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

 Access to full text

 Full (PDF)

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

1. 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
2. R. Gerlach, V. Wünsch, Contributions to polynomial conformal tensors
3. 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