  We revisit the system consisting of a neutron star that harbors a small,
possibly primordial, black hole at its center, focusing on a nonspinning black
hole embedded in a nonrotating neutron star. Extending earlier treatments, we
provide an analytical treatment describing the rate of secular accretion of the
neutron star matter onto the black hole, adopting the relativistic Bondi
accretion formalism for stiff equations of state that we presented elsewhere.
We use these accretion rates to sketch the evolution of the system analytically
until the neutron star is completely consumed. We also perform numerical
simulations in full general relativity for black holes with masses up to nine
orders of magnitude smaller than the neutron star mass, including a simulation
of the entire evolution through collapse for the largest black hole mass. We
construct relativistic initial data for these simulations by generalizing the
black hole puncture method to allow for the presence of matter, and evolve
these data with a code that is optimally designed to resolve the vastly
different length scales present in this problem. We compare our analytic and
numerical results, and provide expressions for the lifetime of neutron stars
harboring such endoparasitic black holes.
