Universality and backreaction in a general-relativistic accretion of   steady fluids
  The spherically symmetric steady accretion of polytropic perfect fluids onto a black hole is the simplest flow model that can demonstrate the effects of backreaction. The analytic and numerical investigation reveals that backreaction keeps intact most of the characteristics of the sonic point. For any such system, with the only free parameter being the relative abundance of the fluid, the mass accretion rate achieves maximal value when the mass of the fluid is universally 1/3 of the total mass. 
Janusz Karkowski, Bogusz Kinasiewicz, Patryk Mach, Edward Malec,   Zdobyslaw Swierczynski