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. As an example we highlight results for $Gamma = 2$, which is often used in numerical simulations to model the EOS of neutron stars. We also discuss a special case with this index, the ultra-relativistic `causal EOS, $P = rho$. The latter serves as a useful limit for the still undetermined neutron-star EOS above nuclear density. The results are useful, for example, to estimate the accretion rate onto a mini-black hole residing at the center of a neutron star.
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