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Huygens’ principle and MAPLE’s NPspinor package. (English) Zbl 1202.83086
Cianci, R. (ed.) et al., Recent developments in general relativity, Genova 2000. Proceedings of the 14th SIGRAV conference on general relativity and gravitational physics, Genova, September 18–22, 2000. Milano: Springer (ISBN 88-470-0162-5/pbk). 151-163 (2002).
Summary: 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 decomposition 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’.
For the entire collection see [Zbl 1063.83501].
MSC:
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
83-04 Software, source code, etc. for problems pertaining to relativity and gravitational theory
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
Software:
Maple; NPspinor
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