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Next-generation detectors are expected to be sensitive to postmerger signalsfrom binary neutron star coalescences and thus to directly probe the remnantdynamics. We investigate the scientific potential of postmerger detections withthe Einstein Telescope using full Bayesian analyses with the state-of-the-artwaveform model ${\tt NRPMw}$. We find that: (i) Postmerger signals withsignal-to-noise ratio (SNR) ${\sim}7$ can be confidently detected with a Bayes'factor of $\log{\cal B}\simeq 5$ ($\rm e$-folded) and the posteriordistributions report informative measurements already at SNR ${\sim}6$ for somenoise realizations. (ii) The postmerger peak frequency $f_2$ can be confidentlyidentified at SNR $7$ with errors of $O(1~{\rm kHz})$, that decrease below$O(100~{\rm Hz})$ for SNR 10. (iii) The remnant's time of collapse to blackhole can be constrained to $O(20~{\rm ms})$ at SNR 10. However, the inferencecan be biased by noise fluctuationsif the latter exceed the signal's amplitudebefore collapse. (iv) Violations of the EOS-insentive relations for $f_2$ canbe detected at SNR $\gtrsim 8$ if the frequency shifts are $\gtrsim 500~{\rmHz}$; they can be smoking guns for EOS softening effects at extreme densities.However, the $f_2$ measurement can be significantly biased by subdominantfrequency components for short-lived remnants. In these cases, an EOS softeningmight be better inferred from the remnant's earlier collapse.

Kilohertz Gravitational Waves from Binary Neutron Star Mergers: Inference of Postmerger Signals with the Einstein Telescope