near the singularity, resulting in a final state of the `entangled entanglement' form involving both matter and gravity.