Abstract: The gravitational waves emitted from a binary neutron star merger, as predicted from general relativistic magneto-hydrodynamics calculations, are sensitive to the appearance of quark matter and the stiffness of the equation of state of QCD matter present in the inner cores of the stars. These astrophysically created extremes of thermodynamics do match, to within 20%, the values of densities and temperatures which are found in relativistic heavy ion collisions, if though at quite different rapidity windows, impact parameters and bombarding energies of the heavy nuclear systems. In this article we combine the results obtained in general relativistic simulations of binary neutron star systems with ones from heavy ion collisions in the lab to pin down the EOS and the phase structure of dense matter. We discuss that the postmerger gravitational wave emission of the neutron star merger remnant might give, in the near future, insides about the properties of the hadron quark transition.