On a Paradox of Gravitational Redshift

Gravitational redshift refers to the increase in wavelength (or reddening) of light as it escapes from a gravitational well. Einstein first derived this phenomenon in 1907 and 1911 by combining special relativity with the equivalence principle. The result was later incorporated into the full framework of general relativity. Today, nearly all textbooks on general relativity, both introductory and advanced, include derivations of gravitational redshift based on the principle of energy conservation. After a thorough review of the most representative of these derivations, we present what appears to be a previously unnoticed paradox affecting the energy-based derivation of gravitational redshift, and we examine its implications.