We generalize a class of magnetically charged black holes holes non-minimally
coupled to two scalar fields previously found by one of us [gr-qc/9910041] to
the case of multiple scalar fields. The black holes possess a novel type of
primary scalar hair, which we call a contingent primary hair: although the
solutions possess degrees of freedom which are not completely determined by the
other charges of the theory, the charges necessarily vanish in the absence of
the magnetic monopole. Only one constraint relates the black hole mass to the
magnetic charge and scalar charges of the theory. We obtain a Smarr-type
thermodynamic relation, and the first law of black hole thermodynamics for the
system. We further explicitly show in the two-scalar-field case that, contrary
to the case of many other hairy black holes, the black hole solutions are
stable to radial perturbations.Comment: 10 pages, RevTeX4, 6 figures, graphicx. v2: Substantial new sections
and results added from authors' joint unpublished manuscript dated 2000,
doubling the length of the paper. v3: references added. v4: Small additions
(extra figures etc) to agree with published versio
