Self-gravitating Superfluids: The Gross-Pitaevskii-Poisson Framework

We provide an overview of the Gross-Pitaevskii-Poisson equation (GPPE) that is used to model self-gravitating superfluid systems, which include gravitationally collapsed boson and axion stars and dark-matter haloes. We outline how this framework can be used to develop minimal models for neutron stars and for pulsars and their glitches. We account not only for vortices in the neutron superfluid inside these stars, but also for the flux tubes in the proton-superconductor subsystem, using a coupled model with the neutron superfluid, proton superconductor, the Maxwell equations for the vector potential ${\bf A}$, and the Poisson equation for self-gravity.