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Neutron stars are quite a way from becoming blackholes. If a star (very roughly) has a mass 8ish times that of our sun it is likely to end as a neutron star - it will blow off its outer layers (more or less explosively) and the core will fall in on itself till atoms cannot remain as atoms and you get ...sorry, you cannot view external links. To see them, please
REGISTER or LOGIN and you would start getting really weird stuff. Even then it is unlikely to be a black hole - but some other form of degenerate matter. The question is how you would get enough matter into the neutron star to change its mass that much. Remember the neutron star is sitting right where a really massive star exploded - quite a lot of the locally available matter will have been attracted and eaten by the star and blown off in the explosion.Even if there is a star neighbour of the neutron star willing to give up its matter to increase the neutron stars mass - there is another fly in the ointment: angular momentum. Angular momentum will stop the matter flowing straight into the neutron star - and the neutron star is so small, that any in falling material ends up on a very shallow spiral into the star (it's basically a slow decay orbit). The material in this spinning accretion disc moves at huge speed and generates huge heat through friction. The huge rotating magnetic field of the neutron star may also mean that the very inside bit of the accretion disk is flung away from the star at the poles.Basically, whilst a huge amount of material might be around the neutron star - the mass of the star itself will not be increased enough to change its nature