Nonexistence of Petrov type III space-times on which Weyl's neutrino equation or Maxwell's equations satisfy Huygens' principle

R. G. McLenaghan; F. D. Sasse

Annales de l'I.H.P. Physique théorique (1996)

  • Volume: 65, Issue: 3, page 253-271
  • ISSN: 0246-0211

How to cite

top

McLenaghan, R. G., and Sasse, F. D.. "Nonexistence of Petrov type III space-times on which Weyl's neutrino equation or Maxwell's equations satisfy Huygens' principle." Annales de l'I.H.P. Physique théorique 65.3 (1996): 253-271. <http://eudml.org/doc/76742>.

@article{McLenaghan1996,
author = {McLenaghan, R. G., Sasse, F. D.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Maxwell equations; Weyl equation; Petrov type III spacetime; Huygens' principle},
language = {eng},
number = {3},
pages = {253-271},
publisher = {Gauthier-Villars},
title = {Nonexistence of Petrov type III space-times on which Weyl's neutrino equation or Maxwell's equations satisfy Huygens' principle},
url = {http://eudml.org/doc/76742},
volume = {65},
year = {1996},
}

TY - JOUR
AU - McLenaghan, R. G.
AU - Sasse, F. D.
TI - Nonexistence of Petrov type III space-times on which Weyl's neutrino equation or Maxwell's equations satisfy Huygens' principle
JO - Annales de l'I.H.P. Physique théorique
PY - 1996
PB - Gauthier-Villars
VL - 65
IS - 3
SP - 253
EP - 271
LA - eng
KW - Maxwell equations; Weyl equation; Petrov type III spacetime; Huygens' principle
UR - http://eudml.org/doc/76742
ER -

References

top
  1. [1] M. Alvarez, Zum huygensschen Prinzip bei einigen Klassen spinorieller Feldgleichungen in gekrümmten Raum-Zeit-Manifaltigkeiten, Diss. A. Päd. Hochshule Erfurt/Mühlhausen, 1991. 
  2. [2] M. Alvarez and V. Wünsch, Zur Gültigkeit des huygensschen Prinzips bei der Weyl-Gleichung und den homogenen Maxwellschen Gleichungen für Metriken vom Petrov-typ N, Wiss. Zeitschr. Päd. Hochsch. Erfurt/Mühlhausen, Math.-Naturwiss., Vol. 27, 1991, pp. 77-91. 
  3. [3] J. Carminati and R.G. Mclenaghan, Some new results on the validity of Huygens' principle for the scalar wave equation on a curved space-time. Article in Gravitation, Geometry and Relativistic Physics, Proceedings of the Journées Relativistes1984, Aussois, France, edited by Laboratoire Gravitation et Cosmologie Relativistes. Institut Henri Poincaré, Lectures Notes in Physics, Vol. 212, Springer Verlag, Berlin, 1984. Zbl0557.53046MR780225
  4. [4] 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
  5. [5] 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
  6. [6] J. Carminati and R.G. Mclenaghan, An explicit determination of 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
  7. [7] J. Carminati and R.G. Mclenaghan, An explicit determination of 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
  8. [8] S.R. Czapor and R.G. Mclenaghan, NP: A Maple package for performing calculations in the Newman-Penrose formalism, Gen. Rel. Gravit., Vol. 19, 1987, pp. 623-635. Zbl0613.53033MR892637
  9. [9] S.R. Czapor, R.G. Mclenaghan and J. Carminati, The automatic conversion of spinor equations to dyad form in MAPLE, Gen. Rel. Gravit., Vol. 24, 1992, pp. 911-928. Zbl0758.53047MR1180241
  10. [10] P. Günther, Zur Gültigkeit des huygensschen Prinzips bei partiellen Differentialgleichungen von normalen hyperbolischen Typus, S.-B. Sachs. Akad. Wiss. Leipzig Math.-Natur K., Vol. 100, 1952, pp. 1-43. Zbl0046.32201MR50136
  11. [11] P. Günther, Einige Sätze über huygenssche Differentialgleichungen, Wiss. Zeitschr. Karl Marx Univ., Math.-natu. ReiheLeipzig, Vol. 14, 1965, pp. 497-507. Zbl0173.12203MR198012
  12. [12] P. Günther, Ein Beispiel einer nichttrivialen huygesschen Differentialgleichungen mit vier unabhängigen Variablen, Arch. Rational Mech. Anal., Vol. 18, 1965, pp. 103-106. Zbl0125.05404MR174865
  13. [13] P. Günther and V. Wünsch, Maxwellsche Gleichungen und huygensches Prinzip I, Math. Nachr., Vol. 63, 1974, pp. 97-121. Zbl0288.35042MR363377
  14. [14] J. Hadamard, Lectures on Cauchy's problem in linear differential equations, Yale University Press, New Haven, 1923. Zbl49.0725.04JFM49.0725.04
  15. [15] H.P. Künzle, Maxwell fields satisfying Huygens' principle, Proc. Cambridge Philos. Soc., Vol. 64, 1968, pp. 779-785. 
  16. [16] 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
  17. [17] R.G. Mclenaghan and J. Leroy, Complex recurrent space-times, Proc. Roy. Soc. London, Vol. A327, 1972, pp. 229-249. Zbl0243.53030MR309517
  18. [18] R.G. Mclenaghan, On the validity of Huygens' principle for second order partial differential equations with four independent variables. Part I: Derivation of necessary conditios, Ann. Inst. Henri Poincaré, Vol. A20, 1974, pp. 153-188. Zbl0287.35058MR361452
  19. [19] R.G. Mclenaghan and T.G.C. Williams, An explicit determination of the Petrov type D space-times on which Weyl's neutrino equation and Maxwell's equations satisfiy Huygens' principle, Ann. Inst. Henri Poincaré, Phys. Théor., Vol. 53, 1990, pp. 217-223. Zbl0709.53053MR1079778
  20. [20] V. Wünsch, Über selbstadjungierte Huygenssche Differentialgleichungen mit vier unabhängigen Variablen, Math. Nachr., Vol. 47, 1970, pp. 131-154. Zbl0211.40803MR298221
  21. [21] V. Wünsch, Maxwellsche Gleichungen und huygensches Prinzip II, Math. Nachr., Vol. 73, 1974, pp. 19-36. Zbl0288.35043MR426807
  22. [22] V. Wünsch, Cauchy-Problem und huygenssches Prinzip bei einigen Klassen spinorieller Feldleichungen I, Beitr. zur Analysis, Vol. 12, 1978, pp. 47-76. Zbl0448.58022MR507097
  23. [23] V. Wünsch, Cauchy-Problem und huygenssches Prinzip bei einigen Klassen spinorieller Feldleichungen II, Beitr. zur Analisys, Vol. 13, 1979, pp. 147-177. Zbl0467.35067MR536225
  24. [24] V. Wünsch, Huygens' principle on Petrov type-D space-times, Ann. Phys., Vol. 46, 1989, pp. 593-597. Zbl0697.53027MR1051239

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.