The Role of Dipole Charges in Black Hole Thermodynamics

Abstract

Modern derivations of the first law of black holes appear to show that the only charges that arise are monopole charges that can be obtained by surface integrals at infinity. However, the recently discovered five dimensional black ring solutions empirically satisfy a first law in which dipole charges appear. We resolve this contradiction and derive a general form of the first law for black rings. Dipole charges do appear together with a corresponding potential. We also include theories with Chern-Simons terms and generalize the first law to other horizon topologies and more generic local charges.