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Exact Brans-Dicke-Bianchi solutions

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Solutions of Einstein's Equations: Techniques and Results

Part of the book series: Lecture Notes in Physics ((LNP,volume 205))

Abstract

Using a new method of reduction of the Brans-Dicke field equations we derive various new vacuum solutions as well as some perfect fluid solutions for the class of spatially homogeneous space-times in a unified manner.Exact solutions are given for the isotropic Friedmann-Robertson-Walker models and for the anisotropic Bianchi types I-IX and for the related Kantowski-Sacks model.

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References

  1. Brans, C., and Dicke, R.: 1961, Phys. Rev. 124, 925.

    Google Scholar 

  2. Weinberg, S.: 1972, Gravitation and Cosmology,Wiley and Sons-,N.Y.

    Google Scholar 

  3. Dirac, P. A. M.: 1937, Nature 1 323.

    Google Scholar 

  4. McIntosh, C. B. G.: 1973, Phys. Lett. 43A, 33.

    Google Scholar 

  5. Carmeli, M.,Charach, Ch., and Feinstein, A.: 1983, PhyB. Lett. 96A, 1.

    Google Scholar 

  6. Carmeli, M.,Charach, Ch., and Feinstein, A.: 1983, Ann.Phys.(USA) 150, 392.

    Google Scholar 

  7. Will, C.: 1980, Theory and Experiment in Gravitational Physics, Cambridge Univ.Press,Cambridge.

    Google Scholar 

  8. Smalley, L.L., and Eby, P.B.: 1976, Nuovo Cimento 35B, 54.

    Google Scholar 

  9. Barker, B. M.: 1978, Astrophys. J. 219, 5.

    Google Scholar 

  10. Will, C.: 1974, In: Experimental Gravitation: Proc.of Course 56 of the International School of Physics“Enrico Fermi”, ed.B.Bertotti, Academic Press, New York.

    Google Scholar 

  11. Wesson, P. S.: Gravity, Particles and Astrophysics, D.Reidel Publ. Co.,Dordrecht,Holland.

    Google Scholar 

  12. Singh, T., and Rai, L. N.: 1983, Gen.Rel.Grav. 15, 875.

    Google Scholar 

  13. Van Nieuwenhuizen, P., and Freedman, D. Z.: 1979, Supergravity, North-Holland, Amsterdam.

    Google Scholar 

  14. Hawking, S. W., and Roček, M.: 1981, Superspate and Supergravity, Camgridge Univ.Press,Cambridge.

    Google Scholar 

  15. Ferrara, S., and Taylor, J. G.: 1982, Supergravity '81,Cambridge Univ.Press,Cambridge.

    Google Scholar 

  16. Ferrara, S., Taylor, J. G., and van Nieuwenhuizen, P.: 1983,Supersymmetry and Supergravity '82,World Scientific,Singapore.

    Google Scholar 

  17. Milewski,B.: 1983, Supersymmetry and Supergravity 1983,World Scientific, Singapore.

    Google Scholar 

  18. Scherk, J.: 1979, In: Supergravity,ed.P.van Nieuwenhuizen, and D.Z. Freedman,North-Holland,Amsterdam.

    Google Scholar 

  19. Lorenz-Petzold, D.: 1984,Universität Konstanz,in preparation.

    Google Scholar 

  20. Freund, P. G. O.: 1982, Nuclear Phys. B209, 146.

    Google Scholar 

  21. Kramer, D., Staphani, H., MacCallum, M. A. H., and Herlt, E.: 1980, Exact Solutions of Einstein's Field Equations,VEB,Deutscher Verlag der Wissenschaften,Berlin, D.D.R.

