3,634 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
On the Thermodynamics of Simple Non-Isentropic Perfect Fluids in General Relativity
We examine the consistency of the thermodynamics of irrotational and
non-isentropic perfect fluids complying with matter conservation by looking at
the integrability conditions of the Gibbs-Duhem relation. We show that the
latter is always integrable for fluids of the following types: (a) static, (b)
isentropic (admits a barotropic equation of state), (c) the source of a
spacetime for which , where is the dimension of the orbit of the
isometry group. This consistency scheme is tested also in two large classes of
known exact solutions for which , in general: perfect fluid Szekeres
solutions (classes I and II). In none of these cases, the Gibbs-Duhem relation
is integrable, in general, though specific particular cases of Szekeres class
II (all complying with ) are identified for which the integrability of
this relation can be achieved. We show that Szekeres class I solutions satisfy
the integrability conditions only in two trivial cases, namely the spherically
symmetric limiting case and the Friedman-Roberson-Walker (FRW) cosmology.
Explicit forms of the state variables and equations of state linking them are
given explicitly and discussed in relation to the FRW limits of the solutions.
We show that fixing free parameters in these solutions by a formal
identification with FRW parameters leads, in all cases examined, to unphysical
temperature evolution laws, quite unrelated to those of their FRW limiting
cosmologies.Comment: 29 pages, Plain.Te
Local thermal equilibrium and ideal gas Stephani universes
The Stephani universes that can be interpreted as an ideal gas evolving in
local thermal equilibrium are determined. Five classes of thermodynamic schemes
are admissible, which give rise to five classes of regular models and three
classes of singular models. No Stephani universes exist representing an exact
solution to a classical ideal gas (one for which the internal energy is
proportional to the temperature). But some Stephani universes may approximate a
classical ideal gas at first order in the temperature: all of them are
obtained. Finally, some features about the physical behavior of the models are
pointed out.Comment: 20 page
Realistic fluids as source for dynamically accreting black holes in a cosmological background
We show that a single imperfect fluid can be used as a source to obtain the
generalized McVittie metric as an exact solution to Einstein's equations. The
mass parameter in this metric varies with time thanks to a mechanism based on
the presence of a temperature gradient. This fully dynamical solution is
interpreted as an accreting black hole in an expanding universe if the metric
asymptotes to Schwarzschild-de Sitter at temporal infinity. We present a simple
but instructive example for the mass function and briefly discuss the structure
of the apparent horizons and the past singularity.Comment: 5 pages, 2 figures. Updated references and minor changes to match the
version accepted for publishing in PR
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
Radial asymptotics of Lemaitre-Tolman-Bondi dust models
We examine the radial asymptotic behavior of spherically symmetric
Lemaitre-Tolman-Bondi dust models by looking at their covariant scalars along
radial rays, which are spacelike geodesics parametrized by proper length
, orthogonal to the 4-velocity and to the orbits of SO(3). By introducing
quasi-local scalars defined as integral functions along the rays, we obtain a
complete and covariant representation of the models, leading to an initial
value parametrization in which all scalars can be given by scaling laws
depending on two metric scale factors and two basic initial value functions.
Considering regular "open" LTB models whose space slices allow for a diverging
, we provide the conditions on the radial coordinate so that its
asymptotic limit corresponds to the limit as . The "asymptotic
state" is then defined as this limit, together with asymptotic series expansion
around it, evaluated for all metric functions, covariant scalars (local and
quasi-local) and their fluctuations. By looking at different sets of initial
conditions, we examine and classify the asymptotic states of parabolic,
hyperbolic and open elliptic models admitting a symmetry center. We show that
in the radial direction the models can be asymptotic to any one of the
following spacetimes: FLRW dust cosmologies with zero or negative spatial
curvature, sections of Minkowski flat space (including Milne's space), sections
of the Schwarzschild--Kruskal manifold or self--similar dust solutions.Comment: 44 pages (including a long appendix), 3 figures, IOP LaTeX style.
Typos corrected and an important reference added. Accepted for publication in
General Relativity and Gravitatio
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
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