Quantum uncertainty in the final state of gravitational collapse

Abstract

THE ratio of the action S to ħ (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/ħ is large compared with unity, and the governing equations are given by δS = 0. Quantum mechanics begins to be important when S ≲ ħ, 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 ≫ ħ) 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 of̄ final states some of̄ which are non-singular.