The river model of gravitational collapse

Abstract

We show that the transformation of a time-evolving spherically symmetric metric tensor into a Painlevé–Gullstrand–Lemaître form brings forth a few curious consequences. The time evolution describes a non-singular gravitational collapse, leading to a bounce and dispersal of all the clustered matter, or a wormhole geometry for certain initial conditions. The null convergence condition is violated only at the onset of bounce or the wormhole formation. As an example, the requirements to develop a Simpson–Visser wormhole/regular black-hole geometry is discussed. The solution can be regarded as a new time-evolving twin of sonic dumb holes found in analog gravity.