prof. Andrzej Trautman

contribution to gravitational waves

  1. (with V. S. Matveev) A criterion for compatibility of conformal and projective structures, Commun. Math. Phys. 329 (2014) 821–825
  2. Editorial note to: J. Ehlers, F. A. E. Pirani and A. Schild, The geometry of free fall and light propagation, General Relativity and Gravitation 44 (2012) 1581–1586
  3. Editorial note to: Władyslaw Ślebodziński, On Hamiltons canonical equations, General Relativity and Gravitation 42 (2010) 2525–2528
  4. Editorial note to: Myron Mathisson, The mechanics of matter particles in general relativity and to: Myron Mathisson, New mechanics of material systems, General Relativity and Gravitation 42 (2010) 985–987
  5. Editorial note to: J. L. Synge, On the deviation of geodesics and null geodesics, particularly in relation to the properties of spaces of constant curvature and indefinite line-element and to: F. A. E. Pirani, Onthe physical significance of the Riemann tensor, General Relativity and Gravitation 41 (2009) 1195–1202
  6. (with T. Sauer) Myron Mathisson: what little we know of his life, Acta Phys. Polon. B Proc. Suppl. 1 (2008) 7–26
  7. Remarks on the history of the notion of Lie differentiation, pages 297–302 in Variations, Geometry and Physics in honour of Demeter Krupkas sixty-fifth birthday, O. Krupkova and D. J. Saunders (Editors), Nova Science Publishers (2008)
  8. Connections and the Dirac operator on spinor bundles, J. Geom. Phys. 58 (2008) 238–252
  9. On eight kinds of spinors, Acta Phys. Polon. B 36 (2005) 121–130
  10. Einstein–Cartan theory, In: Encyclopedia of Mathematical Physics, edited by J.P. Francoise, G. L. Naber and Tsou S. T., Oxford: Elsevier (2006), vol. 2 pages 189–195
  11. Clifford algebras and their representations, In: Encyclopedia of Mathematical Physics, edited by J.-P. Fran ̧coise, G. L. Naber and Tsou S. T., Oxford: Elsevier (2006), vol. 1 pages 518–530
  12. Lectures on general relativity (a “Golden Oldie”), GRG Journal 34 721–762 (2002)
  13. (with M. Bobieński) Pinc and Lipschitz structures on products of manifolds, Ann. Glob. Anal. Geom. 22 291–300 (2002)
  14. Robinson manifolds and the shear-free condition, Int. J. Modern Phys.A 17 (no. 20) 2735-37 (2002)
  15. Spinors in geometry and physics, In: Proc. Intern. Conf. Science and Culture, Losinj 2001, eds. F. Bradamante and G. Furlan, Consorzioper l’Incremento degli Studi e delle Ricerche dei Dipartimenti di Fisica dell’Universita di Trieste
  16. (with P. Nurowski) Robinson manifolds as the Lorentzian analogs of Hermite manifolds, Diff. Geom. Appl. 17 175–195 (2002)
  17. Robinson manifolds and Cauchy–Riemann spaces, Class. Quantum Grav. 19 R1–R10 (2002)
  18. Double covers of pseudo-orthogonal groups, pp. 377–388 in: Clifford Analysis and Its Applications, ed. by F. Brackx et al., Kluwer, Dordrecht, 2001
  19. A conjectured form of the Goldberg–Sachs theorem, Twistor Newsletter 45 50–51 (2000)
  20. (with Th. Friedrich) Spin spaces, Lipschitz groups, and spinor bundles, Ann. Glob. Anal. Geom. 18 221–240 (2000)
  21. Gauge and optical aspects of gravitation, Class. Quantum Grav. 16, A157–A175 (1999)
  22. On complex structures in physics, pp. 487–501 in: ibid
  23. (with P. Nurowski and E. Schucking) Relativistic gravitational fields with close Newtonian analogs, pp. 329–337 in: On Einstein’s Path, A. Harvey (ed), Springer-Verlag, New York, 1999
  24. Reflections and spinors on manifolds, pp. 518–527 in: Proc. of Conference CP453: Particles, Fields, and Gravitation (Łódź, 14–18 May1998), ed. J. Rembieliński, The American Institute of Physics, 1998
  25. Pythagorean spinors and Penrose twistors, pp. 411–419 in: The Geometric Universe: Science, Geometry and the Work of Roger Penrose, ed. by S. A. Huggett, L. J. Mason, K. P. Tod, S. T. Tsou, and N. M. J. Woodhouse, Oxford University Press, Oxford, 1998
