General relativistic accretion with backreaction
  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. Backreaction keeps intact most of the characteristics of the sonic point. For any such system the mass accretion rate achieves maximal value when the mass of the fluid is 1/3 of the total mass. Fixing the total mass of the system, one observes the existence of two weakly accreting regimes, one overabundant and the other poor in fluid content. 
Janusz Karkowski, Bogusz Kinasiewicz, Patryk Mach, Edward Malec,   Zdobyslaw Swierczynski