Quantum uncertainty in the final state of gravitational collapse

Abstract

The ratio of the action S to h (Planck's constant/2π) determines whether the physical system in question is to be treated classically or quantum mechanically. In the area of classical physics the ratio S/h is large compared with unity, and the governing equations are given by δS=0. Quantum mechanics begins to be important when S≲h , and the definitive approach of classical physics is replaced by quantum uncertainty. We discuss here the behaviour of a physical system which is initially in the classical domain (S≫h) but whose later development may well take it into the region of quantum uncertainty. We consider a specific example of this-the gravitational collapse of a spherical dust ball. While classically such a dust ball ends up in a space-time singularity, the corresponding quantum mechanical result suggests a range oƒ^→ final states some oƒ^→ which are non-singular.