Core-collapse supernova matter: light clusters, pasta phase and phase transitions

The pasta phase in core-collapse supernova matter (finite temperatures and fixed proton fractions) is studied within relativistic mean field models. Two different calculations are used for comparison, the Thomas-Fermi (TF) and the Coexisting Phases (CP) approximations. The effects of including light clusters in nuclear matter and the densities at which the transitions between pasta configurations and to uniform matter occur are also investigated. Finally, a comparison with a finite temperature Skyrme-Hartree-Fock calculation is drawn.