Melvin--Bonnor and Bertotti--Robinson spacetimes with Baryonic charge

Abstract: Recently, a novel dictionary relating solutions of the Einstein--Scalar--Maxwell theory to solutions of gauged Skyrme--Maxwell--Einstein models in $(3+1)$ dimensions has been established. This development provides a clear and systematic route to constructing new configurations with nontrivial Baryonic charge and magnetic field, leveraging the fact that the Einstein--Scalar--Maxwell system is considerably more tractable, thanks to powerful solution-generating techniques. In this work, we exploit the framework that allows compact sources dressed by scalar fields to be consistently embedded in external electromagnetic backgrounds, and we construct their dual counterparts carrying Baryonic charge in the Skyrme sector. The resulting Baryonic charge is expressed directly in terms of the parameters characterizing the seed spacetime, and a corresponding quantization condition involving these parameters is explicitly derived. Consequently, the mass and the Baryonic charge are not independent parameters. These results provide a closed analytic formula for the black hole mass parameter in terms of the Baryonic charge and the magnetic field. This relation between the mass parameter and the Baryonic charge is linear for large values of the mass, while significant deviations from linearity arise if the mass takes intermediate values.