Formation of Trapped Surfaces in General Relativity

Abstract

In this thesis we present two results regarding the formation of trapped surfaces in general relativity.

The first is a simplified approach to Christodoulou's breakthrough result which showed that trapped surfaces can form dynamically by the focusing of gravitational radiation from past null infinity.

We extend the methods of Klainerman-Rodnianski, who gave a simplified proof of this result in a finite region.

The second result extends the theorem of Christodoulou by allowing for weaker initial data but still guaranteeing that a trapped surface forms in the casual domain.

In particular, we show that a trapped surface can form dynamically from initial data which is merely ``large" in a scale-invariant way.

The second result is obtained jointly with Luk.