Dynamics of general relativistic spherically symmetric dust thick shells

TL;DR

This paper develops a general formalism to analyze the dynamics of spherically symmetric dust thick shells in general relativity, showing that thickness accelerates collapse compared to thin shell models.

Contribution

It introduces a new scheme to derive the equations of motion for thick shells in arbitrary spherically symmetric spacetimes, extending thin shell dynamics.

Findings

Thick shells collapse faster than thin shells.

The formalism reduces to known thin shell equations in the zero-thickness limit.

The approach applies to shells embedded in different spherically symmetric spacetimes.

Abstract

We consider a spherical thick shell immersed in two different spherically symmetric space-times. Using the fact that the boundaries of the thick shell with two embedding space-times must be nonsingular hypersurfaces, we develop a scheme to obtain the underlying equation of motion for the thick shell in general. As a simple example, the equation of motion of a spherical dustlike shell in vacuum is obtained. To compare our formalism with the thin shell one, the dynamical equation of motion of the thick shell is then expanded to the first order of its thickness. It is easily seen that the thin shell limit of our dynamical equation is exactly that given in the literature for the dynamics of a thin shell. It turns out that the effect of thickness is to speed up the collapse of the shell.