  26. (with M. Cahen and S. Gutt) Pin structures and the Dirac operator on real projective spaces and quadrics, pp. 391–399 in: V. Dietrich et al. (eds.), Clifford Algebras and Their Applications in Mathematical Physics (Proceedings of a conference held in 1996 at Aachen) Kluwer, Dordrecht, 1998
  27. Triviality of the Grassmann bundles on hypersurfaces in Rm+1 , Twistor Newsletter 43, 22–23 (1997)
  28. Clifford and the ‘square root’ ideas, Contemporary Mathematics 203, 3–24 (1997)
  29. A metaphysical remark on variational principles, ibid. 27, 839–848 (1995)
  30. The Dirac operator on hypersurfaces, Acta Phys. Polon. B 26, 1283–1310 (1995)
  31. (with M. Cahen and S. Gutt) Pin structures and the modified Dirac operator, J. Geom. Phys. 17, 283–297 (1995)
  32. (with K.Trautman) Generalized pure spinors, J. Geom. Phys. 15, 1–22 (1994)
  33. Geometric aspects of spinors, pp. 333–344 in: R. Delanghe, F. Brackx and H. Serras, eds., Proceedings of the Third International Conference on Clifford Algebras and their Applications in Mathematical Physics held at Deinze, Kluwer, Dordrecht, 1993
  34. (with I. Robinson) The conformal geometry of complex quadrics and the fractional-linear form of Mobius transformations, J. Math. Phys. 34, 5391–5406 (1993)
  35. Spin structures on hypersurfaces and the spectrum of the Dirac operator on spheres, pp. 25–29 in: Spinors, Twistors, Clifford Algebras and Quantum Deformations, Proc. Conf. (Sobótka, 1992) eds Z Oziewicz et al., Kluwer, Dordrecht, 1993
  36. (with M. Cahen and S. Gutt) Spin structures on real projective quadricsJ. Geom. Phys. 10, 127–154 (1993)
  37. Spinors and the Dirac operator on hypersurfaces. I. General theory, J. Math. Phys. 33, 4011–4019 (1992)
  38. (with W. Kopczyński) Simple spinors and real structures, J. Math. Phys. 33, 550–559 (1992)
  39. (with W. Kopczyński) Spacetima and Gravitation, PWN and J. Wiley, Warszawa and Chichester, 1992
  40. L'echiquier spinoriel, Bull. Cl. Sci. Acad. Roy. Belg. 6e ser., 6–9, 187–194 (1990).
  41. (with I. Robinson) Optical geometry, pp. 454–497 in: New Theories in Physics, Proc. of the XI Warsaw Symp. on Elementary Particle Physics, Kazimierz 23-27 May 1988, ed. by Z. Ajduk et al., World Scientic, Singapore, 1989.
  42. (with L. Dąbrowski) Spinor structures on homogeneous Riemannian spaces, pp. 249–257 in: Spinors in Physics and Geometry, Proc. of Conf., Trieste, 11–13 Sept. 1986, ed. by A. I and G. Furlan, World Scientic, Singapore, 1988
  43. (with P. Budinich) Fock space description of simple spinors, J. Math. Phys. 30, 2125–2131 (1988)
  44. (with P. Budinich) The Spinorial Chessboard, Trieste Notes in Physics, Springer, Berlin, 1988
  45. (with P. Budinich) An introduction to the spinorial chessboard, J. Geom. Phys. 4, 361–390 (1987)
  46. (with P. Hogan) On gravitational radiation from bounded sources, pp. 215–242 in: Gravitation and Geometry, A volume in honour of Ivor Robinson, ed. by W. Rindler and A. I, Bibliopolis, Napoli, 1987
  47. (with I. Robinson) Cauchy–Riemann structures in optical geometry, pp. 317–324 in: Proc. of the Fourth Marcel Grossmann Meeting on General Relativity, ed. by R. Ruffini, Elsevier Science Publ., 1986
  48. (with L. Dąbrowski) Spinor structures on spheres and projective spaces, J. Math. Phys. 27, 2022–2028 (1986)
  49. (with P. Budinich) Remarks on pure spinors, Lett. Math. Phys. 11, 315–324 (1986)
  50. Review of the books by T. Frankel, H. Stephani, and R. M. Wald, Bull. (N. S.) Amer. Math. Soc. 14, 152–158 (1986)
  51. (with I. Robinson) A generalization of the Mariot theorem on congruences of null geodesics, Proc. Roy. Soc. London A405, 41–48 (1986)
  52. (with I. Robinson) Integrable optical geometry, Lett. Math. Phys. 10, 179–182 (1985)
  53. Optical structures in relativistic theories, Asterisque, numero hors serie,401–420 (1985)
  54. Deformations of the Hodge map and optical geometry, J. Geom. Phys. 1, 85–95 (1984)
