The Magnetorotational Instability in the Kerr Metric

Abstract

The magnetorotational instability (MRI) is the leading candidate for driving turbulence, angular momentum transport, and accretion in astrophysical disks. I consider the linear theory of the MRI in a thin, equatorial disk in the Kerr metric. I begin by analyzing a mechanical model for the MRI that consists of two point masses on nearly circular orbits connected by a spring. I then develop a local Cartesian coordinate system for thin, equatorial Kerr disks. In this local model general relativistic effects manifest themselves solely through changes in the Coriolis parameter and in the tidal expansion of the effective potential. The MRI can be analyzed in the context of the local model using nonrelativistic magnetohydrodynamics, and the growth rates agree with those found in the mechanical model. The maximum growth rate measured by a circular orbit observer differs from a naive estimate using Newtonian gravity by a factor that varies between 1 and 4/3 for all radii and for all a/M.