Entropy Bounds and Black Hole Remnants

TL;DR

The paper rederives the universal Bekenstein entropy bound $S \le \frac{2\pi R E}{\hbar}$ for gravitating systems by treating Unruh–Wald buoyancy exactly near a RN black hole, showing the neutral point lies very close to the horizon and that the bound follows from the generalized second law even without relying on the UW restriction. It demonstrates that buoyancy is typically subleading and that the bound is robust to an arbitrarily large number of particle species by including vacuum energies, and it extends the analysis to $D$ dimensions. The authors further argue that black hole remnants cannot bypass the bound, severely constraining their information capacity and challenging their ability to resolve the information paradox. Together, these results reinforce the universality of the entropy bound across gravitating systems, species counts, and dimensionality, and clarify the role of buoyancy in GSL-consistent energy accounting.

Abstract

We rederive the universal bound on entropy with the help of black holes while allowing for Unruh--Wald buoyancy. We consider a box full of entropy lowered towards and then dropped into a Reissner--Nordström black hole in equilibrium with thermal radiation. We avoid the approximation that the buoyant pressure varies slowly across the box, and compute the buoyant force exactly. We find, in agreement with independent investigations, that the neutral point generically lies very near the horizon. A consequence is that in the generic case, the Unruh--Wald entropy restriction is neither necessary nor sufficient for enforcement of the generalized second law. Another consequence is that generically the buoyancy makes only a negligible contribution to the energy bookeeping, so that the original entropy bound is recovered if the generalized second law is assumed to hold. The number of particle species does not figure in the entropy bound, a point that has caused some perplexity. We demonstrate by explicit calculation that, for arbitrarily large number of particle species, the bound is indeed satisfied by cavity thermal radiation in the thermodynamic regime, provided vacuum energies are included. We also show directly that thermal radiation in a cavity in $D$ dimensional space also respects the bound regardless of the value of $D$. As an application of the bound we show that it strongly restricts the information capacity of the posited black hole remnants, so that they cannot serve to resolve the information paradox.