The Magnetorotational Instability in the Kerr Metric

The magnetorotational instability (MRI) is the leading candidate for drivingturbulence, angular momentum transport, and accretion in astrophysical disks. Iconsider the linear theory of the MRI in a thin, equatorial disk in the Kerrmetric. I begin by analyzing a mechanical model for the MRI that consists oftwo point masses on nearly circular orbits connected by a spring. I thendevelop a local Cartesian coordinate system for thin, equatorial Kerr disks. Inthis local model general relativistic effects manifest themselves solelythrough changes in the Coriolis parameter and in the tidal expansion of theeffective potential. The MRI can be analyzed in the context of the local modelusing nonrelativistic magnetohydrodynamics, and the growth rates agree withthose found in the mechanical model. The maximum growth rate measured by acircular orbit observer differs from a naive estimate using Newtonian gravityby a factor that varies between 1 and 4/3 for all radii and for all a/M.Comment: 11 pages, 2 figures, aastex, accepted to Ap