Post-Newtonian spherically symmetrical accretion

The objective of this work is to investigate the influence corrections spherical symmetrical accretion an infinity gas cloud characterized by a polytropic equation into massive object due post-Newtonian approximation. Starting with steady state hydrodynamic equations for mass, mass-energy, and momentum densities, Bernoulli derived. critical values flow velocity, sound velocity radial distance are obtained from system hydrodynamics in coordinates. It was considered that ratio far body speed light order ${a}_{\ensuremath{\infty}}/c={10}^{\ensuremath{-}2}$. analysis solution led following results: Mach number Newtonian have practically same distances distance; decreasing bigger than one accretion; difference between numbers when ${a}_{\ensuremath{\infty}}/c\ensuremath{\ll}{10}^{\ensuremath{-}2}$ insignificant; effect correction terms more perceptive lowest solutions ${a}_{\ensuremath{\infty}}/c>{10}^{\ensuremath{-}2}$ does not lead continuous inflow outflow at point; comparison those follow relativistic shows dependence former numbers.