Magnetic charges and Wald entropy

TL;DR

This paper extends Wald's formalism to analyze the thermodynamics of higher-dimensional black objects with electric and magnetic charges, revealing duality properties in their first laws and Smarr relations.

Contribution

It introduces a method to incorporate electric-magnetic duality into the thermodynamic laws of higher-dimensional black objects within a generalized Einstein-Maxwell framework.

Findings

Derived first laws and Smarr formulas for higher-dimensional black holes and rings.

Clarified the role of electric-magnetic duality in black hole thermodynamics.

Provided a systematic approach to handle magnetic charges in Wald's formalism.

Abstract

Using Wald's formalism, we study the thermodynamics (first laws and Smarr formulae) of asymptotically-flat black holes, rings etc. in a higher-dimensional higher-rank generalization of the Einstein-Maxwell theory. We show how to deal with the electric and magnetic charges of the objects and how the electric-magnetic duality properties of the theory are realized in the first laws and Smarr formulae.