Are there hyperentropic objects ?

By treating the Hawking radiation as a system in thermal equilibrium, Marolf and R. Sorkin have argued that hyperentropic objects (those violating the entropy bounds) would be emitted profusely with the radiation, thus opening a loophole in black hole based arguments for such entropy bounds. We demonstrate, on kinetic grounds, that hyperentropic objects could only be formed extremely slowly, and so would be rare in the Hawking radiance, thus contributing negligibly to its entropy. The arguments based on the generalized second law of thermodynamics then rule out weakly self-gravitating hyperentropic objects and a class of strongly self-gravitating ones.Comment: LaTeX, 4 page

How does the entropy/information bound work ?

According to the universal entropy bound, the entropy (and hence information capacity) of a complete weakly self-gravitating physical system can be bounded exclusively in terms of its circumscribing radius and total gravitating energy. The bound's correctness is supported by explicit statistical calculations of entropy, gedanken experiments involving the generalized second law, and Bousso's covariant holographic bound. On the other hand, it is not always obvious in a particular example how the system avoids having too many states for given energy, and hence violating the bound. We analyze in detail several purported counterexamples of this type (involving systems made of massive particles, systems at low temperature, systems with high degeneracy of the lowest excited states, systems with degenerate ground states, or involving a particle spectrum with proliferation of nearly massless species), and exhibit in each case the mechanism behind the bound's efficacy.Comment: LaTeX, 10 pages. Contribution to the special issue of Foundation of Physics in honor of Asher Peres; C. Fuchs and A. van der Merwe, ed

Boundary conditions and the entropy bound

The entropy-to-energy bound is examined for a quantum scalar field confined to a cavity and satisfying Robin condition on the boundary of the cavity. It is found that near certain points in the space of the parameter defining the boundary condition the lowest eigenfrequency (while non-zero) becomes arbitrarily small. Estimating, according to Bekenstein and Schiffer, the ratio $S/E$ by the $\zeta$-function, $(24\zeta (4))^{1/4}$, we compute $\zeta (4)$ explicitly and find that it is not bounded near those points that signals violation of the bound. We interpret our results as imposing certain constraints on the value of the boundary interaction and estimate the forbidden region in the parameter space of the boundary conditions.Comment: 16 pages, latex, v2: typos corrected, to appear in Phys.Rev.

Entropy Bounds and Black Hole Remnants

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.Comment: 12 pages, UCSBTH-93-2

The Quantum States and the Statistical Entropy of the Charged Black Hole

We quantize the Reissner-Nordstr\"om black hole using an adaptation of Kucha\v{r}'s canonical decomposition of the Kruskal extension of the Schwarzschild black hole. The Wheeler-DeWitt equation turns into a functional Schroedinger equation in Gaussian time by coupling the gravitational field to a reference fluid or dust. The physical phase space of the theory is spanned by the mass, $M$, the charge, $Q$, the physical radius, $R$, the dust proper time, $\tau$, and their canonical momenta. The exact solutions of the functional Schroedinger equation imply that the difference in the areas of the outer and inner horizons is quantized in integer units. This agrees in spirit, but not precisely, with Bekenstein's proposal on the discrete horizon area spectrum of black holes. We also compute the entropy in the microcanonical ensemble and show that the entropy of the Reissner-Nordstr\"om black hole is proportional to this quantized difference in horizon areas.Comment: 31 pages, 3 figures, PHYZZX macros. Comments on the wave-functional in the interior and one reference added. To appear in Phys. Rev.

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

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.Comment: RevTeX, 16 page

Black Hole Radiation and Volume Statistical Entropy

The simplest possible equation for Hawking radiation, and other black hole radiated power is derived in terms of black hole density. Black hole density also leads to the simplest possible model of a gas of elementary constituents confined inside a gravitational bottle of Schwarzchild radius at tremendous pressure, which yields identically the same functional dependence as the traditional black hole entropy. Variations of Sbh can be obtained which depend on the occupancy of phase space cells. A relation is derived between the constituent momenta and the black hole radius which is similar to the Compton wavelength relation.Comment: 11 pages, no figures. Key Words: Black Hole Entropy, Hawking Radiation, Black Hole density. This is a better pdf versio

Selection Rules for Black-Hole Quantum Transitions

We suggest that quantum transitions of black holes comply with selection rules, analogous to those of atomic spectroscopy. In order to identify such rules, we apply Bohr's correspondence principle to the quasinormal ringing frequencies of black holes. In this context, classical ringing frequencies with an asymptotically vanishing real part \omega_R correspond to virtual quanta, and may thus be interpreted as forbidden quantum transitions. With this motivation, we calculate the quasinormal spectrum of neutrino fields in spherically symmetric black-hole spacetimes. It is shown that \omega_R->0 for these resonances, suggesting that the corresponding fermionic transitions are quantum mechanically forbidden.Comment: 4 pages, 2 figure

Bound states and the Bekenstein bound

We explore the validity of the generalized Bekenstein bound, S <= pi M a. We define the entropy S as the logarithm of the number of states which have energy eigenvalue below M and are localized to a flat space region of width a. If boundary conditions that localize field modes are imposed by fiat, then the bound encounters well-known difficulties with negative Casimir energy and large species number, as well as novel problems arising only in the generalized form. In realistic systems, however, finite-size effects contribute additional energy. We study two different models for estimating such contributions. Our analysis suggests that the bound is both valid and nontrivial if interactions are properly included, so that the entropy S counts the bound states of interacting fields.Comment: 35 page

Does the generalized second law require entropy bounds for a charged system?

We calculate the net change in generalized entropy occurring when one carries out the gedanken experiment in which a box initially containing energy $E$, entropy $S$ and charge $Q$ is lowered adiabatically toward a Reissner-Nordstr\"{o}m black hole and then dropped in. This is an extension of the work of Unruh-Wald to a charged system (the contents of the box possesses a charge $Q$). Their previous analysis showed that the effects of acceleration radiation prevent violation of the generalized second law of thermodynamics. In our more generic case, we show that the properties of the thermal atmosphere are equally important when charge is present. Indeed, we prove here that an equilibrium condition for the the thermal atmosphere and the physical properties of ordinary matter are sufficient to enforce the generalized second law. Thus, no additional assumptions concerning entropy bounds on the contents of the box need to be made in this process. The relation between our work and the recent works of Bekenstein and Mayo, and Hod (entropy bound for a charged system) are also discussed.Comment: 18pages, RevTex, no figure