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