Quantum Effects and Spacetime Singularity

Abstract

Conclusions regarding the inevitability of space-time singularities cannot be accepted as final without including the quantum effects which will be important during the final stages of collapse or near initial singularity. We generalise here earlier results on the behaviour of quantum effects in the vicinity of space-time singularity [1, 2, 3, 4] that when the conformal degree of freedom is quantised, the quantum effects diverge near the singularity and that nonsingular, non-classical states can occur with finite probability. A general class of space-times, including spatially homogeneous but anisotropic cases is treated which encompasses most of the interesting classically singular spacetimes such as the collapsing dust-ball solution, Robertson-Walker spacetimes, the general cosmological scenario of Belinskii et al. etc. A consideration to general inhomogeneous spacetimes is also given. The stress-energy tensor is taken to be that of non-interacting material particles and singularities considered are general strong curvature singularities. The wave function of the system is not assumed to have a special form such as a wave packet, and can again have a general form. The quantum effects are seen to be governed by a non-linear differential equation which is analysed to study them near singularity. We use here the operator approach which is intuitively appealing and often more direct as compared to the path integral approach sometimes used [3,4].