Phase transitions in neutron stars and maximum masses

Using the most recent realistic effective interactions for nuclear matter w ith a smooth extrapolation to high densities including causality, we constr ain 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-cir cle dot. from quasi-periodic oscillations in low-mass X-ray binaries are co nfirmed, a soft equation of state as well as strong phase transitions can b e excluded in neutron star cores.