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’

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  1. Catalano Ferraioli, D.; Marvan, M.: The equivalence problem for generic four-dimensional metrics with two commuting Killing vectors (2020)
  2. Bratek, Łukasz; Jałocha, Joanna; Woszczyna, Andrzej: Nakedly singular counterpart of Schwarzschild’s incompressible star. A barotropic continuity condition in the center (2019)
  3. Brooks, D. A.; Mcnutt, D. D.; Simard, J. P.; Musoke, N. K.: Scalar polynomial curvature invariants in the context of the Cartan-Karlhede algorithm (2019)
  4. Cadoni, Mariano; Franzin, Edgardo; Masella, Federico; Tuveri, Matteo: A solution-generating method in Einstein-scalar gravity (2019)
  5. de Haro, Jaume; Aresté Saló, Llibert; Pan, Supriya: Limiting curvature mimetic gravity and its relation to loop quantum cosmology (2019)
  6. Wylleman, L.; Coley, A.; McNutt, D.; Aadne, M.: Observer-based invariants for cosmological models (2019)
  7. Endlich, Solomon; Gorbenko, Victor; Huang, Junwu; Senatore, Leonardo: An effective formalism for testing extensions to general relativity with gravitational waves (2017)
  8. Tian, David Wenjie: Local energy-momentum conservation in scalar-tensor-like gravity with generic curvature invariants (2016)
  9. Woszczyna, Andrzej; Kutschera, Marek; Kubis, Sebastian; Czaja, Wojciech; Plaszczyk, Piotr; Golda, Zdzisław A.: Nakedly singular non-vacuum gravitating equilibrium states (2016)
  10. Smolic, Jelena; Taylor, Marika: Higher derivative effects for 4d AdS gravity (2013)
  11. Beke, David; Palmisano, Giovanni; Speziale, Simone: Pauli-Fierz mass term in modified Plebanski gravity (2012)
  12. Chu, K. C.; Czapor, S. R.; McLenaghan, R. G.: Huygens’ principle and MAPLE’s NPspinor package (2002)
  13. Cianci, R. (ed.); Collina, R. (ed.); Francaviglia, M. (ed.); Fré, P. (ed.): Recent developments in general relativity, Genova 2000. Proceedings of the 14th SIGRAV conference on general relativity and gravitational physics, Genova, September 18--22, 2000 (2002)
  14. Anderson, W. G.; McLenaghan, R. G.; Sasse, F. D.: Huygens’ principle for the non-self-adjoint scalar wave equation on Petrov type III space-times (1999)
  15. Czapor, S. R.; McLenaghan, R. G.; Sasse, F. D.: Complete solution of Hadamard’s problem for the scalar wave equation on Petrov type III space-times (1999)
  16. McLenaghan, R. G.; Sasse, F. D.: Nonexistence of Petrov type III space-times on which Weyl’s neutrino equation or Maxwell’s equations satisfy Huygens’ principle (1996)
  17. Carminati, J.; McLenaghan, R. G.: Algebraic invariants of the Riemann tensor in a four-dimensional Lorentzian space (1991)