    Google Scholar 

  22. Ryan, M. P. Jr., and Shepley, L. C.: 1975, Homogeneous Relativistic Cosmologies,Princeton Univ.Press, New Jersey.

    Google Scholar 

  23. Zel'dovich, Ya. B., and Novikov, I. D.: 1983,Relativistic Astrophysics, Vol. 2, Chicago Press,Chicago.

    Google Scholar 

  24. Ellis, G. F. R., and MacCallum, M. A. H.: 1969, Commun.Math. Phys. 12, 108.

    Google Scholar 

  25. Lorenz, D.: 1981, Acta Phys. Pol. B12, 939.

    Google Scholar 

  26. Fennely, A. J.: 1978, Rept.No: NASA-TM-78151

    Google Scholar 

  27. Lorenz-Petzold, D.: 1984, Astrophys.Space Sci., to appear.

    Google Scholar 

  28. Lorenz, D.: 1980, Phys. Rev. D22, 1848.

    Google Scholar 

  29. Lorenz, D.: 1980, Phys. Lett. 79AA, 19.

    Google Scholar 

  30. Lorenz, D.: 1980, Phys. Lett. 80A, 235.

    Google Scholar 

  31. Lorenz, D.: 1980, Nuovo Cimento Lett. 29, 238.

    Google Scholar 

  32. Lorenz, D.: 1981, Phys. Lett. 83A, 155.

    Google Scholar 

  33. Lorenz, D.: 1981, Gen. Rel. Grav. 13, 795.

    Google Scholar 

  34. Lorenz, D.: 1982, Acta Phys. Pol. B13, 195.

    Google Scholar 

  35. Lorenz, D.: 1982, Phys. Lett. 87A, 486.

    Google Scholar 

  36. Lorenz, D.: 1982, Phys. Lett. 2A, 118.

    Google Scholar 

  37. Lorenz, D.: 1982, Astrophys. Space Sci. 83, 63.

    Google Scholar 

  38. Lorenz, D.: 1982, Astrophys. Space Sci. 85, 59.

    Google Scholar 

  39. Lorenz, D.: 1982, Astrophys. Space Sci. 85, 63.

    Google Scholar 

  40. Lorenz, D.: 1982, Astrophys. Space Sci. 85, 69.

    Google Scholar 

  41. Lorenz, D.: 1982, Gen. Rel. Grav. 14, 691.

    Google Scholar 

  42. Lorenz, D.: 1982, J. Phys. A: Math. Gen. 15, 2809.

    Google Scholar 

  43. Lorenz, D.: 1982, J. Phys. A: Math. Gen. 15, 2997.

    Google Scholar 

  44. Lorenz, D.: 1983, J. Phys. A: Math. Gen. 16, 575.

    Google Scholar 

  45. Lorenz, D.: 1983, Astrophys. Space Sci. 93, 419.

    Google Scholar 

  46. Lorenz, D.: 1983, Acta Phys. Pol. B14, 479.

    Google Scholar 

  47. Lorenz, D.: 1983, Acta Phys. Pol. B14, 723.

    Google Scholar 

  48. Lorenz, D.: 1983, Acta Phys. Pol. B14

    Google Scholar 

  49. Lorenz, D.: 1983, Acta Phys. Pol. B14

    Google Scholar 

  50. Lorenz, D.: 1983, GR 10, 298, Padua.

    Google Scholar 

  51. Lorenz, D., and Reinhardt, M.: 1980, GR 9, 58, Jena.

    Google Scholar 

  52. Lorenz, D., and Zimmermann, R. E.: 1981,Nuovo Cimento Lett.31, 603.

    Google Scholar 

  53. Lorenz-Petzold, D.: 1983, Astrophys. Space Sci. 96, 54 Lorenz-Petzold, D.: 1983, Astrophys. Space Sci. 96

    Google Scholar 

  54. Lorenz-Petzold, D.: 1983, Astrophys. Space Sci. 96

    Google Scholar 

  55. Lorenz-Petzold, D.: 1983, J. Math. Phys. 24, 2632.

    Google Scholar 

  56. O'Hanlon, J., and Tupper, B. O. J.: 1972, Nuovo Cimento 7B, 305.

    Google Scholar 

  57. Chauvet, P.: 1983, Astrophys. Space Sci. 90, 51.

    Google Scholar 

  58. Cerveró, J. M., and Estevez, P. G.: 1983, Gen. Rel. Grav. 15,351.

    Google Scholar 

  59. Lorenz-Petzold, D.: 1983,Astrophys. Space Sci. 96

    Google Scholar 

