Phase transitions in neutron stars and maximum masses

Using the most recent realistic effective interactions for nuclear matter with a smooth extrapolation to high densities including causality, we constrain the equation of state and calculate maximum masses of rotating neutron stars. First- and second-order phase transitions to, e.g., quark matter at high densities are included. If neutron star masses of similar to 2.3 M-circle dot. from quasi-periodic oscillations in low-mass X-ray binaries are confirmed, a soft equation of state as well as strong phase transitions can be excluded in neutron star cores.