Gravitational collapse via Wheeler–DeWitt equation.

We analyze the Wheeler–DeWitt (WDW) equation in the context of a gravitational collapse. The physics of an expanding/collapsing universe and many details of a collapsing star can classically be described by the Robertson–Walker metric in which the WDW equation takes the form of a times-less Schrödinger equation. We set up the corresponding WDW potential for the collapse and study the solutions of the wave function. The results show that the central singularity appearing in classical general relativity is avoided, the density is quantized in terms of the Planck density and the expectation value of the scale factor exhibits a discrete behavior. • Wheeler–DeWitt equation applied to gravitational collapse reveals quantum effects inside black holes. • Classical central singularity in gravitational collapse avoided through quantum mechanics. • Quantization of matter density in gravitational collapse, linked to Planck density. • Wave function behavior indicates discrete quantum dynamics in gravitational collapse scenarios. • Study explores quantum gravity's impact on the late stages of astrophysical system collapse. [ABSTRACT FROM AUTHOR]