  In this paper we examine time-dependent and three-dimensional perturbations
of spherical accretion flow onto a neutron star close to its Eddington limit.
Our treatment assumes a Schwarzschild geometry for the spacetime outside the
neutron star and is fully general relativistic. At all the accretion rates
studied, the response of the accretion flow to perturbations includes weakly
damped oscillatory modes. At sufficiently high luminosities --- but still well
below the Eddington limit --- the flows become unstable to aspherical
perturbations. These unstable radiation hydrodynamic modes resemble the onset
of convection, and allow accretion to occur preferentially through more rapidly
descending columns of gas, while the radiation produced escapes through
neighboring columns in which the gas descends more slowly.
