Shell crossings and the Tolman model

Hellaby, Charles; Lake, Kayll

doi:10.1086/162995

Cited by 148 publications

(238 citation statements)

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“…If they occur between t 1 & t 2 the model evolution is unsatisfactory, but if they occur before t 1 or after t 2 , this may not be of much concern. The conditions on E(M) & t B (M) for avoiding them [7] must also be checked.…”

Section: Discussionmentioning

confidence: 99%

“…Also the space t = const with E(r) < 0 everywhere is not necessarily closed (and the one with E(r) > 0 is not necessarily infinite), see Refs. [7,8].…”

Section: The Lemaître-tolman (L-t) Modelmentioning

confidence: 99%

“…We also, in searching for realistic models, prefer L-T models that are free of shell crossings [7]. This is not because shells of matter cannot collide, but because the L-T co-moving description breaks down there.…”

Section: The Lemaître-tolman (L-t) Modelmentioning

confidence: 99%

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Structure formation in the Lemaître-Tolman model

2001

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Structure formation within the Lemaître-Tolman model is investigated in a general manner. We seek models such that the initial density perturbation within a homogeneous background has a smaller mass than the structure into which it will develop, and the perturbation then accretes more mass during evolution. This is a generalisation of the approach taken by Bonnor in 1956. It is proved that any two spherically symmetric density profiles specified on any two constant time slices can be joined by a Lemaître-Tolman evolution, and exact implicit formulae for the arbitrary functions that determine the resulting L-T model are obtained. Examples of the process are investigated numerically.

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Section: Discussionmentioning

confidence: 99%

“…Also the space t = const with E(r) < 0 everywhere is not necessarily closed (and the one with E(r) > 0 is not necessarily infinite), see Refs. [7,8].…”

Section: The Lemaître-tolman (L-t) Modelmentioning

confidence: 99%

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Structure formation in the Lemaître-Tolman model

2001

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“…Note that if t SC and t SF are sufficiently smooth (in fact only continuous), then the SCS occurs at values of R forming disjoint open subsets. Furthermore, it is possible to identify these open subsets in terms of the initial data E(R), m(R) [13]. The co-ordinate freedom can be used to set r(R, 0) = R, and so the initial density is µ := ρ(R, 0) = m ′ /R 2 .…”

Section: Existence Of Weak Solutionsmentioning

confidence: 99%

Dynamical extensions for shell-crossing singularities

Nolan

2003

Class. Quantum Grav.

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Abstract. We derive global weak solutions of Einstein's equations for spherically symmetric dust-filled space-times which admit shell-crossing singularities. In the marginally bound case, the solutions are weak solutions of a conservation law. In the non-marginally bound case, the equations are solved in a generalized sense involving metric functions of bounded variation. The solutions are not unique to the future of the shell-crossing singularity, which is replaced by a shock wave in the present treatment; the metric is bounded but not continuous.

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“…The conditions on the 3 arbitrary functions of the model that ensure none be present anywhere in an L-T model are given in [8].…”

Section: Use Of Exact Inhomogeneous Models In Astrophysics and Cosmologymentioning

confidence: 99%

Inhomogeneities in the Universe with exact solutions of General Relativity

Célérier

2010

AIP Conference Proceedings

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It is commonly stated that we have entered the era of precision cosmology in which a number of important observations have reached a degree of precision, and a level of agreement with theory, that is comparable with many Earth-based physics experiments. One of the consequences is the need to examine at what point our usual, well-worn assumption of homogeneity associated to the use of perturbation theory begins to compromise the accuracy of our models. It is now a widely accepted fact that the effect of the inhomogeneities observed in the Universe cannot be ignored when one wants to construct an accurate cosmological model. Well-established physics can explain several of the observed phenomena without introducing highly speculative elements, like dark matter, dark energy, exponential expansion at densities never attained in any experiment (i.e. inflation), and the like. Two main classes of methods are currently used to deal with these issues. Averaging, sometimes linked to fitting procedures a la Stoegger and Ellis, provide us with one promising way of solving the problem. Another approach is the use of exact inhomogeneous solutions of General Relativity. This will be developed here.

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Shell crossings and the Tolman model

Cited by 148 publications

References 0 publications

Structure formation in the Lemaître-Tolman model

Structure formation in the Lemaître-Tolman model

Dynamical extensions for shell-crossing singularities

Inhomogeneities in the Universe with exact solutions of General Relativity

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