Mass-redshift Degeneracy for Gravitational-wave Sources in the Vicinity of a Supermassive Black Hole

Retrieving the mass of a gravitational-wave (GW) source is a fundamental but difficult problem because the mass is degenerate with redshift. In astronomy, three types of redshift exist, namely cosmological, Doppler, and gravitational redshift, but the latter two are normally too weak to affect the observation. In this Letter, we show that the current astrophysical models allow binary black holes (BBHs) to merge within $10$ Schwarzschild radii of a supermassive black hole (SMBH). We find that in this case both the Doppler and gravitational redshift are significant, and in the most extreme condition they could increase the “apparent” black-hole mass and distance by a factor of $1.9-3.4$. We show that such a factor is consistent with the distribution in the distance-mass diagram of the ten BBHs detected so far by LIGO/Virgo. We also discuss the difficulties of this redshift scenario caused by the low event rate predicted by the current models, as well the potential solutions.