Gravitational collapse of spherical shells of fluid in the isotropic homogeneous universe

TL;DR

This paper analytically studies the gravitational collapse of thick fluid shells in an isotropic universe, connecting FLRW and black hole metrics, and confirms energy invariance during collapse.

Contribution

It provides new analytic solutions for collapsing fluid shells in a cosmological setting, including cases without interior perfect fluid, and verifies energy conservation.

Findings

Analytic solutions interpolating FLRW and black hole metrics.

Collapse orbits determined by interface conditions and equations of state.

Total energy remains invariant during collapse.

Abstract

We investigate gravitational collapse of thick shell of fluid in the isotropic homogeneous universe without radiation described by the Einstein gravity with cosmological constant. We construct analytic solutions of this kind interpolating the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric and the de-Sitter Schwarzschild black hole one by the Gullstrand-Painlev\'e one. After determining the scale factor for a perfect fluid coexisting with cosmological constant, we determine the orbit of the collapsing shells of fluid from the continuity condition for density and the perpendicular component of pressure at interface. However the continuity condition cannot fix the orbit when there does not exist a perfect fluid inside the shells. In this case we determine the orbit from an equation of state for the fluid consisting a shell near the surface. Finally we confirm that the total energy defined in arXiv:2005.13233 is independent of the given time evolution in this system.