General radially moving references frames in the black hole background

We consider general radially moving frames realized in the background of nonextremal black holes having causal structure similar to that Schwarzschild metric. In doing so, we generalize Lema\^{\i}tre approach, constructing free-falling which are built from reference particles with an arbitrary specific energy $e_{0}$ including $e_{0}<0$ and a special case $e_{0}=0$. The formula 3-velocity freely falling particle $e$ respect frame $% e_{0}$ is presented. point out relation between properties considered near horizon Banados-Silk-West effect indefinite growth collisions. Using our frames, also nonradial motion test regions singularity. time at horizons depending on sign energy.