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Entropy Bounds and Black Hole Remnants
General Relativity and Quantum Cosmology · Submitted 25 Jul 1993
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We rederive the universal bound on entropy with the help of black holes while allowing for Unruh--Wald buoyancy. | contribution 0.94 | 0.94 | 0.10 | asserted 0.99 |
| s1 | We consider a box full of entropy lowered towards and then dropped into a Reissner--Nordstr\"om black hole in equilibrium with thermal radiation. | method 0.76 | 0.81 | 0.03 | asserted 0.81 |
| s2 | We avoid the approximation that the buoyant pressure varies slowly across the box, and compute the buoyant force exactly. | method 0.89 | 0.96 | 0.04 | asserted 0.97 |
| s3 | We find, in agreement with independent investigations, that the neutral point generically lies very near the horizon. | result 1.00 | 0.85 | 0.09 | asserted 1.00 |
| s4 | 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. | interpretation 0.84 | 0.87 | 0.34 | asserted 1.00 |
| s5 | 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. | interpretation 0.68 | 0.90 | 0.24 | asserted 0.98 |
| s6 | The number of particle species does not figure in the entropy bound, a point that has caused some perplexity. | background 0.55 | 0.14 | 0.05 | asserted 0.99 |
| s7 | 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. | result 0.85 | 0.96 | 0.08 | asserted 1.00 |
| s8 | We also show directly that thermal radiation in a cavity in $D$ dimensional space also respects the bound regardless of the value of $D$. | result 0.93 | 0.94 | 0.06 | asserted 1.00 |
| s9 | 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. | result 0.65 | 0.94 | 0.27 | asserted 1.00 |
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Original 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.
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How the literature uses it
28 arXiv papers cite this in 34 sentences
Papers citing it · 22 sentences without a confident label
Cites it as background 11 papers
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Another intriguing approach to understanding cosmic acceleration and possibly resolving tensions draws from gravity-thermodynamics formalism [ref] [ref] , which is once again based on the foundational concepts in black hole physics developed by Hawking and Bekenstein [ref] .
Holographic and Gravity-Thermodynamic Approaches in Entropic Cosmology: Bayesian Assessment using late-time Data · Introduction · 0.89
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For example, information loss or remnant [ref] modifies Statement One; firewall [ref] , ER=EPR [ref] , pre-Hawking radiation [ref] , or some version of the fuzzball [ref] modifies Statement Two; various proposals of nonlocal effects near the horizon [ref] , causal patch complementarity [ref] , or computational complementarity [ref] modify Statement Three.[Various versions of complementarity basically claim that QFT breaks down if one applies it to compare quantities which are in-principle not measurable (or difficult to measure) by the same observer.]
A self-consistency check for unitary propagation of Hawking quanta · Black Hole Information Paradox · 0.95
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This derivation of the bound from the generalized second law of thermodynamics (GSL) was impugned [ref] and defended [ref] in several occasions.
Relative entropy and the Bekenstein bound · Introduction · 0.85
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