Nonexistence of Petrov type III Space-Times on which Weyl's Neutrino Equation or Maxwell's Equations satisfy Huygens' Principle
R. G. McLenaghan, F. D. Sasse
Abstract
Extending previous results we show that there are no Petrov type III space-times on which either the Weyl neutrino equation or Maxwell's equations satisfy Huygens' principle. We prove the result by using Maple's NPspinor package to convert the five-index necessary condition obtained by Alvarez and Wunsch to dyad form. The integrability conditions of the problem lead to a system of polynomial equations. We then apply Maple's grobner package to show that this system has no admissible solutions.
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