A slowly rotating perfect fluid body in an ambient vacuum
  A global model of a slowly rotating perfect fluid ball in general relativity is presented. To second order in the rotation parameter, the junction surface is an ellipsoidal cylinder. The interior is given by a limiting case of the Wahlquist solution, and the vacuum region is not asymptotically flat. The impossibility of joining an asymptotically flat vacuum region has been shown in a preceding work. 
Michael Bradley, Gyula Fodor and Zolt\'an Perj\'es