Global properties of asymptotically de Sitter and Anti de Sitter spacetimes

In the first part of this work we show a uniqueness result for globally hyperbolic spacetimes with a spacelike conformal boundary satisfying the vacuum Einstein equations with positive cosmological constant. Then we present applications of this result in the contexts of cosmic censorship and the initial value problem in general relativity. Further extensions of this result to non-vacuum solutions of the Einstein equations are also studied. On the other hand, the second half of this thesis deals with spacetimes with timelike boundary. We first develop the causal theory of such spacetimes and then use it to prove a quasi-local version of the principle of topological censorship.