A concise introduction to trapped surface formation in general relativity

TL;DR

This paper provides a pedagogical overview of the mathematical formalism used to study trapped surface formation in general relativity, focusing on the optical structure and key analyses by Christodoulou and others.

Contribution

It synthesizes the complex mathematical formalism of trapped surface formation, making it accessible for further research and understanding in the field.

Findings

Rigorous mathematical analysis of trapped surface formation

Optical structure formalism in general relativity

Clarification of nonlinear equations involved

Abstract

Trapped surface formation in general relativity can be studied through a coupled set of nonlinear equations, where various terms can be neglected, as was proved by a rigorous mathematical analysis of Christodoulou. This paper is devoted to a pedagogical synthesis of the mathematical formalism employed in this analysis, i.e. the optical structure of general relativity investigated by Christodoulou, Klainerman and other authors after them.