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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
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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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R. G. McLenaghan, F. D. Sasse. 2005-04-13. Nonexistence of Petrov type III Space-Times on which Weyl's Neutrino Equation or Maxwell's Equations satisfy Huygens' Principle. https://arxiv.org/abs/math-ph/0504040

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