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

J. Carminati; R. G. McLenaghan

Annales de l'I.H.P. Physique théorique (1987)

  • Volume: 47, Issue: 4, page 337-354
  • ISSN: 0246-0211

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Carminati, J., and McLenaghan, R. G.. "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." Annales de l'I.H.P. Physique théorique 47.4 (1987): 337-354. <http://eudml.org/doc/76382>.

@article{Carminati1987,
author = {Carminati, J., McLenaghan, R. G.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Petrov type D space-times; Huygens' principle},
language = {eng},
number = {4},
pages = {337-354},
publisher = {Gauthier-Villars},
title = {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},
url = {http://eudml.org/doc/76382},
volume = {47},
year = {1987},
}

TY - JOUR
AU - Carminati, J.
AU - McLenaghan, R. G.
TI - 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
JO - Annales de l'I.H.P. Physique théorique
PY - 1987
PB - Gauthier-Villars
VL - 47
IS - 4
SP - 337
EP - 354
LA - eng
KW - Petrov type D space-times; Huygens' principle
UR - http://eudml.org/doc/76382
ER -

References

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  1. [1] B. Buchberger, A Survey on the Method of Gröbner Bases for Solving Problems in Connection with Systems of Multivariate Polynomials. Article in the Second RIKEN International Symposium on Symbolic and Algebraic Computation by Computers, edited by N. Inada and T. Soma. World Scientific Publishing Co., Singapore, 1984, p. 69-83. Zbl0645.68057MR835951
  2. [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 Relativistes1984, Aussois, France, edited by Laboratoire Gravitation et Cosmologie Relativistes. Institut Henri Poincaré. Lecture Notes in Physics, t. 212, Springer-Verlag, Berlin, 1984. Zbl0557.53046MR780225
  3. [3] 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., t. 105 A, 1984, p. 351-354. Zbl0694.35074MR766032
  4. [4] 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. Zbl0595.35067MR839281
  5. [5] J. Carminati and R.G. Mclenaghan, The validity of Huygens' principle for the conformally invariant scalar wave equation, Maxwell's equations and Weyl's neutrino equation on Petrov type D and type III space-times. Phys. Lett., t. 118 A, 1986, p. 322-324. MR867005
  6. [6] B.W. Char, K.O. Geddes, W.M. Gentleman, G.H. Gonnet, The design of MAPLE: a compact, portable, and powerful computer algebra system, Proc. EUROCAL' 83. Lectures Notes in Computer Science, t. 162, 1983, p. 101. 
  7. [7] S.R. Czapor, Private communication. 
  8. [8] R. Debever, Le rayonnement gravitationnel : le tenseur de Riemann en relativité générale. Cah. Phys., t. 168-169, 1964, p. 303-349. MR187877
  9. [9] 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. Zbl0046.32201MR50136
  10. [10] P. Günther, Ein Beispiel einer nichttrivalen Huygensschen Differentialgleichungen mit vier unabhängigen Variablen. Arch. Rational Mech. Anal., t. 18, 1965, p. 103-106. Zbl0125.05404MR174865
  11. [11] P. Günther, Eigine Sätze über Huygenssche Differentialgleichungen. Wiss. Zeitschr. Karl Marx Univ. Math.-Natu. Reihe Leipzig, t. 14, 1965, p. 498-507. Zbl0173.12203MR198012
  12. [12] P. Günther and V. Wünsch, Maxwellsche Gleichungen und Huygenssches PrinzipI. Math. Nach., t. 63, 1974, p. 97-121. Zbl0288.35042MR363377
  13. [13] J. Hadamard, Lectures on Cauchy's problem in linear partial differential equations. Yale University Press, New Haven, 1923. Zbl49.0725.04JFM49.0725.04
  14. [14] H.P. Künzle, Maxwell fields satisfying Huygens' principle. Proc. Cambridge Philos. Soc., t. 64, 1968, p. 770-785. 
  15. [15] 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. Zbl0182.13403MR234700
  16. [16] R.G. Mclenaghan and J. Leroy, Complex recurrent space-times. Proc. Roy. Soc. London, t. A 327, 1972, p. 229-249. Zbl0243.53030MR309517
  17. [17] 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. A 20, 1974, p. 153-188. Zbl0287.35058MR361452
  18. [18] R.G. Mclenaghan, Huygens' principle. Ann. Inst. Henri Poincaré, t. A 27, 1982, p. 211-236. Zbl0528.35057MR694586
  19. [19] 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. Zbl0108.40905MR141500
  20. [20] R. Penrose, A spinor approach to general relativity. Ann. Physics, t. 10, 1960, p. 171- 201. Zbl0091.21404MR115765
  21. [21] A.Z. Petrov, Einstein-Raume. Academic Verlag, Berlin, 1964. MR162594
  22. [22] 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. 
  23. [23] B. Rinke and V. Wünsch, Zum Huygensschen Prinzip bei der skalaren Wellengleichung. Beitr. zur Analysis, t. 18, 1981, p. 43-75. Zbl0501.53010MR650138
  24. [24] V. Wünsch, Über selbstadjungierte Huygenssche Differentialgleichungen mit vier unabhängigen Variablen. Math. Nachr., t. 47, 1970, p. 131-154. Zbl0211.40803MR298221
  25. [25] V. Wünsch, Maxwellsche Gleichungen und Huygenssches Prinzip II. Math. Nach., t. 73, 1976, p. 19-36. Zbl0288.35043MR426807
  26. [26] V. Wünsch, Über eine Klasse Konforminvarianter Tensoren. Math. Nach., t. 73, 1976, p. 37-58. Zbl0287.53014MR433342
  27. [27] V. Wünsch, Cauchy-problem und Huygenssches Prinzip bei einigen Klassen spinorieller Feldgleichungen I. Beitr. zur Analysis, t. 12, 1978, p. 47-76. Zbl0448.58022MR507097
  28. [28] V. Wünsch, Cauchy-Problem und Huygenssches Prinzip bei einigen Klassen spinorieller Feldgleichungen II. Beitr. zur Analysis, t. 13, 1979, p. 147-177. Zbl0467.35067MR536225

Citations in EuDML Documents

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  1. J. Carminati, R. G. McLenaghan, An explicit determination of the space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. Part III : Petrov type III space-times
  2. R. G. McLenaghan, G. C. Williams, An explicit determination of the Petrov type D spacetimes on which Weyl's neutrino equation and Maxwell's equations satisfy Huygens' principle
  3. R. G. McLenaghan, F. D. Sasse, Nonexistence of Petrov type III space-times on which Weyl's neutrino equation or Maxwell's equations satisfy Huygens' principle
  4. J. Carminati, S. R. Czapor, R. G. McLenaghan, G. C. Williams, Consequences of the validity of Huygens' principle for the conformally invariant scalar wave equation, Weyl's neutrino equation and Maxwell's equations on Petrov type II space-times
  5. R. G. McLenaghan, T. F. Walton, 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
  6. 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
  7. W. G. Anderson, R. G. McLenaghan, On the validity of Huygens' principle for second order partial differential equations with four independent variables. II. A sixth necessary condition

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