Radial oscillations of a radiation-supported levitating shell in Eddington luminosity neutron stars

In general relativity, it has been shown that radiation-supported atmospheres exist outside the surface of a radiating spherical body close to a radius where the gravitational and radiative forces balance each other. We calculate the frequency of oscillation of the incompressible radial mode of such a thin atmospheric shell and show that in the optically thin case, this particular mode is overdamped by radiation drag.