SUPERCONDUCTING P-BRANES AND EXTREMAL BLACK-HOLES - ART. NO. 084009

In Einstein-Maxwell theory, magnetic flux lines are ''expelled'' from a black hole as extremality is approached, in the sense that the compo nent of the field strength normal to the horizon goes to zero. Thus, e xtremal black holes are found to exhibit the sort of ''Meissner effect '' which is characteristic of superconducting media. We review some of the evidence for this effect and present new evidence for it using re cently found black hole solutions in string theory and Kaluza-Klein th eory. We also present some new solutions, which arise naturally in str ing theory, which are non-superconducting extremal black holes. We pre sent a nice geometrical interpretation of these effects derived by loo king carefully at the higher dimensional configurations from which the lower dimensional black hole solutions are obtained. We show that oth er extremal solitonic objects in string theory (such as p-branes) can also display superconducting properties. In particular, we argue that the relativistic London equation will hold on the world volume of ''li ght'' superconducting p-branes (which are embedded in hat space), and that minimally coupled zero modes will propagate in the adS factor of the near-horizon geometries of ''heavy,'' or gravitating, superconduct ing p-branes. [S0556-2821(98)09518-6].