We describe a family of static black-hole solutions arising in a theory with Einstein gravity coupled to electromagnetism and an axionlike scalar field. These solutions carry both electric and magnetic charge. In addition, the scalar field is spatially varying outside the horizon. Since this nontrivial scalar field is not required by any conservation law, these solutions shed further light on the black-hole no-hair conjecture.
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Lee et al. (1991) studied this question.
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