Quantum fluctuations near the classical space-time singularity

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 fluctuations quantitatively. The cases discussed are (i) the gravitational col- lapse 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 non- singular solutions can occur with finite probabilities.