Optical structures in relativistic theories
Élie Cartan et les mathématiques d'aujourd'hui - Lyon, 25-29 juin 1984, Astérisque no. S131  (1985), p. 401-420
@incollection{AST_1985__S131__401_0,
     author = {Trautman, Andrzej},
     title = {Optical structures in relativistic theories},
     booktitle = {\'Elie Cartan et les math\'ematiques d'aujourd'hui - Lyon, 25-29 juin 1984},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {S131},
     year = {1985},
     pages = {401-420},
     zbl = {0599.53055},
     mrnumber = {837209},
     language = {en},
     url = {http://www.numdam.org/item/AST_1985__S131__401_0}
}
Trautman, Andrzej. Optical structures in relativistic theories, in Élie Cartan et les mathématiques d'aujourd'hui - Lyon, 25-29 juin 1984, Astérisque, no. S131 (1985), pp. 401-420. http://www.numdam.org/item/AST_1985__S131__401_0/

[1]Cartan (É.). - Leçons sur la théorie des spineurs, Actualités Sci. Indust. n°643 and 701, Paris, Hermann, 1938. | JFM 64.1382.04 | Zbl 0022.17101

[2] Cartan (É.). - Sur les espaces conformes généralisés et l'Univers optique, C.R. Acad. Sci. Paris, t. 174, 1922, p. 857-859. | JFM 48.0854.04

[3] Robinson (I.). - Null electromagnetic fields, J. Math. Phys., t. 2, 1959, p. 290-291. | Article | MR 127369

[4] Robinson (I.) and Trautman (A.). - Spherical gravitational waves in general relativity, Proc. Roy. Soc. London Ser. A, t.265, 1962, p. 463-473. | Article | MR 135928 | Zbl 0099.42902

[5.] Kerr (R. P.). - Gravitational field of a spinning mass as an example of algebraically special metrics, Phys. Rev. Lett., t. 11, 1963, p. 237-238. | Article | MR 156674 | Zbl 0112.21904

[6.] Kramer (D.), Stephani (H.), Maccallum (M.) and Herlt (E.). - Exact Solutions of Einstein's Field Equations. - Cambridge and Berlin, Cambridge University Press and Deutscher Verlag der Wissenschaften, 1980. | MR 614593 | Zbl 0449.53018

[7] Trautman (A.). - Un théorème sur les champs de Yang-Mills isotropes, C.R. Acad. Sci. Paris, t. 297, 1983, p. 209-212. | MR 725409 | Zbl 0531.53060

[8] Goldberg (J. N.) and Sachs (R. K.). - A theorem on Petrov types, Acta Phys. Polon., t. 22 Suppl., 1962, p. 13-23. | MR 156679 | Zbl 0113.44807

[9] Robinson (I.) and Schild (A.). - Generalization of a theorem by GOLDBERG and SACHS, J. Math. Phys., t. 4, 1963, p. 484-489. | Article | MR 149937 | Zbl 0114.43903

[10] Köhler (E.) and Walker (M.). - A remark on the generalized Goldberg-Sachs theorem, GRG Journal, t. 5, 1975, p. 507-512. | Article | MR 429017

[11] Sachs (R. K.). - Gravitational waves in general relativity VI, The outgoing radiation condition, Proc. Roy. Soc. London Ser. A, t. 264, 1961, p. 309-338 | Article | MR 156678 | Zbl 0098.19204

Sachs (R. K.). - Distance and the asymptotic behaviour of waves in general relativity in "Recent developments in General Relativity", volume dedicated to Leopold Infeld, New York and Warsaw, Pergamon Press and PWN, 1962. | MR 164707

[12] Newman (E. T.) and Penrose (R.). - An approach to gravitational radiation by a method of spin coefficients, J. Math. Phys., t. 3, 1962, p. 566-578. | Article | MR 141500 | Zbl 0108.40905

[13] Penrose (R.). - Zero rest-mass fields including gravitation : asymptotic behaviour, Proc. Roy. Soc. London Ser. A, t. 284, 1965, p. 159-203. | Article | MR 175590 | Zbl 0129.41202

[14] Frolov (V. P.). - The Newman-Penrose method in the theory of general relativity. Proc. (Trudy) of the P.N. Lebedev Physics Inst. vol. 96 (transl. from Russian), New York and London, Consultants Bureau, 1979.

[15] Esposito (F. P.) and Witten (L.) (Eds.).- Asymptotic structure of space-time. New York and London, Plenum Press, 1977. | Article | MR 465030

[16] Xanthopoulos (B. C.). - Exact vacuum solutions of Einstein's equation from linearized solutions, J. Math. Phys., t. 19, 1978, p. 1607-1609. | Article | MR 524253 | Zbl 0978.83509

[17] Kerr (R. P.) and Schild (A.). - A new class of vacuum solutions of the Einstein field equations, in : "Atti del Convegno sulla Relatività Generale : Problemi dell'energia e onde gravitazionali", pp. 1-12, Firenze, G. Barbèra, Editore, 1965.

