2,491 research outputs found
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
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
Ideal gas sources for the Lemaitre-Tolman-Bondi metrics
New exact solutions emerge by replacing the dust source of the
Lem\^aitre-Tolman-Bondi metrics with a viscous fluid satisfying the monatomic
gas equation of state. The solutions have a consistent thermodynamical
interpretation. The most general transport equation of Extended Irreversible
Thermodynamics is satisfied, with phenomenological coefficients bearing a close
resemblance to those characterizing a non relativistic Maxwell-Bolzmann gas.Comment: 7 pages, Plain TeX with IOP macros, important corrections to previous
version, 3 figures (to appear in Classical and Quantum Gravity, June 1998
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
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
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
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
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