Hertz and Debye potentials and electromagnetic fields in general relativity

Abstract

In this paper the authors extend 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. They classify all Hertzian schemes 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. They then apply their results to several Debye schemes and present a new scheme which can be used in Petrov type-D spacetimes. 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.