  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. This is a new
messenger observable 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 to 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.
