2,227 research outputs found
Towards a physical interpretation for the Stephani Universes
A physicaly reasonable interpretation is provided for the perfect fluid,
sphericaly symmetric, conformally flat ``Stephani Universes''. The free
parameters of this class of exact solutions are determined so that the ideal
gas relation is identicaly fulfiled, while the full equation of state
of a classical monatomic ideal gas and a matter-radiation mixture holds up to a
good approximation in a near dust, matter dominated regime. Only the models
having spacelike slices with positive curvature admit a regular evolution
domain that avoids an unphysical singularity. In the matter dominated regime
these models are dynamicaly and observationaly indistinguishable from
``standard'' FLRW cosmology with a dust source.Comment: 17 pages, 2 figures, LaTeX with revtex style, submitted to General
Relativity and Gravitatio
Evolution of radial profiles in regular Lemaitre-Tolman-Bondi dust models
We undertake a comprehensive and rigorous analytic study of the evolution of
radial profiles of covariant scalars in regular Lemaitre-Tolman-Bondi dust
models. We consider specifically the phenomenon of "profile inversions" in
which an initial clump profile of density, spatial curvature or the expansion
scalar, might evolve into a void profile (and vice versa). Previous work in the
literature on models with density void profiles and/or allowing for density
profile inversions is given full generalization, with some erroneous results
corrected. We prove rigorously that if an evolution without shell crossings is
assumed, then only the 'clump to void' inversion can occur in density profiles,
and only in hyperbolic models or regions with negative spatial curvature. The
profiles of spatial curvature follow similar patterns as those of the density,
with 'clump to void' inversions only possible for hyperbolic models or regions.
However, profiles of the expansion scalar are less restrictive, with profile
inversions necessarily taking place in elliptic models. We also examine radial
profiles in special LTB configurations: closed elliptic models, models with a
simultaneous big bang singularity, as well as a locally collapsing elliptic
region surrounded by an expanding hyperbolic background. The general analytic
statements that we obtain allow for setting up the right initial conditions to
construct fully regular LTB models with any specific qualitative requirements
for the profiles of all scalars and their time evolution. The results presented
can be very useful in guiding future numerical work on these models and in
revising previous analytic work on all their applications.Comment: Final version to appear in Classical and Quantum Gravity. Readers
eager to know the results and implications without having to go through the
technical detail are recommended to go directly to the summary and discussion
in the final section (section 11). Typos have been corrected and an important
reference has been adde
Weighed scalar averaging in LTB dust models, part I: statistical fluctuations and gravitational entropy
We introduce a weighed scalar average formalism ("q-average") for the study
of the theoretical properties and the dynamics of spherically symmetric
Lemaitre-Tolman-Bondi (LTB) dust models models. The "q-scalars" that emerge by
applying the q-averages to the density, Hubble expansion and spatial curvature
(which are common to FLRW models) are directly expressible in terms of
curvature and kinematic invariants and identically satisfy FLRW evolution laws
without the back-reaction terms that characterize Buchert's average. The local
and non-local fluctuations and perturbations with respect to the q-average
convey the effects of inhomogeneity through the ratio of curvature and
kinematic invariants and the magnitude of radial gradients. All curvature and
kinematic proper tensors that characterize the models are expressible as
irreducible algebraic expansions on the metric and 4-velocity, whose
coefficients are the q-scalars and their linear and quadratic local
fluctuations. All invariant contractions of these tensors are quadratic
fluctuations, whose q-averages are directly and exactly related to statistical
correlation moments of the density and Hubble expansion scalar. We explore the
application of this formalism to a definition of a gravitational entropy
functional proposed by Hosoya et al (2004 Phys. Rev. Lett. 92 141302). We show
that a positive entropy production follows from a negative correlation between
fluctuations of the density and Hubble scalar, providing a brief outline on its
fulfillment in various LTB models and regions. While the q-average formalism is
specially suited for LTB and Szekeres models, it may provide a valuable
theoretical insight on the properties of scalar averaging in inhomogeneous
spacetimes in general.Comment: 27 pages in IOP format, 1 figure. Matches version accepted for
publication in Classical and Quantum Gravit
Lattice Boltzmann Model for Axisymmetric Multiphase Flows
In this paper, a lattice Boltzmann (LB) model is presented for axisymmetric
multiphase flows. Source terms are added to a two-dimensional standard lattice
Boltzmann equation (LBE) for multiphase flows such that the emergent dynamics
can be transformed into the axisymmetric cylindrical coordinate system. The
source terms are temporally and spatially dependent and represent the
axisymmetric contribution of the order parameter of fluid phases and inertial,
