On the mathematical character of the relativistic transfer moment equations

General--relativistic, frequency--dependent radiative transfer in spherical,differentially--moving media is considered. In particular we investigate thecharacter of the differential operator defined by the first two momentequations in the stationary case. We prove that the moment equations form ahyperbolic system when the logarithmic velocity gradient is positive, providedthat a reasonable condition on the Eddington factors is met. The operator,however, may become elliptic in accretion flows and, in general, when gravityis taken into account. Finally we show that, in an optically thick medium, oneof the characteristics becomes infinite when the flow velocity equals $\pmc/\sqrt 3$. Both high--speed, stationary inflows and outflows may thereforecontain regions which are ``causally'' disconnected.Comment: 16 pages, PlainTex, accepted for publication in MNRA