Advertisement

Czechoslovak Journal of Physics B

, Volume 19, Issue 4, pp 419–442 | Cite as

Conservation laws in general relativity

  • J. Horský
  • J. Novotný
Review Paper

Abstract

In recent years an increased interest in General Relativity Theory (GRT) has been apparent among theoretical physicists, mathematicians, astronomers and geophysicists. At the same time, the necessity of rinding a final and generally satisfactory solution of a very important problem, namely that of conservation laws, has become topical. Surprising difficulties have been encountered in the attempt to transfer these concepts to General Relativity Theory. In the course of a few years a comprehensive literature has resulted and now the time is ripe for a thorough summary of the results attained so far.

Keywords

General Relativity Theory Theoretical Physicist Satisfactory Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Trautman A., Pirani F. A. E., Bondi H.: Lectures on General Relativity. Brandeis Summer Institute in Theoretical Physics. New Jersey 1964.Google Scholar
  2. [2]
    Trautman A.: Bull. Acad. Polon. Sci. Cl. III (1958), 407.Google Scholar
  3. [3]
    Eisenhart L. P.: Riemannian Geometry. Princeton 1964.Google Scholar
  4. [4]
    Bergmann P. G.: Phys. Rev.75 (1949), 680.Google Scholar
  5. [5]
    Bogoljubov N. N., Širkov D. V.: Introduction to the Quantized Field Theory (in Russian). Moscow 1957.Google Scholar
  6. [6]
    Bergmann P. G., Thomson R.: Phys. Rev. 89 (1955), 400.Google Scholar
  7. [7]
    Trautman A.:in Gravitation. New York 1962.Google Scholar
  8. [8]
    Noether E.: E.: Gött. Nachr. 235, 1918.Google Scholar
  9. [9]
    Hilbert D.: Gött. Nachr. 3, 395, 1915 and Math. Ann. 92, 1, 1924.Google Scholar
  10. [10]
    Schmutzer E.: Zs. Naturf.16a. (1961), 825.Google Scholar
  11. [10a]
    Schröder U. E.: Fortschr. Phys.16 (1968), 357.Google Scholar
  12. [11]
    Bergmann P. G., Schiller R.: Phys. Rev.89 (1953), 4.Google Scholar
  13. [12]
    Landau L. D., Lifšic E. M.: Theory of Field (in Russian). Moscow 1960.Google Scholar
  14. [13]
    Lorentz H. A.: Proc. Acad. Amsterdam20 (1916), 2.Google Scholar
  15. [14]
    Belinfante F. J.: Physica7 (1940), 449.Google Scholar
  16. [15]
    Bičák J.: Czech. J. Phys.B 15 (1965), 81.Google Scholar
  17. [16]
    Suttorp L. G., de Groot S. R.: Phys. Lett. Vol.21, No. 3 (1966), 297.Google Scholar
  18. [17]
    Synge J. L.: Relativity. The General Theory. Amsterdam 1960.Google Scholar
  19. [18]
    Møller C.: Ann. of Phys.4 (1958), 347.Google Scholar
  20. [19]
    Bergmann P. G., Janis A., Newman E., Goldberg I.: Phys. Rev.103 (1956), 807.Google Scholar
  21. [20]
    Bergmann P. G.: Phys. Rev.112 (1958), 287.Google Scholar
  22. [21]
    Komar A.: Phys. Rev.113 (1959), 934.Google Scholar
  23. [22]
    Cattaneo C.: Ann. Inst. H. Poincare, Vol.IV., No. 1 (1966), 1.Google Scholar
  24. [23]
    Fok V. A.: Theory of Space, Time and Gravitation (in Russian). Moscow 1961.Google Scholar
  25. [24]
    Pirani F. A. E.: Phys. Rev.105 (1957), 1089.Google Scholar
  26. [25]
    Fok V. A.: Revs. Mod. Phys.29 (1957), 325.Google Scholar
  27. [26]
    Dirac P. A. M.: Phys. Rev.114 (1959), 924.Google Scholar
  28. [27]
    Arnowit R., Desser S., Misner C. W.: Ann. of Phys.11 (1960), 116.Google Scholar
  29. [28]
    Komar A.: Phys Rev.127 (1962), 1411.Google Scholar
  30. [29]
    Komar A.: Phys Rev.129 (1963), 1873.Google Scholar
  31. [30]
    Petrov A. Z.: Einstein's Spaces (in Russian) Moscow 1961.Google Scholar
  32. [31]
