  The remnant star of a neutron star merger is an anticipated loud source of
kiloHertz gravitational waves that conveys unique information on the equation
of state of hot matter at extreme densities. Observations of such signals are
hampered by the photon shot noise of ground-based interferometers and pose a
challenge for gravitational-wave astronomy. We develop an analytical
time-domain waveform model for postmerger signals informed by numerical
relativity simulations. The model completes effective-one-body waveforms for
quasi-circular nonspinning binaries in the kiloHertz regime. We show that a
template-based analysis can detect postmerger signals with a minimal
signal-to-noise ratios (SNR) of 8, corresponding to GW170817-like events for
third-generation interferometers. Using Bayesian model selection and the
complete inspiral-merger-postmerger waveform model it is possible to infer
whether the merger outcome is a prompt collapse to a black hole or a remnant
star. In the latter case, the radius of the maximum mass (most compact)
nonrotating neutron star can be determined to kilometer precision. We
demonstrate the feasibility of inferring the stiffness of the equation of state
at extreme densities using the quasiuniversal relations deduced from
numerical-relativity simulations.
