Advertisement

Black Holes and the Unification of Asymmetries

  • Benjamin Gal-Or
Chapter

Abstract

Of all the conceptions of cosmology and astrophysics, perhaps the most intriguing is the black hole (or “frozen star,” as it is sometimes called): a hole in space with a definite edge, over which anything can fall in — but nothing can escape, because of a gravitational field so strong that even radiation is irreversibly trapped and held by it; a thermodynamic sink which drastically curves space and twists time.

Keywords

Black Hole Neutron Star Gravitational Field Event Horizon Gravitational Collapse 
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 (To Part III)

  1. 1.
    Gal-Or, B., Found. Phys., 6, 407 (1976); 6, 623 (1976).CrossRefGoogle Scholar
  2. 2.
    Gal-Or, B., ed., Modern Developments in Thermodynamics, Wiley, N.Y. (1974). Stuart, E. B., Gal-Or, B., and Brainard, A. J., eds., A Critical Review of Thermodynamics, Mono Book, Baltimore (1970) (Proceedings of International Symposium, sponsored by NSF, “A Critical Review of the Foundations of Relativistic and Classical Thermodynamics,” at Pittsburgh, Pa., April 7–9 (1969).Google Scholar
  3. 3.
    Gold, T., in Recent Developments in General Relativity, Pergamon Press, N.Y. (1962), p. 225; in The Nature of Time (Gold, T., ed.), Cornell University Press, N.Y. (1967), pp. 1, 128, 229; in Ref. 1, pp. 63.Google Scholar
  4. 4.
    Narlikar, J. V., in The Nature of Time (Gold, T., ed.), Cornell University Press, N.Y. (1967), pp. 25, 28, 62; Pure and Appl. Chem. 22, 449, 543 (1970); with Hoyle, F., Nature 222, 1040 (1969); Proc. Roy. Soc. A 277, 1 (1963); Ann. Phys. 54, 207 (1969), 62, 44 (1971).Google Scholar
  5. 5.
    Gal-Or, B., Science 176, 11–17 (1972); Nature 230, (1971); 234, 217 (1971).Google Scholar
  6. 6.
    Gal-Or, B., “Entropy, Fallacy, and the Origin of Irreversibility,” Annals, N.Y. Acad. Sci. 196 (A6), pp. 305–325, October 4 (1972) [N.Y. A.S. Award Paper (1971)].Google Scholar
  7. 7.
    Gal-Or, B., “The New Philosophy of Thermodynamics,” in Entropy and Information in Science and Philosophy (Zeman, J., ed.), Czechoslovak Academy of Sciences, Elsevier (1974). Space Sci. Review; In press.Google Scholar
  8. 8.
    Ellis, H. G., Found. Phys., 4, 311 (1974).CrossRefGoogle Scholar
  9. 9.
    Rosenfeld, L., in The Nature of Time (Gold, T., ed.), Cornell University Press, N.Y. (1967), pp. 135, 187, 191, 194, 227, 230, 242.Google Scholar
  10. 10.
    Bergmann, P. G., in The Nature of Time (Gold, T., ed.), Cornell University Press, N.Y. (1967), pp. 40, 185, 189, 233, 241.Google Scholar
  11. 11.
    Beauregard, O. Costa de, in Ref. 2, pp. 75.Google Scholar
  12. 12.
    Aharony, A. (with Ne’eman, Y.), Int. Jour. Theoret. Phys. 3, 437 (1970); Lettere al Nuovo Cimento, Serie I, 4, 862 (1970) in Ref. 1, pp. 95.Google Scholar
  13. 13.
    Landau, L. D. and Lifshitz, E. M., Statistical Physics, Addison-Wesley, Reading, Pa. pp. 13, 29 (1969).Google Scholar
  14. 14.
    Prigogine, I., in A Critical Review of Thermodynamics (Stuart, Gal-Or and Brainard, eds.), Mono Book, Baltimore, p. 461 (1967).Google Scholar
  15. 15.
    Tolman, R. C., Relativity Thermodynamics and Cosmology, Oxford Press (1933), pp. 221, 301, 323, 328, 395, 421, 440.Google Scholar
  16. 16.
    Narlikar, J. V., in Ref. 1, pp. 53.Google Scholar
  17. 17.