  60. Nariai, H.: 1972, Prog. Theor. Phys. 47, 1824.

    Google Scholar 

  61. Nariai, H.: 1972, Prog. Theor. Phys. 48, 703.

    Google Scholar 

  62. Matzner, R. A., Ryan, M. P., and Toton, E. T.: 1973,Nuovo Cimento 14B, 161.

    Google Scholar 

  63. Ruban, V. A., and Finkelstein,A.M.: 1972,Nuovo Cimento.,Lett.5,289.

    Google Scholar 

  64. Belinskii, V. A., and Khalatnikov, I. M.: 1972, Zh. Eksp. Teor. Fiz. 63, 1121 (Sov. Phys.-JETP 36, 591)

    Google Scholar 

  65. Shri Ram: 1983, Astrophys. Space Sci. 94, 307.

    Google Scholar 

  66. Shri Ram: 1983, Gen. Rel. Grav. 15, 635.

    Google Scholar 

  67. Shri Ram, and Singh, D. K.: 1983, Astrophys. Space Sci. 95, 219.

    Google Scholar 

  68. Johri, V. B. and Goswami, G. K.: 1983, Aust. J. Phys. 34, 261.

    Google Scholar 

  69. Dyllong, U.: 1983, Astron. Nachr.(Germany) 304, 163.

    Google Scholar 

  70. Lorenz-Petzold, D.: 1984, Astrophys. Space Sci., to appear.

    Google Scholar 

  71. Lorenz-Petzold, D.: 1984, Gen. Rel. Grav., to appear.

    Google Scholar 

  72. Lorenz-Petzold, D.: 1984, Astrophys. Space Sci., to appear.

    Google Scholar 

  73. Lorenz-Petzold, D.: 1984, Aunt. J. Phys., to appear.

    Google Scholar 

  74. Lorenz-Petzold, D.: 1984, Phys. Rev. D., to appear

    Google Scholar 

  75. Chakravarti, S. P., and De, U. K.: 1983, Atron. Astrophys. 121, 1.

    Google Scholar 

  76. Lorenz-Petzold, D.: 1984, Astron. Astrophys., to appear.

    Google Scholar 

  77. Ruban, V. A., and Finkelstein, A. M.: 1975, Gen. Rel.Grav. 6, 601.

    Google Scholar 

  78. Johri, V. B., and Goswami, G. K.: 1981, Aunt. J. Phys. 34, 261.

    Google Scholar 

  79. Raychaudhuri, A. K.: 1975, Prog. Theor, Phys. 53, 1360.

    Google Scholar 

  80. Raychaudhuri, A. K.: 1979, Theoretical Cosmology,Clarendon Press, Oxford.

    Google Scholar 

  81. Johri, V. B., and Goswami, G. K.: 1980, J. Math. Phys. 21, 2269.

    Google Scholar 

  82. Singh, T., Rai, L. N., and Singh, T.: 1983, Astrophys. Space Sci. 96, 95.

    Google Scholar 

  83. Chakraborty, S. K.: 1983, J. Math. Phys. 24, 1359.

    Google Scholar 

  84. Banerjee, A., and Santos, N. O.: 1982, Nuovo Cimento 67B, 31.

    Google Scholar 

  85. Dicke, R.: 1962, Phys. Rev. 125, 2163.

    Google Scholar 

  86. Lorenz-Petzold, D.: 1984, Prog. Theor. Phys., to appear.

    Google Scholar 

  87. Lorenz-Petzold, D.: 1984, Astrophys. Space Sci., to appear.

    Google Scholar 

  88. Kinnersley, W.: 1975, In:GR 7, ed. by Shaviv, G., and Rosen, J., Wiley and Sons, New York.

    Google Scholar 

  89. Sneddon, G. E., and McIntosh, C. B. G.: 1974, Aust.J.Phys. 27,411.

    Google Scholar 

  90. Tabensky, R., and Taub, A. H.: 1973, Commun.Math. Phys. 29, 61.

    Google Scholar 

  91. Wainwright, J., Ince, W. C. W., and Marshman, B. J.: 1979, Gen. Rel. Grav. 10, 259.

    Google Scholar 

  92. Vajk, J. P.: 1969, J. Math. Phys.10, 1145.

    Google Scholar 

  93. Harrison, E. R.: 1967, Mon. Not. Roy. Astr. Soc. 137, 69.

    Google Scholar 

  94. Maartens, R., and Nel, S. D.: 1978, Commun. Math. Phys. 59, 273.

