On Existence and Properties of Rotating Star Solutions to the Euler-Poisson Equations

The Euler-Poisson equations are used in astrophysics to model rotating gaseous stars. Auchmuty and Beals in 1971 first found a family of rotating star solutions by solving a variational free boundary problem. A great many results followed to generalize the solutions to more diverse situations. Recent interests in extrasolar planet structures require extension of the picture to include a solid rocky core together with its gravitational potential. In this dissertation, we discuss various extensions of the classical rotating star results to incorporate a solid core. We also study the effect of a non-isentropic equation of state on the structure of the rotating star solutions.