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
Annales de l'I.H.P. Physique théorique, Volume 48 (1988) no. 3, pp. 267-280.
@article{AIHPA_1988__48_3_267_0,
     author = {McLenaghan, R. G. and Walton, T. F.},
     title = {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},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {267--280},
     publisher = {Gauthier-Villars},
     volume = {48},
     number = {3},
     year = {1988},
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     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1988__48_3_267_0/}
}
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McLenaghan, R. G.; Walton, T. F. 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. Annales de l'I.H.P. Physique théorique, Volume 48 (1988) no. 3, pp. 267-280. http://www.numdam.org/item/AIHPA_1988__48_3_267_0/

[1] L. Asgeirsson, Some hints on Huygens' principle and Hadamard's conjecture. Comm. Pure Appl. Math., t. 9, 1956, p. 307-326. | MR | Zbl

[2] 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, Lecture Notes in Physics, t. 212, Springer-Verlag, Berlin, 1984. | MR | Zbl

[3] 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., t. 44, 1986, p. 115-153. | Numdam | MR | Zbl

[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 II: Petrov type D space-times. Ann. Inst. Henri Poincaré, Phys. Théor., t. 47, 1987, p. 337-354. | Numdam | MR | Zbl

[5] J. Carminati and R.G. Mclenaghan, An explicit determination of the spacetimes on which the conformally invariant scalar wave equation satisfies Huygens' principle. Part III: Petrov type III space-times. Ann. Inst. Henri Poincaré, Phys. Théor., in press. | Numdam | Zbl

[6] R. Debever, Le rayonnement gravitationnel : le tenseur de Riemann en relativité générale. Cah. Phys., t. 168-169, 1964, p. 303-349. | MR

[7] P. Günther, Zur Gültigkeit des Huygensschen Princips bei partiellen Differentialgleichungen von normalen hyperbolischen Typus. S.-B. Sachs. Akad. Wiss. Leipzig Math.-Natur.,K., t. 100, 1952, p. 1-43. | MR | Zbl

[8] P. Günther, Ein Beispiel einer nichttrivalen Huygensschen Differentialgleichungen mit vier unabhängigen Variablen. Arch. Rational Mech. Anal., t. 18, 1965, p. 103- 106. | MR | Zbl

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

[10] J. Hadamard, The problem of diffusion of waves. Ann. of Math., t. 43, 1942, p. 510-522. | MR | Zbl

[11] E. Hölder, Poissonsche Wellenformel in nichteuclidischen Räumen. Ber. Verh. Sachs. Akad. Wiss. Leipzig, t. 99, 1938, p. 55-66. | JFM | Zbl

[12] M. Mathisson, Le problème de M. Hadamard relatif à la diffusion des ondes. Acta Math., t. 71, 1939, p. 249-282. | MR | Zbl

[13] R.G. Mclenaghan, An explicit determination of the empty space-times on which the wave equation satisfies Huygens' principle. Proc. Cambridge Philos. Soc., t. 65, 1969, p. 139-155. | MR | Zbl

[14] R. G McLENAGHAN and J. Leroy, Complex recurrent spacetimes. Proc. Roy. Soc. London, t. A327, 1972, p. 229-249. | Zbl

[15] 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, t. A20, 1974, p. 153-188. | Numdam | MR | Zbl

[16] R.G. Mclenaghan, Huygens' principle. Ann. Inst. Henri Poincaré, t. A27, 1982, p. 211-236. | Numdam | MR | Zbl

[17] E.T. Newman and R. Penrose, An approach to gravitational radiation by a method of spin coefficients. J. Math. Phys., t. 3, 1962, p. 566-578. | MR | Zbl

[18] R. Penrose, A spinor approach to general relativity. Ann. Physics, t. 10, 1960, p. 171-201. | MR | Zbl

[19] A.Z. Petrov, Einstein-Raume. Academic Verlag, Berlin, 1964. | MR

[20] F.A.E. Pirani, Introduction to gravitational radiation theory. Article in Lectures on General Relativity, edited by S. Deser and W. Ford, Brandeis Summer Institute in Theoretical Physics, t. 1, 1964, Prentice-Hall, New York.

[21] B. Rinke and V. Wünsch, Zum Huygensschen Prinzip bei der skalaren Wellengleichung. Beitr. zur Analysis, t. 18, 1981, p. 43-75. | MR | Zbl

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

[23] V. Wünsch, Über eine Klasse Konforminvariater Tensoren. Math. Nach., t. 73, 1976, p. 37-58. | MR | Zbl