In this chapter, we will introduce the Topological Censorship.
It is now accepted that the Earth is round. We live on a sphere but in our everyday life we just do geometry with three-dimensional Euclidian space!
It works because, at our scale, the surface of the Earth is almost flat. It is the same idea used to define a manifold , i.e. a space locally similar to 
.
On manifolds we use differential geometry which is not necessary with the Euclidian metric (
) when we need to talk about effects that see the difference.
When we observe the universe around us, we see a trivial spatial topology! It is continuously deformable to a three-dimensional Euclidian space.
But the solutions of the Einstein equation are not so simple! General Relativity allows the spacetime to have a complicated structure with singularities.
There is an apparent contradiction. Then, why did we not observe topology in our spacetime ?
The answer can be that it does not exist... A more interesting possibility is it cannot be seen. This is called the topological censorship conjecture.
This was proved in 1993 by
Friedman, Schleich and Witt ([4] and appendix
page ). The subject of this
report is to study some aspects of this censorship. First we will discuss some notions require in the understanding of the theorem that we want to prove in the next part. After this required understanding of how the proof works we will be able to generalize it to some other kind of spacetime.
