Some examples of trapped surfaces

TL;DR

This paper provides simple, illustrative examples of trapped surfaces in various gravitational collapse scenarios to aid understanding of this key concept in general relativity.

Contribution

It introduces accessible pen-and-paper examples of trapped surfaces from different models, enhancing visualization and comprehension.

Findings

Examples from time-symmetric initial data

Examples from 2+1 dimensions

Examples from collapsing null shells and Vaidya solution

Abstract

We present some simple pen and paper examples of trapped surfaces in order to help visualising this key concept of the theory of gravitational collapse. We collect these examples from time-symmetric initial data, 2+1 dimensions, collapsing null shells, and the Vaidya solution.