    Google Scholar 

  95. Ruban, V. A.: 1978,Preprint No. 412, Leningrad Institute of Nuclear Physics, B.P. Konstantinova.

    Google Scholar 

  96. Ruban, V. A.: 1977,Zh.Eksp.Teor.Fiz. 72,1201(Sov.Phys.-JETP45,629).

    Google Scholar 

  97. Ruban, V. A.: 1977, Preprint No. 327, Leningrad Institute of Nucclear Physics, B.P. Konstantinova.

    Google Scholar 

  98. Barrow, J. D.: 1978, Nature 272, 211.

    Google Scholar 

  99. Lorenz-Petzold, D.: 1984, Acta Phys. Pol., to appear.

    Google Scholar 

  100. Anderson, J. L.: 1971, Phys. Rev. D3, 1689

    Google Scholar 

  101. Misner, W., Thorne, K. S., and Wheeler, J. A.: 1973, Graviation, Freeman,San Francisco.

    Google Scholar 

  102. Collins, C. B., and Ellis, G. F. R.: 1979, Phys. Rep. 56, 65.

    Google Scholar 

  103. Dehnen, H., and Obregón, O.: 1971, Astrophys. Space Sci. 14, 454.

    Google Scholar 

  104. Dehnen, H., and Obregón, O.: 1972, Astrophys. Space Sci. 15, 326.

    Google Scholar 

  105. Dehnen, H., and Obregon, O.: 1972, Astrophys. Space Sci. 15, 338.

    Google Scholar 

  106. Lessner, G.: 1974, Astrophys. Space Sci. 30, L5.

    Google Scholar 

  107. Lessner, G.: 1974, Gen. Rel. Grav. 5, 699.

    Google Scholar 

  108. Gurevich, L. E., Finkelstein, A. M., and Ruban, V. A.: 1973, Astrophys. Space Sci. 22, 231.

    Google Scholar 

  109. Lorenz-Petzold, D.: 1984, Ann. Phys.(N.Y.), to appear.

    Google Scholar 

  110. Nariai, H.: 1968, Prog. Theor. Phys. 40, 49.

    Google Scholar 

  111. Nariai, H.: 1969, Prog. Theor, Phys. 42, 544.

    Google Scholar 

  112. Lorenz-Petzold, D.: 1984, Astrophys. Space Sci., to appear.

    Google Scholar 

  113. Ruban, V. A., and Finkelstein, A. M.: 1976, Astrofizika 12, 371.

    Google Scholar 

  114. Tolman, R. C.: 1931, Phys. Rev. 37, 377.

    Google Scholar 

  115. Tolman, R. C.: 1931, Phys. Rev. 38, 1758.

    Google Scholar 

  116. Obregón, O, and Chauvet, P.: 1978, Astrophys. Space Sci. 56, 335.

    Google Scholar 

  117. Lorenz-Petzold, D.: 1984, Astrophys. Space Sci,, to appear.

    Google Scholar 

  118. Jordan, P.: 1952, Zeits. Phys. 132, 655.

    Google Scholar 

  119. Jordan, P.: 1955, Schwerkraft und Weltall, 2.Auflg.,Vieweg & Sohn, Braunschweig

    Google Scholar 

  120. Miyazaki, A.: 1978, Phys. Rev. Lett. 40, 725.

    Google Scholar 

  121. Miyazaki, A.: 1978, Phys. Rev. Lett. 40, 1055.

    Google Scholar 

  122. Miyazaki, A.: 1978, Prog. Theor. Phys. 60, 321.

    Google Scholar 

  123. Miyazaki, A.: 1979, Phys. Rev. D19, 2861.

    Google Scholar 

  124. Miyazaki, A.: 1981, Phys. Rev. D23 3085.

    Google Scholar 

  125. Miyazaki, A.: 1982, Il Nuovo Cimento 68 B, 126.

    Google Scholar 

  126. Dicke, R. H.: 1968, Astrophys. J. 152, 1.

    Google Scholar 

  127. Bishop, N. T.: 1976, Mon.Not. R. Astr. Soc. 176, 241.

    Google Scholar 

  128. Brill, D. R.: 1962, In: Evidence for Gravitational Theories, International School of Physics “Enrico Fermi”,Course XX, ed.by C. Moller, AcademicPress,New York and London.

