Exact evolution of discrete relativistic cosmological models

Clifton, Timothy; Gregoris, Daniele; Rosquist, Kjell; Tavakol, Reza

doi:10.1088/1475-7516/2013/11/010

Cited by 47 publications

(142 citation statements)

References 45 publications

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“…Unfortunately it cannot be used in our case because it is infinite, due to of the infinite volume inside the black holes. In [29,20,22], where only regular lattice configurations are considered, the size is defined by matching the size of the lattice cell to a corresponding lattice cell in the FLRW model. This is not possible in the general case where no symmetries are present and no curves are geometrically distinguished.…”

Section: Flrw Fitting and Effective Parametersmentioning

confidence: 99%

“…H 8 is identical to the original regular 8-black-hole model R 8 and all subsequent configurations inherit the whole group of discrete symmetries of R 8 . In particular, it is noteworthy that the edges of the big quasi-cubes in all H N are locally rotationally symmetric curves in the sense of [22] and the exact, relativistic evolution along them can be investigated using the same methods.…”

Section: Construction Of the Sequencementioning

confidence: 99%

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Backreaction and continuum limit in a closed universe filled with black holes

Korzyński

2014

Class. Quantum Grav.

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Abstract. We discuss the continuum limit of the initial data for a vacuum, closed cosmological model with black holes as the only sources of the gravitational field. The model we consider is an exact solution of the constraint equations and represents a vacuum universe with a number of black holes placed on a spatial slice of S 3 topology considered at the moment of its largest expansion when the black holes are momentary at rest. We explain how and under what conditions the FLRW metric arises as the continuum limit when the number of black holes contained in the model goes to infinity. We also discuss the relation between the effective cosmological parameters of the model, inferred from the large scale geometry of the spacetime, and the masses of individual black holes. In particular, we prove an estimate for the difference between the total effective mass of the system and the sum of the masses of all black holes, thus quantifying the effects of the inhomogeneities in the matter distribution or the cosmological backreaction.

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Section: Flrw Fitting and Effective Parametersmentioning

confidence: 99%

Section: Construction Of the Sequencementioning

confidence: 99%

Backreaction and continuum limit in a closed universe filled with black holes

Korzyński

2014

Class. Quantum Grav.

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“…The black hole lattice universe is often used as one of tools to evaluate effects of local non-linear inhomogeneities on the global expansion. Recently, black hole lattice universe models have been revisited by several authors [2][3][4][5][6][7][8][9][10][11][12]. Time symmetric initial data for N-black hole systems on a virtual 3-sphere have been analyzed in Refs.…”

Section: Introductionmentioning

confidence: 99%

Black hole universe with a cosmological constant

Yoo

Okawa²

2014

Phys. Rev. D

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Time evolution of a black hole lattice universe with a positive cosmological constant Λ is simulated. The vacuum Einstein equations are numerically solved in a cubic box with a black hole in the center. Periodic boundary conditions on all pairs of opposite faces are imposed. Configurations of marginally trapped surfaces are analyzed. We describe the time evolution of not only black hole horizons, but also cosmological horizons. Defining the effective scale factor by using the area of a surface of the cubic box, we compare it with that in the spatially flat dust dominated FLRW universe with the same value of Λ. It is found that the behaviour of the effective scale factor is well approximated by that in the FLRW universe. Our result suggests that local inhomogeneities do not significantly affect the global expansion law of the universe irrespective of the value of Λ. * Electronic address: yoo@gravity.phys.nagoya-u.ac.jp † Electronic address: hirotada.okawa@ist.utl.pt 2

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“…, n − 1. For n ≥ 3 it can be shown that curves associated with such a discrete symmetry group have the LRS property [6] while for n = 2 this does not follow (see discussion in [5] and [7]). Vectors and tensors satisfying (9) have the following properties when evaluated along LRS curves:…”

Section: Locally Rotationally Symmetric Curvesmentioning

confidence: 99%

“…[3]). A new avenue to address this issue was recently opened by considering a universe filled with Schwarzschild black holes as sources [4][5][6][7][8][9]. The idea is to first specify the sources as initial data on a time-symmetric spatial hypersurface with spherical topology.…”

Section: Introductionmentioning

confidence: 99%

Analytic analysis of irregular discrete universes

Jolin

Rosquist

2018

Gen Relativ Gravit

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In this work we investigate the dynamics of cosmological models with spherical topology containing up to 600 Schwarzschild black holes arranged in an irregular manner. We solve the field equations by tessellating the 3-sphere into eight identical cells, each having a single edge which is shared by all cells. The shared edge is enforced to be locally rotationally symmetric, thereby allowing for solving the dynamics to high accuracy along this edge. Each cell will then carry an identical (up to parity) configuration which can however have an arbitrarily random distribution. The dynamics of such models is compared to that of previous works on regularly distributed black holes as well as with the standard isotropic dust models of the FLRW type. The irregular models are shown to have richer dynamics than that of the regular models. The randomization of the distribution of the black holes is done both without bias and also with a certain clustering bias. The geometry of the initial configuration of our models is shown to be qualitatively different from the regular case in the way it approaches the isotropic model.

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Exact evolution of discrete relativistic cosmological models

Cited by 47 publications

References 45 publications

Backreaction and continuum limit in a closed universe filled with black holes

Backreaction and continuum limit in a closed universe filled with black holes

Black hole universe with a cosmological constant

Analytic analysis of irregular discrete universes

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