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) (Q1098018)

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.