Trapped and Released: Black Hole Mergers in Active Galactic Nuclei

Stellar-mass black holes in active galactic nuclei (AGN) are potential major sources of gravitational waves, contributing to both LIGO-Virgo-KAGRA binary mergers and future LISA-band extreme mass ratio inspirals. Migration traps - regions where hydrodynamic torques cancel out - may significantly affect these black holes' ability to merge.  We investigate how black holes can escape these traps through merger outcomes, finding that while gravitational wave recoil kicks can temporarily displace merged black holes, gas drag quickly realigns them. However, we identify a more effective escape mechanism: once a black hole exceeds a critical mass, it opens a gap in the AGN disk, eliminating the trap. This process is particularly efficient in low-mass AGN relevant for LISA observations. We find migration traps exist only within AGN luminosities between 10^{43.5} and 10^{45.5} erg/s, with an even narrower range allowing growth into the pair instability mass gap. This characteristic luminosity scale could provide an indirect test of the AGN channel for binary black hole mergers.