So the thing that paper does is it assumes you can make warp bubbles in any reference frame. The original paper makes one warp bubble and this doesn't lead to anything paradoxical.
But if I can make two warp bubbles in two different frames, I can make a round trip that arrives before it starts.
So you need to violate special relativity in a global way to avoid these issues. You have to have a spacetime where only certain warp geometries are possible.
I apologize for being a bit impatient before, these issues are subtle. The only real way to get it is to bear with the math onesself.
But if I can make two warp bubbles in two different frames, I can make a round trip that arrives before it starts.
So you need to violate special relativity in a global way to avoid these issues. You have to have a spacetime where only certain warp geometries are possible.
I apologize for being a bit impatient before, these issues are subtle. The only real way to get it is to bear with the math onesself.