We investigate the viability of a new type of compact star whose main constituent is a Bose-Einstein condensate of charged pions. Several different setups are considered, where a gas of charged leptons and neutrinos is also present. The pionic equation of state is obtained from lattice QCD simulations in the presence of an isospin chemical potential and requires no modeling of the nuclear force. The gravitationally bound configurations of these systems are found by solving the Tolman-Oppenheimer-Volkoff equations. We discuss weak decays within the pion condensed phase and elaborate on the generation mechanism of such objects.

If a first-order phase transition separates nuclear and quark matter at large baryon density, an interface between these two phases has a nonzero surface tension. We calculate this surface tension within a nucleon-meson model for domain walls and bubbles. Various methods and approximations are discussed and compared, including a numerical evaluation of the spatial profile of the interface. We also compute the surface tension at the other first-order phase transitions of the model: the nuclear liquid-gas transition and, in the parameter regime where it exists, the direct transition from the vacuum to the (approximately) chirally symmetric phase. Identifying the chirally symmetric phase with quark matter -our model does not contain explicit quark degrees of freedom -we find maximal surface tensions of the vacuum-quark transition ΣVQ ∼ 15 MeV/fm 2 , relevant for the surface of quark stars, and of the nuclear-quark transition ΣNQ ∼ 10 MeV/fm 2 , relevant for hybrid stars and for quark matter nucleation in supernovae and neutron star mergers.

The fundamental nature of dark matter is entirely unknown. A compelling candidate is Twin Higgs mirror matter, invisible hidden-sector cousins of the Standard Model particles and forces. This predicts mirror neutron stars made entirely of mirror nuclear matter. We find their structure using realistic equations of state, robustly modified based on first-principle quantum chromodynamic calculations, for the first time. This allows us to predict their gravitational wave signals, demonstrating an impressive discovery potential and ability to probe dark sectors connected to the hierarchy problem.