We present a formulation of electromagnetism in vacuum and in the presence of an arbitrary gravitational eld, based on Clifford analysis over a pseudo-Riemannian space with signature (1,3). We show that it is possibleto solve the direct electromagnetic radiation problem in four dimensional form, without invoking electromagneticpotentials and solely by analytical means. Our method reveals that the full electromagnetic eld can be completelyexpressed in terms of a particular solution of the underlying scalar wave equation, so that calculating the customaryGreen's dyadic is super uous.