  We report about the possibility for interacting Kerr sources to exist in two
different states - black holes or naked singularities - both states
characterized by the same masses and angular momenta. Another surprising
discovery reported by us is that in spite of the absence of balance between two
Kerr black holes, the latter nevertheless can repel each other, which provides
a good opportunity for experimental detection of the spin-spin repulsive force
through the observation of astrophysical black-hole binaries.
