Applied Analysis Seminar Stability of Liquid Lane–Emden Stars

A star is a lump of fluid surrounded by a vacuum, where internal pressure acts to expand the fluid while self-gravity acts to compress it. The classical (Newtonian) model describing these dynamics is the Euler–Poisson system: the compressible Euler equations coupled with the Poisson equation within a free-boundary framework. Two important classes of spherically symmetric solutions are the Lane–Emden stars, which represent time-independent stars in hydrostatic equilibrium, and the Goldreich–Weber stars, which describe expanding and collapsing bodies (modeling phenomena such as supernovae). In our universe, we observe both stable stars like our Sun and unstable ones that, for example, collapse into black holes. This motivates the study of the stability of these stellar solutions. While the stability and instability of classical gaseous Lane–Emden stars have been extensively studied, the classical gaseous model fails to exhibit certain relevant relativistic effects. I will discuss my recent results concerning liquid stars with the stiffened gas equation of state (p = \rho^\gamma - 1) and how it connects with, and behaves similarly to, the relativistic model given by the Einstein–Euler system.