    There are authors who, unaware of the fundamental problem, hopelessly seek (cf. also [391) the origin of irreversibility in the Hamiltonian and the interaction terms in it [cf., e.g., Hove, L. van, Physica 21,517 (1955); 25,269 (1969)]; or in the coarse graining of phase space, which is required to take account of the fact that all measurements are macroscopic [cf., e.g., Landsberg, P. T., Thermodynamics with Quantum Statistical Illustrations,Interscience (1961); Proc. Roy. Soc. A262,100 (1961); or in passage to the limit of an infinite number of degrees of freedom [cf., e.g., Balescu, R. in [2] p. 473; Physica 36,433 (1967); Phys. Lett. 27A,249 (1967)]; or in interpretations of the Liouville equation [cf., e.g., Prigogine, I., in [2], p. 1; or in the impossibility of completely isolating a system from the rest of the universe [cf., e.g., Blatt, J. M., Prog. Theoret. Phys. 22,745 (1959)].Google Scholar
  18. 18.
    Misner, C. W., Phys. Rev. 186, 1328 (1969).MATHCrossRefGoogle Scholar
  19. 19.
    Beauregard, O. Costa de, Le Second Principe de la Science du Temps, Editions du Seuil, Paris (1963); Pure and Appl. Chem. 22, 540 (1970).Google Scholar
  20. 20.
    Adams, E. N., Phys. Rev. 120, 675 (1960).MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Beauregard, O. Costa de, in Proceedings of the International Congress for Logic, Methodology and the Philosophy of Science (Bar-Hillel, Y., ed.), North Holland, 313 (1964).Google Scholar
  22. 22.
    Gal-Or, B., Science 178, 1119 (1972).CrossRefGoogle Scholar
  23. 23.
    Feigl, H. and Maxwell, G., eds., Current Issues in the Philosophy of Science, Holt, Rinehart and Minneapolis (1962).Google Scholar
  24. 24.
    Grunbaum, A., Philosophical Problems of Space and Time, Knopf, N.Y. (1963); (Gold, T., ed.), Cornell University Press, N.Y., p. 149 (1967).Google Scholar
  25. 25.
    Hogarth, J. E. in The Nature of Time (Gold, T., ed.), Cornell University Press, N.Y., p. 7 (1967).Google Scholar
  26. 26.
    Layzer, D., in The Nature of Time ( Gold, T., ed.), Cornell University Press, N.Y. (1967).Google Scholar
  27. 27.
    Mehlberg, H., in Current Issues in the Philosophy of Science (Feigl and Maxwell, eds.), Holt, Rinehart and Winston, N.Y., p. 105 (1961).Google Scholar
  28. 28.
    Ne’eman, Y. in Ref. 1, pp. 91.Google Scholar
  29. 29.
    Penrose, O. and Percival, I. C., Proc. Phys. Soc. 79, Part 3, No. 509, p. 605 (1962).MathSciNetGoogle Scholar
  30. 30.
    Prigogine, I., in [2], pp. 3, 203, 461, 505.Google Scholar
  31. 31.
    Reichenbach, H., The Direction of Time, University of California Press, Berkeley (1956); The Philosophy of Space and Time, Dover, N.Y. (1958).Google Scholar
  32. 32.
    Tisza, L., in [2], pp. 107, 206, 510.Google Scholar
  33. 33.
    Watanabe, S., in The Voices of Time (Fraser, J. T., ed.), George Braziller, N.Y. 1966, p. 543; Progr. Theoret. Phys. (Kyoto) Suppl., Extra No., p. 135 (1965).Google Scholar
  34. 34.
    Wheeler, J. A., in The Nature of Time (Gold, T., ed.), Cornell University Press, N.Y. 1967, pp. 90, 233, 235.Google Scholar
  35. 35.
    Whitrow, G. J., The Natural Philosophy of Time, Nelson, London, 1961.MATHGoogle Scholar
  36. 36.
    Loschmidt, J., Wiener Ber. 73, 139 (1876); 75, 67 (1877).Google Scholar
  37. 37.
    Zermelo, E., Ann. Phys. 57, (1896); 59; 793 (1896).MATHCrossRefGoogle Scholar
  38. 38.
    Zel’dovich, Y. B., JETP Lett. 12, 307 (1970).Google Scholar
  39. 39.
    Penrose, O., Foundations of Statistical Mechanics, Pergamon, Oxford 1970.MATHGoogle Scholar
  40. 40.
