In Einstein-Maxwell theory, magnetic flux lines are `expelled' from a black
hole as extremality is approached, in the sense that the component of the field
strength normal to the horizon goes to zero. Thus, extremal 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 do
present new evidence for it using recently found black hole solutions in string
theory and Kaluza-Klein theory. We also present some new solutions, which arise
naturally in string theory, which are non-superconducting extremal black holes.
We present a nice geometrical interpretation of these effects derived by
looking carefully at the higher dimensional configurations from which the lower
dimensional black hole solutions are obtained. We show that other 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 worldvolume of `light' superconducting
p-branes (which are embedded in flat space), and that minimally coupled zero
modes will propagate in the adS factor of the near-horizon geometries of
`heavy', or gravitating, superconducting p-branes.Comment: 22 pages, 2 figure
