Global Continuation and the Theory of Rotating Stars

This paper gives a condensed review of the history of solutions to the Euler-Poisson equations modeling equilibrium states of rotating stars and galaxies, leading to a recent result of Walter Strauss and the author. This result constructs a connected set of rotating star solutions for larger and larger rotation speed, so that the supports of the stars become unbounded if we assume an equation of state $p={\rho }^{\gamma }$, $4\mathrm{/}3<\gamma <2$. On the other hand, if $6\mathrm{/}5<\gamma <4\mathrm{/}3$, we show that either the supports of the stars become unbounded, or the density somewhere within the stars becomes unbounded. This is the first global continuation result for rotating stars that displays singularity formation within the solution set.