On the Mathematical Character of the Relativistic Transfer Moment Equations

Abstract

General--relativistic, frequency--dependent radiative transfer in spherical, differentially--moving media is considered. In particular we investigate the character of the differential operator defined by the first two moment equations in the stationary case. We prove that the moment equations form a hyperbolic system when the logarithmic velocity gradient is positive, provided that a reasonable condition on the Eddington factors is met. The operator, however, may become elliptic in accretion flows and, in general, when gravity is taken into account. Finally we show that, in an optically thick medium, one of the characteristics becomes infinite when the flow velocity equals $\pm c/\sqrt 3$. Both high--speed, stationary inflows and outflows may therefore contain regions which are ``causally'' disconnected.