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Accretion onto black holes inside neutron stars with piecewise-polytropic equations of state: analytic and numerical treatments

We consider spherically symmetric accretion onto a small, possibly primordial, black hole residing at the center of a neutron star governed by a cold nuclear equation of state (EOS). We generalize the relativistic Bondi solution for such EOSs, approximated by piecewise polytropes, and thereby obtain analytical expressions for the steady-state matter profiles and accretion rates. We compare these rates with those found by time-dependent, general relativistic hydrodynamical simulations upon relaxation and find excellent agreement. We consider several different candidate EOSs, neutron star masses and central densities and find that the accretion rates vary only little, resulting in an accretion rate that depends primarily on the black hole mass, and only weakly on the properties of the neutron star.