Evolution of radial profiles in regular Lemaitre-Tolman-Bondi dust models

Sussman, Roberto A.

doi:10.48550/arxiv.1005.0717

Cited by 11 publications

(52 citation statements)

References 38 publications

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“…Obtaining numerically Ω b , Ω m , Ω e , δ (b) , δ (m) , δ (e) , δ (H) and H q (ξ, r i ), it is possible to obtain the rest of the scalars that characterize the LTB metric: the QL baryonic, CDM and DE densities as (18), the spatial curvature and its fluctuation δ (κ) from the constraints (20), and the corresponding local scalars A = H, K, ρ b , ρ m , ρ e , J from…”

Section: Critical Points (ωmentioning

confidence: 99%

“…Thus, the initial conditions considered in the numerical work must avoid an evolution towards a shell crossing, i.e., Γ > 0 must hold throughout the evolution. For LTB dust solutions with Λ = 0 it is possible to state analytic restrictions on initial conditions to guarantee an evolution with no shell crossings ( [15,16,17,20]), but for the solutions with nonzero pressure that we are considering here this can only be achieved by numerical trial and error of initial conditions.…”

Section: Ql Scalars Scaling Laws and Shell-cross Singularitiesmentioning

confidence: 99%

“…However, these exact solutions are also compatible with nonzero pressures (something that it is often not known). In particular, it is possible to define a class of "quasi-local scalars" (QL scalars [19,20,21,22]) that allow for a clear, yet complete, description of the theoretical properties and evolution of sources with zero and nonzero pressure in terms of averages of standard covariant scalars satisfying FLRW dynamics, with the deviation from a FLRW background described by fluctuations with respect to the QL scalars [21], all this with both the QL scalars and fluctuations being coordinate independent covariant quantities [22]). The QL scalars and their fluctuations transform Einstein's field equations for LTB models into evolution equations that can be set up as a self-consistent dynamical system (e.g., as has been done for dust models without and with a cosmological constant term, in [23,24] and [25] respectively).…”

Section: Introductionmentioning

confidence: 99%

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Evolution equations dynamical system of the Lemaître--Tolman--Bondi metric containing coupled dark energy

Blanquet-Jaramillo,

Sussman,

Aguero

et al. 2022

Preprint

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We consider inhomogeneous spherically symmetric models based on the Lemaître-Tolman-Bondi (LTB) metric, assuming as its source an interactive mixture of ordinary baryonic matter, cold dark matter and dark energy with a coupling term proportional to the addition of energy densities of both dark fluids. We reduce Einstein's field equations to a first order 7-dimensional autonomous dynamical system of evolution equations and algebraic constraints. We study in detail the evolution of the energy density and spatial curvature profiles along the phase space by means of two subspace projections: a three-dimensional projection associated with the solutions of the Friedman-Lemaître-Robertson-Walker metric (invariant subspace) and a four-dimensional projection describing the evolution of the inhomogeneous fluctuations. We also classify and study the critical points of the system in comparison with previous work on similar sources, as well as solving numerically the equations for initial energy density and curvature profiles that lead to a spherical bounce whose collapsing time we estimate appropriately.

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Section: Critical Points (ωmentioning

confidence: 99%

Section: Ql Scalars Scaling Laws and Shell-cross Singularitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Evolution equations dynamical system of the Lemaître--Tolman--Bondi metric containing coupled dark energy

Blanquet-Jaramillo,

Sussman,

Aguero

et al. 2022

Preprint

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show abstract

“…These solutions have been extensively studied (with zero and nonzero cosmological constant) and used in a wide range of astrophysical and cosmological modelling (see extensive reviews in [22,23,24,25]). In particular, a better understanding of their theoretical properties follows by describing their dynamics in terms of "quasi-local scalars" [26,27,28,29] (to be denoted henceforth as "q-scalars"), which are related to averages of standard covariant scalars and satisfy FLRW dynamical equations and scaling laws [28].…”

Section: Introductionmentioning

confidence: 99%

Interactive mixture of inhomogeneous dark fluids driven by dark energy: a dynamical system analysis

