The interaction between a weak magnetic field and a slowly rotating black hole

Abstract
We solve Maxwell’s equations in the vacuum space-time of the slowly rotating black hole (terms of second and higher order in angular momentum are ignored), with a homogeneous magnetic field aligned at angle γ to the rotation axis as boundary condition far from the hole, assuming that the field is always so weak as to have no influence upon the background metric. The solution is used to find the change of angular momentum of the hole. The component perpendicular to the field decreases exponentially with time according to the law J ⊥ = ( J ⊥ ) initial exp ( – t ז -1 ) where ז -1 = 1 6/3π G 2 c -5 (mass of hole) (magnetic field energy density at infinity), while the component parallel to the field remains constant. The axis of rotation of the black hole is thus caused to come into alignment with the magnetic field, although so gradually as to render remote the prospect of observational confirmation for any easily conceived astrophysical situation. With the chosen boundary condition on the field, no energy emerges from the hole, kinetic energy of rotation being transformed instead into irreducible mass.

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