The Role of Dipole Charges in Black Hole Thermodynamics

TL;DR

The paper investigates how dipole charges can enter the first law of black hole thermodynamics in higher dimensions. It shows that the Sudarsky-Wald derivation's assumption of a globally defined potential omits dipole contributions, which appear when the potential is not globally defined due to horizon topology. It derives a corrected first law for five-dimensional dipole rings, including a dipole term, and extends the formalism to minimal 5D supergravity with Chern-Simons terms. It further generalizes to higher dimensions with p-form fields, predicting local charges on general horizon topologies and providing a unified first-law framework. The results broaden the scope of charges appearing in black hole thermodynamics and suggest new directions for higher-dimensional solutions.

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.