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traveling back in time is not mathematically disallowed by the general relativity.
in fact there is a lot of work done on the topic, and lots of potential scenarios proposed (which usually involve describing the space-time warped into weird 4D shapes). what GR does tell you is what kind of matter/energy would produce such spaces (since in GR these two are intertwined), and that's kind of where common sense works again: most proposed geometries do require either negative energy densities or mathematical singularities (which to be fair are not impossible, but we kinda never seen that, aside from dark energy).
on the other hand -- faster-than-light travel is also possible -- albeit with similar constraints.
Moving mass backwards through time isn't strictly mathematically disallowed. Idk what it's going to look like when it arrives, though.
What does a Tachyon even look like?
i didn't mean purely mathematically. but from the physics standpoint. in other words, if you provide enough dark energy and shape it into a specific configuration, it will generate space-time where time travel is possible in practice.
"How much ya got?"
"Well, it's a purely theoretical substance. But theoretically we've got more of that than all the regular energy in the known universe."
I want to say that'll be the easy part, but I guess it really depends how abstract of a shape we're talking about and how malleable dark energy ends up being.