86 research outputs found
The LQC evolution operator of FRW universe with positive cosmological constant
The self-adjointness of an evolution operator
corresponding to the model of flat FRW universe with massless scalar field and
cosmological constant quantized in the framework of Loop Quantum Cosmology is
studied in the case . It is shown, that for
\Lambda<\Lambda_c\approx 10.3 \lPl^{-2} the operator admits many self-adjoint
extensions, each of the purely discrete spectrum. On the other hand for
the operator is essentially self-adjoint, however the
physical Hilbert space of the model does not contain any physically interesting
states.Comment: RevTex4, 8 page
Geometric Characterizations of the Kerr Isolated Horizon
We formulate conditions on the geometry of a non-expanding horizon
which are sufficient for the space-time metric to coincide on with the
Kerr metric. We introduce an invariant which can be used as a measure of how
different the geometry of a given non-expanding horizon is from the geometry of
the Kerr horizon. Directly, our results concern the space-time metric at \IH
at the zeroth and the first orders. Combained with the results of Ashtekar,
Beetle and Lewandowski, our conditions can be used to compare the space-time
geometry at the non-expanding horizon with that of Kerr to every order. The
results should be useful to numerical relativity in analyzing the sense in
which the final black hole horizon produced by a collapse or a merger
approaches the Kerr horizon.Comment: 11 pages, relevance of the results for the numerical relativity
explained, mistakes correcte
Effective dynamics of the hybrid quantization of the Gowdy T^3 universe
The quantum dynamics of the linearly polarized Gowdy T^3 model (compact
inhomogeneous universes admitting linearly polarized gravitational waves) is
analyzed within Loop Quantum Cosmology by means of an effective dynamics. The
analysis, performed via analytical and numerical methods, proves that the
behavior found in the evolution of vacuum (homogeneous) Bianchi I universes is
preserved qualitatively also in the presence of inhomogeneities. More
precisely, the initial singularity is replaced by a big bounce which joins
deterministically two large classical universes. In addition, we show that the
size of the universe at the bounce is at least of the same order of magnitude
(roughly speaking) as the size of the corresponding homogeneous universe
obtained in the absence of gravitational waves. In particular, a precise lower
bound for the ratio of these two sizes is found. Finally, the comparison of the
amplitudes of the gravitational wave modes in the distant future and past shows
that, statistically (i.e., for large samples of universes), the difference in
amplitude is enhanced for nearly homogeneous universes, whereas this difference
vanishes in inhomogeneity dominated cases. The presented analysis constitutes
the first systematic effective study of an inhomogeneous system within Loop
Quantum Cosmology, and it proves the robustness of the results obtained for
homogeneous cosmologies in this context.Comment: 21 pages, 11 figures, RevTex4-1 + BibTe
Physical evolution in Loop Quantum Cosmology: The example of vacuum Bianchi I
We use the vacuum Bianchi I model as an example to investigate the concept of
physical evolution in Loop Quantum Cosmology (LQC) in the absence of the
massless scalar field which has been used so far in the literature as an
internal time. In order to retrieve the system dynamics when no such a suitable
clock field is present, we explore different constructions of families of
unitarily related partial observables. These observables are parameterized,
respectively, by: (i) one of the components of the densitized triad, and (ii)
its conjugate momentum; each of them playing the role of an evolution
parameter. Exploiting the properties of the considered example, we investigate
in detail the domains of applicability of each construction. In both cases the
observables possess a neat physical interpretation only in an approximate
sense. However, whereas in case (i) such interpretation is reasonably accurate
only for a portion of the evolution of the universe, in case (ii) it remains so
during all the evolution (at least in the physically interesting cases). The
constructed families of observables are next used to describe the evolution of
the Bianchi I universe. The performed analysis confirms the robustness of the
bounces, also in absence of matter fields, as well as the preservation of the
semiclassicality through them. The concept of evolution studied here and the
presented construction of observables are applicable to a wide class of models
in LQC, including quantizations of the Bianchi I model obtained with other
prescriptions for the improved dynamics.Comment: RevTex4, 22 pages, 4 figure
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