Magnetic field corrections to inspiral waveforms appear at -2 PN and -3 PN orders and mimic power-law environmental gravity but can be distinguished above a transition density of about 10^{-4} kg/m^3 for Bonnor-Melvin cases using multi-event statistics.
Barausse, The evolution of massive black holes and their spins in their galactic hosts , Monthly Notices of the Royal Astronomical Society 423 (2012) 2533 ⚶2557
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Distinguishability of magnetic massive black holes from environmental mimics with inspiral gravitational waves
Magnetic field corrections to inspiral waveforms appear at -2 PN and -3 PN orders and mimic power-law environmental gravity but can be distinguished above a transition density of about 10^{-4} kg/m^3 for Bonnor-Melvin cases using multi-event statistics.