Doppler, gravitational and cosmological redshifts

TL;DR

This paper clarifies the derivation of Doppler, gravitational, and cosmological redshifts by emphasizing the importance of considering both energy and momentum conservation, correcting prior oversights.

Contribution

It introduces a consistent formulation for all three redshift types, addressing gaps in previous derivations and referencing relevant literature.

Findings

Both energy and momentum considerations are essential for accurate redshift derivations.

The paper provides a unified framework for Doppler, gravitational, and cosmological redshifts.

It corrects previous claims by emphasizing comprehensive physical considerations.

Abstract

Ortiz and Ibarra-Castor (2024) have presented a "Generalized redshift formula" taking account of only energy conservation considerations. Contrary to their claim, we emphasize to invoke both energy and momentum considerations in order to deduce all three types of redshift (Doppler, gravitational and cosmological). We formulate our views on the three physical e ects in a consistent manner in addition to addressing the lack of relevant references in Ref. (Ortiz and Ibarra-Castor, 2024)