Abstract

The divergence in the energy density of zero-point radiation can be removed by addition of self-gravitational potential energy density, provided that the resulting finite energy density closes the universe at radius R. Gravitational renormalization removes also the divergence of the self-energy of the electron. The black hole condition is satisfied at r = R, for both internal and external motion. Extended Newtonian cosmology in flat space-time is valid only with coordinate-dependent units. The equivalent Einstein cosmology (with constant units) is that of de Sitter space-time. Being a black hole, the universe is perfectly isolated from the rest of the cosmos, and is one of an infinity of universes. A universe is to be regarded as an isolated system surrounding any test mass m whose boundary surface adjusts so as to produce at m in the rest frame of m a constant gravitational potential irrespective of the distribution of surrounding matter.