    Phipps, T. E., Jr., Found. Phys. 3, 435 (1973).CrossRefGoogle Scholar
  41. 41.
    Kovetz, A. and Shaviv, G., Astrophysics and Space Science 6, 396 (1970); 7, 416 (1970).Google Scholar
  42. 42.
    Dicke, R. H., Phys. Today 20, 55 (1967).CrossRefGoogle Scholar
  43. 43.
    Cox, A. N., “Stellar Absorption Coefficients and Opacities, in Stars and Stellar Systems ( Kuiper, G. P., ed.), Vol. VIII, University of Chicago Press, 1965, pp. 195–263.Google Scholar
  44. 44.
    Reeves, H., “Stellar Energy Sources,” Ibid. pp. 113–193.Google Scholar
  45. 45.
    Sciama, D. W., “The Recent Renaissance of Observational Cosmology,” in Relativity and Gravitation ( Kuper, C. G. and Peres, A., eds.), Gordon and Breach, N.Y. 1971, p. 283.Google Scholar
  46. 46.
    Einstein, A., in Albert Einstein, Philosopher-Scientist ( Paul Arthur Shilpp, ed.), Harper Torchbooks, N.Y. 1959, Vol. II, p. 687.Google Scholar
  47. 47.
    Sandage, A., Quart. J. Radio-A.str. Soc. 13, 282 (1972).Google Scholar
  48. 48.
    Weinberg, S., Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley, N.Y. 1972, pp. 597.Google Scholar
  49. 49.
    Ledoux, P., “Stellar Stability,” in Stars and Stellar Systems ( Kuiper, G. P. ed.), Vol. VIII, University of Chicago Press, 1965, pp. 499–574.Google Scholar
  50. 50.
    Truesdell, C., Rational Thermodynamics, McGraw-Hill, N.Y. 1969, pp. 30, 57, 106, 193.Google Scholar
  51. 51.
    Gringorten, I. I. and Kantor, A. J., in Handbook of Geophysics and Space Environments ( Valley, S. L. ed.), McGraw-Hill, N.Y. 1965.Google Scholar
  52. 52.
    Huang, S. S. and Struve, O., “Stellar Rotation and Atmospheric Turbulence,” in Stars and Stellar Systems ( Kuiper, G. P. ed.), Vol. VI, University of Chicago Press, 1960, pp. 321–369.Google Scholar
  53. 53.
    Bondi, H., in The Nature of Time (Gold, T., ed.), Cornell University Press, N.Y. 1967; Cosmology, Cambridge University Press, 1961.Google Scholar
  54. 54.
    Heelan, P., Quantum Mechanics and Objectivity, Nijhoff, The Hague 1965, 1, 95 (1970).Google Scholar
  55. 55.
    Popper, K., in Quantum Theory and Reality ( Bunge, M., ed.), Springer, N.Y. 1967, p. 7.Google Scholar
  56. 56.
    Bunge, M., Ibid, p. 107.Google Scholar
  57. 57.
    Motz, L., Ap. J. 112, 362 (1952); Astrophysics and Stellar Structure, Waltham, Mass. 1970.Google Scholar
  58. 58.
    Katz, A., Principles of Statistical Mechanics, Freeman, San Francisco 1967.Google Scholar
  59. 59.
    Cocke, W. J., Phys. Rev. 160 (5), 1165 (1967).Google Scholar
  60. 60.
    Conant, D. R., in A Critical Review of Thermodynamics ( Stuart, E. B., Gal-Or, B. eds.), Mono Book, Baltimore (1970), p. 507.Google Scholar
  61. 61.
    De Groot, S. R. and Mazur, P., Non-Equilibrium Thermodynamics, North Holland 1962.Google Scholar
  62. 62.
    Sciama, D. W., Modern Cosmology, Cambridge University Press, N.Y. 1971.Google Scholar
  63. 63.
    Peebles, P. J. E., Physical Cosmology, Princeton University Press, Princeton 1971.Google Scholar
  64. 64.
    Sachs, R. G., Science 176, 587 (1972).CrossRefGoogle Scholar
  65. 65.
    Christenson, J. H., Cronin, J. W., Fitch, V. L., and Turlay, R., Phys. Rev. Lett. 13, 138 (1964); Phys. Rev. B. 140, 74 (1965).CrossRefGoogle Scholar
  66. 66.
    Lee, T. D. and Yang, C. N., Phys. Rev. 104, 254 (1956); Wu, C. S., Amber, E., Hayward, R. W., Hoppes, D. D., and Hudson, R. P., Phys. Rev. 105, 1413 (1957).MathSciNetCrossRefGoogle Scholar
  67. Dass, G. V., Prepring TH. 1373-CERN (1971).Google Scholar
