indistinguishable from the chirp signals of those more massive BBHs residing in a vacuum environment. Such fake massive objects in the milli-Hertz band, if not appropriately accounted for in the future, may alter our understanding of the formation, evolution, and detection of BBHs.'
author:
- Xian Chen
- 'Ze-Yuan Xuan'
- Peng Peng
title: 'Fake massive black holes in the milli-Hertz gravitational-wave band'
---

Introduction {#sec:intro}
============

The majority of the black holes (BHs) detected by the ground-based gravitational wave (GW) observatories (i.e, LIGO and Virgo) turn out to be several times more massive than those previously detected in X-ray binaries [@ligo18a]. Such a discrepancy has important implications for the formation and evolution of stellar-mass binary BHs [BBHs, @ligo16astro]. However, mass is not a direct observable in GW astronomy. It is inferred either from the chirp signal, i.e., an increase of the GW frequency with time, or from the merger and ringdown signals. If the signal gets distorted, either at the moment of generation or during the propagation, an error would be induced in the measurement of the mass.

Redshift is such a disturbing factor. It stretches the signal during its propagation. As a result, mass ($m$) is degenerate with 