# Is it possible for the phase of electric charge to change over large general relativistic distances?

Jackson provides examples of how magnetic charge and electric charge form together to create complex charge, \begin{align} \rho = \rho_e+i\rho_m \end{align} which gives rise to the complex faraday field \begin{align} \boldsymbol{F}=\boldsymbol{E}+i\boldsymbol{B} \end{align} I assume magnetic charge has not been observed on a local scale, however is it possible to bend space such that two charges are observed to have different phases over vast cosmic distances. For example \begin{align} \rho = \rho_e e^{i r/\lambda} \end{align}

If every electromagnetic charge has the same ratio of magnetic and electric charge then you can rotate that complex charge $\rho=\rho_e+i\rho_m$ (and a duality rotation for the fields) to get a purely real (electric) charge with the normal maxwell equations.