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The selfgravity of an infalling gas can alter significantly the accretion ofgases. In the case of spherically symmetric steady flows of polytropic perfectfluids the mass accretion rate achieves maximal value when the mass of thefluid is 1/3 of the total mass. There are two weakly accreting regimes, oneover-abundant and the other poor in fluid content. The analysis within thenewtonian gravity suggests that selfgravitating fluids can be unstable, incontrast to the accretion of test fluids.Comment: Typos corrected. Talk given at the 42nd Karpacz Winter School of  Theoretical Physics, Ladek, Poland February 2006 on Current Mathematical  Topics in Gravitation and Cosmolog

SELFGRAVITATION IN A GENERAL-RELATIVISTIC ACCRETION OF STEADY FLUIDS