An explicit determination of the Petrov type D spacetimes on which Weyl's neutrino equation and Maxwell's equations satisfy Huygens' principle

R. G. McLenaghan; G. C. Williams

Annales de l'I.H.P. Physique théorique (1990)

  • Volume: 53, Issue: 2, page 217-223
  • ISSN: 0246-0211

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McLenaghan, R. G., and Williams, G. C.. "An explicit determination of the Petrov type D spacetimes on which Weyl's neutrino equation and Maxwell's equations satisfy Huygens' principle." Annales de l'I.H.P. Physique théorique 53.2 (1990): 217-223. <http://eudml.org/doc/76501>.

@article{McLenaghan1990,
author = {McLenaghan, R. G., Williams, G. C.},
journal = {Annales de l'I.H.P. Physique théorique},
language = {eng},
number = {2},
pages = {217-223},
publisher = {Gauthier-Villars},
title = {An explicit determination of the Petrov type D spacetimes on which Weyl's neutrino equation and Maxwell's equations satisfy Huygens' principle},
url = {http://eudml.org/doc/76501},
volume = {53},
year = {1990},
}

TY - JOUR
AU - McLenaghan, R. G.
AU - Williams, G. C.
TI - An explicit determination of the Petrov type D spacetimes on which Weyl's neutrino equation and Maxwell's equations satisfy Huygens' principle
JO - Annales de l'I.H.P. Physique théorique
PY - 1990
PB - Gauthier-Villars
VL - 53
IS - 2
SP - 217
EP - 223
LA - eng
UR - http://eudml.org/doc/76501
ER -

