  We perform three-dimensional relativistic hydrodynamical simulations of the
coalescence of strange stars (SSs) and explore the possibility to decide on the
strange matter hypothesis by means of gravitational-wave (GW) measurements.
Selfbinding of strange quark matter (SQM) and the generally more compact stars
yield features that clearly distinguish SS from neutron star (NS) mergers, e.g.
hampering tidal disruption during the plunge of quark stars. Furthermore,
instead of forming dilute halos around the remnant as in the case of NS
mergers, the coalescence of SSs results in a differentially rotating
hypermassive object with a sharp surface layer surrounded by a geometrically
thin, clumpy high-density SQM disk. We also investigate the importance of
including non-zero temperature equations of state (EoSs) in NS and SS merger
simulations. In both cases we find a crucial sensitivity of the dynamics and
outcome of the coalescence to thermal effects, which, e.g., determine the outer
remnant structure and the delay time of the dense remnant core to black hole
collapse. For comparing and classifying the GW signals, we use a number of
characteristic quantities like the maximum frequency during inspiral or the
dominant frequency of oscillations of the postmerger remnant. In general, these
frequencies are higher for SS mergers. If not, additional features of the GW
luminosity spectrum may help to discriminate coalescence events of the
different types. Future GW measurements may thus help to decide on the
existence of SQM stars. (abridged)
