Absence of Observed Unspeakably Large Black Holes Tells Us the Curvature of Space

Abstract

Using black-hole arguments with widely accepted premises, we show that it is extremely improbable that space is Euclidean, and that it is unspeakably improbable that space is hyperbolic. Independently, using an argument which makes no appeal to black holes, but only to the ratio of volumes in hyperbolic space of Hubble volumes from different times, we prove that space is not hyperbolic. We conclude by discussing some implications of these results, when conjoined with the assumption that the entropy of a black hole is the hidden information about its internal configuration.