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

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