Abstract We discuss the modes of the Alfvén waves in the accretion disk with a toroidal magnetic field in black hole low mass X-ray binaries in a rotating frame. By solving the perturbed general relativistic magnetohydrodynamic equations in the rotating frame, we find two stable modes of the Alfvén wave which are the same as those in the fiducial observer frame. This gives a feasible way to transform between the two different frames, which validates the possible Alfvén wave modes in the accreting celestial bodies with a toroidal magnetic field.
Keywords accretion, accretion disks — magnetohydrodynamics — relativity
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