  Gravitational waves from binary neutron star (BNS) mergers can constrain
nuclear matter models predicting the neutron star's equation of state (EOS).
Matter effects on the inspiral-merger signal are encoded in the multipolar
tidal polarizability parameters, whose leading order combination is sufficient
to capture to high accuracy the key features of the merger waveform (e.g.~the
merger frequency). Similar EOS-insensitive relations exist for the post-merger
signal and can be used to model the emission from the remnant. Several works
suggested that the appearance of new degrees of freedom or phase transitions in
high-density post-merger matter can be inferred by observing a violation of
these EOS-insensitive relations. Here, we demonstrate a Bayesian method to test
such an EOS-insensitive relation between the tidal polarizability parameters
(or any other equivalent parameter) and the dominant post-merger frequency,
using information either up to merger or from the post-merger signal.
Technically, the method is similar to tests of General Relativity with binary
black holes that verify the inspiral-merger-ringdown consistency. However,
differently from the latter, BNS pre/post-merger consistency tests are
conceptually less informative and they only address the consistency (or the
breaking) of the assumed EOS-insensitive relation. Specifically, we discuss how
such tests cannot conclusively discriminate between an EOS not respecting such
relation and the appearance of new degrees of freedom (or phase transitions) in
high-density matter.
