Lightlike simultaneity, comoving observers and distances in general relativity

TL;DR

This paper introduces a new framework for understanding simultaneity, velocities, and distances in general relativity using lightlike simultaneity, unifying concepts like Doppler effect, gravitational redshift, and various distance measures.

Contribution

It defines a condition for comoving observers based on lightlike simultaneity and introduces a generalized distance concept applicable in various space-times.

Findings

Comoving observers see the same light ray with identical frequency and direction.

Gravitational redshift is shown as a special case of the Doppler effect.

Affine distance generalizes proper radial distance and aligns with Hubble law in Robertson-Walker space-times.

Abstract

We state a condition for an observer to be comoving with another observer in general relativity, based on the concept of lightlike simultaneity. Taking into account this condition, we study relative velocities, Doppler effect and light aberration. We obtain that comoving observers observe the same light ray with the same frequency and direction, and so gravitational redshift effect is a particular case of Doppler effect. We also define a distance between an observer and the events that it observes, that coincides with the known affine distance. We show that affine distance is a particular case of radar distance in the Minkowski space-time and generalizes the proper radial distance in the Schwarzschild space-time. Finally, we show that affine distance gives us a new concept of distance in Robertson-Walker space-times, according to Hubble law.