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Nonexistence of Petrov type III space-times on which Weyl’s neutrino equation or Maxwell’s equations satisfy Huygens’ principle. (English) Zbl 0869.53061
The paper is part of a program to find all Huygens-type equations among the conformally invariant hyperbolic field equations on a four-dimensional spacetime. More precisely, this is the sixth paper of a series; it considers Maxwell’s equations for electromagnetism and Weyl’s equation for neutrinos. It shows that Huygens’ principle is never valid on a spacetime of Petrov type III. To that aim the known necessary conditions, up to the five-index condition found by Alvarez and Wünsch, are translated into spinor form by means of the Maple package NPspinor. Some Newman-Penrose spinor coefficients are the variables of the new polynomial system; the latter is solved by means of the Maple package grobner.

MSC:
53Z05 Applications of differential geometry to physics
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
83-04 Software, source code, etc. for problems pertaining to relativity and gravitational theory
83C50 Electromagnetic fields in general relativity and gravitational theory
Software:
Maple; NP; NPspinor
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References:
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