viscous and surface tension forces. A model which is effectively explicit and
second order is obtained. This is achieved by taking into account the discrete
lattice effects in the Chapman-Enskog multiscale analysis, so that the
macroscopic axisymmetric mass and momentum equations for multiphase flows are
recovered self-consistently. The model is extended to incorporate reduced
compressibility effects. Axisymmetric equilibrium drop formation and
oscillations, breakup and formation of satellite droplets from viscous liquid
cylindrical jets through Rayleigh capillary instability and drop collisions are
presented. Comparisons of the computed results with available data show
satisfactory agreement.Comment: 17 pages, 11 figures, to be published in Physical Review
Back-reaction and effective acceleration in generic LTB dust models
We provide a thorough examination of the conditions for the existence of
back-reaction and an "effective" acceleration (in the context of Buchert's
averaging formalism) in regular generic spherically symmetric
Lemaitre-Tolman-Bondi (LTB) dust models. By considering arbitrary spherical
comoving domains, we verify rigorously the fulfillment of these conditions
expressed in terms of suitable scalar variables that are evaluated at the
boundary of every domain. Effective deceleration necessarily occurs in all
domains in: (a) the asymptotic radial range of models converging to a FLRW
background, (b) the asymptotic time range of non-vacuum hyperbolic models, (c)
LTB self-similar solutions and (d) near a simultaneous big bang. Accelerating
domains are proven to exist in the following scenarios: (i) central vacuum
regions, (ii) central (non-vacuum) density voids, (iii) the intermediate radial
range of models converging to a FLRW background, (iv) the asymptotic radial
range of models converging to a Minkowski vacuum and (v) domains near and/or
intersecting a non-simultaneous big bang. All these scenarios occur in
hyperbolic models with negative averaged and local spatial curvature, though
scenarios (iv) and (v) are also possible in low density regions of a class of
elliptic models in which local spatial curvature is negative but its average is
positive. Rough numerical estimates between -0.003 and -0.5 were found for the
effective deceleration parameter. While the existence of accelerating domains
cannot be ruled out in models converging to an Einstein de Sitter background
and in domains undergoing gravitational collapse, the conditions for this are
very restrictive. The results obtained may provide important theoretical clues
on the effects of back-reaction and averaging in more general non-spherical
models.Comment: Final version accepted for publication in Classical and Quantum
Gravity. 47 pages in IOP LaTeX macros, 12 pdf figure
Atmospheric greenhouse gases retrieved from SCIAMACHY: comparison to ground-based FTS measurements and model results
SCIAMACHY onboard ENVISAT (launched in 2002) enables the retrieval of global long-term column-averaged dry air mole fractions of the two most important anthropogenic greenhouse gases carbon dioxide and methane (denoted XCO_2 and XCH_4). In order to assess the quality of the greenhouse gas data obtained with the recently introduced v2 of the scientific retrieval algorithm WFM-DOAS, we present validations with ground-based Fourier Transform Spectrometer (FTS) measurements and comparisons with model results at eight Total Carbon Column Observing Network (TCCON) sites providing realistic error estimates of the satellite data. Such validation is a prerequisite to assess the suitability of data sets for their use in inverse modelling.
It is shown that there are generally no significant differences between the carbon dioxide annual increases of SCIAMACHY and the assimilation system CarbonTracker (2.00 ± 0.16 ppm yr^(−1) compared to 1.94 ± 0.03 ppm yr−1 on global average). The XCO_2 seasonal cycle amplitudes derived from SCIAMACHY are typically larger than those from TCCON which are in turn larger than those from CarbonTracker. The absolute values of the northern hemispheric TCCON seasonal cycle amplitudes are closer to SCIAMACHY than to CarbonTracker and the corresponding differences are not significant when compared with SCIAMACHY, whereas they can be significant for a subset of the analysed TCCON sites when compared with CarbonTracker. At Darwin we find discrepancies of the seasonal cycle derived from SCIAMACHY compared to the other data sets which can probably be ascribed to occurrences of undetected thin clouds. Based on the comparison with the reference data, we conclude that the carbon dioxide data set can be characterised by a regional relative precision (mean standard deviation of the differences) of about 2.2 ppm and a relative accuracy (standard deviation of the mean differences) of 1.1–1.2 ppm for monthly average composites within a radius of 500 km.
For methane, prior to November 2005, the regional relative precision amounts to 12 ppb and the relative accuracy is about 3 ppb for monthly composite averages within the same radius. The loss of some spectral detector pixels results in a degradation of performance thereafter in the spectral range currently used for the methane column retrieval. This leads to larger scatter and lower XCH_4 values are retrieved in the tropics for the subsequent time period degrading the relative accuracy. As a result, the overall relative precision is estimated to be 17 ppb and the relative accuracy is in the range of about 10–20 ppb for monthly averages within a radius of 500 km.
