329 research outputs found
Comparison of area spectra in loop quantum gravity
We compare two area spectra proposed in loop quantum gravity in different
approaches to compute the entropy of the Schwarzschild black hole. We describe
the black hole in general microcanonical and canonical area ensembles for these
spectra. We show that in the canonical ensemble, the results for all
statistical quantities for any spectrum can be reproduced by a heuristic
picture of Bekenstein up to second order. For one of these spectra - the
equally-spaced spectrum - in light of a proposed connection of the black hole
area spectrum to the quasinormal mode spectrum and following hep-th/0304135, we
present explicit calculations to argue that this spectrum is completely
consistent with this connection. This follows without requiring a change in the
gauge group of the spin degrees of freedom in this formalism from SU(2) to
SO(3). We also show that independent of the area spectrum, the degeneracy of
the area observable is bounded by , where is measured in
Planck units and is a constant of order unity.Comment: 8 pages, Revtex 4, version to appear in Classical and Quantum Gravit
Time-reversal frameness and superselection
We show that appropriate superpositions of motional states are a reference
frame resource that enables breaking of time -reversal superselection so that
two parties lacking knowledge about the other's direction of time can still
communicate. We identify the time-reversal reference frame resource states and
determine the corresponding frameness monotone, which connects time-reversal
frameness to entanglement. In contradistinction to other studies of reference
frame quantum resources, this is the first analysis that involves an
antiunitary rather than unitary representation.Comment: 10 p
Building blocks of a black hole
What is the nature of the energy spectrum of a black hole ? The algebraic
approach to black hole quantization requires the horizon area eigenvalues to be
equally spaced. As stressed long ago by by Mukhanov, such eigenvalues must be
exponentially degenerate with respect to the area quantum number if one is to
understand black hole entropy as reflecting degeneracy of the observable
states. Here we construct the black hole states by means of a pair of "creation
operators" subject to a particular simple algebra, a slight generalization of
that for the harmonic oscillator. We then prove rigorously that the n-th area
eigenvalue is exactly 2 raised to the n-fold degenerate. Thus black hole
entropy qua logarithm of the number of states for fixed horizon area comes out
proportional to that area.Comment: PhysRevTeX, 14 page
Thermal Fluctuations and Black Hole Entropy
In this paper, we consider the effect of thermal fluctuations on the entropy
of both neutral and charged black holes. We emphasize the distinction between
fixed and fluctuating charge systems; using a canonical ensemble to describe
the former and a grand canonical ensemble to study the latter. Our novel
approach is based on the philosophy that the black hole quantum spectrum is an
essential component in any such calculation. For definiteness, we employ a
uniformly spaced area spectrum, which has been advocated by Bekenstein and
others in the literature. The generic results are applied to some specific
models; in particular, various limiting cases of an (arbitrary-dimensional)
AdS-Reissner-Nordstrom black hole. We find that the leading-order quantum
correction to the entropy can consistently be expressed as the logarithm of the
classical quantity. For a small AdS curvature parameter and zero net charge, it
is shown that, independent of the dimension, the logarithmic prefactor is +1/2
when the charge is fixed but +1 when the charge is fluctuating.We also
demonstrate that, in the grand canonical framework, the fluctuations in the
charge are large, , even when .
A further implication of this framework is that an asymptotically flat,
non-extremal black hole can never achieve a state of thermal equilibrium.Comment: 25 pages, Revtex; references added and corrected, and some minor
change
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
Area spectra of the rotating BTZ black hole from quasinormal modes
Following Bekenstein's suggestion that the horizon area of a black hole
should be quantized, the discrete spectrum of the horizon area has been
investigated in various ways. By considering the quasinormal mode of a black
hole, we obtain the transition frequency of the black hole, analogous to the
case of a hydrogen atom, in the semiclassical limit. According to Bohr's
correspondence principle, this transition frequency at large quantum number is
equal to classical oscillation frequency. For the corresponding classical
system of periodic motion with this oscillation frequency, an action variable
is identified and quantized via Bohr-Sommerfeld quantization, from which the
quantized spectrum of the horizon area is obtained. This method can be applied
for black holes with discrete quasinormal modes. As an example, we apply the
method for the both non-rotating and rotating BTZ black holes and obtain that
the spectrum of the horizon area is equally spaced and independent of the
cosmological constant for both cases
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