Detectable Environmental Effects in GW190521-like Black-Hole Binaries with LISA

GW190521 is the compact binary with the largest masses observed to date, with at least one black hole in the pair-instability gap. This event has also been claimed to be associated with an optical flare observed by the Zwicky Transient Facility in an active galactic nucleus (AGN), possibly due to the postmerger motion of the merger remnant in the AGN gaseous disk. The Laser Interferometer Space Antenna (LISA) may detect up to ten such gas-rich black-hole binaries months to years before their detection by Laser Interferometer Gravitational Wave Observatory or Virgo-like interferometers, localizing them in the sky within ≈1°^{2}. LISA will also measure directly deviations from purely vacuum and stationary waveforms arising from gas accretion, dynamical friction, and orbital motion around the AGN's massive black hole (acceleration, strong lensing, and Doppler modulation). LISA will therefore be crucial to enable us to point electromagnetic telescopes ahead of time toward this novel class of gas-rich sources, to gain direct insight on their physics, and to disentangle environmental effects from corrections to general relativity that may also appear in the waveforms at low frequencies.