One of the few possibilities of time travel is a rotating charged black hole. Once one goes in orbit of the black hole, they can escape, but only into a different part of the universe. This does not require you to fly into or through a black hole. The region of space that they are ejected to could be a different area of space or a different time, since these are both dimensions of our world. The problem with this theory is that there are no charged rotating black holes. It is slightly plausible that one could shoot projectiles into a charged black hole to cause it to rotate; however, at some point, the mass of the projectiles required to speed of the black hole any further would be infinite. Therefore, this project is impossible.