JournalszaaVol. 16, No. 1pp. 37–58

An Explicit Determination of the Non-self-adjoint Wave Equations that Satisfy Huygens’ Principle on Petrov Type III Background Space-times

  • W.G. Anderson

    University of Alberta, Edmonton, Canada
  • Raymond G. McLenaghan

    University of Waterloo, Canada
  • Tom G. Walton

    Waterloo, Ontario, Canada
An Explicit Determination of the Non-self-adjoint Wave Equations that Satisfy Huygens’ Principle on Petrov Type III Background Space-times cover
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Abstract

It is shown that the validity of Huygens’ principle for the non-self-adjoint wave equation on a Petrov type Ill space-time implies that the space-time is conformally related to one in which every repeated null vector field of the Weyl tensor is recurrent. It is further shown that, given a certain mild assumption imposed on the covariant derivative of the Weyl curvature spinor, there are no Petrov type III space-times on which the non-self-adjoint scalar wave equation satisfies Huygens’ Principle.

Cite this article

W.G. Anderson, Raymond G. McLenaghan, Tom G. Walton, An Explicit Determination of the Non-self-adjoint Wave Equations that Satisfy Huygens’ Principle on Petrov Type III Background Space-times. Z. Anal. Anwend. 16 (1997), no. 1, pp. 37–58

DOI 10.4171/ZAA/748