through each point and then compute their effect on the particle motion. Numerical examples are given in Section \[examples\] and the concluding section ends with several remarks and plans for further study. Note that we use geometrized units in which $c=1$ and $G=1$, Greek indices take the values $0,1,2,3$ and Latin indices $1,2,3$, and partial derivatives are indicated by a comma.

“Vertical" geodesic radiation flux in a Schwarzschild field {#flux}
===========================================================

A thin accretion disc in the equatorial plane would certainly emit radiation in all directions, but it is perhaps a natural zero-order approximation to assume that most of the flux is directed perpendicularly to this plane. Actually, [@BisnovatyiKB-77] calculated, for a particle at any given location, the radiation force by integrating contributions from all directions over the whole Novikov-Thorne disc, and found a “cosine law" peaked along the vertical axis. However, since the disc itself orbits around the centre (in fact extremely fast in the case of very compact centre), the radiation it emits should have some angular momentum, but we will still set this angular momentum to zero here, not only for simplicity, but mainly because otherwise the radiation could not reach the vicinity of the axis. Thus 