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We study the oscillations of relativistic stars, incorporating key physicsassociated with internal composition, thermal gradients and crust elasticity.Our aim is to develop a formalism which is able to account for thestate-of-the-art understanding of the complex physics associated with thesesystems. As a first step, we build models using a modern equation of stateincluding composition gradients and density discontinuities associated withinternal phase-transitions (like the crust-core transition and the point wheremuons first appear in the core). In order to understand the nature of theoscillation spectrum, we carry out cooling simulations to provide realisticsnapshots of the temperature distribution in the interior as the star evolvesthrough adolescence. The associated thermal pressure is incorporated in theperturbation analysis, and we discuss the presence of $g$-modes arising as aresult of thermal effects. We also consider interface modes due tophase-transitions and the gradual formation of the star's crust and theemergence of a set of shear modes.

Seismology of adolescent neutron stars: Accounting for thermal effects and crust elasticity