The idea of the universe as a black hole revisited

Abstract

The Friedmann equation for a homogeneous and isotropic universe model with a cosmological constant yields the eventual maximal expansion of a closed dust universe. On the other hand, from the line element for the false vacuum outside a spherically matter distribution we obtain the generalized Schwarzschild radius, i.e., the position of the event horizon. It has been argued that the mathematical similarity of these two quantities cannot be a coincidence, but means that the universe is inside a black hole. We show that this interpretation is wrong. Matching the two metrics, we find what we intuitively expect: our expanding universe cannot be inside the event horizon of the vacuum metric.