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

摘要

The geometry of three-dimensional space guides the search for a better modelthan the blackhole with its unwelcome singularity. An elementary constructionproduces on the 4-manifold of 2-spheres in a Riemannian 3-space a space-timemetric invariant under uniform conformal transformations of the 3-space. Whenthe 3-space is Euclidean, the metric reduces to de Sitter's expanding universemetric. Generalization yields a space-time metric that retains the `exponentialexpansion property' of the de Sitter metric. A strictly geometric actionprinciple gives field equations which, because they do not adhere to Einstein'searly confounding of energy and inertial mass with gravitating mass, admitsolutions that escape the Penrose-Hawking singularity theorems. A sphericallysymmetric solution that is asymptotic to the Schwarzschild blackhole metrichas, in place of a horizon and a singularity, an Einstein-Rosen `bridge', or`tunnel', connecting two asymptotically Euclidean regions. On one side thegravitational center attracts, and is dark but not black; on the other side itrepels, and is bright. Travel and signaling from either side to the other viathe tunnel are possible. Analysis of the Einstein tensor of this `darkhole' (or`darkhole-brighthole') suggests that not all energy produces gravity, and thatcalling energy `negative', or its relationship to geometry `exotic', isunjustified.