Here we will recall some definitions about trapped surfaces. This will be needed for the proof we will explain in the second part of the report.
One can see that this surface is in a
gravitational field so intense than even outgoing light cannot
escape. And as nothing travel faster than light the matter
inside 
is trapped.
There are some other less restrictive definitions; One is used in the Topological Censorship theorem .
A picture that one can have in mind for trapped surface is the vortex formed by water drainning from a bathtub. Indeed everything in the bath is attracted by it. To escape one need a velocity greater than the one of the water flowing down the vortex. For the bath it is physically possible to escape, but for a trapped surface the speed of light is not enough to escape, then all the matter must stay inside the trapped surface.
As there is a conjugate point for all radially outward null geodesics from the trapped surface, this whole region of space is collapsing. It seems logical that a singularity is formed. This is proved in the singularity theorems (see for example [3] or chapter 
).
