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The high-frequency quasi-periodic oscillations (HFQPOs) that punctuate thelight curves of X-ray binary systems present a window onto the intrinsicproperties of stellar-mass black holes and hence a testbed for generalrelativity. One explanation for these features is that relativistic distortionof the accretion disc's differential rotation creates a trapping region inwhich inertial waves (r-modes) might grow to observable amplitudes. Localanalyses, however, predict that large-scale magnetic fields push this trappingregion to the inner disc edge, where conditions may be unfavorable for r-modegrowth. We revisit this problem from a pseudo-Newtonian but fully globalperspective, deriving linearized equations describing a relativistic,magnetized accretion flow, and calculating normal modes with and withoutvertical density stratification. In an unstratified model, the choice ofvertical wavenumber determines the extent to which vertical magnetic fieldsdrive the r-modes toward the inner edge. In a global model fully incorporatingdensity stratification, we confirm that this susceptibility to magnetic fieldsdepends on disc thickness. Our calculations suggest that in thin discs, r-modesmay remain independent of the inner disc edge for vertical magnetic fields withplasma betas as low as $\beta\approx 100-300$. We posit that the appearance ofr-modes in observations may be more determined by a competition betweenexcitation and damping mechanisms near the ISCO than the modification of thetrapping region by magnetic fields.

Quasi-periodic oscillations and the global modes of relativistic, MHD accretion discs