Huygens' principle for the non-self-adjoint scalar wave equation on Petrov type III space-times
Annales de l'I.H.P. Physique théorique, Tome 70 (1999) no. 3, pp. 259-276. 
@article{AIHPA_1999__70_3_259_0,
     author = {Anderson, W. G. and McLenaghan, R. G. and Sasse, F. D.},
     title = {Huygens' principle for the non-self-adjoint scalar wave equation on {Petrov} type {III} space-times},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {259--276},
     publisher = {Gauthier-Villars},
     volume = {70},
     number = {3},
     year = {1999},
     mrnumber = {1718182},
     zbl = {0956.83005},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1999__70_3_259_0/}
}
TY  - JOUR
AU  - Anderson, W. G.
AU  - McLenaghan, R. G.
AU  - Sasse, F. D.
TI  - Huygens' principle for the non-self-adjoint scalar wave equation on Petrov type III space-times
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1999
SP  - 259
EP  - 276
VL  - 70
IS  - 3
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1999__70_3_259_0/
LA  - en
ID  - AIHPA_1999__70_3_259_0
ER  - 
%0 Journal Article
%A Anderson, W. G.
%A McLenaghan, R. G.
%A Sasse, F. D.
%T Huygens' principle for the non-self-adjoint scalar wave equation on Petrov type III space-times
%J Annales de l'I.H.P. Physique théorique
%D 1999
%P 259-276
%V 70
%N 3
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1999__70_3_259_0/
%G en
%F AIHPA_1999__70_3_259_0
Anderson, W. G.; McLenaghan, R. G.; Sasse, F. D. Huygens' principle for the non-self-adjoint scalar wave equation on Petrov type III space-times. Annales de l'I.H.P. Physique théorique, Tome 70 (1999) no. 3, pp. 259-276. http://www.numdam.org/item/AIHPA_1999__70_3_259_0/

[1] W. Anderson, Contributions to the study of Huygens' Principle for non-self-adjoint scalar wave equations on curved space-time, M. Math. Thesis, University of Waterloo, 1991.

[2] W.G. Anderson and R.G. Mclenaghan, On the validity of Huygens' principle for second order partial differential equations with four independent variables. II. - A sixth necessary condition, Ann. Inst. Henri Poincaré, Phys. Théor., 60, 1994, pp. 373-432. | Numdam | MR | Zbl

[3] W.G. Anderson, R.G. Mclenaghan and T.F. Walton, An explicit determination of the Non-self-adjoint wave equations that satisfy Huygens' principle on Petrov type III background space-times, Zeitschrift für Analysis und ihre Anwendungen - Journal for Analysis and its Applications, 16, 1996, pp. 37-58. | MR | Zbl

[4] S.R. Czapor and R.G. Mclenaghan, NP: A Maple package for performing calculations in the Newman-Penrose formalism. Gen. Rel. Gravit., 19, 1987, pp. 623-635. | MR | Zbl

[5] S.R. Czapor, Gröbner Basis Methods for Solving Algebraic Equations, Research Report CS-89-51, 1989, Department of Computer Science, University of Waterloo, Ontario, Canada.

[6] S.R. Czapor, R.G. Mclenaghan and J. Carminati, The automatic conversion of spinor equations to dyad form in MAPLE, Gen. Rel. Gravit., 24, 1992, pp. 911-928. | MR | Zbl

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

[8] 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, A20, 1974, pp. 153-188. | Numdam | MR | Zbl

[9] R.G. Mclenaghan, Huygens' principle, Ann. Inst. Henri Poincaré 27, 1982, pp. 211-236. | Numdam | MR | Zbl

[10] R.G. Mclenaghan and T.F. Walton, An explicit determination of the non-self-adjoint wave equations on a curved space-time that satisfies Huygens' principle. Part I: Petrov type N background space-times, Ann. Inst. Henri Poincaré, Phys. Théor., 48, 1988, pp. 267-280. | Numdam | MR | Zbl

[11] 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., 53, 1990, pp. 217-223. | Numdam | MR | Zbl

[12] R.G. Mclenaghan and F.D. Sasse, Nonexistence of Petrov type III space-times on which Weyl's neutrino equation or Maxwell's equations satisfy Huygens' principle, Ann. Inst. Henri Poincaré, Phys. Théor., 65, 1996, pp. 253-271. | Numdam | MR | Zbl

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

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

[15] F.A.E. Pirani, in Lectures on General Relativity, S. Deser and W. Ford, ed., Prentice-Hall, New Jersey, 1964.

[16] F.D. Sasse, Huygens' Principle for Relativistic Wave Equations on Petrov type III Space-Times, Ph.D. Thesis, University of Waterloo, 1997.

[17] T.F. Walton, The validity of Huygens' Principle for the non-self-adjoint scalar wave equations on curved space-time, M. Math. Thesis, University of Waterloo, 1988.

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

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