2018

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We examine the evolution of an inhomogeneous mixture of non-relativistic pressureless cold dark matter (CDM), coupled to dark energy (DE) characterised by the equation of state parameter w < −1/3, with the interaction term proportional to the DE density. This coupled mixture is the source of a spherically symmetric Lemaître-Tolman-Bondi (LTB) metric admitting an asymptotic Friedman-Lemaître-Robertson-Walker (FLRW) background. Einstein's equations reduce to a 5-dimensional autonomous dynamical system involving quasi-local variables related to suitable averages of covariant scalars and their fluctuations. The phase space evolution around the critical points (past/future attractors and five saddles) is examined in detail. For all parameter values and both directions of energy flow (CDM to DE and DE to CDM) the phase space trajectories are compatible with a physically plausible early cosmic times behaviour near the past attractor. This result compares favourably with mixtures with interaction driven by the CDM density, whose past evolution is unphysical for DE to CDM energy flow. Numerical examples are provided describing the evolution of an initial profile that can be associated with idealised structure formation scenarios.

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“…Another important feature of the LTB space-time is a possibility of describing voids formation (see [3] including a historical review of voids discovery). And even more cosmological and theoretical applications of that remarkable solution can be found in [4].…”

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confidence: 96%

A Weak Solution of Einstein Equations for Expanding Dust

Tegai¹

2012

The Twelfth Marcel Grossmann Meeting

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An expanding spherically symmetric dust cloud is considered in a framework of general relativity. Initial conditions leading to a shell-crossing singularity are chosen. The way to construct a weak solution for such a case is proposed. Suggested method consists in cutting off the region containing the shell-crossing and matching the remaining parts of space-time at a thin shell. Junction conditions determine the motion of that thin shell. The singular part of dust stress-energy tensor is nontrivial only after the shell-crossing occurs. Before that the solution coincides with Lemaitre -TolmanBondi one. A toy model representing an underdensed region in Universe is discussed. One of the less studied properties of the LTB solution is the formation of shell-crossing singularities (SCS) for certain initial conditions. The cause for it is the intersection of initially different dust layers resulting in diverging and even negative density. The employing of frameworks other then a co-moving one merely brings the metric tensor to a regular form [5] but can't remove the singularity because it is in fact a physical but not a coordinate effect. For that reason the initial conditions leading to a SCS are usually avoided even if it seems unfortunate.The nature of SCS was investigated by different authors [6-9] and the conclusion is that it has a different ("weak" or "inessential") type from a shell-focusing singularity and therefore the solution can be extended beyond the SCS. The first example of such an extension was provided in [6] for a rather special case of spacetime. Further works [8,10] suggest the extension to be a weak solution of Einstein equations. In [11] such weak solutions are derived treating SCS as a shock wave and using Rankine -Hugoniot conditions. Unlike the classical solution the weak one is not unique to the future of the shell-crossing singularity even for well posed initial conditions. There is a weak or extended solution which has singular part in stress-energy tensor and there is still * Electronic address: tegai s f@inbox.ru a classical solution which is a special case of a weak solution with only regular distributions involved.Here we introduce another way to find a weak solution employing Israel -Darmois -Lichnerowicz junction formalism [12]. The idea is to cut out the unphysical regions with negative density and match the remaining parts of the space-time at a thin shell. Of course models with thin shells are nothing new in cosmology and were first studied in [13]. However the important difference is that the thin shell in present work arises from smooth initial conditions.Israel -Darmois -Lichnerowicz matching procedure can be viewed as a consequence of dealing with field equations in a framework of tensor distributions [14]. The same is true for relativistic Rankine -Hugoniot equations which are identical to O'Brien -Singe conditions while written in general form of energy and momentum conservation across the junction surface [15]. Thus relying on the matching scheme one can expect to get the sam...

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Evolution of radial profiles in regular Lemaitre-Tolman-Bondi dust models

Cited by 11 publications

References 38 publications

Evolution equations dynamical system of the Lemaître--Tolman--Bondi metric containing coupled dark energy

Evolution equations dynamical system of the Lemaître--Tolman--Bondi metric containing coupled dark energy

Interactive mixture of inhomogeneous dark fluids driven by dark energy: a dynamical system analysis

A Weak Solution of Einstein Equations for Expanding Dust

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