    Google Scholar 

  129. Morganstern, R. E.: 1971, Phys. Rev, D4, 278.

    Google Scholar 

  130. Morganstern, R. E.: 1971, Phys. Rev. D3, 2946.

    Google Scholar 

  131. Morganstern, R. E.: 1973, Phys. Rev. D7, 1570.

    Google Scholar 

  132. Morganstern, R. E.: 1974, Astrophys. J. 191, 39.

    Google Scholar 

  133. Greenstein, G. S.: 1968, Astrophys.Lett. 1, 139.

    Google Scholar 

  134. Greenstein, G. S.: 1968, Astrophys. Space Sci. 2, 155.

    Google Scholar 

  135. Oechionero, F., and Vagnetti, F.: 1975, Astr.Astrophys. 44, 333.

    Google Scholar 

  136. Kasner, E.: 1921, Am. J. Math. 43, 217.

    Google Scholar 

  137. Taub, A.H.: 1951, Ann. Math. 53, 472.

    Google Scholar 

  138. Collins, C. B.: 1971, Commun. Math. Phys. 23, 137.

    Google Scholar 

  139. Collins, C. B., and Stewart, J. M.: 1971, Mon. Not. R. Astr. Soc. 153, 419.

    Google Scholar 

  140. Kantowski, R.: 1966, PhD thesis University of Texas.

    Google Scholar 

  141. Kantowski, R., and Sachs, R. K.: 1966, J. Math. Phys. 7, 443.

    Google Scholar 

  142. Collins, C. B.: 1977, J. Math. Phys. 18, 2116.

    Google Scholar 

  143. Fangudes, H. V.: 1982, Lett.Math. Phys. 6, 417.

    Google Scholar 

  144. Hangudes, H. V.: 1983, Phys. Rev. Lett. 51, 517.

    Google Scholar 

  145. Eangudes, H. V.: 1983, Astrophys. Lett. 23, 161.

    Google Scholar 

  146. Demaret, J., and Hanquin, J. L.: 1982, Phys. Rev, D26, 3359.

    Google Scholar 

  147. Bray, M.: 1983, C. R. Acad. Sc. Paris, t. 296, II 221.

    Google Scholar 

  148. Bray,M.: 1983, C. R. Acad. Sc. Paris, t. 296, II 317.

    Google Scholar 

  149. Harvey, A., and Tsoubelis, D.: 1977, Phys. Rev. D15, 2734.

    Google Scholar 

  150. Lorenz-Petzold, D.: 1984, Math. Proc. Cambridge Phil. Soc.,to app.

    Google Scholar 

  151. Lorenz-Petzold, D.: 1984, Math. Proc. Cambridge Phil. Soc.,to app.

    Google Scholar 

  152. Joseph, V. A.: 1966, Proc. Cambridge Phil. Soc., 62, 87.

    Google Scholar 

  153. Batakis, N. A., and Tsoubelis, D.: Phys. Lett. 85A, 261.

    Google Scholar 

  154. 154Batakis, N. A., and Tsoubelis, D.: Phys. Rev. D26, 2611.

