  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.
