Electromagnetic dual Einstein-Maxwell-scalar models

Electromagnetic duality is discussed in the context of Einstein-Maxwell-scalar (EMS) models including axionic-type couplings. This family of models introduces two non-minimal coupling functions $f(\phi)$ and $g(\phi)$, depending on a real scalar field $\phi$. Interpreting the scalar field as a medium, one naturally defines constitutive relations as in relativistic non-linear electrodynamics. Requiring these constitutive relations to be invariant under the $SO(2)$ electromagnetic duality rotations of Maxwell's theory, defines 1-parameter, closed $\textit{duality orbits}$ in the space of EMS models, connecting different electromagnetic fields in "dual" models with different coupling functions, but leaving both the scalar field and the spacetime geometry invariant. This mapping works as a solution generating technique, extending any given solution of a specific model to a (different) solution for any of the dual models along the whole duality orbit. We illustrate this technique by considering the duality orbits seeded by specific EMS models wherein solitonic and black hole solutions are known. For dilatonic models, specific rotations are equivalent to $S$-duality.