Q1098018
type: Item
instance of: scholarly article
title: Zur Gültigkeit des Huygensschen Prinzips bei hyperbolischen Differentialgleichungssystemen in statischen Raum-Zeiten. (Validity of Huygens' principle for hyperbolic differential equation systems in static space times)
zbMATH Open document ID: 0636.35073
DOI: 10.4171/ZAA/259
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1987-01-01T00:00:00Z
review text: Known necessary conditions for the validity of Huygens' principle for the self-adjoint scalar wave equation, for Maxwell's and Weyl's equations are examined in static space-times. To this end we use a three-dimensional Newman-Penrose-formalism which was suggested by \textit{Z. Perjés} [J. Math. Phys. 11, 3383-3391 (1970)]. Two of the main results are: (i) Huygens' principle does not hold in static Petrov-type D space-times. (ii) A static space-time in which two of the three types of equations mentioned above satisfy Huygens' principle is conformally flat. A result analogous to i) for Petrov-type I space-times has been derived only under additional assumptions. The Huygensian space-times are determined explicitly for a number of examples of static metrics known from General Relativity.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 83C50
zbMATH DE Number: 4036331
zbMATH Keywords: Huygens' principle
zbMATH Keywords: static space-times
zbMATH Keywords: Newman-Penrose-formalism
author: Reinhard Illge
MaRDI profile type: Publication
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label: Zur Gültigkeit des Huygensschen Prinzips bei hyperbolischen Differentialgleichungssystemen in statischen Raum-Zeiten. (Validity of Huygens' principle for hyperbolic differential equation systems in static space times)
description: scientific article; zbMATH DE number 4036331