Dynamical interiors of black-bounce spacetimes

Abstract

Using the Israel-Darmois junction conditions, we obtain a class of regular dynamical interiors to the recently proposed black-bounce spacetimes which regularises the Schwarzschild singularity by introducing a regularisation parameter. We show that a regularised Friedmann-Lemaitre-Robertson-Walker like interior geometry can not be matched smoothly with the exterior black-bounce spacetime through a timelike hypersurface, as there always exists a thin shell of non-zero energy-momentum tensor at the matching hypersurface. We obtain the expressions for the energy density and pressure corresponding to the thin-shell surface energy-momentum tensor in terms of the regularisation parameter and derive an evolution equation for the scale factor of the interior geometry by imposing physical conditions on these components. We also discuss the formation of the event horizon inside the interior in the case when the initial conditions are such that the situation describes a collapsing matter cloud. We elaborate upon the physical implications of these results.