Flow and Peculiar Velocities for Generic Motion in Spherically Symmetric Black Holes

In this methodological paper we consider geodesic motion of particles in spherically symmetric black hole space-times.We develop an approach based on splitting the velocity of a freely falling particle to the flow velocity, which depends only on the metric, and a deviation from it (a peculiar velocity). It applies to a wide class of spherically symmetric metrics and is exploited under the horizon of the Schwarzschild black hole. The present work generalizes previous results obtained for pure radial motion. Now, the motion is, in general, nonradial, so that an observer can have a nonzero angular momentum. This approach enables us to give simple physical interpretation of redshifts (blueshifts) inside the horizon including the region near the singularity and agrees with the recent results obtained by direct calculations.

Automated summary

This methodological paper extends previous results obtained for pure radial motion to consider the geodesic motion of particles in spherically symmetric black hole space-times, including nonradial motion and the possibility of an observer having nonzero angular momentum. The approach provides a simple physical interpretation of redshifts (blueshifts) inside the horizon, including the region near the singularity, and is consistent with recent results obtained by direct calculations.