Novel phases and transitions in Color Flavor Locked matter

We analyze the phases of dense quark matter at nonzero quark masses. We map out the phase diagrams for charged quark matter as well as charge neutral matter containing leptons. We find that in Color Flavor Locked (CFL) quark matter, the symmetric phase with equal numbers of $u$, $d$ and $s$ quarks is unlikely to occur in nature. Various less symmetric phases with additional meson condensates may play a role in neutron star cores, however, in agreement with the analysis of Bedaque and Sch\"afer. We discuss the implications of these novel color superconducting quark matter phases and their transitions for neutron stars.