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An explicit determination of the space-times on which the conformally invariant scalar wave equation satisfies Huygens’ principle. III: Petrov type III space-times. (English) Zbl 0706.35131

Summary: [For part I, see ibid. 44, 115-153 (1986; Zbl 0595.35067).]
It is shown that the validity of Huygens’ principle for the conformally invariant scalar wave equation, Maxwell’s equations or Weyl’s neutrino equation on a Petrov type III space-time, implies that the space-time is conformally related to one on which the repeated principal null vector field of the Weyl tensor, is recurrent. Further, it is proven tat if a certain mild assumption which is shown to be suggested by the necessary conditions, is imposed on the covariant derivative of the Weyl tensor, then there are no Petrov type III space-times on which any of the above equations satisfies Huygens’ principle.

MSC:

35Q75 PDEs in connection with relativity and gravitational theory
35L05 Wave equation
83C99 General relativity

Citations:

Zbl 0595.35067

Software:

Maple; NP
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Full Text: Numdam EuDML

References:

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