Weyl中微子方程或Maxwell方程满足惠更斯原理的Petrov型III时空的不存在性
Nonexistence of Petrov type III Space-Times on which Weyl's Neutrino Equation or Maxwell's Equations satisfy Huygens' Principle
摘要：
推广以往的结果，我们表明，没有彼得罗夫III型时空上的Weyl中微子方程或麦克斯韦方程满足惠更斯原理。利用Maple的NPspinor包将Alvarez和Wunsch的五指标必要条件转化为并矢形式，证明了这一结果.问题的可积性条件导致一个多项式方程组。然后，我们应用Maple的grobner包，以表明该系统没有容许的解决方案。
英文摘要：
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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