Equilibrium of two rotating charged black holes and the Dirac string

The two-body problem of rotating charged black holes is studied in terms of the stationary axisymmetric electrovac solution obtained from Ernst's charging transformation of the two-Kerr-NUT family. The electromagnetic effect turns out to be unessential (except the static case) to the conditions for equilibrium which assure the regularity of the symmetry axis. Although the system has no net magnetic charge, the rotation generates the Dirac string linking two black holes in consequence of the distorted gravitational field. Then, via the Komar integrals, we can show that each black hole does not satisfy the usual mass formula. (author)