We identify the condition for smoothness at the center of spherically symmetric solutions of Einstein’s original equations (without the cosmological constant), and use this to derive a universal phase portrait which describes general, smooth, spherically symmetric solutions near the center of symmetry when the pressure $p=0$. In this phase portrait, the critical $k=0$, $p=0$ Friedmann spacetime appears as an unstable saddle rest point. This phase portrait tells us that the Friedmann spacetime is unstable to spherical perturbations when the pressure drops to zero, no matter what point is taken to be the center, and in this sense it is unobservable by redshift vs luminosity measurements looking outward from any point. Moreover, the unstable manifold of the saddle rest point corresponding to Friedmann describes the evolution of smooth perturbations, and we show that this evolution creates local uniformly expanding spacetimes which, in the under-dense case, create precisely the same range of quadratic corrections to redshift vs luminosity as does Dark Energy in the form of a nonzero cosmological constant. Thus the anomalous accelerations inferred from the supernova data are not only consistent with Einstein’s original theory of GR, but are a prediction of it.

This is joint work with Joel Smoller and Zeke Vogler.