[18] Trautman (A.). - Deformations of the Hodge map and optical geometry, J. Geometry and Physics, t. 1, 1984, p. 85-95. | Article | MR 794981 | Zbl 0591.53055

[19] Robinson (I.) and Trautman (A.). - Optical geometry (in preparation). | Zbl 0583.53030

[20] Petrov (A. Z.). - Classification of spaces defining gravitational fields, Scientific Notices Kazan State Univ., t. 114, N°8, 1954, p. 55-69 (Russian). | MR 76401 | Zbl 0972.83007

[21] Pirani (F. A. E.). - Invariant formulation of gravitational radiation theory, Phys. Rev, t. 105, 1957, p. 1089-1099. | Article | MR 96537 | Zbl 0077.41901

[22] Debever (R.). - La super-énergie en relativité générale, Bull. Soc. Math. Belg., t. 10, 1958, p. 112-147. | MR 127939 | Zbl 0091.21204

[23] Lichnerowicz (A.). - Sur les ondes et radiations gravitationnelles, C.R. Acad. Sci. Paris, t. 246, 1958, p. 893-896. | MR 93384 | Zbl 0078.43301

[24] Bel (L.). - Sur la radiation gravitationnelle, C.R. Acad. Sci. Paris, t. 247, 1958, p. 1094-1096. | MR 99871 | Zbl 0082.41204

[25] Penrose (R.). - A spinor approach to general relativity, Ann. Phys. (N.Y.), t. 10, 1960, p. 171-201. | Article | MR 115765 | Zbl 0091.21404

[26] Bateman (H.). - The transformation of coordinates which can be used to transform one physical problem into another, Proc. Lond. Math. Soc., t. 8, 1910, p. 469-488. | Article | JFM 41.0943.01 | MR 1577445

[27] D'Inverno (R. A.) and Stachel (J.). - Conformal two-structure as the gravitational degrees of freedom in general relativity, J. Math. Phys., t. 19, 1978, p. 2447-60. | Article | MR 512965

[28] Jordan (P.), Ehlers (J.) and Sachs (R. K.). - Beiträge zur Theorie der reinen Gravitationsstrahlung, Akad. Wiss. Mainz, Abh. Math.-Naturwiss. Kl., t. 1, 1961, p. 3-62. | MR 156681 | Zbl 0124.22205

[29] Cahen (M.) and Leroy (J.). - Exact solutions of Einstein-Maxwell equations, J. Math. Mech., t. 16, 1966, p. 501-508. | MR 204127 | Zbl 0152.45902

[30] Cahen (M.), Debever (R.) and Defrise (L.). - A complex vectorial formalism in general relativity, J. Math. Mech., t. 16, 1967, p. 761-786. | MR 207370 | Zbl 0149.23401

[31] O'Neill (B.). - Semi-Riemannian geometry with applications to relativity. - New York, Academic Press, 1983. | MR 719023 | Zbl 0531.53051

[32] Robinson (I.), Robinson (J. R.) and Zund (J. D.). - Degenerate gravitational fields with twisting rays, J. Math. Mech., t. 18, 1969, p. 881-892. | MR 238549 | Zbl 0177.28702

[33] Vaidya (P. C.). - A generalized Kerr-Schild solution of Einstein's equations, Proc. Camb. Phil. Soc., t. 75, 1974, p. 383-390. | Article | MR 343853 | Zbl 0278.53043

[34] Hauser (I.). - Type-N gravitational field with twist, Phys. Rev. Lett., t. 33, 1974, p. 1112-3. | Article | MR 384039 | Zbl 0942.83513

[35] Plebanski (J. F.) and Hacyan (S.). - Null geodesic surfaces and the Goldberg-Sachs theorem in complex Riemannian spaces, J. Math. Phys., t. 16, 1975, p. 2403-2407. | Article | MR 389135 | Zbl 0314.53013

[36] Plebanski (J. F.) and Robinson (I.). - Left-degenerate vacuum metrics, Phys. Rev. Lett., t. 37, 1976, p. 493-5. | Article | MR 411476

[37] Fulp (R. O.), Sommers (P.) and Norris (L. K.). - Algebraically special Yang-Mills solutions without sources, J. Math. Phys., t. 22, 1981, p. 2040-54. | Article | MR 631159 | Zbl 0476.53018

[38] Sternberg (S.). - Lectures on differential geometry. - Englewood Cliffs, N.J., Prentice-Hall, 1964. | MR 193578 | Zbl 0129.13102

