  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.
