Generalised Harrison transformations and black diholes in Einstein-ModMax

TL;DR

This paper develops generalized Harrison transformations for Einstein-ModMax theory, enabling the generation of new solutions including black diholes, and extends these techniques to Einstein-dilaton-ModMax theory, enriching the solution space of non-linear electrodynamics coupled to gravity.

Contribution

It introduces generalized Harrison transformations that preserve specific sectors in Einstein-ModMax theory and applies them to derive new solutions like black diholes, also extending to Einstein-dilaton-ModMax theory.

Findings

Rederived known solutions in Einstein-ModMax theory.

Constructed a new black dihole solution with opposite magnetic charges.

Extended solution techniques to Einstein-dilaton-ModMax theory.

Abstract

Einstein-Maxwell theory has powerful solution generating techniques which include Harrison transformations in the Ernst formalism. We construct generalized Harrison transformations that preserve the purely magnetic or purely electric sector in Einstein-ModMax (EMM) theory. Thus, they serve as solution generating techniques within these sectors for this model of non-linear electrodynamics minimally coupled to gravity. As an application we rederive several known exact solutions of EMM and a new solution, black diholes, describing two extremal BHs in equilibrium, with opposite magnetic charges, whose attraction is balanced by their embedding in the Melvin magnetic universe of this model. As a further generalization, we consider Einstein-dilaton-ModMax theory, and provide the extremal charged BHs and black diholes also in this model.