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Eternity is unstable

Abstract

We show that if the Universe expands forever, it will become increasingly irregular in the far future. In particular, we demonstrate that the Hawking black hole evaporation process causes a vortical instability to develop in spatially homogeneous spacetimes which are approximately k = 0 Friedmann universes. We associate the increase of irregularity with the increase of gravitational field entropy, and thus provide a novel picture of the universal heat death.

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References

  1. Collins, C. B. & Hawking, S. W. Astrophys. J. 180, 317 (1973).

    Article  ADS  MathSciNet  Google Scholar 

  2. Misner, C. W. Astrophys. J. 151, 431 (1968).

    Article  ADS  Google Scholar 

  3. Barrow, J. D. & Matzner, R. A. Mon. Not. R. astr. Soc. 181, 719 (1977).

    Article  ADS  CAS  Google Scholar 

  4. Davies, P. C. W. Phys. Lett. 68 B, 402 (1977).

    Article  Google Scholar 

  5. Davies, P. C. W., Fulling, S. A., Christensen, S. M. & Bunch, T. S. Ann. Phys. 109, 108 (1977).

    Article  ADS  Google Scholar 

  6. Dicke, R. H. Nature 192, 440 (1961).

    Article  ADS  Google Scholar 

  7. Carter, B. Confrontation of Cosmological Theories with Observational Data, (ed. Longair, M. S.) (Reidel, Dordrecht, 1974).

    Google Scholar 

  8. Barrow, J. D. & Tipler, F. J. The Anthropic Cosmological Principle (in preparation)

  9. Bekenstein, J. D. Phys. Rev. D9, 3292 (1974).

    Article  ADS  Google Scholar 

  10. Hawking, S. W. Commun. Math. Phys. 43, 199 (1975).

    Article  ADS  Google Scholar 

  11. Bekenstein, J. D. Phys. Rev. D5, 1239 & 2403 (1972).

    ADS  MathSciNet  Google Scholar 

  12. Rees, M. J. Observatory 89, 193 (1969).

    ADS  Google Scholar 

  13. Davies, P. C. W. Mon. Not. R. astr. Soc. 161, (1973).

  14. Mendoza, E. in Reflections on the Motive Power of Fire by Sadi Camot (Dover, New York, 1960).

    Google Scholar 

  15. Thomson, W. Phil. Mag. 4, 304 (1852).

    Article  Google Scholar 

  16. Helmholz, H. Von, On the Interaction of Natural Forces (1854) in Popular Sci entific lectures(ed. Kline M.,) (Dover, New York, 1961).

    Google Scholar 

  17. Clausius, R. Ann. Physik 125, 353 (1865).

    Article  ADS  Google Scholar 

  18. Clausius, R. Phil. Mag. 35, 405 (1868).

    Article  Google Scholar 

  19. Brush, S. G. The Kind of Motion We Call Heat: A History of the Kinetic Theory of Gases in the 19th Century (North Holland, Amsterdam, 1976).

    Google Scholar 

  20. Brush, S. G. The Temperature of History: Phases of Science and Culture in the Nineteenth Century (Franklin, New York, 1978).

    Google Scholar 

  21. Jeans, J. H. The Universe Around Us, (Cambridge University Press, 1930).

    MATH  Google Scholar 

  22. Eddington, A. S. The Nature of the Physical World (Cambridge University Press, 1928).

    MATH  Google Scholar 

  23. Eddington, A. S. Nature 127, 447 (1931).

    Article  ADS  Google Scholar 

  24. Misner, C. W., Thorne, K. S. & Wheeler, J. A. Gravitation (Freeman, San Francisco, 1973).

    Google Scholar 

  25. Landau, L., Lifshitz, E. M. The Classical Theory of Field 4th edn (Pergamon, Oxford, 1975).

    MATH  Google Scholar 

  26. Islam, J. Q. JIR. Astr. Soc. 18, 3 (1977).

    ADS  Google Scholar 

  27. Saslaw, W. C. Publ. astr. Soc. Pacific 85, 5 (1973).

    Article  ADS  Google Scholar 

  28. Saslaw, W. C., in IAU Symp. No. 58 (ed. Shakeshaft, J. R.) (Reidel, Dordrecht, 1974).

  29. Chandrasekhar, S. Principles of Stellar Dynamics (Dover, New York, 1960).

    MATH  Google Scholar 

  30. Spitzer, L., Härm, R. Astrophys. J. 127, 544. (1958).

    Article  ADS  Google Scholar 

  31. Harrison, B. K., Thorne, K. S., Wakano, M. & Wheeler, J. A. Gravitation Theory and Gravitational Collapse (Chicago, University Press, 1965).

