Lecture XXI: Radial pulsations and stability

Having constructed the equilibrium stellar configurations, we are now poised to ask whether they are stable to small perturbations. This leads us to the subject of relativistic stellar pulsations. One may classify such pulsations by their angular dependence: when we investigate the full subject we will find modes of every spherical harmonic index l ≥ 0. However, for the cold stars of interest to us the only unstable objects are those with purely radial (l = 0) unstable modes. In particular, the sequence of stars in between white dwarfs and neutron stars (whose cores are made of the mixed nuclei-in-neutron-gas phase) is unstable against radial oscillations: if infinitesimally perturbed, such an object either implodes to a neutron star, or explodes into a cloud of neutron-rich radioactive matter. Reading: