Primordial black holes captured by neutron stars: simulations in general relativity

We present self-consistent numerical simulations in general relativity of putative primordial black holes inside neutron stars. Complementing a companion paper in which we assumed the black hole mass $m$ to be much smaller than the mass $M_*$ of the neutron star, thereby justifying a point-mass treatment, we here consider black holes with masses large enough so that their effect on the neutron star cannot be neglected. We develop and employ several new numerical techniques, including initial data describing boosted black holes in neutron-star spacetimes, a relativistic determination of the escape speed, and a gauge condition that keeps the black hole hole at a fixed coordinate location. We then perform numerical simulations that highlight different aspects of the capture of primordial black holes by neutron stars. In particular, we simulate the initial passage of the black hole through the star, demonstrating that the neutron star remains dynamically stable provided the black-hole mass is sufficiently small, $m \lesssim 0.05 M_*$. We also model the late evolution of a black hole oscillating about the center of an initially stable neutron star while accreting stellar mass and ultimately triggering gravitational collapse.