Particles under radiation thrust in Schwarzschild space-time: a flux perpendicular to the equatorial plane

Motivated by the picture of a thin accretion disc around a black hole, radiating mainly in the direction perpendicular to its plane, we study the motion of test particles interacting with a test geodesic radiation flux propagating perpendicular to the equatorial plane in a Schwarzschild space-time. We assume that the interaction (kind of Poynting-Robertson effect) is modelled by an effective term corresponding to a Thomson-type radiation drag. After approximating the individual photon trajectories in quite an accurate way, we solve the continuity equation (up to linear order in M) in order to find a consistent radiation-flux density, prescribing a certain plausible equatorial profile. The combined effect of gravitation and radiation is illustrated on several figures; they confirm that the particles are generically strongly influenced by the flux, in particular, they are both collimated and accelerated in the direction perpendicular to the disc, but the acceleration received in this manner is not enough to explain highly relativistic outflows emanating from some black-hole-disc sources. Main improvement needed is a more realistic description of the radiation-particle interaction, allowing for Compton-type frequency-dependent effect and particle heating/cooling.