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The inner crust of a mature neutron star is composed of an elastic lattice ofneutron-rich nuclei penetrated by free neutrons. These neutrons can flowrelative to the crust once the star cools below the superfluid transitiontemperature. In order to model the dynamics of this system, which is relevantfor a range of problems from pulsar glitches to magnetar seismology andcontinuous gravitational-wave emission from rotating deformed neutron stars, weneed to understand general relativistic Lagrangian perturbation theory forelastic matter coupled to a superfluid component. This paper develops therelevant formalism to the level required for astrophysical applications.

The dynamics of neutron star crusts: Lagrangian perturbation theory for a relativistic superfluid-elastic system