Huygens’ Principle and MAPLE’s NPspinor Package
With the assistance of the computer algebra system MAPLE’s NPspinor package, two propositions are proved regarding the validity of Huygens’ principle for the non-self- adjoint scalar wave equation on a Petrov type D spacetime. A decom-position of the problem is given according to the alignment of the principal spinors of the Maxwell and Weyl spinors. The first proposition states that the validity of Huygens’ principle implies a certain product involving four of the spin coefficients is real. The second proposition states that if the associated Maxwell spinor of a non-self-adjoint scalar wave operator is algebraically degenerate and its principal spinor is aligned with one of the doubly degenerate Weyl principal spinors, then that wave operator cannot be Huygens’.
KeywordsProposition State Weyl Spinor Scalar Wave Equation Petrov Type Nonvanishing Component
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