Non-Archimedean character of quantum buoyancy and the generalized second law of thermodynamics

TL;DR

This paper revises the understanding of quantum buoyancy near black holes, showing it is weaker than previously thought, which impacts the validity of the generalized second law of thermodynamics and introduces new bounds on entropy.

Contribution

It introduces a diffractive scattering approach to calculate quantum buoyancy, challenging prior fluid-based models and clarifies conditions for the generalized second law's validity.

Findings

Quantum buoyancy is weaker than in the fluid model.

The optimal drop point for objects is near the horizon.

The universal entropy bound suffices for the second law when near the horizon.

Abstract

Quantum buoyancy has been proposed as the mechanism protecting the generalized second law when an entropy--bearing object is slowly lowered towards a black hole and then dropped in. We point out that the original derivation of the buoyant force from a fluid picture of the acceleration radiation is invalid unless the object is almost at the horizon, because otherwise typical wavelengths in the radiation are larger than the object. The buoyant force is here calculated from the diffractive scattering of waves off the object, and found to be weaker than in the original theory. As a consequence, the argument justifying the generalized second law from buoyancy cannot be completed unless the optimal drop point is next to the horizon. The universal bound on entropy is always a sufficient condition for operation of the generalized second law, and can be derived from that law when the optimal drop point is close to the horizon. We also compute the quantum buoyancy of an elementary charged particle; it turns out to be negligible for energetic considerations. Finally, we speculate on the significance of the absence from the bound of any mention of the number of particle species in nature.