  We examine whether the accretion of dark matter onto neutron stars could ever
have any visible external effects. Captured dark matter which subsequently
annihilates will heat the neutron stars, although it seems the effect will be
too small to heat close neutron stars at an observable rate whilst those at the
galactic centre are obscured by dust. Non-annihilating dark matter would
accumulate at the centre of the neutron star. In a very dense region of dark
matter such as that which may be found at the centre of the galaxy, a neutron
star might accrete enough to cause it to collapse within a period of time less
than the age of the Universe. We calculate what value of the stable dark
matter-nucleon cross section would cause this to occur for a large range of
masses.
