Active galactic nuclei, gravitational redshifts, and cosmological tensions

Gravitational redshift is a classical effect of Einstein's General Relativity, already measured in stars, quasars and clusters of galaxies. We here identify the signature of gravitational redshift in the emission lines of active galaxies due to supermassive black holes and discuss their impact on cosmological inference from type Ia supernovae. Firstly, from the full width at half maximum of $H_{\beta}$ lines of 75 Seyfert type I galaxies of the AGN Black Hole Mass Database, we derive a gravitational redshift $z_g = (2.4 \pm 0.9) \times 10^{-4}$. Expanding this analysis to 86755 quasars from DR14 of SDSS we have a mean value $z_g \approx 2.7 \times 10^{-4}$. Then, by comparing the redshifts of 34 lines measured at the central and outer regions of LINER galaxies in the SAMI survey we obtain $z_g = (0.68 \pm 0.09) \times 10^{-4}$. These numbers are compatible with central black holes of $\approx 10^9$ solar masses and broad line regions of $\approx 1$~pc. For non-AGN galaxies the gravitational redshift is compatible with zero and, as they constitute most of SNe Ia host galaxies, the impact on the cosmological parameters is negligible.