Let $(M, g)$ be a smooth Lorenzian time-oriented manifold.
Is it possible for the Lorenzian metric induced topology to be different from that of the manifold topology, without CTCs?
We know that the two topologies are not necessarily the same and such matching can happen iff the spacetime is strongly causal.
So if the answer is yes and there exists such spacetime, they surely are not strongly causal.
I want to know how far this mismatch of topologies can go while avoiding CTCs. (avoiding also the case of "up to a metric fluctuation that can create a CTC")
Or does any topological mismatch/deviation result in CTCs(directly or up to metric fluctuation)?
Or in general:
Is there any relation at all between topological deviation, and the existence of CTCs(also up to a metric fluctuation) one way or another?