Generalized observers and velocity measurements in General Relativity

TL;DR

This paper proposes a generalized framework for defining velocities in General Relativity, ensuring physically consistent measurements near black holes, and clarifies that freely falling particles remain subluminal at the event horizon.

Contribution

It introduces a new method for velocity measurement using generalized observers, resolving unphysical interpretations in previous approaches.

Findings

Freely falling particles are always less than the speed of light at the Schwarzschild horizon.

The proposed observer set provides a consistent way to measure velocities in curved spacetime.

The approach clarifies the physical interpretation of velocities near black holes.

Abstract

To resolve some unphysical interpretations related to velocity measurements by static observers, we discuss the use of generalized observer sets, give a prescription for defining the speed of test particles relative to those observers and show that, for any locally inertial frame, the speed of a freely falling material particle is always less than the speed of light at the Schwarzschild black hole surface.