  55. A simple proof of the Robinson theorem, pp. 327–335 in: Proc. Journees Relativistes 1983, Torino 5-8 May 1983, ed. by S. Benenti et al., Pitagora Ed., Bologna, 1985
  56. Differential Geometry for Physicists  (Stony Brook Lectures), Bibliopolis, Napoli, 1984
  57. Einstein and the geometrization of physics, pp. 9–15 in: Aspetti Matematici della Teoria della Relativita, Proc. Atti dei Convegni Lincei No. 57, Accademia Nazionale dei Lincei, Roma, 1983
  58. Un theoreme sur les champs de Yang–Mills isotropes, CR Acad. Sci. Paris 297, 209–212 (1983)
  59. (with J. Lewandowski and J. Tafel) Geometrical aspects of gauge conditions, Lett. Math. Phys. 7, 347–352 (1983)
  60. The Einstein–Cartan theory (summary), pp. 225–227 in: Proc. of the 9th Intern. Conf. on GRG, Jena 1980, ed. by E. Schmutzer, Deutsche Verlag der Wissen., Berlin, 1983
  61. (with I. Robinson) Conformal geometry of flows in n dimensions, J. Math. Phys. 24, 1425–1429 (1983)
  62. (with J. Tafel) Can poles change color?, J. Math. Phys. 24, 1087–1092 (1983)
  63. Yang-Mills theory and gravitation: A comparison, pp. 179–189 in: Geo metric Techniques in Gauge Theories, Proc. Scheveningen 1981, ed. By R. Martini and E. M. de Jager, Lecture Notes in Math. 926, Springer, Berlin, 1982
  64. (with M. E. Mayer) A brief introduction to the geometry of gauge fields, Acta Phys. Austriaca, Suppl. 23, 433–476 (1981)
  65. Geometrical aspects of gauge configurations, Acta Phys. Austriaca, Suppl. 23, 401–432 (1981)
  66. Radiation of energy and change in color of a point source of the Yang–Mills field, Phys. Rev. Lett. 46, 875–877 (1981)
  67. Comments on the paper by Elie Cartan: Sur une generalisation de la notion de courbure de Riemann et les espacesa torsion, pp. 493–496 in: ibid.
  68. Generalities on geometric theories of gravitation, pp. 1–4 in: Cosmology and gravitation: Spin, torsion, rotation, and supergravity, ed. by P. G. Bergmann and V. de Sabbata, Plenum, New York, 1980
  69. On groups of gauge transformations, pp. 114–120 in: Geometrical and Topological Methods in Gauge Theories, Proc. of Conf. Montreal 1979, Lecture Notes in Phys. No. 129, ed. by J. P. Harnad and S. Shnider, Springer, Berlin. 1980
  70. Fibre bundles, gauge fields, and gravitation, pp. 287–308 in: General Relativity and Gravitation, vol. I, ed. by A. Held, Plenum, New York, 1980
  71. A class of null solutions to Yang-Mills equations, J. Phys. A: Math. Gen. 13, L1–L4 (1980)
  72. The geometry of gauge fields, Czech. J. Phys. B29, 107–116 (1979)
  73. On gauge transformations and symmetries, Bull. Acad. Polon. Sci., ser. sci. math., astr. et phys. 27, 7–13 (1979)
  74. Motion and radiation according to the theory of general relativity, pp. 17–31 in: Leopold Infeld, His Life and Scientific Work, ed. by E. Infeld, PWN, Warszawa, 1978
  75. (with J. Nowakowski) Natural connections on Stiefel bundles are sourceless gauge fields, J. Math. Phys. 19, 1100–1103 (1978)
  76. Solutions of the Maxwell and Yang–Mills equations associated with Hopf fibrings, Intern. J. Theor. Phys. 16, 561–565 (1977)
  77. A classification of space-time structures, Rep. Math. Phys. (Torun) 10, 297–310 (1976)
  78. Energy, gravitation and cosmology, pp. 133–141 in: Proc. of the Third General Conference of the European Physical Society, Bucharest 9–12 Sept. 1975, Publ. by EPS, Petit–Lancy; Czech transl. in Cesk. Casopis pro fyziku A26, 464–472 (1976)
  79. Recent advances in the Einstein-Cartan theory, Ann. New York Acad. Sci. 262, 241–245 (1975)
  80. (with W. Adamowicz) The principle of equivalence for spin, Bull. Acad. Polon. Sci., ser. sci. math., astr. et phys. 23, 339–342 (1975)
  81. (with D. Krupka) General invariance of Lagrangian structures, Bull. Acad. Polon. Sci., ser. sci. math., astr. et phys. 22, 207–211 (1974)
  82. The Einstein–Cartan theory of gravitation, pp. 161–170 in: Ondes et Radiations Gravitationnelles, Coll. Intern. du CNRS, Paris 18–22 juin 1973 du CNRS, Paris, 1974
