Flow and peculiar velocities for generic motion in spherically symmetric black holes

TL;DR

This paper introduces a new method to analyze particle motion in spherically symmetric black holes by decomposing velocities into flow and peculiar components, providing insights into redshift phenomena inside horizons.

Contribution

It generalizes previous radial motion results to nonradial cases, applicable to various metrics, and offers a physical interpretation of redshift inside black hole horizons.

Findings

Applicable to a wide class of spherically symmetric metrics

Provides a simple physical interpretation of redshift inside horizons

Generalizes previous radial motion results to nonradial motion

Abstract

In this methodological paper we consider geodesic motion of particles in a 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 a metric, and 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 redshift (blueshift) inside the horizon including the region near the singularity and agrees with the recent results obtained by direct calculations.