A classical instability of Reissner-Nordström solutions and the fate of magnetically charged black holes.

Working in the context of spontaneously broken gauge theories, we show that the magnetically charged Reissner-Nordström solution develops a classical instability if the horizon is sufficiently small. This instability has significant implications for the evolution of a magnetically charged black hole. In particular, it leads to the possibility that such a hole could evaporate completely, leaving in its place a nonsingular magnetic monopole. This work was supported in part by the US Department of Energy (VPN and EJW), by NASA (EJW) under grant NAGW-2381 and by an NSF Presidential Young Investigator Award (KL). * Alfred P. Sloan Fellow. The Reissner-Nordström solution to the coupled Einstein-Maxwell equations describes a spherically symmetric black hole endowed with electric or magnetic charge. Although the solution makes mathematical sense in a theory involving only gravity and the electromagnetic field, its physical motivation is somewhat tenuous unless the theory also contains particles carrying such charges. This remark has little consequence in the case of electric charge, since one only need add a field whose elementary particles are electrically charged. The addition of magnetic charge to the theory is less trivial, but can be accomplished by enlarging the structure of the theory so that electromagnetism emerges as the unbroken subgroup of a spontaneously broken gauge theory in which magnetic monopoles arise as topologically nontrivial classical solution [1]. The incorporation of these additional fields into the Reissner-Nordström solution is rather straightforward [2], and changes neither the metric nor the magnetic field. However, as we will show in this letter, the presence of these fields can render this solution unstable. This instability arises at the level of the classical field equations and does not depend on any quantum mechanical process. It has important implications for the ultimate fate of magnetically charged black holes. The magnetically charged Reissner-Nordström solution to the Maxwell-Einstein equations has a radial magnetic field with magnitude QM/r 2 and a metric which may be written as ds = Bdt −Adr − rdθ − r sinθdφ (1) where B = A = 1− 2MG r + 4πGQ2M r ≡ BRN (2) There is a physical singularity at r = 0 which is hidden within a horizon at