The impact of AGN environmental effects on testing general relativity with space-borne gravitational wave detector
The space-borne gravitational wave detectors such as TianQin offers a new window to test General Relativity by observing the early inspiral phase of stellar-mass binary black holes. A key concern arises if these stellar-mass binary black holes reside in gaseous environments such as active galactic nucleus accretion disks, where environmental effects imprint detectable modulations on the gravitational waveform. Using Bayesian inference on simulated signals containing both environmental and dipole deviation, we have assessed the extent to which the presence of environmental effects affects the detectability of dipole radiation. Our results demonstrate that even in the presence of strong environmental coupling, the dipole parameter can be recovered with high precision, and the evidence for dipole radiation remains distinguishable. Crucially, we find that the existence of environmental effects does not fundamentally impede the identification of dipole radiation, provided both effects are simultaneously modelled in the inference process. This study establishes that future tests of modified gravity with space-borne observatories can remain robust even for sources in astrophysical environments.