# Penrose Singularity Theorem

1. Apr 26, 2012

### PLuz

Can anyone help me with this?

1. The problem statement, all variables and given/known data

Explain why Penrose's singularity theorem does not apply to each of the following geodesi-
cally complete Lorentzian manifolds:
(a) Minkowski's spacetime;
(b) Einstein's universe;
(c) de Sitter's universe;
(d) Anti-de Sitter spacetime.

2. Relevant Information

Here is what the theorem says:

"Let (M,g) be a globally hyperbolic Lorentzian manifold. If (M,g) has a noncompact connected Cauchy surface, the null energy condition is satisfied and exists a closed trapped null surface, then (M,g) is singular."

3. The attempt at a solution
Well, I believe for a) the answer is that there aren't any closed trapped surfaces.
b) I believe it's the same as a).
d)It isn't globally hyperbolic.

but for c) am not sure. There are closed traped surfaces, right? And it is globbaly hyperbolic then that leaves, there aren't any noncompact connected Cauchy surfaces? Can any one explain why?

Thanks

Last edited: Apr 26, 2012