Geroch's splitting theorem
In the theory of causal structure on Lorentzian manifolds, Geroch's theorem or Geroch's splitting theorem (first proved by Robert Geroch) gives a topological characterization of globally hyperbolic spacetimes.
Let be a globally hyperbolic spacetime. Then is strongly causal and there exists a global "time function" on the manifold, i.e. a continuous, surjective map such that: