Black-Hole Winds with a Variable Eddington Factor

We solve one-dimentinal spherically symmetric, optically thick black-hole winds under general relativity with the help of a variable Eddington factor, f(tau, beta), where tau is the optical depth and beta is the flow velocity normalized by the speed of light. Relativistic radiation hydrodynamics under the moment formalism has several complex problems, such as a closure relation. Conventional relativistic moment equations closed with the traditional Eddington approximation in the comoving frame have a singularity, beyond which the flow cannot be accelerated. In order to avoid such a pathological behavior inherent in the relativistic moment formalism, we use a variable Eddington factor that depends on the flow velocity as well as the optical depth, for the case of spherically symmetric flow. We find luminous winds that can be accelerated by radiation pressure from a close vicinity to a black hole up to nearly the speed of light in a general-relativistic gravitational field.