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The no-hair theorem precludes the existence of black holes with a scalar charge. We explicitly construct static spherically symmetric solutions of the Einstein equation in the presence of massless dilaton and gauge fieldsm relevant to higher-dimensional Kaluza-Klein and superstring theories. Except the special case of the wormhole solution, all non-trivial solutions contain naked singularities not covered by an event horizon. Time-dependent perturbation, however, shows the instability of these solutions, caused by the dilaton field.
Koikawa et al. (Wed,) studied this question.