Nonexistence of Petrov type III Space-Times on which Weyl's Neutrino Equation or Maxwell's Equations satisfy Huygens' Principle

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.

14 pages

Cited by in corpus (2)

• Complete Solution of Hadamard's Problem for the Scalar Wave Equation on Petrov type III Space-Times
• Huygens' Principle for the Non-Self-Adjoint Scalar Wave Equation on Petrov type III Space-Times