We already know that spacetime has local curvature, so it’s possible that spacetimes curvature isn’t static. How this affects or interacts with time isn’t clear, since we don’t really understand what spacetime is or how it comes to be.
I think if both of you aren't aware, this talk on the concept of time orientability might be interesting exploration on this: https://yewtu.be/watch?v=Mk7vkhT0UCM