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The Classical Singularity Theorems and Their Quantum Loopholes

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Abstract

The singularity theorems of classical general relativity are briefly reviewed. The extent to which their conclusions might still apply when quantum theory is taken into account is discussed. There are two distinct quantum loopholes: quantum violation of the classical energy conditions, and the presence of quantum fluctuations of the spacetime geometry. The possible significance of each is discussed.

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REFERENCES

  • Belinsky, V. A. and Khalatnikov, I. M. (1969). Soviet Physics-JETP, 29, 911.

    Google Scholar 

  • Belinsky, V. A., Lifshitz, E. M., and Khalatnikov, I. M. (1970). Advances in Physics, 19, 525.

    Google Scholar 

  • Borde, A. (1987). Classical and Quantum Gravity 4, 343.

    Google Scholar 

  • Borde, A., Guth, A. H., and Vilenkin, A. (2001). Preprint gr-qc/0110012.

  • Flanagan, E. E. (1997). Physical Review D 56, 4922[gr-qc/9706006].

    Google Scholar 

  • Fewster, C. J. (2000). Classical and Quantum Gravity 17, 1897[gr-qc/9910060].

    Google Scholar 

  • Fewster, C. J. and Eveson, S. P. (1998). Physical Review D 58, 084010[gr-qc/9805024].

    Google Scholar 

  • Ford, L. H. (1978). Proceedings of the Royal Society of London A 364, 227.

    Google Scholar 

  • Ford, L. H. (1991). Physical Review D 43, 3972.

    Google Scholar 

  • Ford, L. H. (1995). Physical Review D 51, 1692[gr-qc/9410047].

    Google Scholar 

  • Ford, L. H. and Roman, T. A. (1995). Physical Review D 51, 4277[gr-qc/9410043].

    Google Scholar 

  • Ford, L. H. and Roman, T. A. (1996). Physical Review D 53, 5496[gr-qc/9510071].

    Google Scholar 

  • Ford, L. H. and Roman, T. A. (1997). Physical Review D 55, 2082[gr-qc/9607003].

    Google Scholar 

  • Frolov, V., Markov, M., and Mukhanov, V. (1990). Physical Review D 41, 383.

    Google Scholar 

  • Galloway, G. J. (1981). Manuscripta Mathematics 31, 297.

    Google Scholar 

  • Hawking, S. W. and Ellis, G. F. R. (1973). The large scale structure of space-time, Cambridge University Press, Cambridge, UK.

    Google Scholar 

  • Hu, B. L. and Verdaguer, E. (2002). Preprint gr-qc/0211090.

  • Jackel, M.-T. and Reynaud, S. (1995). Annalen Physics 4, 68[quant-ph/0101116].

    Google Scholar 

  • Kuo, C.-I. and Ford, L. H. (1993). Physical Review D 47, 4510[gr-qc/9304008].

    Google Scholar 

  • Lifshitz, E. M. and Khalatnikov, I. M. (1963). Advances in Physics, 12, 185.

    Google Scholar 

  • Martin, R. and Verdaguer, E. (2000). Physical Review D 61, 124024[gr-qc/0001098].

    Google Scholar 

  • Parentani, R. (2001). Physical Review D 63, 041503[gr-qc/0009011].

    Google Scholar 

  • Parker, L. and Fulling, S. A. (1973). Physical Review D 7, 2357.

    Google Scholar 

  • Penrose, R. (1965). Physical Review Letters 14, 57.

    Google Scholar 

  • Pfenning, M. J. and Ford, L. H. (1997a). Physical Review D 55, 4813[gr-qc/9608005].

    Google Scholar 

  • Pfenning, M. J. and Ford, L. H. (1997b). Classical and Quantum Gravity 14, 1743[gr-qc/9702026].

    Google Scholar 

  • Pfenning, M. J. and Ford, L. H. (1998). Physical Review D 57, 3489[gr-qc/9710055].

    Google Scholar 

  • Roman, T. A. (1988). Physical Review D 37, 546.

    Google Scholar 

  • Saa, A., Gunzig, E., Brenig, L., Faraoni, V., Rocha Filho, T. M., and Figueiredo, A. (2001). International Journal of Theoretical Physics 40, 2295.

    Google Scholar 

  • Shiokawa, K. (2000). Physical Review D 62, 024002[hep-th/0001088].

    Google Scholar 

  • Sopova, V. and Ford, L. H. (2002). Physical Review D 66, 045026[quant-ph/0204125].

    Google Scholar 

  • Tipler, F. J. (1979). Physical Review D 17, 2521.

    Google Scholar 

  • Wald, R. M. (1984). General Relativity, University of Chicago Press, Chicago, IL, Chap. 9, Singularities.

    Google Scholar 

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Ford, L.H. The Classical Singularity Theorems and Their Quantum Loopholes. International Journal of Theoretical Physics 42, 1219–1227 (2003). https://doi.org/10.1023/A:1025754515197

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