Possibility of Kinematic Axisymmetric Dynamos near Rotating Black Holes

The kinematic theory of axisymmetric dynamos in the accretion disk of a rotating black hole differs in some important aspects from the nonrelativistic formulation; the gravitomagnetic potential couples the equations of the magnetic flux and current, rendering invalid the argument used in the proof of Cowling's antidynamo theorem. We prove that in this case no similar theorem may exist by showing that a sharp gradient in the angular velocity of the disk may cause a dynamo effect localized near the equatorial plane.