Darkholes: Nicer than blackholes - with a bright side, too (Does energy produce gravity?)

Abstract

The geometry of three-dimensional space guides the search for a better model than the blackhole with its unwelcome singularity. An elementary construction produces on the 4-manifold of 2-spheres in a Riemannian 3-space a space-time metric invariant under uniform conformal transformations of the 3-space. When the 3-space is Euclidean, the metric reduces to de Sitter's expanding universe metric. Generalization yields a space-time metric that retains the `exponential expansion property' of the de Sitter metric. A strictly geometric action principle gives field equations which, because they do not adhere to Einstein's early confounding of energy and inertial mass with gravitating mass, admit solutions that escape the Penrose-Hawking singularity theorems. A spherically symmetric solution that is asymptotic to the Schwarzschild blackhole metric has, in place of a horizon and a singularity, an Einstein-Rosen `bridge', or `tunnel', connecting two asymptotically Euclidean regions. On one side the gravitational center attracts, and is dark but not black; on the other side it repels, and is bright. Travel and signaling from either side to the other via the tunnel are possible. Analysis of the Einstein tensor of this `darkhole' (or `darkhole-brighthole') suggests that not all energy produces gravity, and that calling energy `negative', or its relationship to geometry `exotic', is unjustified.