Abstract
The status of a classical space-time singularity, when quantum effects are taken into account, has remained a matter of intense interest ever since the epochmaking paper of DeWitt [1] on quantum gravity. We examine here the evolution of quantum fluctuations in the vicinity of the singularity arising out of the classical collapse of a homogeneous dust cloud. As opposed to the pathintegral method used to quantize the conformal degree of freedom (see, e.g., [3] or [4]), we use here the traditional operator approach to the quantum theory which is much more direct and appealing while achieving an additional generalization that the wave function of the system is assumed to have a completely general form. It is shown that the quantum uncertainty diverges in the limit of approach to the classically singular epoch and that nonsingular, nonclassical states can occur with finite probability.
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References
DeWitt, B. (1967).Phys. Rev.,160, 1113.
Gotay, M. J., and Demaret, J. (1983).Phys. Rev. D,28, 2402.
Narlikar, J. V. (1978).Mon. Not. R. Astr. Soc.,183, 159.
Joshi, P. S., and Narlikar, J. V. (1986).Int. J. Mod. Phys. A,1, 243.
Brill, D. (1975). InQuantum Theory and Structure of Time and Space, L. Castell, M. Drieschner, and C. F. von Weizsäcker, eds. (Carl Hansen Verlag, München, Wien).
Joshi, P. S. (1986). InTopological Properties and Global Structure of Spacetime, P. G. Bergmann, ed. (Plenum Press, New York).
Oppenheimer, J., and Snyder, H. (1939).Phys. Rev.,56, 455.
Messiah, A. (1973).Quantum Mechanics, Vol. I (North Holland Publishers, Amsterdam).
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Joshi, P.S., Joshi, S.S. Quantum effects in a homogeneous dust cloud collapse. Gen Relat Gravit 19, 1033–1042 (1987). https://doi.org/10.1007/BF00759582
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DOI: https://doi.org/10.1007/BF00759582