Black Hole Lattices Under the Microscope

TL;DR

This paper investigates the local curvature of initial data for multiple black hole configurations on a 3-sphere, revealing that asymptotic regions resemble Schwarzschild black holes and that random arrangements exhibit slightly reduced cosmological backreaction.

Contribution

It provides a detailed analysis of the local curvature in black hole lattice initial data, comparing regular and random configurations and their effects on cosmological backreaction.

Findings

Asymptotic regions are close to Schwarzschild geometry.

Random configurations have slightly smaller cosmological backreaction.

Region between black holes shows interesting curvature behavior.

Abstract

It is known how to choose initial data for Einstein's equations describing an arbitrary number of black holes at a moment of time symmetry. This idea has been used to give insight into the cosmological averaging problem. We study the local curvature of the initial data space, for configurations of 8, 120, or 600 black holes obtained by choosing points either regularly or randomly on the 3-sphere. We conclude that the asymptotic regions are remarkably close to that of Schwarzschild, while the region in between shows interesting behaviour. The cosmological back reaction as defined in the recent literature is actually a bit smaller for the random configurations.