689 research outputs found
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
High-order gauge-invariant perturbations of a spherical spacetime
We complete the formulation of a general framework for the analysis of
high-order nonspherical perturbations of a four-dimensional spherical spacetime
by including a gauge-invariant description of the perturbations. We present a
general algorithm to construct these invariants and provide explicit formulas
for the case of second-order metric perturbations. We show that the well-known
problem of lack of invariance for the first-order perturbations with l=0,1
propagates to increasing values of l for perturbations of higher order, owing
to mode coupling. We also discuss in which circumstances it is possible to
construct the invariants
Conserved quantities in isotropic loop quantum cosmology
We develop an action principle for those models arising from isotropic loop
quantum cosmology, and show that there is a natural conserved quantity for
the discrete difference equation arising from the Hamiltonian constraint. This
quantity relates the semi-classical limit of the wavefunction at large
values of the spatial volume, but opposite triad orientations. Moreover, there
is a similar quantity for generic difference equations of one parameter arising
from a self-adjoint operator.Comment: 6 pages, to be published in Europhysics Letter
Big Bounce and inhomogeneities
The dynamics of an inhomogeneous universe is studied with the methods of Loop
Quantum Cosmology as an example of the quantization of vacuum cosmological
spacetimes containing gravitational waves (Gowdy spacetimes). The analysis
performed at the effective level shows that: (i) The initial Big Bang
singularity is replaced (as in the case of homogeneous cosmological models) by
a Big Bounce, joining deterministically two large universes, (ii) the universe
size at the bounce is at least of the same order of magnitude as that of the
background homogeneous universe, (iii) for each gravitational wave mode, the
difference in amplitude at very early and very late times has a vanishing
statistical average when the bounce dynamics is strongly dominated by the
inhomogeneities, whereas this average is positive when the dynamics is in a
near-vacuum regime, so that statistically the inhomogeneities are amplified.Comment: RevTex4, 4 pages, 2 figure
Corrigendum to "Assessment of tsunami hazards for the Central American Pacific coast from southern Mexico to northern Peru" published in Nat. Hazards Earth Syst. Sci., 14, 1889–1903, 2014
No abstract available
Assessment of tsunami hazards for the Central American Pacific coast from southern Mexico to northern Peru
Abstract. Central America (CA), from Guatemala to Panama, has been struck by at least 52 tsunamis between 1539 and 2013, and in the extended region from Mexico to northern Peru (denoted as ECA, Extended Central America in this paper) the number of recorded tsunamis in the same time span is more than 100, most of which were triggered by earthquakes located in the Middle American Trench that runs parallel to the Pacific coast. The most severe event in the catalogue is the tsunami that occurred on 2 September 1992 off Nicaragua, with run-up measured in the range of 5–10 m in several places along the Nicaraguan coast. The aim of this paper is to assess the tsunami hazard on the Pacific coast of this extended region, and to this purpose a hybrid probabilistic-deterministic analysis is performed, that is adequate for tsunamis generated by earthquakes. More specifically, the probabilistic approach is used to compute the Gutenberg–Richter coefficients of the main seismic tsunamigenic zones of the area and to estimate the annual rate of occurrence of tsunamigenic earthquakes and their corresponding return period. The output of the probabilistic part of the method is taken as input by the deterministic part, which is applied to calculate the tsunami run-up distribution along the coast
Second and higher-order perturbations of a spherical spacetime
The Gerlach and Sengupta (GS) formalism of coordinate-invariant, first-order,
spherical and nonspherical perturbations around an arbitrary spherical
spacetime is generalized to higher orders, focusing on second-order
perturbation theory. The GS harmonics are generalized to an arbitrary number of
indices on the unit sphere and a formula is given for their products. The
formalism is optimized for its implementation in a computer algebra system,
something that becomes essential in practice given the size and complexity of
the equations. All evolution equations for the second-order perturbations, as
well as the conservation equations for the energy-momentum tensor at this
perturbation order, are given in covariant form, in Regge-Wheeler gauge.Comment: Accepted for publication in Physical Review
The Euro-Mediterranean Tsunami Catalogue
A unified catalogue containing 290 tsunamis generated in the European
and Mediterranean seas since 6150 B.C. to current days is presented. It is
the result of a systematic and detailed review of all the regional cata-
logues available in literature covering the study area, each of them hav-
ing their own format and level of accuracy. The realization of a single
catalogue covering a so wide area and involving several countries was a
complex task that posed a series of challenges, being the standardization
and the quality of the data the most demanding. A “reliability” value
was used to rate equally the quality of the data for each event and this pa-
rameter was assigned based on the trustworthiness of the information
related to the generating cause, the tsunami description accuracy and also
on the availability of coeval bibliographical sources. Following these cri-
teria we included in the catalogue events whose reliability ranges from 0
(“very improbable tsunami”) to 4 (“definite tsunami”). About 900 docu-
mentary sources, including historical documents, books, scientific reports,
newspapers and previous catalogues, support the tsunami data and de-
scriptions gathered in this catalogue. As a result, in the present paper a list
of the 290 tsunamis with their main parameters is reported. The online
version of the catalogue, available at http://roma2.rm.ingv.it/en/faci
lities/data_bases/52/catalogue_of_the_euro-mediterranean_tsunamis,
provides additional information such as detailed descriptions, pictures,
etc. and the complete list of bibliographical sources. Most of the included
events have a high reliability value (3= “probable” and 4= “definite”)
which makes the Euro-Mediterranean Tsunami Catalogue an essential
tool for the implementation of tsunami hazard and risk assessment
Mode coupling of Schwarzschild perturbations: Ringdown frequencies
Within linearized perturbation theory, black holes decay to their final
stationary state through the well-known spectrum of quasinormal modes. Here we
numerically study whether nonlinearities change this picture. For that purpose
we study the ringdown frequencies of gauge-invariant second-order gravitational
perturbations induced by self-coupling of linearized perturbations of
Schwarzschild black holes. We do so through high-accuracy simulations in the
time domain of first and second-order Regge-Wheeler-Zerilli type equations, for
a variety of initial data sets. We consider first-order even-parity
perturbations and odd-parity ones, and all
the multipoles that they generate through self-coupling. For all of them and
all the initial data sets considered we find that ---in contrast to previous
predictions in the literature--- the numerical decay frequencies of
second-order perturbations are the same ones of linearized theory, and we
explain the observed behavior. This would indicate, in particular, that when
modeling or searching for ringdown gravitational waves, appropriately including
the standard quasinormal modes already takes into account nonlinear effects
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