Velocity addition formulas in Robertson-Walker spacetimes

TL;DR

This paper derives velocity addition formulas in Robertson-Walker spacetimes, extending special relativity results to cosmological models and highlighting differences among various geometric relative velocities.

Contribution

It introduces universal velocity addition formulas for multiple relative velocities in Robertson-Walker spacetimes, generalizing special relativity to cosmological contexts.

Findings

Spectroscopic velocity follows special relativity addition law.

Explicit examples of velocity addition formulas are provided.

Special relativity formulas are recovered as a special case.

Abstract

Universal velocity addition formulas analogous to the well-known formula in special relativity are found for four geometrically defined relative velocities in a large class of Robertson-Walker spacetimes. Explicit examples are given. The special relativity result is recovered as a special case, and it is shown that the spectroscopic relative velocity, in contrast to three other geometric relative velocities, follows the same addition law as in special relativity for comoving observers in Robertson-Walker cosmologies.