Relativistic Bondi accretion for stiff equations of state*

We revisit Bondi accretion - steady-state, adiabatic, spherical gas flow onto a Schwarzschild black hole at rest in an asymptotically homogeneous medium - for stiff polytropic equations of state (EOSs) with adiabatic indices $\Gamma > 5/3$. A general relativistic treatment is required to determine their accretion rates, for which we provide exact expressions. We discuss several qualitative differences between results for soft and stiff EOSs - including the appearance of a minimum steady-state accretion rate for EOSs with $\Gamma \geq 5/3$ - and explore limiting cases in order to examine these differences. Our results are useful, for example, to estimate the accretion rate onto a mini-black hole residing at the center of a neutron star.