    Pirani F. A. E.: in Colloque international sur les theories relativities de la gravitation. Royamount 1959.Google Scholar
  33. [32]
    Freud P.: Ann. Math.40 (1939), 417.Google Scholar
  34. [33]
    Tolman R. C.: Relativity. Thermodynamics and Cosmology Oxford 1934.Google Scholar
  35. [34]
    Goldberg J. N.: Phys. Rev.111 (1958), 315.Google Scholar
  36. [35]
    Pauli W.: Theory of Relativity. London 1958.Google Scholar
  37. [36]
    Møller C.: The Theory of Relativity. Oxford 1961.Google Scholar
  38. [37]
    Einstein A.: Berl. Ber. 448, 1918.Google Scholar
  39. [38]
    Klein F.: Gött. Nachr. 394, 1918.Google Scholar
  40. [39]
    Trautman A.: Lectures on General Relativity. King's College. London 1958.Google Scholar
  41. [40]
    Einstein A.: Ann. d. Phys.49 (1916), 769.Google Scholar
  42. [41]
    Lichnerowicz A.: CRA246 (1958), 893.Google Scholar
  43. [42]
    Pirani F. A. E.: Phys. Rev.105 (1957), 1089.Google Scholar
  44. [43]
    Brill D.: Ann. of Phys.7 (1959), 466.Google Scholar
  45. [44]
    Peres A.: Phys. Rev.128 (1962), 2471.Google Scholar
  46. [45]
    Weber J., Wheeler J. A.: Rev. Mod. Phys.29 (1957), 3, 509.Google Scholar
  47. [46]
    Marder R.: Proc. Roy. Soc.A244 (1958), 524.Google Scholar
  48. [47]
    Papapetrou A., Schöpf H. G.: CRA251 (1960), 2889.Google Scholar
  49. [48]
    Bondi H., van der Burg M. G. J., Metzner A. V. K.: Proc. Roy. Soc.A269 (1962), 21.Google Scholar
  50. [49]
    Kuchař K., Langer J.: Czech. J. Phys.B 13 (1963), 233.Google Scholar
  51. [50]
    Bonazzola M. S.: CRA259 (1964), 1011.Google Scholar
  52. [51]
    Trautman A.: Usp. Fiz. Nauk89 (1966), 3.Google Scholar
  53. [52]
    Eddington A. S.: Proc. Roy. Soc.A102 (1923), 268.Google Scholar
  54. [53]
    Bonnor W. B.: Phil. Trans. Roy. Soc.AXXX (1954), 994.Google Scholar
  55. [54]
    Burcev P.: Czech. J. Phys.B11 (1961), 385.Google Scholar
  56. [55]
    Weber J.: Phys. Rev.117 (1960), 306.Google Scholar
  57. [56]
    Weber J.: General Relativity and Gravitational Waves. New York 1961.Google Scholar
  58. [57]
    Weber J.: Gravitational Radiation Experiments. Preprint 1. 1963.Google Scholar
  59. [58]
    Bauer H.: Phys. Zs.19 (1918), 163.Google Scholar
  60. [59]
    Møller C.: Max Planck Festschrift. Berlin 1958.Google Scholar
  61. [60]
    Møller C.: Mat. Fyz. Skr. Dan. Vid. Selsk.14 (1951), 31.Google Scholar
  62. [61]
    Møller C.: Ann. of Phys.12 (1961), 118.Google Scholar
  63. [62]
    Novotný J.: Thesis. J. E. Purkyně University Brno 1967.Google Scholar
  64. [63]
    Burcev P., Horský J.: Czech. J. Phys.B 16 (1966), 529.Google Scholar
  65. [64]
    Mickevič N. V.: Ann.Phys.1 (1958), 319.Google Scholar
  66. [65]
    Zelmanov A.: Dokchl. Akad. Nauk107, No. 6 (1956).Google Scholar
  67. [66]
    Novikov I. D.: Věstn. Mosk. Univ. No. 2 (1960).Google Scholar
  68. [67]
    Mickevič N. V.:Lecture at the 1st Russian Conf. on Gravitation. Moscow 1961.Google Scholar
  69. [68]
    Mickevič N. V.: Trudy Univ. Družby Narodov11 (1965), 58.Google Scholar
  70. [69]
    Rosen N.: Phys. Rev.47 (1940), 147.Google Scholar
  71. [70]
    Rayski J.: Acta Phys. Polon.9 (1961), 33.Google Scholar
  72. [71]
    Rayski J.: Acta Phys. Polon.20 (1961), 509.Google Scholar
  73. [72]
    Horský J.: Phys. Lett. Vol.22 No. 3 (1966), 282.Google Scholar
  74. [73]
    Horský J.: Czech. J. Phys.B 16 (1966), 175.Google Scholar
  75. [74]
    Rylov Ju.: Ann. d. Phys.12 (1964), 329.Google Scholar
  76. [75]
    Magnusson M.: Mat. Fyz. Skr. Vid. Dan. Selsk. No. 6 (1960), 32.Google Scholar
  77. [76]
    Møller C.: Mat. Skr. Vid. Dan. Selsk. No 10 (1961).Google Scholar
