Entropy Bounds and Black Hole Remnants

TL;DR

This paper reexamines the entropy bounds related to black holes, incorporating Unruh--Wald buoyancy effects, and demonstrates that the bounds hold under various conditions, impacting theories about black hole remnants and the information paradox.

Contribution

The paper provides an exact calculation of buoyant forces near black holes and shows the universality of entropy bounds regardless of particle species or dimensions.

Findings

The neutral point is near the horizon in general.

The original entropy bound is recovered if the GSL holds.

Black hole remnants cannot resolve the information paradox.

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--Nordstr\"om 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.