If you can travel to the past, the past co-exists, in a certain sense, with the present. If the past co-exists with the present, it cannot do so dynamically (since you already exist in the present dynamically), the past is static. So if you “arrive” in the past you are simply frozen, the “frontier of change” being far away in the future, because you are not some special god-person who carries the “frontier of change” with you. (Which means you can’t really “arrive” in the past, since it’s a dynamic process.)

No change of the past can take place, unless some sort of meta-time exists, because the change of the past must “occur” (hint, hint) outside of our time (part of our spacetime), relative to the old state of the spacetime. Such a change can only be meaningful - if at all - outside of our spacetime, in a meta-time. Anything involving a change of the spacetime involves dynamics relative to something outside of the spacetime.

The usual time travel films/books accept the “frontier of change” in the present, then move it with the personages to the past, although this makes no sense. In these films/books it’s the “present” moment as experienced by the heroes that counts, but why? It has no special physical significance.