The Black Hole Universe, Part I

Abstract

The original Friedmann (1922) and Lemaitre (1927) cosmological model corresponds to a classical solution of General Relativity (GR), with the same uniform (FLRW) metric as the standard cosmology, but bounded to a sphere of radius R and empty space outside. We study the junction conditions for R to show that a co-moving observer, like us, located anywhere inside R, measures the same background and has the same past light-cone as an observer in an infinite FLRW with the same density. We also estimate the mass M inside R and show that in the observed universe R<rS≡2 GM, which corresponds to a Black Hole Universe (BHU). We argue that this original Friedmann–Lemaitre model can explain the observed cosmic acceleration without the need of Dark Energy, because rS acts like a cosmological constant Λ=3/r2S. The same solution can describe the interior of a stellar or galactic BHs. In co-moving coordinates the BHU is expanding while in physical or proper coordinates it is asymptotically static. Such frame duality corresponds to a simple Lorentz transformation. The BHU therefore provides a physical BH solution with an asymptotically deSitter metric interior that merges into a Schwarzschild metric exterior without discontinuities.