Gravitational Redshift from Galaxy Clusters - a Relativistic Approach

Gravitational redshift is one of Einstein’s first predictions. On cosmological scales, we observe that the light emitted by Bright Central Galaxies at the bottom of a cluster’s gravitational potential is more redshifted than the average member galaxy. A first detection of this signal was made in 2011, but later studies questioned its interpretation, highlighting additional kinematic contributions. In this talk, I will present a fully relativistic derivation of these effects and compare it with previous studies. With a proper theoretical understanding, this effect provides a unique opportunity to test the equivalence principle at Mpc scales.