Superconducting p-branes and Extremal Black Holes

TL;DR

The paper investigates the superconducting-like Meissner effect in extremal black holes and p-branes within string theory, providing new solutions and a geometric interpretation of their electromagnetic properties.

Contribution

It presents new evidence and solutions for superconducting extremal black holes and p-branes, along with a geometric interpretation of these effects in higher-dimensional theories.

Findings

Extremal black holes exhibit a Meissner effect similar to superconductors.

New solutions of non-superconducting extremal black holes are found in string theory.

Superconducting properties are extended to p-branes, with implications for their worldvolume physics.

Abstract

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.