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An explicit determination of the empty space-times on which the wave equation satisfies Huygens' principle†

Published online by Cambridge University Press:  24 October 2008

R. G. McLenaghan
R. G. McLenaghan
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge‡
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Abstract

The validity of Huygens' principle in the sense of Hadamard's ‘minor premise’ is investigated for scalar wave equations on curved space-time. A new necessary condition for its validity in empty space-time is derived from Hadamard's necessary and sufficient condition using a covariant Taylor expansion in normal coordinates. A two component spinor calculus is then employed to show that this necessary condition implies that the plane wave space-times and Minkowski space are the only empty space-times on which the scalar wave equation satisfies Huygens' principle.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 1 , January 1969 , pp. 139 - 155
Copyright
Copyright © Cambridge Philosophical Society 1969

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