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

Understand

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 $1.9-3.4$.