  A rotating stationary solution of the vacuum Einstein equations with a
cosmological constant is exhibited which reduces to de Sitter's interior
cosmological solution when the angular momentum goes to zero. This solution is
locally isomorphic to de Sitter space, but as one approaches the axis of
rotation a conical event horizon appears that signals the appearance of a new
phase of space-time. This suggests that in reality rotating compact objects
have a vortex structure similar to that conjectured for rotating superfluid
droplets. In the limit of slow rotation the vortex core would be nearly
cylindrical and the space-time inside the core would be Godel-like. The
exterior space-time will resemble the Kerr solution for equatorial latitudes,
but significant deviations from Kerr are expected for polar latitudes.
