Huygens' principle and characteristic propagation property for waves in curved space-times

Fields satisfying a wave equation on a curved space‐time can be accompanied by tails propagating inside the light cone. A formal characterization of tails is given, and the relationship of the tail‐free property with the characteristic propagation property (CPP) discussed in the literature is clarified. The scalar wave equation satisfies the CPP independently of the tail‐free property only in the case of minimal coupling in two space‐time dimensions. The peculiar feature of electromagnetic radiation, for which pure gauge tails in the potential can occur, is pointed out.