MAGIC - how MAtter's extreme phases can be revealed in Gravitational wave observations and in relativistic heavy Ion Collision experiments

Nearly one hundred years after Albert Einstein developed the field equations of general relativity and predicted the existence of gravitational waves, a gravitational wave event from a binary neutron star merger (GW170817) was detected in August 2017 by the LIGO/VIRGO collaboration. During the thereon analysis of the gravitational wave data, the equation of state of elementary matter could be constrained in the regime of high densities/temperatures. Recent simulations show, that the appearance of a hadron to quark phase transition in the interior region of a hybrid star merger remnant might change the overall properties of the merger event and could be detectable in future. On the one hand, 4D-simulations of binary neutron star mergers show that these astrophysical systems represent optimal laboratories to investigate the phase structure of quantum chromodynamics. On the other hand, accelerators like the FAIR facility at GSI Helmholtzzentrum allow one to study the properties of the quark-gluon plasma produced in relativistic collisions of heavy ions. This article combines a survey of recent advancements in two rather distinct fields, which reveal - on first sight - a surprising similarity of both, namely relativistic collisions of nuclei and of neutron star mergers. (paper)