Contributions to the Study of the Validity of Huygens' Principle for the Non-self-adjoint Scalar Wave Equation on Petrov Type D Spacetimes

[摘要] This thesis makes contributions to the solution of Hadamard;;s problem through an examination of the question of the validity of Huygens;;principle for the non-self-adjoint scalar wave equation on a Petrov type D spacetime.The problem is split into five further sub-cases based on the alignment of the Maxwell and Weyl principal spinors of the underlying spacetime.Two of these sub-cases are considered, one of which is proved to be incompatible with Huygens;; principle, while for the other, it is shown that Huygens;; principle implies that the two principal null congruences of the Weyl tensor are geodesic and shear-free. Furthermore, an unpublished result of McLenaghan regarding symmetric spacetimes of Petrov type D is independently verified.This result suggests the possible existence of counter-examples of the Carminati-McLenaghan conjecture.

[发布机构] University of Waterloo

[效力级别] Huygens"

[关键词] Mathematics;Huygens"principle;non-self-adjoint;scalar wave equation;Petrov type D