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The equation of motion announced in the title was already deduced for thecases the inner metric being flat and the shell being negligibly small (testmatter), using surface layers and geodesic trajectories resp. Here we derivethe general equation of motion and solve it in closed form for the case ofparabolic motion. Especially the motion near the horizon and near thesingularity are examined.

Motion of a thin spherically symmetric Shell of Dust in the Schwarzschild field