  The spherically symmetric steady accretion of polytropic perfect fluids onto
a black hole is the simplest flow model that can demonstrate effects of
backreaction (selfgravity). It has been discovered 16 years ago that
backreaction does not influence some ("intensive") characteristics of sonic
points, under suitable conditions. Herein we consider a wider class of
equations of state, with polytropic indices in the range (1,2], and establish
detailed boundary conditions that allow one to prove this fact. We find also
numerical examples showing limits of our analytic criteria - if suitable
analytic conditions are not satisfied, then selfgravity influences all
characteristics of sonic points. That fact constrains the applicability of the
recent proposal of Baumgarte and Shapiro to estimate the lifetime of black
holes within compact stellar objects.
