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Quantum fluctuations near the classical space-time singularity

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Abstract

The method of path integration is used to study the effects of quantum fluctuations in the space-time geometry near the classical singularity of general relativity. It is shown that in certain special cases explicit Feynman propagators can be constructed which enable us to evaluate these fluctuationsquantitatively. The cases discussed are (i) the gravitational collapse of a uniform dust ball, (ii) the Friedmann cosmologies, (iii) the axisymmetric Bianchi type I cosmological model, and (iv) the general anisotropic Bianchi type I cosmological model. In all cases discussed here the quantum uncertainty grows to infinity as the classical space-time singularity is approached. In this wider regime of quantum gravitation nonsingular solutions can occur with finite probabilities.

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References

  1. Hawking, S. W., and Ellis, G. F. R. (1973).The Large Scale Structure of Space-time (Cambridge University Press, London).

    Google Scholar 

  2. Hawking, S. W. (1974).Nature,248, 30.

    Google Scholar 

  3. Isham, C. J., Penrose, R., and Sciama, D. W. (1975).Quantum Gravity (Clarendon Press, Oxford).

    Google Scholar 

  4. Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973).Gravitation (W. H. Freeman, San Francisco).

    Google Scholar 

  5. Feynman, R. P., and Hibbs, A. R. (1965).Quantum Mechanics and Path Integrals (McGraw-Hill, New York).

    Google Scholar 

  6. Hawking, S. W., and Gibbons, G. W. (1977).Phys. Rev. D,15, 2752.

    Google Scholar 

  7. De Witt, B. S. (1967).Phys. Rev.,162, 1239.

    Google Scholar 

  8. Narlikar, J. V. (1978).Mon. Not. R. Astron. Soc.,183, 159.

    Google Scholar 

  9. Hoyle, F., and Narlikar, J. V. (1970).Nature,228, 544.

    Google Scholar 

  10. De Witt, C. (1976).Ann. Phys.,97, 307.

    Google Scholar 

  11. Bateman, H. (1954).Higher Transcendental Functions, ed. A. Erdelye (McGraw-Hill, New York), Vol. I, p. 163.

    Google Scholar 

  12. Misner, C. W. (1972). InMagic without Magic, ed. J. R. Klauder (W. H. Freeman, San Francisco), p. 441.

    Google Scholar 

  13. MacCallum, M. A. H. (1975). InQuantum Gravity, ed. C. J. Isham, R. Penrose, and D. W. Sciama (Clarendon Press, Oxford), p. 174.

    Google Scholar 

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  1. Tata Institute of Fundamental Research, 400 005, Bombay, India

    J. V. Narlikar

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  1. J. V. Narlikar
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Narlikar, J.V. Quantum fluctuations near the classical space-time singularity. Gen Relat Gravit 10, 883–896 (1979). https://doi.org/10.1007/BF00756752

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  • DOI: https://doi.org/10.1007/BF00756752

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