Transition to light-like trajectories in thin shell dynamics

TL;DR

The paper studies how a massive thin shell in a spherically symmetric spacetime transitions to a light-like trajectory, exploring conditions that allow it to evade collapse or continue collapsing after becoming null.

Contribution

It generalizes the transition to null trajectories for thin shells in arbitrary spherically symmetric spacetimes and discusses mechanisms for shell persistence or continued collapse.

Findings

Transition to null occurs generically in spherically symmetric geometries.

Surface pressure can enable shells to evade the Schwarzschild radius.

Shell collapse can continue if the exterior geometry is more general.

Abstract

It was recently shown that a massive thin shell that is sandwiched between a flat interior and an exterior geometry given by the outgoing Vaidya metric becomes null in a finite proper time. We investigate this transition for a general spherically-symmetric metric outside the shell and find that it occurs generically. Once the shell is null its persistence on a null trajectory can be ensured by several mechanisms that we describe. Using the outgoing Vaidya metric as an example we show that if a dust shell acquires surface pressure on its transition to a null trajectory it can evade the Schwarzschild radius through its collapse. Alternatively, the pressureless collapse may continue if the exterior geometry acquires a more general form.