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

## TL;DR

This paper explores how gravitational and Doppler redshifts near supermassive black holes can significantly bias the inferred mass and distance of gravitational-wave sources, potentially explaining some observed data.

## Contribution

It demonstrates that redshift effects near supermassive black holes can cause substantial overestimation of GW source masses, a factor previously considered negligible.

## Key findings

- Redshift effects can increase apparent black hole mass by up to 3.4 times.
- Current GW detections are consistent with sources merging near SMBHs considering redshift effects.
- Low event rate challenges the redshift scenario but potential solutions are discussed.

## Abstract

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.