Time Travel: Why Only to CTC's Creation?

[Starlover]

In theorized travel to the past -- in particular with a closed timelike curve (CTC), why is it possible to only go back in time to the point at which the CTC was created?

Questions related to this would be:
1) Can space curve into a CTC if it was not originally in a CTC?
2) How can we be sure that we (or Earth) are not already in a CTC? (Is it because there is no gravity source powerful enough to create a CTC, in our immediate vicinity?)

 

[Matterwave]

As time travel to the past is thought to be forbidden, and CTCs are thought to be forbidden in physical space times, this thread is just speculation.

1) Space can't curve into a CTC, a CTC is a specific everywhere forward directed time-like curve in space-time which turns in on itself.

2) Things don't keep repeating, i.e. we don't keep going back to the same events, so by observation, we can deduce we are not in a CTC.