See Hayward 2013 for a recent comprehensive review, and Faraoni 2013 for one with special attention to its relevance to cosmology.
Likewise, a reverse application of the Schrödinger equation will take us from the later state back to the original initial state.
A spacetime, then, is said to be singular if it possesses a path such that the specified parameter associated with that path cannot increase without bound as one traverses the entirety of the maximally extended path.