1,605 research outputs found
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
by the -function, , we compute
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 dimensional space also respects the bound
regardless of the value of . 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, , the charge, , the physical radius, , the dust proper time,
, 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 ,
entropy and charge 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 ). 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
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