    Google Scholar 

  155. Roy, S. R., and Singh, J. P.: 1983, Astrophys. Space Sci. 96

    Google Scholar 

  156. Lorenz-Petzold, D.: 1984, Acta Phys. Pol., to appear.

    Google Scholar 

  157. Collinson, C. D., and French, D. C.: 1967, J. Math. Phys. 8, 701.

    Google Scholar 

  158. Siklos, S. T. C.: 1978, Commun. Math. Phys. 58, 255.

    Google Scholar 

  159. Siklos, S. T. C.: 1981, J. Phys. A: Math. Gen. 14, 395.

    Google Scholar 

  160. Lorenz-Petzold, D.: 1984, Classical and Quantum Grav., to appear.

    Google Scholar 

  161. MacCallum, M. A. H.: 1971, Commun. Math. Phys. 20, 57.

    Google Scholar 

  162. Ruban, V. A.: 1978, Preprint No. 411, Leningrad Institute of Nuclear Physics, B.P. Konstantinova.

    Google Scholar 

  163. Ruban, V. A., Ushakov, A. Yu., and Chernin, A. D.: 1981, Zh. Eksp. Teor, Fiz. 80, 816 (Sov. Phys.-JETP 53, 413).

    Google Scholar 

  164. Belinskii, V. A., Khalatnikov, I. M., and Lifshitz, E. M.: 1982, Adv. Phys. 31, 639.

    Google Scholar 

  165. Batakis, N. A.: 1981, Phys. Rev. D23, 1681.

    Google Scholar 

  166. Siklos, S. T. C.: 1980, Phys. Lett. 76A, 19.

    Google Scholar 

  167. Siklos, S. T. C.: 1981, Gen. Rel. Grav. 13, 433.

    Google Scholar 

  168. Evans, A. B.: 1974, Nature, 252, 109.

    Google Scholar 

  169. Evans, A. B.: 1978, Month. Not. R. Ast. Soc. 183, 727.

    Google Scholar 

  170. Spokoiny, B. L.: Phys. Lett. 81A, 493.

    Google Scholar 

  171. Spokoiny, B. L.: Gen. Rel. Grav. 14, 279.

    Google Scholar 

  172. Carmeli, M, and Charach, Ch.: 1980, Phys. Lett. 75A, 333.

    Google Scholar 

  173. Carmeli, M., Charach, Ch., and Malin, S.: Phys. Rep. 76, 79.

    Google Scholar 

  174. Roy, S. R.,and Tiwari, O. P.: 1982, J. Phys. A: Math. Gen. 15, 1747.

    Google Scholar 

  175. Roy, S. R., and Singh, J. P.: 1983, Acta Phys. Aust. 55, 57.

    Google Scholar 

  176. 176Rosquist, K.: 1983, Phys. Lett. 97A, 145.

    Google Scholar 

  177. Rosquist, K.: 1983,Preprint,Univ. Stockholm.

    Google Scholar 

  178. Tsoubelis, D.: 1979, Phys. Rev. D20, 3004.

    Google Scholar 

  179. Tsoubelis, D.: 1981, Phys. Rev. D23, 823.

    Google Scholar 

  180. Ram, S., and Singh, D. K.: 1983, Astrophys. Space Sci. 96

    Google Scholar 

  181. Lorenz-Petzold, D.: 1984, Acta Phys. Aust., to appear.

    Google Scholar 

  182. Dunn, K. A., and Tupper, B. O. J.: 1976, Astrophys. J. 204, 322.

    Google Scholar 

  183. 183Dunn, K. A., and Tupper, B. O. J.: 1978, Astrophys. J. 222, 405.

    Google Scholar 

  184. Tupper, B. O. J.: 1977, Astrophys. J. 216, 192.

    Google Scholar 

  185. MacCallum, M. A. H.: 1977, Astrophys. J. 212, 946.

    Google Scholar 

  186. Lukash, V. N.: 1974, Zh. Eksp. Teor. Fiz. 67, 1594 (Sov. Phys.JETP 40, 792).

    Google Scholar 

  187. 187Lukash, V. N.: 1974, ZhETF Pis. Red. 19, 499.

    Google Scholar 

  188. Lukash, V. N.: 1974, Astron. Zh. 51, 281 (Sov. Astron. 18, 164).

    Google Scholar 

  189. 189Lukash, V. N.: 1976, Il Nuovo Cimento 35B, 268.

    Google Scholar 

  190. Jantzen, R. T.: 1980, Ann. Phys. (N.Y.) 127, 302.

    Google Scholar 

  191. Lorenz-Petzold, D.: 1984, Universität Konstanz.

    Google Scholar 

  192. Doroshkevich, A. G., Lukash, V, N., and Novikov, I. D.: 1973, Zh. Eksper. Teor. Fiz. 64, 1457 (Sov. Phys.-JETP 37, 739).

