Analytic Analysis of Irregular Discrete Universes
arXiv:1802.07135 · doi:10.1007/s10714-018-2436-7
Abstract
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 (LRS), 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
arXiv comment25 pages, 22 figures, v.2 is updated with couple of new references, discusses related work and fixed some spelling errors
References in corpus (14)
- Backreaction in late-time cosmology
- The universe seen at different scales
- Is there proof that backreaction of inhomogeneities is irrelevant in cosmology?
- General Relativistic 1+3 Orthonormal Frame Approach Revisited
- What is dust? - Physical foundations of the averaging problem in cosmology
- Topological Lensing in Spherical Spaces
- An exact quantification of backreaction in relativistic cosmology
- Evolution of a periodic eight-black-hole lattice in numerical relativity
- Exact Evolution of Discrete Relativistic Cosmological Models
- Backreaction and continuum limit in a closed universe filled with black holes
- Black-Hole Lattices as Cosmological Models
- On the vacuum Einstein equations along curves with a discrete local rotational and reflection symmetry
- Nonlinear effects of general relativity from multiscale structure
- The Magnetic Part of the Weyl Tensor, and the Expansion of Discrete Universes