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, Tome 65 (1996) no. 3, pp. 253-271.
@article{AIHPA_1996__65_3_253_0,
     author = {McLenaghan, R. G. and Sasse, F. D.},
     title = {Nonexistence of {Petrov} type {III} space-times on which {Weyl's} neutrino equation or {Maxwell's} equations satisfy {Huygens'} principle},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {253--271},
     publisher = {Gauthier-Villars},
     volume = {65},
     number = {3},
     year = {1996},
     mrnumber = {1420704},
     zbl = {0869.53061},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1996__65_3_253_0/}
}
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
SP  - 253
EP  - 271
VL  - 65
IS  - 3
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1996__65_3_253_0/
LA  - en
ID  - AIHPA_1996__65_3_253_0
ER  - 
%0 Journal Article
%A McLenaghan, R. G.
%A Sasse, F. D.
%T Nonexistence of Petrov type III space-times on which Weyl's neutrino equation or Maxwell's equations satisfy Huygens' principle
%J Annales de l'I.H.P. Physique théorique
%D 1996
%P 253-271
%V 65
%N 3
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1996__65_3_253_0/
%G en
%F AIHPA_1996__65_3_253_0
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. Annales de l'I.H.P. Physique théorique, Tome 65 (1996) no. 3, pp. 253-271. http://www.numdam.org/item/AIHPA_1996__65_3_253_0/

[1] M. Alvarez, Zum huygensschen Prinzip bei einigen Klassen spinorieller Feldgleichungen in gekrümmten Raum-Zeit-Manifaltigkeiten, Diss. A. Päd. Hochshule Erfurt/Mühlhausen, 1991.

[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] 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 Relativistes 1984, Aussois, France, edited by Laboratoire Gravitation et Cosmologie Relativistes. Institut Henri Poincaré, Lectures Notes in Physics, Vol. 212, Springer Verlag, Berlin, 1984. | MR | Zbl

[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. | MR

[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. | Numdam | MR | Zbl

[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. | Numdam | MR | Zbl

[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. | Numdam | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[11] P. Günther, Einige Sätze über huygenssche Differentialgleichungen, Wiss. Zeitschr. Karl Marx Univ., Math.-natu. Reihe Leipzig, Vol. 14, 1965, pp. 497-507. | MR | Zbl

[12] P. Günther, Ein Beispiel einer nichttrivialen huygesschen Differentialgleichungen mit vier unabhängigen Variablen, Arch. Rational Mech. Anal., Vol. 18, 1965, pp. 103-106. | MR | Zbl

[13] P. Günther and V. Wünsch, Maxwellsche Gleichungen und huygensches Prinzip I, Math. Nachr., Vol. 63, 1974, pp. 97-121. | MR | Zbl

[14] J. Hadamard, Lectures on Cauchy's problem in linear differential equations, Yale University Press, New Haven, 1923. | JFM

[15] H.P. Künzle, Maxwell fields satisfying Huygens' principle, Proc. Cambridge Philos. Soc., Vol. 64, 1968, pp. 779-785.

[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. | MR | Zbl

[17] R.G. Mclenaghan and J. Leroy, Complex recurrent space-times, Proc. Roy. Soc. London, Vol. A327, 1972, pp. 229-249. | MR | Zbl

[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. | EuDML | Numdam | MR | Zbl

[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. | EuDML | Numdam | MR | Zbl

[20] V. Wünsch, Über selbstadjungierte Huygenssche Differentialgleichungen mit vier unabhängigen Variablen, Math. Nachr., Vol. 47, 1970, pp. 131-154. | MR | Zbl

[21] V. Wünsch, Maxwellsche Gleichungen und huygensches Prinzip II, Math. Nachr., Vol. 73, 1974, pp. 19-36. | MR | Zbl

[22] V. Wünsch, Cauchy-Problem und huygenssches Prinzip bei einigen Klassen spinorieller Feldleichungen I, Beitr. zur Analysis, Vol. 12, 1978, pp. 47-76. | MR | Zbl

[23] V. Wünsch, Cauchy-Problem und huygenssches Prinzip bei einigen Klassen spinorieller Feldleichungen II, Beitr. zur Analisys, Vol. 13, 1979, pp. 147-177. | MR | Zbl

[24] V. Wünsch, Huygens' principle on Petrov type-D space-times, Ann. Phys., Vol. 46, 1989, pp. 593-597. | MR | Zbl