867 research outputs found
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
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
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
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
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.
Entropy bounds for charged and rotating systems
It was shown in a previous work that, for systems in which the entropy is an
extensive function of the energy and volume, the Bekenstein and the holographic
entropy bounds predict new results. In this paper, we go further and derive
improved upper bounds to the entropy of {\it extensive} charged and rotating
systems. Furthermore, it is shown that for charged and rotating systems
(including non-extensive ones), the total energy that appear in both the
Bekenstein entropy bound (BEB) and the causal entropy bound (CEB) can be
replaced by the {\it internal} energy of the system. In addition, we propose
possible corrections to the BEB and the CEB.Comment: 12 pages, revte
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
How Fast Does Information Leak out from a Black Hole?
Hawking's radiance, even as computed without account of backreaction, departs
from blackbody form due to the mode dependence of the barrier penetration
factor. Thus the radiation is not the maximal entropy radiation for given
energy. By comparing estimates of the actual entropy emission rate with the
maximal entropy rate for the given power, and using standard ideas from
communication theory, we set an upper bound on the permitted information
outflow rate. This is several times the rates of black hole entropy decrease or
radiation entropy production. Thus, if subtle quantum effects not heretofore
accounted for code information in the radiance, the information that was
thought to be irreparably lost down the black hole may gradually leak back out
from the black hole environs over the full duration of the hole's evaporation.Comment: 8 pages, plain TeX, UCSBTH-93-0
Stars and (Furry) Black Holes in Lorentz Breaking Massive Gravity
We study the exact spherically symmetric solutions in a class of
Lorentz-breaking massive gravity theories, using the effective-theory approach
where the graviton mass is generated by the interaction with a suitable set of
Stuckelberg fields. We find explicitly the exact black hole solutions which
generalizes the familiar Schwarzschild one, which shows a non-analytic hair in
the form of a power-like term r^\gamma. For realistic self-gravitating bodies,
we find interesting features, linked to the effective violation of the Gauss
law: i) the total gravitational mass appearing in the standard 1/r term gets a
multiplicative renormalization proportional to the area of the body itself; ii)
the magnitude of the power-like hairy correction is also linked to size of the
body. The novel features can be ascribed to presence of the goldstones fluid
turned on by matter inside the body; its equation of state approaching that of
dark energy near the center. The goldstones fluid also changes the matter
equilibrium pressure, leading to an upper limit for the graviton mass, m <~
10^-28 - 10^29 eV, derived from the largest stable gravitational bound states
in the Universe.Comment: 22 pages, 4 Figures. Final version to be published in PRD. Typos
corrected, comments adde
A note on the quantization of a multi-horizon black hole
We consider the quasinormal spectrum of a charged scalar field in the
(charged) Reissner-Nordstrom spacetime, which has two horizons. The spectrum is
characterized by two distinct families of asymptotic resonances. We suggest and
demonstrate the according to Bohr's correspondence principle and in agreement
with the Bekenstein-Mukhanov quantization scheme, one of these resonances
corresponds to a fundamental change of Delta A=4hbar ln2 in the surface area of
the black-hole outer horizon. The second asymptotic resonance is associated
with a fundamental change of Delta Atot=4hbar ln3 in the total area of the
black hole (in the sum of the surface areas of the inner and outer horizons),
in accordance with a suggestion of Makela and Repo.Comment: 6 page
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