Velocity measurements in General Relativity revisited

TL;DR

This paper revisits velocity measurements in General Relativity, demonstrating that test particles at a black hole's event horizon move at speeds less than light using generalized metrics and observer sets.

Contribution

It extends previous analyses by employing more general metrics and observer sets to clarify velocity measurements at black hole horizons.

Findings

Velocity of test particles at the horizon is less than light speed.

Generalized metrics and observers resolve unphysical interpretations.

Provides pedagogical insights into velocity measurements in curved spacetime.

Abstract

In this work we generalize an earlier treatment of the measurements of velocities at the event horizon of a black hole. This is intended as a pedagogical exercise as well as one more contribution to the resolution of some unphysical interpretations related to velocity measurements by generalized observers. We now use a more general metric and, non-geodesic observer sets to show that the velocity of a test particle at the event horizon is less than the speed of light.