It is shown that the validity of Huygens’ principle for the non-self-adjoint wave equation on a Petrov type Ill space-time implies that the space-time is conformally related to one in which every repeated null vector field of the Weyl tensor is recurrent. It is further shown that, given a certain mild assumption imposed on the covariant derivative of the Weyl curvature spinor, there are no Petrov type III space-times on which the non-self-adjoint scalar wave equation satisfies Huygens’ Principle.
Cite this article
W.G. Anderson, Raymond G. McLenaghan, Tom G. Walton, An Explicit Determination of the Non-self-adjoint Wave Equations that Satisfy Huygens’ Principle on Petrov Type III Background Space-times. Z. Anal. Anwend. 16 (1997), no. 1, pp. 37–58DOI 10.4171/ZAA/748