  In general relativity static gaseous atmospheres may be in hydrostatic
balance in the absence of a supporting stellar surface, provided that the
luminosity is close to the Eddington value. We construct analytic models of
optically thin, spherically symmetric shells supported by the radiation
pressure of a luminous central body in the Schwarzschild metric. Opacity is
assumed to be dominated by Thomson scattering. The inner parts of the
atmospheres, where the luminosity locally has supercritical values, are
characterized by a density and pressure inversion. The atmospheres are
convectively and Rayleigh-Taylor stable, and there is no outflow of gas.