  68. 68.
    Olbers, H. W. M., Bodes Jahrbuch, 110 (1826).Google Scholar
  69. 69.
    Halley, Edmund, Phil. Trans. Roy. Soc. (London) 31 (1720).Google Scholar
  70. 70.
    Fowler, W. A. and Hoyle, F. Ap. J. Suppl. 9, 201 (1964).CrossRefGoogle Scholar
  71. 71.
    Colgate, S. A. and White, R. H., Ap. J. 143, 626 (1966).CrossRefGoogle Scholar
  72. 72.
    Arnett, W. D., Canad. J. Phys. 44, 2553 (1966).CrossRefGoogle Scholar
  73. 73.
    Schwartz, R. A., Ann. Phys. 43, 42 (1967).CrossRefGoogle Scholar
  74. 74.
    Rakavy, G., Shaviv, G. and Zinamon, Z., Ap. J. 150, 131 (1967).CrossRefGoogle Scholar
  75. 75.
    Clayton, D. D., Principles of Stellar Evolution and Nucleosynthesis, McGraw-Hill, N.Y. 1968.Google Scholar
  76. 76.
    Gal-Or, B. et al., Intern. J. Heat and Mass Transfer 14, 727 (1971).CrossRefGoogle Scholar
  77. 77.
    Wheeler, J. A. and Feynman, R. P., Rev. Mod. Phys. 17, 157 (1945).CrossRefGoogle Scholar
  78. 78.
    Feynman, R. P., Rev. Mod. Phys. 20, 367 (1948).MathSciNetCrossRefGoogle Scholar
  79. 79.
    Feynman, R. P. and Hibbs, A. R., Quantum Mechanics and Path Integrals, McGraw-Hill, N.Y. 1965.Google Scholar
  80. 80.
    Lemaitre, G., Ann. Soc. Sci. (Bruxelles) 47A, 49 (1927).Google Scholar
  81. 81.
    Friedmann, A., Zeits f: Physik 10, 377 (1922).CrossRefGoogle Scholar
  82. 82.
    Dudley, H. C., Lettere al Nuovo Cimento 5(3), 231 (1972); Phys. Lett., in press (1972); Nuovo Cimento 4B,68 (1971).Google Scholar
  83. 83.
    Arnold, V. I. and Avez, A., Problemes Ergodiques de la Mechanics, Benjamin, N.Y. 1968.Google Scholar
  84. 84.
    Farquhar, I., Ergodic Theory in Statistical Mechanics, Wiley, N.Y. 1964.Google Scholar
  85. 85.
    Sinai, Y. G., “On the Foundations of the Ergodic Hypothesis for a Dynamical System in Statistical Gechanics,” Soviet Mathematics 4, 1818 (1963).MathSciNetGoogle Scholar
  86. 86.
    Ungarish, M., Internal Report, Technion-Israel Inst. of Tech., Aug. 1972.Google Scholar
  87. 87.
    Eringen, A. C., in A Critical Review of Thermodynamics, Mono Book (Stuart, E. B., Gal-Or, B., eds. ), Baltimore (1970) p. 483.Google Scholar
  88. 88.
    Kestin, J. and Rice, J. R., ibid. p. 282.Google Scholar
  89. 89.
    Bohm, D., Phys. Rev. 85, 166, 180 (1952).MathSciNetCrossRefGoogle Scholar
  90. 90.
    de Broglie, L., Founvations of Physics, Vol. 1, p. 1, 1970.Google Scholar
  91. 91.
    Finzi, A., “Is Dissipation of the Energy of Orbital Motion the Source of the Radiant Energy of Novae?.” Technion Prepring Series No. MT-89, Sept. 1971.Google Scholar
  92. 92.
    Cohen, J. M. and Cameron, A. G. W., Nature 224, 566 (1969).CrossRefGoogle Scholar
  93. 93.
    Ostriker, J. P. and Gunn, J. E., Ap. J. 157, 1395 (1969); 160, 979 (1970).Google Scholar
  94. 94.
    Finzi, A. and Wolf, R. A., Ap. J. (Letters) 155, 107 (1969); 150, 115 (1967).Google Scholar
  95. 95.
    Kulsrud, R. M., Ap. J. 163, 567 (1971).CrossRefGoogle Scholar
  96. 96.
    Pacini, F., Nature 219, 145 (1968).CrossRefGoogle Scholar
  97. 97.
    Goldreich, P. and Julian, W. H., Ap. J. 157, 869 (1969).CrossRefGoogle Scholar
  98. 98.
    Zel’dovich, Y. B., in Advances in Astronomy and Astrophysics, Vol. 3, Academic Press, N.Y. 1965, pp. 241–375.Google Scholar
  99. 99.
    Janossy, L., Theory of Relativity Based on Physical Reality, Akademiai Kiado, Budapest, 1971, pp. 17, 49.Google Scholar
  100. 100.
    Einstein, A., Verh. d. Schweizer, Nat. Ges. 105, Teil II, pp. 85–93.Google Scholar
