Persistence in black hole lattice cosmological models

Abstract: Dynamical solutions for an evolving multiple network of black holes near a cosmological bounce dominated by a scalar field are investigated. In particular, we consider the class of black hole lattice models in a hyperspherical cosmology, and we focus on the special case of eight regularly-spaced black holes with equal masses when the model parameter $\kappa > 1$. We first derive exact time evolving solutions of instantaneously-static models, by utilizing perturbative solutions of the constraint equations that can then be used to develop exact 4D dynamical solutions of the Einstein field equations. We use the notion of a geometric horizon, which can be characterized by curvature invariants, to determine the black hole horizon. We explicitly compute the invariants for the exact dynamical models obtained. As an application, we discuss whether black holes can persist in such a universe that collapses and then subsequently bounces into a new expansionary phase. We find evidence that in the physical models under investigation (and particularly for $\kappa > 1$) the individual black holes do not merge before nor at the bounce, so that consequently black holes can indeed persist through the bounce.