STATIC BLACK-HOLE SOLUTIONS WITHOUT ROTATIONAL SYMMETRY

We construct static black hole solutions that have no rotational symme try. These arise in theories (including the standard electroweak model ) that contain charged vector mesons with mass m not equal 0. In such theories, a magnetically charged Reissner-Nordstrom black hole with a horizon radius less than a critical value of order m(-1) is classicall y unstable against the development of a nonzero vector meson held just outside the horizon, indicating the existence of static black hole so lutions with vector meson hair. For the case of unit magnetic charge, spherically symmetric solutions of this type have previously been stud ied. For other values of the magnetic charge, general arguments show t hat any new solution with hair cannot be spherically symmetric. In thi s paper we develop and apply a perturbative scheme (which may have app licability in other contexts) for constructing such solutions in the c ase where the Reissner-Nordstrom solution is just barely unstable. For a few low values of the magnetic charge the black holes retain a rota tional symmetry about a single axis, but this axial symmetry disappear s for higher charges. While the vector meson fields vanish exponential ly at distances greater than O(m(-1)), the magnetic field and the metr ic have higher multipole components that decrease only as powers of th e distance from the black hole.