The emitted gravitational waves from 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. This is a new observable messenger from outer space, which does provide direct signals for the phase structure of strongly interacting QCD matter at high baryon density and high temperature. These astrophysically created extremes of thermodynamics do match, to within 20%, the values of densities and temperatures which we find in relativistic hydrodynamics and transport theory of heavy ion collisions at the existing laboratories, if though at quite different rapidity windows, impact parameters and bombarding energies of the heavy nuclear systems. We demonstrate how one unified equation of state can be constructed and used for both neutron star physics and hot QCD matter excited at laboratory facilities. The similarity in underlying QCD physics allows the gravitational wave signals from future advanced LIGO and Virgo events be combined with the analysis of high multiplicity fluctuations and flow measurements in heavy ion detectors in the lab to pin down the EoS and the phase structure of dense matter.