Fast radio bursts (FRBs) are a newly discovered class of radio transients
that emerge from cosmological sources and last for ∼ a few milliseconds.
However, their origin remains a highly debated topic in astronomy. Among the
plethora of cataclysmic events proposed as potential progenitors, binary
neutron star (BNS) mergers have risen as compelling candidates for at least
some subset of apparently non-repeating FRBs. However, this connection should
not be drawn solely on the basis of chance coincidence probability. In this
study, we delineate necessary criteria that must be met when considering an
association between FRBs and BNS mergers, focusing on the post-merger ejecta
environment. To underscore the significance of these criteria, we scrutinize
the proposed association between GW190425 and FRB20190425A. Our investigation
meticulously accounts for the challenging condition that the FRB signal must
traverse the dense merger ejecta without significant attenuation to remain
detectable at 400 MHz. Furthermore, we find that if the FRB is indeed linked to
the gravitational wave event, the GW data strongly support a highly off-axis
configuration, with a probability of the BNS merger viewing angle p(θv> 30∘) to be ≈ 99.99%. Our findings therefore strongly
exclude an on-axis system, which we find, on the other hand, to be required in
order for this FRB to be detectable. Hence, we conclude that GW190425 is not
related to FRB20190425A. We also discuss implications of our results for future
detections of coincident multi-messenger observations of FRBs from BNS remnants
and GW events and argue that BNS merger remnants cannot account for the
formation of > 1% of FRB sources. This observation suggests that short
gamma-ray bursts should not be used to explain global attributes of the FRB
host population.Comment: 9 pages, 4 figures. Submitte