362 research outputs found
Existence of a Semiclassical Approximation in Loop Quantum Gravity
We consider a spherical symmetric black hole in the Schwarzschild metric and
apply Bohr-Sommerfeld quantization to determine the energy levels. The
canonical partition function is then computed and we show that the entropy
coincides with the Bekenstein-Hawking formula when the maximal number of states
for the black hole is the same as computed in loop quantum gravity, proving in
this case the existence of a semiclassical limit and obtaining an independent
derivation of the Barbero-Immirzi parameter.Comment: 6 pages, no figures. Final version accepted for publication in
General Relativity and Gravitatio
Bose Condensation and the BTZ Black Hole
Although all popular approaches to quantum gravity are able to recover the
Bekenstein-Hawking entropy-area law in the thermodynamic limit, there are
significant differences in their descriptions of the microstates and in the
application of statistics. Therefore they can have significantly different
phenomenological implications. For example, requiring indistinguishability of
the elementary degrees of freedom should lead to changes in the black hole's
radiative porperties away from the thermodynamic limit and at low temperatures.
We demonstrate this for the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole. The
energy eigenstates and statistical entropy in the thermodynamic limit of the
BTZ black hole were obtained earlier by us via symmetry reduced canonical
quantum gravity. In that model the BTZ black hole behaves as a system of
Bosonic mass shells moving in a one dimensional harmonic trap. Bose
condensation does not occur in the thermodynamic limit but this system
possesses a finite critical temperature, , and exhibits a large condensate
fraction below when the number of shells is finite.Comment: 5 pages, 5 figures. Published versio
Renormalization and black hole entropy in Loop Quantum Gravity
Microscopic state counting for a black hole in Loop Quantum Gravity yields a
result proportional to horizon area, and inversely proportional to Newton's
constant and the Immirzi parameter. It is argued here that before this result
can be compared to the Bekenstein-Hawking entropy of a macroscopic black hole,
the scale dependence of both Newton's constant and the area must be accounted
for. The two entropies could then agree for any value of the Immirzi parameter,
if a certain renormalization property holds.Comment: 8 pages; v2: references added, typos corrected, version to appear in
CQ
Geon black holes and quantum field theory
Black hole spacetimes that are topological geons in the sense of Sorkin can
be constructed by taking a quotient of a stationary black hole that has a
bifurcate Killing horizon. We discuss the geometric properties of these geon
black holes and the Hawking-Unruh effect on them. We in particular show how
correlations in the Hawking-Unruh effect reveal to an exterior observer
features of the geometry that are classically confined to the regions behind
the horizons.Comment: 11 pages. Talk given at the First Mediterranean Conference on
Classical and Quantum Gravity, Kolymbari (Crete, Greece), September 2009.
Dedicated to Rafael Sorkin. v2: typesetting bug fixe
Entropy calculation for a toy black hole
In this note we carry out the counting of states for a black hole in loop
quantum gravity, however assuming an equidistant area spectrum. We find that
this toy-model is exactly solvable, and we show that its behavior is very
similar to that of the correct model. Thus this toy-model can be used as a nice
and simplifying `laboratory' for questions about the full theory.Comment: 18 pages, 4 figures. v2: Corrected mistake in bibliography, added
appendix with further result
Entropy-Corrected Holographic Dark Energy
The holographic dark energy (HDE) is now an interesting candidate of dark
energy, which has been studied extensively in the literature. In the derivation
of HDE, the black hole entropy plays an important role. In fact, the
entropy-area relation can be modified due to loop quantum gravity or other
reasons. With the modified entropy-area relation, we propose the so-called
``entropy-corrected holographic dark energy'' (ECHDE) in the present work. We
consider many aspects of ECHDE and find some interesting results. In addition,
we briefly consider the so-called ``entropy-corrected agegraphic dark energy''
(ECADE).Comment: 11 pages, 2 tables, revtex4; v2: references adde
Effective State Metamorphosis in Semi-Classical Loop Quantum Cosmology
Modification to the behavior of geometrical density at short scales is a key
result of loop quantum cosmology, responsible for an interesting phenomenology
in the very early universe. We demonstrate the way matter with arbitrary scale
factor dependence in Hamiltonian incorporates this change in its effective
dynamics in the loop modified phase. For generic matter, the equation of state
starts varying near a critical scale factor, becomes negative below it and
violates strong energy condition. This opens a new avenue to generalize various
phenomenological applications in loop quantum cosmology. We show that different
ways to define energy density may yield radically different results, especially
for the case corresponding to classical dust. We also discuss implications for
frequency dispersion induced by modification to geometric density at small
scales.Comment: Revised version; includes expanded discussion of natural
trans-Planckian modifications to frequency dispersion and robustness to
quantization ambiguities. To appear in Class. Quant. Gra
Gibbs' paradox and black-hole entropy
In statistical mechanics Gibbs' paradox is avoided if the particles of a gas
are assumed to be indistinguishable. The resulting entropy then agrees with the
empirically tested thermodynamic entropy up to a term proportional to the
logarithm of the particle number. We discuss here how analogous situations
arise in the statistical foundation of black-hole entropy. Depending on the
underlying approach to quantum gravity, the fundamental objects to be counted
have to be assumed indistinguishable or not in order to arrive at the
Bekenstein--Hawking entropy. We also show that the logarithmic corrections to
this entropy, including their signs, can be understood along the lines of
standard statistical mechanics. We illustrate the general concepts within the
area quantization model of Bekenstein and Mukhanov.Comment: Contribution to Mashhoon festschrift, 13 pages, 4 figure
The Early Universe in Loop Quantum Cosmology
Loop quantum cosmology applies techniques derived for a background
independent quantization of general relativity to cosmological situations and
draws conclusions for the very early universe. Direct implications for the
singularity problem as well as phenomenology in the context of inflation or
bouncing universes result, which will be reviewed here. The discussion focuses
on recent new results for structure formation and generalizations of the
methods.Comment: 10 pages, 3 figures, plenary talk at VI Mexican School on Gravitation
and Mathematical Physics, Nov 21-27, 200
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