[39] Kobayashi (S.). - Transformations groups in differential geometry. - Berlin, Springer-Verlag, 1972. | Article | MR 355886 | Zbl 0829.53023

[40] Robinson (I.) and Trautman (A.). - Conformal geometry of flows in n dimensions, J. Math. Phys, t. 24, 1983, p. 1425-29. | Article | MR 708658 | Zbl 0518.58035

[41] Penrose (R.). - Twistor algebra, J. Math. Phys., t. 8, 1967, p. 345-366. | Article | MR 216828 | Zbl 0163.22602

[42] Penrose (R.) - On the origins of twistor theory, article in "Gravitation and Geometry" (W. Rindler and A. Trautman, eds.), a volume dedicated to Ivor Robinson, Napoli, Bibliopolis, 1986. | MR 938546 | Zbl 0656.53005

[43] Bôcher (M.). - The infinite regions of various geometries, Bull. Amer. Math. Soc., t. 20, 1914, p. 185-200. | Article | JFM 45.0780.03 | MR 1559463

[44] Weyl (H.). - Mathematische Analyse des Raumproblems, Anhang 1. - Berlin, Springer-Verlag, 1923. | Article | JFM 49.0494.02 | MR 676653

[45] Coxeter (H. S. M.). - The representation of a conformal space on a quadric, Ann. of Math., t. 37, 1936, p. 416-426. | Article | JFM 62.0730.02 | MR 1503288 | Zbl 0014.22501

[46] Kuiper (N. H.). - On conformal, flat spaces in the large, Ann. of Math., t. 50, 1949, p. 916-924. | Article | MR 31310 | Zbl 0041.09303

[47] Penrose (R.) - The light cone at infinity, in "Proc. on theory of gravitation 1962" (L. Infeld, ed.), Paris and Warsaw, Gauthier-Villars and PWN, 1964.

[48] Uhlmann (A.). - The closure of Minkowski space, Acta. Phys. Polon., t. 24, 1963, p. 295-6. | MR 162596 | Zbl 0115.42303

[49] Trautman (A.). - A simple proof of the Robinson theorem, in : "Journées Relativistes 1983", Proc. of the conference, (S. Benenti et al., eds.), Bologna, Pitagora Editrice, 1985.

[50] Kinnersley (W.) and Walker (M.). - Uniformly accelerating charged mass in general relativity, Phys. Rev. D, t. 2, 1970, p. 1359-70. | Article | MR 317709 | Zbl 1227.83026

[51] Kinnersley (W.). - Recent progress in exact solutions, in : "General Relativity and Gravitation", Proc. of GR7, Tel-Aviv, June 1974 (G. Shaviv and J. Rosen, eds.), New York and Jerusalem, J. Wiley and Israel Univ. Press, 1975. | MR 433363

[52] Newman (E. T.). - Lienard-Wiechert fields and general relativity, J. Math. Phys., t. 15, 1974, p. 44-45. | Article | MR 408687

[53] Tafel (J.) and Trautman (A.). - Can poles change color ?, J. Math. Phys., t. 24, 1983, p. 1087-92. | Article | MR 702083

[54] Penrose (R.) and Rindler (W.). - Spinors and space-time. - Cambridge, Cambridge University Press, Vol. I : 1984. | MR 776784

Penrose (R.) and Rindler (W.). - Spinors and space-time. - Cambridge, Cambridge University Press, Vol. II : 1985.

[55] Penrose (R.) and Maccallum (M. A. H.). - Twistor theory : an approach to the quantisation of fields and space-time, Phys. Reports C, t. 6, 1972, p. 241-316. | Article | MR 475660

[56] Tafel (J.). - On the Robinson theorem and shearfree geodesic null congruences, Lett. Math. Phys., t. 10, 1985, p. 33-39. | Article | MR 796997 | Zbl 0584.53032

[57] Lewy (H.). - An example of a smooth linear partial differential equation without solution, Ann. of Math., t. 66, 1957, p. 155-158. | Article | MR 88629 | Zbl 0078.08104

[58] Robinson (I.) and Trautman (A.). - Integrable optical geometry, Lett. Math. Phys. (in print). | MR 815241 | Zbl 0583.53030

[59] Robinson (I.) and Trautman (A.). - A generalization of Mariot's theorem on congruences of null geodesics, Proc. Roy. Soc. London, (in print). | MR 844746 | Zbl 0588.53018

[60] Robinson (I.) and Trautman (A.). - Cauchy-Riemann structures in optical geometry, in : Proc. of the 4th Marcel Grossmann Meeting on General Relativity, Rome, June 17-21, 1985 (R. Ruffini, ed.), Amsterdam, North-Holland, (in print). | MR 879758