Erm…relativity is quite mute on the subject of whether or not artificial gravity is possible or not. Quite simply we do not know.
One way to propel a ship to a good fraction of the speed of light that is doable with today’s knowledge is with a microwave laser generated from a solar power station in orbit. The beam would shine on a microwave reflective carbon mesh and accelerate it to high speeds. The ship doesn’t have to carry any fuel, and thus is far easier to accelerate. There’s a rather good article on it in the Jan/Feb issue of the Planetary Report. Not having to carry around reaction mass makes the mission much easier.