  78. [77]
    Møller C.: Mat. Fyz. Skr. Vid. Dan. Selsk. No. 3 (1964).Google Scholar
  79. [78]
    See citation [48].Google Scholar
  80. [79]
    Sachs R. K.: Proc. Roy. Soc.A270 (1962), 103.Google Scholar
  81. [80]
    Møller C.:in Atti del convegno sulla Relativita Generale. Firenze 1964.Google Scholar
  82. [81]
    Møller C.: Nordita publications No. 190 (1966).Google Scholar
  83. [82]
    Pellegrini C., Plebanski J.: J. Mat. Fyz. Skr. Vid. Dan. Selsk.2 (1962).Google Scholar
  84. [83]
    Møller C.: Nordita publications No. 136 (1964).Google Scholar
  85. [84]
    See also citation [77].Google Scholar
  86. [85]
    Schwinger J.: Phys. Rev.130 (1963), 1253.Google Scholar
  87. [86]
    Ivaněnko D.:in Elementary Particles and Compensating Fields (in Russian). Moscow 1964.Google Scholar
  88. [87]
    Ivaněnko D.:in Gravitation and Topology (in Russian). Moscow 1966.Google Scholar
  89. [88]
    Rosen N.: Ann. of Phys.22 (1963), 1.Google Scholar
  90. [89]
    Rosen N.: in Atti del convegno sulla Relativita Generale. Firenze 1964.Google Scholar
  91. [90]
    Cornish F. H. J.: Proc. Roy. Soc.282 (1964), 358.Google Scholar
  92. [91]
    Cornish F. H. J.: Proc. Roy. Soc.282 (1965), 270.Google Scholar
  93. [92]
    Papapetrou A.: Proc. Roy. Irish Acad.52A (1948), 11.Google Scholar
  94. [93]
    Rylov Ju.: Věstn. Mosk. Univ. No. 6 (1962), 45.Google Scholar
  95. [94]
    Rylov Ju.: Ann. d. Phys.12 (1964), 329.Google Scholar
  96. [95]
    Rylov Ju.: Izvěstija Vuzov, Matěmatika No. 3 (1962), 131.Google Scholar
  97. [96]
    Rylov Ju.: Věstnik Mosk. Univ. No. 3 (1963), 55.Google Scholar
  98. [97]
    Vu Thant Khiet: Věstn. Mosk. Univ. No. 3 (1966), 17.Google Scholar
  99. [98]
    Arnowitt R., Deser S., Misner C. W.: Phys. Rev.122 (1961), 997.Google Scholar
  100. [99]
    Arnowitt R., Deser S., Misner C. W.:in Gravitation. New York 1962.Google Scholar
  101. [100]
    Anderson L. J.:in Gravitation and Relativity. New York—Amsterdam 1964.Google Scholar
  102. [101]
    Arnowitt R., Deser S., Misner C. W.:in Recent Developments in General Relativity. Warsaw 1962.Google Scholar
  103. [102]
    Dirac P. A. M.: Proc. Roy. Soc.A246 (1958), 333.Google Scholar
  104. [103]
    Pirani F. A. E.: Phys. Rev.105 (1957), 1089.Google Scholar
  105. [104]
    Matte A.: Canad. J. Math. Tom5, (1953), 1.Google Scholar
  106. [105]
    Synge J. L.: Proc. Roy. Irish Acad. Tom 58, 4, 1957. A quite different and interesting attempt is made by J. L. Synge in Nature, Vol. 215, No. 5096, 102, 1067.Google Scholar
  107. [106]
    Bel L.: Cahiers de Phys. Tom16 (1962), 59.Google Scholar
  108. [107]
    Robinson L.: Lecture at King's College. London 1956.Google Scholar
  109. [108]
    Bonazzola S.: Preprint 1965.Google Scholar
  110. [109]
    Fomin P. I.: Ukr. Fyz. Zhurn.9 (1966), 946.Google Scholar
  111. [110]
    M ø1ler C.: in Report of the Conference on Elementary Particles, Kyoto 1965.Google Scholar
  112. [112]
    Mickevič N. V.: Dokhl. Acad. Nauk USSR (1967), 809.Google Scholar
  113. [112]
    Sexl R. U.: Phys. Lett. Vol.20 No. 4 (1966), 376.Google Scholar
  114. [113]
    Frankfurt U. I.: The Special and the General Theories of Relativity (Historical Studies in Russian). Moscow 1968.Google Scholar
  115. [114]
    De Witt.: Phys. Rev. I-160, 1113, II-162, 1195, III-162, 1239, 1967.Google Scholar

Copyright information

© Nakladatelstvi Československé akademie véd 1969

Authors and Affiliations

  • J. Horský
    • 1
  • J. Novotný
    • 1
  1. 1.Faculty of ScienceJ. E. Purkyně UniversityBrnoCzechoslovakia

Personalised recommendations