Is Cowling's Anti-dynamo Theorem Valid near a Rotating Black Hole?

The kinematic evolution of axisymmetric magnetic and electric elds near a rotating black hole is investigated numerically in Kerr geometry. In the cases investigated it is found that a magnetic eld cannot be sustained against Ohmic dissipation. In at space, this result is known as Cowling's anti-dynamo theorem. No support is found for the possibility that a gravitomagnetic dynamo eeect could lead to self-excited axisymmetric solutions. In practice, therefore, Cowling's anti-dynamo theorem, may still hold in Kerr geometry, although here the original proof can no longer be applied.