# Relative velocity with respect to event horizon

Consider a cloud of particles falling into a black hole. How does the relative velocity between two such particles, one which is already at the event horizon and one that is still some distance away from the event horizon, depend on the distance between them, as considered in the reference frame of the particle that is still some distance away from the event horizon?

• I don't think it matters whether the observer is infalling or not: they never see anything cross the horizon until they do. They do see things get asymptotically close to the horizon and, as you say, the recession velocity then goes asymptotically to $c$. – tfb Oct 12 '16 at 20:35