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Zbl 0645.53047
McLenaghan, R.G.; Walton, T.F.
An explicit determination of the non-self-adjoint wave equations on curved space-time that satisfy Huygens' principle. I: Petrov type N background space-times. (English)
[J] Ann. Inst. Henri Poincaré, Phys. Théor. 48, No.3, 267-280 (1988). ISSN 0246-0211

It is shown that the validity of Huygens' principle for the non-self- adjoint wave equation on a general Petrov type N space-time implies that the equation is equivalent to the conformally invariant scalar wave equation on the exact plane wave space-time. This result solves Hadamard's problem for this class of equations since it is known that the latter equation is the only self-adjoint Huygens' equation on type N space-times.

MSC 2000:: *53B50 Appl. of local differential geometry to physics
83C10 Equations of motion
35L05 Wave equation

Keywords: Huygens' principle; non-self-adjoint wave equation; Petrov type; space- time; Hadamard's problem

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