  The magnetohydrodynamic dynamo equation is derived within general relativity,
using the covariant 1+3 approach, for a plasma with finite electric
conductivity. This formalism allows for a clear division and interpretation of
plasma and gravitational effects, and we have not restricted to a particular
spacetime geometry. The results should be of interest in astrophysics and
cosmology, and the formulation is well suited to gauge invariant perturbation
theory. Moreover, the dynamo equation is presented in some specific limits. In
particular, we consider the interaction of gravitational waves with magnetic
fields, and present results for the evolution of the linearly growing
electromagnetic induction field, as well as the diffusive damping of these
fields.
