Force-free fields from Hertz potentials

We show a correspondence between magnetic fields that are eigenvectors of the curl operator and certain solutions to the source-free Maxwell equations. When the eigenvalue of the curl is non-constant then the corresponding Maxwell system must be solved in a non-flat spacetime. We show how the generalized Hertz potential method of solving Maxwell's equations in curved spacetimes can be applied to determine eigenvectors of the curl. In the case of a constant eigenvalue the Chandrasekhar-Kendall eigenfunctions are recovered. For non-constant eigenvalue we use the formalism to produce some new force-free fields.