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We consider a luminous relativistic star.In the GR framework,the static balance between the radiation pressure and the effective gravity is realized for a specific radius,forming an equilibrium sphere – the Eddington Capture Sphere(ECS).In the test particle limit,for a specific range of luminosities,the ECS location changes from the star surface to infinity.We address the ECS formation issue from the hydrodynamical point of view,developing two models of the static gaseous atmospheres.The simple model is an optically thin polytropic atmosphere for which only the Thomson scattering is taken into account.The second model is based on the local thermal equilibrium assumption,it involves Klein-Nishina scattering and photon absorption processes,uses M1 closure scheme and allows to treat atmospheres of general optical depth.In both cases we find the static solutions with the density peak present and locally super-Eddingtonian radiation luminosity.We indicate the application of this research in the context of the photosphere expansion X-ray bursts.