INSTABILITIES OF MAGNETICALLY CHARGED BLACK-HOLES

The stability of the magnetically charged Reissner-Nordström black hole solution is investigated in the context of a theory with massive charged vector mesons. By exploiting the spherical symmetry of the problem, the linear perturbations about the Reissner-Nordström solution can be decomposed into modes of definite angular momentum J. For each value of J, unstable modes appear if the horizon radius is less than a critical value that depends on an anomalous magnetic moment coupling g and the monopole magnetic charge q/e. It is shown that such a critical radius exists (except in the case q=1/2 with 0≤g≤2), provided only that the vector meson mass is not too close to the Planck mass. The value of the critical radius is determined numerically for a number of values of J. The instabilities found here imply the existence of stable solutions with nonzero vector fields (''hair'') outside the horizon; unless q=1 and g>0, these will not be spherically symmetric. © 1995 The American Physical Society.