    Google Scholar 

  32. Zeldovich, Y. B. Mon. Not. R. astr. Soc 160, 1P (1972).

    Article  ADS  Google Scholar 

  33. Page, D. N. Phys. Rev. D13, 198 (1976).

    Article  ADS  CAS  Google Scholar 

  34. Carr, B. J. Astrophys. J. 206, 8 (1976).

    Article  ADS  CAS  Google Scholar 

  35. Novikov, I. D. & Thorne, K. S. in Black Holes (eds. de Witt, C. & De Witt, B.) (Gordon and Breach, New York, 1973).

    Google Scholar 

  36. Kropp, W. P. & Reines, F. Phys. Rev. 137, 740 (1965).

    Article  ADS  CAS  Google Scholar 

  37. Zeldovich, Y. B. Phys. Lett. 59A, 254 (1976).

    Article  Google Scholar 

  38. Zeldovich, Y. B. Sov. Phys. JETP. 45, 9 (1977).

    ADS  Google Scholar 

  39. Novikov, S. P. Sov. Phys. JETP. 35, 1031 (1972).

    ADS  Google Scholar 

  40. Hawking, S. W. & Ellis, G. F. R. The Large Scale Structure of Space-Time (Cambridge University Press, 1973).

    Book  Google Scholar 

  41. Tipler, F. J. Phys. Rev. D17, 2521 (1978).

    ADS  MathSciNet  Google Scholar 

  42. Zeldovich, Y. B. & Pitajevski, L. P. Commun Math. Phys. 23, 185 (1971).

    Article  ADS  Google Scholar 

  43. Bonnor, W. B. Mon. Not. R. astr. Soc. 167, 55 (1974).

    Article  ADS  Google Scholar 

  44. Bonnor, W. B. & Tommimura, N. Mon. Not. R. astr. Soc. 175, 85 (1976).

    Article  ADS  Google Scholar 

  45. Collins, C. B. & Hawking, S. W. Mon. Not. R. astr. Soc. 162, 307 (1973).

    Article  ADS  Google Scholar 

  46. Raychaudhuri, A. Phys. Rev. 98, 1123 (1955).

    Article  ADS  MathSciNet  Google Scholar 

  47. Ellis, G. F. R. General Relativity and Cosmology (ed. Sachs, R. K.) (Academic, New York. 1973).

    Google Scholar 

  48. MacCallum, M. A. H. Phys. Lett. 40 A, 325 (1972).

    Article  Google Scholar 

  49. Estabrook, F. B., Wahlquist, H. D. & Behr, C. B., J. Math. Phys. 2, 497 (1968).

    Article  ADS  Google Scholar 

  50. Ellis, G. F. R. & MacCallum, M. A. H. Commun Math. Phys. 12, 108 (1969).

    Article  ADS  Google Scholar 

  51. Hawking, S. W. Astrophys. J. 145, 544 (1966).

    Article  ADS  Google Scholar 

  52. Ruzmaikin, A. A., Ruzmaikina, T. V., Sov. Phys. JETP 29, 934 (1969).

    ADS  Google Scholar 

  53. Batakis, N., Cohen, J. M. Phys. Rev. D12, 1544 (1975).

    ADS  MathSciNet  Google Scholar 

  54. Tipler, F. J. Astrophys. J. 209, 12 (1976).

    Article  ADS  Google Scholar 

  55. Gott, J. R., Rees, M. J. Astr. Astrophys. 45, 365 (1975).

    ADS  Google Scholar 

  56. Siklos, S. T. C. Commun. Math. Phys. 58, 255 (1978).

    Article  ADS  MathSciNet  Google Scholar 

  57. Hawking, S. W. Phys. Rev. D14, 2460 (1976).

    ADS  MathSciNet  Google Scholar 

  58. Penrose, R. in Theoretical Principles in Astrophysics and Relativity, (eds Lebovitz, N. R. Reid, W. M. & Vandervoort, P. O.) (Chicago University Press, 1978).

    Google Scholar 

  59. Penrose, R. in Einstein Centenary Volume (eds Hawking, S. W. & Israel, W.) (Cambridge University Press, in the press).

  60. Misner, C. W. Phys. Rev. 186, 1328 (1969).

    Article  ADS  Google Scholar 

  61. York, J. W. Phys. Rev. Lett. 28, 1082 (1972).

    Article  ADS  Google Scholar 

  62. Marsden, J. E. & Tipler, F. J. (1978) (in preparation).

  63. Goddard, A. J. Commun. Math. Phys. 54, 278 (1977).

    Article  ADS  Google Scholar 

  64. Davies, P. C. W. The Physics of Time Asymmetry, (University of California, Berkeley, 1975).

    Book  Google Scholar 

Download references

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Barrow, J., Tipler, F. Eternity is unstable. Nature 276, 453–459 (1978). https://doi.org/10.1038/276453a0

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