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 of the Schwarzschild metric. In doing so, we generalize the Lemaitre approach, constructing free-falling frames which are built from the reference particles with an arbitrary specific energy e(0) including e(0) < 0 and a special case e(0) = 0. The general formula of 3-velocity of a freely falling particle with the specific energy e with respect to a frame with e0 is presented. We point out the relation between the properties of considered frames near a horizon and the Banados-Silk-West effect of an indefinite growth of energy of particle collisions. Using our radially moving frames, we consider also nonradial motion of test particles including the regions near the horizon and singularity. We also point out the properties of the Lemaitre time at horizons depending on the frame and sign of particle energy.

Automated summary

We study general radially moving frames in the background of nonextremal black holes similar to the Schwarzschild metric. We generalize the Lemaitre approach and construct free-falling frames composed of reference particles with arbitrary specific energy, including negative energy. We provide the general formula for the 3-velocity of a freely falling particle with respect to a frame with a specific energy. We investigate the relation between the properties of these frames near a horizon and the Banados-Silk-West effect of indefinite growth of energy of particle collisions. Using our radially moving frames, we also consider the nonradial motion of test particles, including regions near the horizon and singularity. We discuss the properties of the Lemaitre time at horizons depending on the frame and sign of particle energy.