Dyons with potentials: duality and black hole thermodynamics

TL;DR

This paper develops a duality-invariant formalism for dyons that eliminates string singularities and extends to curved space, providing new insights into black hole thermodynamics and charge conservation.

Contribution

It introduces a modified double potential formalism with additional potentials, resolving singularities in dyonic black holes and linking thermodynamics to horizon-protected singularities.

Findings

Dyons can be described without string singularities in this formalism.

Black hole singularities are hidden behind horizons, ensuring regular thermodynamic behavior.

The theory generalizes to curved spacetime, maintaining duality invariance.

Abstract

A modified version of the double potential formalism for the electrodynamics of dyons is constructed. Besides the two vector potentials, this manifestly duality invariant formulation involves four additional potentials, scalar potentials which appear as Lagrange multipliers for the electric and magnetic Gauss constraints and potentials for the longitudinal electric and magnetic fields. In this framework, a static dyon appears as a Coulomb-like solution without string singularities. Dirac strings are needed only for the Lorentz force law, not for Maxwell's equations. The magnetic charge no longer appears as a topological conservation law but as a surface integral on a par with electric charge. The theory is generalized to curved space. As in flat space, the string singularities of dyonic black holes are resolved. As a consequence all singularities are protected by the horizon and the thermodynamics is shown to follow from standard arguments in the grand canonical ensemble.