Hertz and Debye potentials and electromagnetic fields in general relativity

Earlier work on the application of curved space Hertz and Debye bivector potentials to the solution of Maxwell's equations for source-free electromagnetic test fields in general relativity is extended; all Hertzian schemes are classified by considering bivector potentials which are eigenvectors of the Hodge duality operator. This approach has the advantage of simplifying the task of solving the system of coupled equations which determine the Hertz potential. Results are applied to several Debye schemes and a new scheme which can be used in Petrov type-D spacetimes is presented. For each of these schemes, the one-component wave equation for the potential is given with respect to the null tetrad/Newman-Penrose formalism and, for the first time, with respect to an orthonormal basis.