Evolution of a periodic eight-black-hole lattice in numerical relativity

Abstract

Abstract. The idea of black-hole lattices as models for the large-scale structure of the universe has been under scrutiny for several decades, and some of the properties of these systems have been elucidated recently in the context of the problem of cosmological backreaction. The complete, three-dimensional and fully relativistic evolution of these system has, however, never been tackled. We explicitly construct the first of these solutions by numerically integrating Einstein's equation in the case of an eight-black-hole lattice with the topology of S 3 .

Integration of inhomogeneous cosmological spacetimes in the BSSN formalism

“…However, it has also been applied to cosmological problems in the early universe, such as critical collapse in a radiation fluid [5,6], black hole lattices (eg. [7]), and more (for a recent review, see [8]). Here we examine the performance of the BSSN formalism in the context of a matter-dominated cosmological spacetime, and draw comparisons between FLRW spacetimes and perturbed FLRW spacetimes.…”

Black hole universe with a cosmological constant

“…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.…”

“…Time evolution of the 8-black hole system has been performed and analyzed in Ref. [7]. Initial data for a black hole inside a cubic box with a periodic boundary condition have been constructed and analyzed in Refs.…”

“…[3,8], and those time evolutions have been investigated in Refs. [2,7]. We call this cubic lattice model the "black hole universe" in this paper.…”

Solving the Einstein constraints in periodic spaces with a multigrid approach

“…the collection introduced in [1]). Numerical studies in classical, latetime cosmology, examples of which can be found thoughout the history of Numerical Relativity [2,3,4,5,6], have also seen a surge both in demand [7,8,9,10,11,12,13] and in results [14,15].…”