  We consider properties of the trajectory with the zero momentum inside a
spherically symmetric black hole. We work mostly in the Painlev\'{e}%
-Gullstrand frame and use the concept of the "river model of black hole". This
consept allows us to decompose (in a "cosmological manner") the geodesic motion
of a test particle into a "flow" of the frame and a peculiar motion with
respect to this frame. After this decomposition the application of standard
formulae of special relativity for kinematic processes becomes possible. The
present paper expands the notion of peculiar velocities to the region under the
horzion and exploits it for the description of two physical processess - high
energy collisions and redshift. Using this approach we (i) present a novel
description of particle collisions occuring near black hole horizons inside the
event horizon. In particular, we show that the trajectory under discussion is
relevant for ultra-high energy collisions. (ii) In the framework of the river
model, we derive a simple formula (both outside and inside the horizon) for the
redshift in the case of radial motion. It represents the product of two
factors. One of them is responsible for pure gravitational part whereas the
other one gives the Doppler shift due to peculiar motion with respect to the
"flow".
