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Zeitschrift für Analysis und ihre Anwendungen


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Volume 16, Issue 1, 1997, pp. 37–58
DOI: 10.4171/ZAA/748

Published online: 1997-03-31

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

W.G. Anderson[1], Raymond G. McLenaghan[2] and Tom G. Walton[3]

(1) University of Alberta, Edmonton, Canada
(2) University of Waterloo, Canada
(3) Waterloo, Ontario, Canada

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.

Keywords: Huygens’ principle, scalar wave equation, Petrov type III space-times

Anderson W.G., McLenaghan Raymond, Walton Tom: 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), 37-58. doi: 10.4171/ZAA/748