Continua of steadily rotating stars

I will survey some recent mathematical work on rotating stars that is joint with Yilun (Allen) Wu and also partly with Juhi Jang. The rotating star is modeled as a compressible fluid subject to gravity. Under certain conditions there exists a large family of solutions on which the supports of the stars become unbounded. The stars have a fixed mass and they rotate around a fixed axis.  Their speeds of rotation vary along the family.  I will also mention some more elaborate models, including one that permits the entropy to be variable.