Accretion of γ > 5/3 gas by a Schwarzschild black hole

Causality demands that all spherical accretion flows into a Schwarzschild black hole pass through a critical point. In Michel's relativistic generalization of Bondi's theory, there are three such points, but only one of these is physical for a given polytropic equation of state. For a gas with γ<5/3, the only critical points is the one found by Bondi, which lies well outside the event horizon (rsub(s)). There is a relativistic critical point for a 5/3<γ<3 gas, which lies near, but outside rsub(s). All critical points are computed to lie within rs for γ>3; but it is shown that this is equivalent to the sound speed being superluminal ar r > rs. Therefore, the equation of state for such a gas must soften before reaching rs. Given any physical equation of state, the critical flow determines a unique accretion rate. (orig.)