Temporal Novice
Interesting, several of you are on the right track. The repercussions of time travel are not what they seem. If I may offer this bit of advice: Time does not need to be dependent on other factors but only itself.
Could you elaborate please.

Which repercussions do you speak of?

As far as it's dependency on other factors, velocity does indeed have a very real, demonstrated and measured effect on the rate of time's passing, particularly in the presence of gravity wells.

The existence of "time" whatever it is, or how you choose to describe it, is not dependent on anything but itself, but the rate of its "passing" most certainly IS effected by the laws of Special AND General Relativity.

Time dilation, while not being "time travel" per se, is a very easily demonstrated aspect OF Relativity, showing that it's measured "flow" does seem to be dependent on the frame of reference one measures it from. Particularly with reference to relative velocities.

Also, are you familiar with the concept of "Frame Dragging"? This one demonstrates the effects of GRAVITY on time when the body is spinning. Most pronounced of course in the case of the spinning black hole.