  83. On the structure of the Einstein-Cartan equations, Symp. Math. 12, 139–162 (1973)
  84. Theory of gravitation, pp. 179–198 in: The Physicist’s Conception of Nature, ed. by J. Mehra, D. Reidel Publ. Co., Dordrecht, 1973
  85. Summary of the GR6 Conference, GRG Journal 3, 167–174 (1972)
  86. On the Einstein–Cartan equations, Bull. Acad. Polon. Sci., ser. Sci. math., astr. et phys. 20 Part I: 185–190, Part II: 503–506, Part III: 895–896 (1972), 21 Part IV: 345–346 (1973)
  87. Invariance of Lagrangian systems, pp. 85–99 in: General Relativity, Papers in honour of J. L. Synge, ed. by L. O’Raifeartaigh, Clarendon Press, Oxford, 1972
  88. Riemannian bundles, Bull. Acad. Polon. Sci., ser. sci. math., astr. Et phys. 18, 667–672 (1970)
  89. Fibre bundles associated with space-time, Rep. Math. Phys. (Torun) 1, 29–34 (1970)
  90. Noether equations and conservation laws, Commun Math. Phys. 6, 248–261 (1967)
  91. General theory of relativity (in Russian), Uspekhi Fiz. Nauk 89, 3–33 (1966); English transl.: Sov. Phys. Uspekhi, 319–339, Nov.–Dec. 1966
  92. Comparison of Newtonian and relativistic theories of gravitation, pp. 413–425 in: Perspectives in Geometry and Relativity, Essays in honor of V. Hlavaty, ed. by B. Hoffmann, Indiana Univ. Press, Bloomington, 1966
  93. (with H. Bondi and F. A. E. Pirani) Lectures on General Relativity, Brandeis Summer Institute in Theoretical Physics, 1964 (vol. I), Prentice–Hall, Englewood Cliffs, 1964 
  94. Sur la theorie newtonienne de la gravitation, CR Acad. Sci. Paris 257, 617–620 (1963)
  95. Conservation laws in general relativity, pp. 169–198 in: Gravitation, ed. by L. Witten, J. Wiley, New York, 1962
  96. (with I. Robinson) Exact degenerate solutions of Einstein’s equations, pp. 107–114 in: Proceedings on Theory of Gravitation, Proc. Intern. GRG Conf., Jablonna 25–31 July 1962, ed. by L. Infeld, Gauthier–Villars and PWN, Paris and Warsaw, 1964
  97. On the propagation of information by waves, pp. 459–463 in: Recent Developments in General Relativity, a volume in honour of L. Infeld, Pergamon Press and PWN, London and Warsaw, 1962
  98. Analytic solutions of Lorentz-invariant linear equations, ibid. A270, 326–328 (1962)
  99. (with I. Robinson) Some spherical gravitational waves in general relativity, Proc. Roy. Soc. London A265, 463–473 (1962)
  100. Sur les lois de conservation dans les espaces de Riemann, pp. 113–117 in: Les theories relativistes de la gravitation, Proc. Coll. Intern. du CNRS, Royaumont 21–27 juin 1959, Ed. du CNRS, Paris, 1962.
  101. (with I. Robinson) Spherical gravitational waves, Phys. Rev. Lett. 4, 431–432 (1960)
  102. On gravitational radiation damping, ibid. 6, 627–633 (1958)
  103. Radiation and boundary conditions in the theory of gravitation, ibid. 6, 407–412 (1958)
  104. Boundary conditions at infinity for physical theories, Bull. Acad. Polon. Sci., ser. sci. math., astr. et phys. 6, 403–406 (1958)
  105. Sur la propagation des discontinuites du tenseur de Riemann, CR Acad. Sci. Paris 246, 1500–1502 (1958)
  106. Proof of non-existence of periodic gravitational fields representing radiation, ibid. 5, 1115–1117 (1957)
  107. On the conservation theorems and co-ordinate systems in general relativity, ibid. 5, 721–727 (1957)
  108. Discontinuities of field derivatives and radiation in covariant theories, ibid. 5, 273–277 (1957)
  109. Killing equations and conservation theorems, ibid. 4, 679–682 (1956)
  110. On the conservation theorems and equations of motion in covariant field theories, ibid. 4, 675–678 (1956)
  111. Solution of one-body problem by the Einstein-Infeld approximation method, ibid. 4, 443–446 (1956)
  112. On a generalisation of the Einstein–Infeld approximation method, ibid. 4, 439–442 (1956)
  113. On the proofs of ‘backward’ uniqueness for some non-conservative fields describable by differential equations of the hyperbolic type, Bull. Acad. Polon. Sci. Cl III 3, 307–312 (1955)