Apparent motion of a spherical shell collapsing onto a black hole

TL;DR

This paper models the collapse of a spherical shell onto a black hole, demonstrating that an observer at infinity perceives the shell as freezing outside the event horizon, with apparent sizes approaching a specific limit.

Contribution

It corrects previous claims by showing the shell never crosses the horizon from an external observer's perspective and details the evolution of the shell's apparent size during collapse.

Findings

Observer at infinity sees the shell freeze outside the horizon.

Apparent sizes of shell surfaces approach 3√3 GM/c^2 asymptotically.

Collapse dynamics include non-monotonic changes in apparent size.

Abstract

We model the collapse of a spherically symmetric, constant density, pressureless shell onto a preexisting black hole. Contrary to a recent claim of Liu and Zhang (2009), we show that an observer at infinity never sees any part of the shell cross the event horizon. The entire shell appears to "freeze" outside the black hole. We find that during intermediate stages of the collapse, the change in apparent size of the inner surface is non-monotonic. However, at late times, the apparent sizes of the inner and outer surfaces of the shell both approach 3\sqrt{3}GM/c^2 asymptotically, where M is the combined mass of the initial black hole and the shell.