  101. Margenau, H., Philosophy of Science 30,1 (1963); 30,138 (1963); Phys. Today 7, 6 (1954).Google Scholar
  102. 102.
    Heisenberg, W., Physical Principles of Quantum Theory, University of Chicago Press, 1931.Google Scholar
  103. 103.
    Schulman, L., Phys. Rev.,in press; in Modern Developments in Thermodynamics,Wiley, N.Y., p. 81 (1974).Google Scholar
  104. 104.
    Witten, L., ed., Gravitation, Wiley, N.Y. 1962.MATHGoogle Scholar
  105. 105.
    Sperber, G., Found. Phys. 4, p. 163 (1974).CrossRefGoogle Scholar
  106. 106.
    Kyrala, A., Ibid, p. 31.Google Scholar
  107. 107.
    Rothstein, J., Ibid, p. 83.Google Scholar
  108. 108.
    Nordtvedt, K. L., Science 178, 1157 (1972).CrossRefGoogle Scholar
  109. 109.
    Oboukhov, A. M. and Golitsyn, G. S., Space Research XI, Akademie-Verlag, Berlin 1971, p. 121.Google Scholar
  110. 110.
    Zel’dovich, Y. B. and Novikov, I. D., Relativistic Astrophysics-I,University of Chicago Press, 1971. 1 l I.Google Scholar
  111. 111.
    Kantor, W., Found. Phys. 4,105 (1974).Google Scholar
  112. 112.
    Novotny, E., Introduction to Stellar Atmospheres and Interiors, Oxford University Press 1973.Google Scholar
  113. 113.
    Paczynsky, B. E., Acta Astron. 20, 47 (1970); Astrophys. Lett. 11, 53 (1972).Google Scholar
  114. 114.
    Barkat, Z., Ap. J. 163, 433 (1971).CrossRefGoogle Scholar
  115. 115.
    Barkat, Z., Wheeler, J. C., and Buehler, J. R., Ap. J. 171, 651 (1972); Astrophys. Lett. 8, 21 (1971).Google Scholar
  116. 116.
    Arnett, W. D., Ap. and Space Sci. 5, 180 (1969); Ap. J. 53, 341 (1968).CrossRefGoogle Scholar
  117. 117.
    Wilson, J. R., Ap. J. 163, 209 (1971).CrossRefGoogle Scholar
  118. 118.
    Tsuruta, S. and Cameron, A. G. W., Ap. and Space Sci. 7, 374 (1970); 14, . 79 (1971).Google Scholar
  119. 119.
    Arnett, W. D., Truran, J. W., and Woolsey, S. E., Ap. J. 16587 (1971).Google Scholar
  120. 120.
    Hawking, S. W. in 6th Texas Symp. on Relativistic Astrophysics, Annals, New York Academy of Sciences, 224, 268 (1973).Google Scholar
  121. 121.
    Davies, P. C. W., The Physics of Time Asymmetry, University of California Press, Berkeley, 1974.Google Scholar
  122. 122.
    Jackiw, Rev. Mod. Phys. 49, 681 (1977); with C. Rebbi, Phys. Rev. Let. 36, 1116 (1976); 37, 122 (1976); Phys. Rev. D 13, 3398 (1976);MathSciNetGoogle Scholar
  123. 123.
    tHooft, G., Phys. Rev. Let. 37, 8 (1976); Nuclear Phys. B79, 276 (1974);Google Scholar
  124. 124.
    Narlikar, J. V., General Relativity and Cosmology, MacMillan, London, 1979.Google Scholar
  125. 125.
    Hawking, S. W. and W. Israel, eds., General Relativity, Cambridge, 1979.Google Scholar
  126. 126.
    M. Rowan-Robinson, Cosmology, 2nd ed. Oxford, 1981.Google Scholar
  127. 127.
    G. Bath, ed. The State of the Universe, Oxford, 1980.Google Scholar
  128. 128.
    P. T. Landsberg and D. A. Evans, Mathematical Cosmology: An Introduction, Oxford, 1979.Google Scholar
  129. 129.
    G. Burbidge and A. Hewitt, eds. Telescopes for the 1980s, Palo Alto: Annual Reviews, 1981.Google Scholar
  130. 130.
    J. Vervier and R.V.F. Janssens, Spinor Symmetry and supersymmetry, Phys. Lett., 108B: 1, 1982.Google Scholar
  131. 131.
    L.W. Alvarez, et al, Science, 208, 1095, 1980.CrossRefGoogle Scholar

Copyright information

© Benjamin Gal-Or 1983

Authors and Affiliations

  • Benjamin Gal-Or

There are no affiliations available

Personalised recommendations