    Google Scholar 

  193. Jantzen, R. T.: 1979, Commun. Math. Phys. 64, 211.

    Google Scholar 

  194. Jantzen, R. T.: 1980, Il Nuovo Cimento 55B, 161.

    Google Scholar 

  195. Jantzen, R. T.: 1980, Ann. Inst. H. Poincaré,Vol. XXXIII, 121.

    Google Scholar 

  196. Jantzen, R. T.: 1982, J. Math. Phys. 23, 1137.

    Google Scholar 

  197. Jantzen, R. T.: 1982, J. Math. Phys. 23, 1741.

    Google Scholar 

  198. Jantzen, R. T.: 1983, Ann., Phys. (N.Y.) 145, 378.

    Google Scholar 

  199. Jantzen, R. T.: 1983, Preprint. No. 1829, Cambridge,Massachusetts.

    Google Scholar 

  200. Demiafiski, M, and Grishchuk, L. P.: 1972, Commun. Math. Phys. 25, 233.

    Google Scholar 

  201. Borzeskowski, v. H.-H., and Müller, V.: 1978, Ann. Phys. 35, 361.

    Google Scholar 

  202. Paul, H. G.: 1983, Astron. Nachr. 304, 13.

    Google Scholar 

  203. Peresetskii, A. A.: 1976, Uspekhi Mat. Nauk 31, 251.

    Google Scholar 

  204. Peresetskii, A. A.: 1977, Mat. Zam 21, 71 (Russ.Math.Notes 21, 39).

    Google Scholar 

  205. Fennelly, A. J.: 1983, Gen. Rel. Grav. 15, 467.

    Google Scholar 

  206. Melvin, M. A.: 1975, Ann. N.Y. Acad. Sci. 262, 253.

    Google Scholar 

  207. Barnes, A.: 1978, J. Phys. A.: Math. Gen. 11, 1303.

    Google Scholar 

  208. Jantzen, R. T.: 1980, Il Nuovo Cimento 59B, 287.

    Google Scholar 

  209. Collins, C. B:; and Hawking, S. W.: 1973,Mon.Not.R.astr.S.162,307.

    Google Scholar 

  210. Collins, C. B., and Hawking, S. W.: 1973, Astrophys. J. 239, 317.

    Google Scholar 

  211. Doroshkevich, A. G., Lukash, V. N., and Novikov, I. D.: 1974, Astron. Zh. 51, 940 (Sov. Astron. 18, 554).

    Google Scholar 

  212. Caderni, N.,and Fabbri, R.: 1979, Phys. Rev. D20, 1251.

    Google Scholar 

  213. Adams, P. J., Helling, R. W., Zimmerman, R. L., Farhoosh, H., and Zeldich, S.: 1982, Astrophys. J. 253, 1.

    Google Scholar 

  214. Zardecki, A.: 1983, Phys. Rev. D28, 1235.

    Google Scholar 

  215. Barrow, J. D., Juskiewiecz, R., and Sonoda, D. H.: 1983, Nature 305, 397.

    Google Scholar 

  216. Bogoyavlenskii O. I.: 1975, Teor. Math. Fiz. 27, 184 (Theor. Math. Phys. 27, 414).

    Google Scholar 

  217. Bogoyavlenskii, O. I.: 1976, Zh.Eksp. Teor. Fiz. 70, 361 (Sov. Phys.-JETP 43, 187).

    Google Scholar 

  218. Bogoyavlenskii, O. I.: 1976, Trudy Seminara I, G. Petrovskii, Moscow State University 2, 67.

    Google Scholar 

  219. Bogoyavlenskii, O. I.: 1977, Dokl. Akad. Nauk. 232, 189 (Sov. Phys. Dokl. 22, 78).

    Google Scholar 

  220. Bogoyavlenskii, O. I.: 1980, Methods of Qualitative Theory of Dynamical Systems in Astrophysics and Gas Dynamics, Nauka, Moscow

