Zur Gültigkeit des Huygensschen Prinzips bei hyperbolischen Differentialgleichungssytemen in statischen Raum-Zeiten

Abstract

The already 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 by the help of the spinor calculus. One result is, that Huygens’ principle does not hold in Riemannian spaces, whose metric tensor is static and whose Weyl spinor is of Petrov type D. If two of the three considered types of equations satisfy Huygens’ principle in a static space-time, then the conformal curvature tensor vanishes.