References

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  1. [1] J. Carminati and R.G. Mclenaghan, Determination of All Petrov type N Space-Times on which the Conformally Invariant Scalar Wave Equation Satisfies Huygens' Principle, Phys. Lett., Vol. 105A, 1984, pp. 351-354. Zbl0694.35074MR766032
  2. [2] J. Carminati and R.G. Mclenaghan, An Explicit Determination of the Petrov Type N Space-Times on which the Conformally Invariant Scalar Wave Equation Satisfies Huygens' Principle, Ann. Inst. Henri Poincaré, Phys. Théor., Vol. 44, 1986, pp. 115- 153. Zbl0595.35067MR839281
  3. [3] J. Carminati and R.G. Mclenaghan, An Explicit Determination of the Space-times on which the Conformally Invariant Scalar Wave Equation Satisfies Huygens' Principle, Part II: Petrov Type D Space-Times, Ann. Inst. Henri Poincaré, Phys. Théor., Vol. 47, 1987, pp. 337-354. Zbl0694.35074MR933681
  4. [4] J. Carminati and R.G. Mclenaghan, An Explicit Determination of the Space-Times on which the Conformally Invariant Scalar Wave Equation Satisfies Huygens' Principle, Part III: Petrov type III space-times, Ann. Inst. Henri Poincaré, Phys. Théor., Vol. 48, 1988, pp. 77-96. Zbl0706.35131MR947160
  5. [5] P. GüntherZur Gültigkeit des Huygensschen Princips bei partiellen Differentialgleichungen von normalen hyperbolischen Typus, S.-B.Sachs. Akad. Wiss. Leipzig Math.- Natur K., Vol. 100, 1952, pp. 1-43. Zbl0046.32201MR50136
  6. [6] P. Günther, Ein Beispiel einer nichttrivalen Huygensschen Differentialgleichungen mit vier unabhängigen Variablen, Arch. Rational Mech. Anal., Vol. 18, 1965, pp. 103-106. Zbl0125.05404MR174865
  7. [7] P. Günther, Einige Sätze über Huygenssche Differentialgleichungen, Wiss. Zeitschr. Karl Marx Univ., Math.-Natu. Reihe Leipzig, Vol. 14, 1965, pp. 498-507. Zbl0173.12203MR198012
  8. [8] P. Günther and V. Wünsch, Maxwellsche Gleichungen und Huygenssches Prinzip I, Math. Nach., Vol. 63, 1974, pp.97-121. Zbl0288.35042MR363377
  9. [9] J. Hadamard, Lectures on Cauchy's problem in linear partial differential equations, Yale University Press, New Haven, 1923. Zbl49.0725.04JFM49.0725.04
  10. [10] C.N. Kozameh, E.T. Newman and K.P. Tod, Conformal Einstein Spaces, General Relativity and Gravitation, Vol. 17, 1985, pp. 343-352. Zbl0564.53011MR788800
  11. [11] H.P. Künzle, Maxwell Fields Satisfying Huygens' Principle, Proc. Cambridge Philos. Soc., Vol. 64, 1968, pp. 770-785. 
  12. [12] R.G. Mclenaghan, An Explicit Determination of the Empty Space-Times on which the Wave Equation Satisfies Huygens' Principle, Proc. Cambridge Philos. Soc., Vol. 65, 1969, pp. 139-155. Zbl0182.13403MR234700
  13. [13] R.G. Mclenaghan and J. Leroy. Complex recurrent space-times, Proc. R. Soc. Lond., Vol. A 327, 1972, pp. 229-249. Zbl0243.53030MR309517
  14. [14] R.G. Mclenaghan, On the Validity of Huygens' Principle for Second Order Partial Differential Equations with Four Independent Variables. Part I: Derivation of Necessary Conditions, Ann. Inst. Henri Poincaré, Vol. A20, 1974, pp. 153-188. Zbl0287.35058MR361452
  15. [15] R.G. Mclenaghan and T.F. Walton, An Explicit Determination of the Non-Self-Adjoint Wave Equations on Curved Space-Time that Satisfy Huygens' Principle, Part I: Petrov Type N. Background Space-Times, Ann. Inst. Henri Poincaré, Phys. Théor., Vol. 48, 1988, pp. 267-280. Zbl0645.53047MR950268
  16. [16] B. Rinke and V. Wünsch, Zum Huygensschen Prinzip bei der skalaren Wellengleichung, Beitr. Analysis, Vol. 18, 1981, pp.43-75. Zbl0501.53010MR650138
  17. [17] V. Wünsch, Über selbstadjungierte Huygenssche Differentialgleichungen mit vier unabhängigen Variablen, Math. Nachr., Vol. 47, 1970, pp. 131-154. Zbl0211.40803MR298221
  18. [18] V. Wünsch, Cauchy-Problem und Huygenssches Prinzip bei einigen Klassen spinorieller Feldgleichungen I, Beitr. Analysis, Vol. 12, 1978, pp. 47-76. Zbl0448.58022MR507097
  19. [19] V. Wünsch, Cauchy-problem und Huygenssches Prinzip bei einigen Klassen spinorieller Feldgleichungen II, Beitr. Analysis, Vol. 13, 1979, pp. 147-177. Zbl0467.35067MR536225
  20. [20] V. Wünsch, Huygens' Principle on Petrov Type-D Space-times, Ann. Phys., Vol. 46, 1989, pp. 593-597. Zbl0697.53027MR1051239

Citations in EuDML Documents

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  1. V. Wünsch, Huygens' principle on Petrov type N space-times
  2. W. G. Anderson, R. G. McLenaghan, F. D. Sasse, Huygens' principle for the non-self-adjoint scalar wave equation on Petrov type III space-times
  3. R. G. McLenaghan, F. D. Sasse, Nonexistence of Petrov type III space-times on which Weyl's neutrino equation or Maxwell's equations satisfy Huygens' principle
  4. V. Wünsch, Moments and Huygens' principle for conformally invariant field equations in curved space-times
  5. J. Carminati, S. R. Czapor, R. G. McLenaghan, G. C. Williams, Consequences of the validity of Huygens' principle for the conformally invariant scalar wave equation, Weyl's neutrino equation and Maxwell's equations on Petrov type II space-times
  6. S. R. Czapor, R. G. McLenaghan, F. D. Sasse, Complete solution of Hadamard's problem for the scalar wave equation on Petrov type III space-times
  7. W. G. Anderson, R. G. McLenaghan, On the validity of Huygens' principle for second order partial differential equations with four independent variables. II. A sixth necessary condition

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