The derived estimates show that the SCIAMACHY XCH_4 data set before November 2005 is suitable for regional source/sink determination and regional-scale flux uncertainty reduction via inverse modelling worldwide. In addition, the XCO2 monthly data potentially provide valuable information in continental regions, where there is sparse sampling by surface flask measurements
Exact inhomogeneous cosmologies whose source is a radiation-matter mixture with consistent thermodynamics
We derive a new class of exact solutions of Einstein's equations providing a
physically plausible hydrodynamical description of cosmological matter in the
radiative era (), between nucleosynthesis and decoupling.
The solutions are characterized by the Lema\^{\i}tre-Tolman -Bondi metric with
a viscous fluid source, subjected to the following conditions: (a) the
equilibrium state variables satisfy the equation of state of a mixture of an
ultra-relativistic and a non-relativistic ideal gases, where the internal
energy of the latter has been neglected, (b) the particle numbers of the
mixture components are independently conserved, (c) the viscous stress is
consistent with the transport equation and entropy balance law of Extended
Irreversible Thermodynamics, with the coefficient of shear viscosity provided
by Kinetic Theory for the `radiative gas' model. The fulfilment of (a), (b) and
(c) restricts initial conditions in terms of an initial value function,
, related to the average of spatial gradients of the
fluctuations of photon entropy per baryon in the initial hypersurface.
Constraints on the observed anisotropy of the microwave cosmic radiation and
the condition that decoupling occurs at K yield
an estimated value: which can be associated
with a bound on promordial entropy fluctuations. The Jeans mass at decoupling
is of the same order of magnitude as that of baryon dominated perturbation
models ()Comment: LaTeX with revtex (PRD macros). Contains 9 figures (ps). To be
published in Physics Review
Luminosity distance and redshift in the Szekeres inhomogeneous cosmological models
The Szekeres inhomogeneous models can be used to model the true lumpy
universe that we observe. This family of exact solutions to Einstein's
equations was originally derived with a general metric that has no symmetries.
In this work, we develop and use a framework to integrate the angular diameter
and luminosity distances in the general Szekeres models. We use the affine null
geodesic equations in order to derive a set of first-order ordinary
differential equations that can be integrated numerically to calculate the
partial derivatives of the null vector components. These equations allow the
integration in all generality of the distances in the Szekeres models and some
examples are given. The redshift is determined from simultaneous integration of
the null geodesic equations. This work does not assume spherical or axial
symmetry, and the results will be useful for comparisons of the general
Szekeres inhomogeneous models to current and future cosmological data.Comment: 14 pages, 1 figure, matches JCAP accepted versio
Lemaitre-Tolman-Bondi dust spacetimes: Symmetry properties and some extensions to the dissipative case
We consider extensions of Lemaitre-Tolman-Bondi (LTB) spacetimes to the
dissipative case. For doing that we previously carry out a systematic study on
LTB. This study is based on two different aspects of LTB. On the one hand, a
symmetry property of LTB will be presented. On the other hand, the description
of LTB in terms of some fundamental scalar functions (structure scalars)
appearing in the orthogonal splitting of Riemann tensor will be provided. We
shall consider as "natural" generalizations of LTB (hereafter referred to as
GLTB) either those metrics admitting some similar kind of symmetry as LTB, or
those sharing structure scalars with similar dependence on the metric.Comment: 13 pages RevTex. To appear in Phys. Rev. D. Some references corrected
and update
Late-time evolution of nonlinear gravitational collapse
We study numerically the fully nonlinear gravitational collapse of a
self-gravitating, minimally-coupled, massless scalar field in spherical
symmetry. Our numerical code is based on double-null coordinates and on free
evolution of the metric functions: The evolution equations are integrated
numerically, whereas the constraint equations are only monitored. The numerical
code is stable (unlike recent claims) and second-order accurate. We use this
code to study the late-time asymptotic behavior at fixed (outside the black
hole), along the event horizon, and along future null infinity. In all three
asymptotic regions we find that, after the decay of the quasi-normal modes, the
perturbations are dominated by inverse power-law tails. The corresponding power
indices agree with the integer values predicted by linearized theory. We also
study the case of a charged black hole nonlinearly perturbed by a (neutral)
self-gravitating scalar field, and find the same type of behavior---i.e.,
quasi-normal modes followed by inverse power-law tails, with the same indices
as in the uncharged case.Comment: 14 pages, standard LaTeX, 18 Encapsulated PostScript figures. A new
convergence test and a determination of QN ringing were added, in addition to
correction of typos and update of reference
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