Advertisement

Huygens’ Principle and MAPLE’s NPspinor Package

  • Chu K. C. 
  • Czapor S. R. 
  • McLenaghan R. G. 
Conference paper

Abstract

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’.

Keywords

Proposition State Weyl Spinor Scalar Wave Equation Petrov Type Nonvanishing Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Friedlander, F.G. (1975): The Wave Equation on a Curved Space-time. Cambridge University Press, CambridgeMATHGoogle Scholar
  2. 2.
    Czapor, S.R., McLenaghan, R.G., Sasse, F.D. (1999): Ann. Inst. Henri Poincaré 71, 595MathSciNetMATHGoogle Scholar
  3. 3.
    Chu, K.C. (2000): Contributions to the Study of the Validity of Huygens’ Principle for the Non-self-adjoint Scalar Wave Equation on Petrov Type D Spacetimes. M. Math. Thesis, University of Waterloo, Waterloo, Ontario, CanadaGoogle Scholar
  4. 4.
    Anderson, WG. (1991): Contributions to the Study of Huygens’ Principle for Non-self-adjoint Scalar Wave Equations on Curved Space-times. M. Math. Thesis, University of Waterloo, Waterloo, Ontario, CanadaGoogle Scholar
  5. 5.
    Anderson, W.G., McLenaghan, R.G. (1994): Ann. Inst. Henri Poincaré 60, 373MathSciNetMATHGoogle Scholar
  6. 6.
    Carminati, J., McLenaghan, R.G. (1986): Ann. Inst. Henri Poincaré 44, 115MathSciNetMATHGoogle Scholar
  7. 7.
    McLenaghan, R.G., Walton, T.F. (1988): Ann. Inst. Henri Poincaré 48, 267MathSciNetMATHGoogle Scholar
  8. 8.
    Günther, P. (1952): Ber. Verh. Sachs. Akad. Wiss. Leipzig 100, 1Google Scholar
  9. 9.
    McLenaghan, R.G. (1974): Ann. Inst. Henri Poincaré 20, 153MathSciNetMATHGoogle Scholar
  10. 10.
    Czapor, S.R., McLenaghan, R.G. (1987): General Relativity and Gravitation 19, 623MathSciNetADSMATHCrossRefGoogle Scholar
  11. 11.
    Czapor, S.R., McLenaghan, R.G., Carminati, J. (1991): General Relativity and Gravitation 24, 911MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    Adams, W.W, Loustaunau, P. (1994): Introduction to Gröbner Bases. American Mathematical Society, ProvidenceMATHGoogle Scholar
  13. 13.
    Geddes, K.O., Czapor, S.R., Labahn, G. (1992): Algorithms for Computer Algebra. Kluwer Academic Publishers, BostonMATHCrossRefGoogle Scholar
  14. 14.
    Czapor, S.R. (1988): Gröbner Basis Methods for Solving Algebraic Equations. Doctoral Thesis, University of Waterloo, Waterloo, Ontario, CanadaGoogle Scholar
  15. 15.
    Czapor, S.R. (1989): J. Symbolic Computation 7, 49MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia 2002

Authors and Affiliations

  • Chu K. C. 
    • 1
  • Czapor S. R. 
    • 2
  • McLenaghan R. G. 
    • 3
  1. 1.Department of Mathematics, University of Utah, Salt Lake City, Utah, USA, and Dipartimento di FisicaUniversità di Roma “Tor Vergata”RomaItaly
  2. 2.Department of Mathematics and Computer ScienceLaurentian UniversityOntarioCanada
  3. 3.Department of Applied MathematicsUniversity of WaterlooW. Waterloo OntarioCanada

Personalised recommendations