Piecewise silence in discrete cosmological models

Abstract

We consider a family of cosmological models in which all mass is confined to a regular lattice of identical black holes. By exploiting the reflection symmetry about planes that bisect these lattices into identical halves, we are able to consider the evolution of a number of geometrically distinguished surfaces that exist within each of them. We find that the evolution equations for the reflection symmetric surfaces can be written as a simple set of Friedmann-like equations, with source terms that behave like a set of interacting effective fluids. We then show that gravitational waves are effectively trapped within small chambers for all time, and are not free to propagate throughout the space-time. Each chamber therefore evolves as if it were in isolation from the rest of the universe. We call this phenomenon 'piecewise silence'.

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.…”

Post-Newtonian cosmological models

“…The existence of a radiation-like term has also been found previously in other models. Firstly, in the case of regularly arranged black holes in a lattice under reflective symmetric boundary conditions 14 , and secondly in the case of the short wavelength approximation for fluctuations around a background metric 15 .…”

On the energy content of electromagnetic and gravitational plane waves through super-energy tensors

“…(2.6)). The latter then turns out to be P (g) 29) and is timelike. As stated above, replacing in region IV u → u + and v → v + allows the extension of the metric to the whole spacetime ds 2 I = − 4dudv + dx 2 + dy 2 ,…”