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A hypermassive neutron star (HMNS) is a neutron star with sufficient mass to collapse into a black hole, basically, more massive than the Tolman-Oppenheimer-Volkoff limit. It immediately collapses (e.g., well within a second) unless rotation counteracts the effect of gravity and delays the collapse. The term supramassive neutron star (SMNS or sometimes spelled supermassive neutron star) has a similar meaning: it is used for such an overly-massive neutron star, sometimes intended to mean "longer-lived than a HMNS" and sometimes assuming HMNS to be a sub-type.
Such neutron stars are of interest because they may exist for a short time in the midst of a neutron star merger, and their short existence can affect the observable phenomena, both electromagnetic radiation and gravitational waves. GW170817's merger appears to be such a case. Such neutron stars might also be a source of some as-yet-unexplained phenomena, e.g., some gamma-ray bursts. They are also of interest because of the possibility that some might further persist due to rotation, which has some potential in explaining other observations, such as-yet unexplained transients which might be due to subsequent collapses. The term blitzar was coined for such rotating massive neutron stars with magnetic fields (thus likely pulsars) when such a collapse was put forward as a possible source of fast radio bursts.