The Role of Dipole Charges in Black Hole Thermodynamics

TL;DR

This paper resolves the apparent contradiction in black hole thermodynamics by demonstrating that dipole charges, alongside monopole charges, are integral to the first law, especially in five-dimensional black rings with various topologies.

Contribution

It derives a general first law for black rings that includes dipole charges and extends the framework to theories with Chern-Simons terms and diverse horizon topologies.

Findings

Dipole charges are essential in the first law of black hole thermodynamics.

The first law is generalized to include theories with Chern-Simons terms.

The framework applies to various horizon topologies and local charges.

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.