On the gravitational redshifts of spectral lines - A critico-historical study

TL;DR

This paper critically examines the historical and mathematical foundations of gravitational redshift, confirming through rigorous computation that the frequency of emitted electromagnetic waves remains unchanged during propagation.

Contribution

It provides a detailed critique and rigorous proof of the invariance of gravitationally redshifted frequencies, clarifying misconceptions in traditional treatments.

Findings

Confirmed that gravitationally redshifted frequency remains unaltered during propagation

Provided a rigorous mathematical proof using Whittaker's computation

Highlighted inaccuracies in customary qualitative explanations

Abstract

A beautiful, detailed computation by Whittaker has enabled us to prove in a rigorous way that the gravitationally redshifted frequency of a monochromatic e.m. wave sent forth at the surface of a celestial body is propagated unaltered from the emitting source to terrestrial observers. We remark that in the customary treatments only qualitative and inaccurate justifications of this fact are given.