    Google Scholar 

  221. Bogoyavlenskii, O. I., and Novikov, S. P.: 1973, Zh. Eksp. Teor. Fiz. 64, 1475 (sov. Phys.-JETP 37, 747).

    Google Scholar 

  222. Bogoyavlenskii, O. I., and Novikov, S. P.: 1975, Trudy Seminara I. G. Petrovskii, Moscow State University 1, 7.

    Google Scholar 

  223. Bogoyavlenskii, O. I., and Novikov, S. P.: 1976, Usp. Mat. Nauk, 31, 33 (Russian Math. Survey 31, 31).

    Google Scholar 

  224. Novikov, S. P.: 1972, Zh. Eksp. Teor. Fiz. 62, 1977 (Sov. Phys.JETP 35, 1031

    Google Scholar 

  225. Grigoryan, S. D.: 1979, Mat. Zam 26, 235( Math. Notes 26, 610)

    Google Scholar 

  226. Ryan, M. P. Jr., Waller, S. M., and Shepley, L. C.: 1982, Astrophys. J. 254, 425.

    Google Scholar 

  227. Ruban, V. A.: 1982, Astron. Zh. 59, 1044 (Sov. Astron. 26, 632).

    Google Scholar 

  228. Scares, I. D., and Assad, M. J. D.: 1978, Phys. Lett. 66A,359

    Google Scholar 

  229. Assad, M.J. D., and Soares, I. D.: 1983, Phys. Rev. D28, 1858.

    Google Scholar 

  230. Barrow, J. D., and Tipler, F. J.: 1979, Phys. Rep. 56, 371.

    Google Scholar 

  231. Barrow, J. D.: 1982, Phys. Rep. 85, 1.

    Google Scholar 

  232. Barrow, J. D.: 1981, Phys. Rev. Lett. 46, 963.

    Google Scholar 

  233. Barrow, J. D.: 1981, Phys. Rev. Lett. 446, 1436.

    Google Scholar 

  234. Chernoff, D. F., and Barrow, J. D.: 1983, Phys. Rev. Lett. 50, 134.

    Google Scholar 

  235. 235Elskens, Y.: 1983, Phys. Rev. D28, 1033.

    Google Scholar 

  236. Sirousee-Zia, H.: 1982, Gen. Rel. Grav. 14, 751.

    Google Scholar 

  237. Harvey, A.: 1983, Phys. Rev. D28, 2121.

    Google Scholar 

  238. Collins, C. B., Glass, E. N., and Wilkinson, D. A.: 1980, Gen. Rel. Grav. 12, 805.

    Google Scholar 

  239. MacCallum, M. A. H.: 1973, In: Cargese Lectures, Vol. 6, 61, ed. by E. Schatzman, Gordon and Breach, New York.

    Google Scholar 

  240. MacCallum, M. A. H.: 1979, Rend. Sem. Mat.,Torino Vol. 36, 27.

    Google Scholar 

  241. MacCallum, M. A. H.: 1979, In: General Relativity: an Einstein Centenary Survey, ed. by S. W. Hawking, and W. Israel, Cambridge Univ. Press, Cambridge.

    Google Scholar 

  242. MacCallum, M. A. H.: 1979, In: Physics of the Expanding Universe, Lecture Notes in Physics, ed. by M. Demianski, Vol. 109, Springer-Verlag, Berlin.

    Google Scholar 

  243. MacCallum, M. A. H.: 1980, In: Essays in General Relativity,. ed. by F. J. Tipler, Academic Press, New York.

    Google Scholar 

  244. MacCallum, M. A. H.: 1982, In: The Origin and Evolution of the Universe, ed. by V. De Sabbata, World Scientific,Singapore.

    Google Scholar 

  245. MacCallum, M. A. H.: 1983, In: The Origin and Evolution of Galaxies, ed. by B. J. T. Jones, and J. E. Jones, D. Reidel Publ. Co. Dordrecht, Holland

    Google Scholar 

  246. MacCallum, M. A. H.: 1983, In: Unified Field Theoriesof More than 4 Dimensions, ed. by. V. De Sabbata, and E. Schmutzer, World Scientific, Singapore.

    Google Scholar 

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  1. Fakultät für Physik, Universität Konstanz, D-7750, Konstanz, Germany

    Dieter Lorenz-Petzold

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C. Hoenselaers W. Dietz

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Lorenz-Petzold, D. (1984). Exact Brans-Dicke-Bianchi solutions. In: Hoenselaers, C., Dietz, W. (eds) Solutions of Einstein's Equations: Techniques and Results. Lecture Notes in Physics, vol 205. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-13366-6_19

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  • DOI: https://doi.org/10.1007/3-540-13366-6_19

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