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Third-generation gravitational wave (GW) observatories such as EinsteinTelescope (ET) and Cosmic Explorer (CE) will be ideal instruments to probe thestructure of neutron stars through the GWs they emit when undergoing binarycoalescence. In this work we make predictions about how well ET in particularwill enable us to reconstruct the neutron star equation of state throughobservations of tens of binary neutron star coalescences with signal-to-noiseratios in the hundreds. We restrict ourselves to information that can beextracted from the inspiral, which includes tidal effects and possibly r-moderesonances. In treating the latter we go beyond the Newtonian approximation,introducing and utilizing new universal relations. We find that the ability toobserve resonant r-modes would have a noticeable impact on neutron starequation of state measurements with ET.

Determining the equation of state of neutron stars with Einstein  Telescope using tidal effects and r-mode excitations from a population of  binary inspirals