A stationary distribution of matter outside a Kerr black hole will cause the angular momentum of the black hole to decrease with time provided the distribution is not symmetric about the axis defined by the black hole's angular momentum. The rate of decrease of angular momentum is calculated in the case that (a) the effects of the exterior matter can be treated as a perturbation to the Kerr geometry and (b) the angular momentum of the black hole is small.

• Received 13 October 1972

DOI:https://doi.org/10.1103/PhysRevD.8.1010