  It is an interesting open problem whether two non-extremal rotating and
electrically charged black holes can be in physical equilibrium, which might be
possible due to a balance between the gravitational attraction and the
spin-spin and electrical repulsions. Exact candidate solutions were
constructed, but it is unclear whether they are physically acceptable. These
solutions were obtained by assuming a particular behaviour on the symmetry
axis. However, it was not known whether the assumed form of the axis data
covers the general case or whether data of some other type need to be
considered as well. By studying a boundary value problem for the axisymmetric
and stationary Einstein-Maxwell equations, we address this question and derive
the most general form of permissible axis potentials for possible equilibrium
configurations.
