I tried to do some research about the time travel thing. As far as I've understood while the person is in the space ship he turns around, accellerates, and he will feel that he is in a gravitational field. Being in a gravitational field, causes time to go slower. Thus for him time will go slower for him and faster on earth, while observers from earth predict the same, that time goes slower for him and faster for them. However this accelleration lasts only a very short amount of time compared to the whole trip. Therefor he will only feel as if he is in a gravitational field slowing his time only for as long as he accellerates. After he is finished accellerating both observers will experience that the other persons clock is slower, right?
So is it only the time during the accelleration that the person in the rockets time is really going relatively slower, or his time is really going relatively slower the whole trip?
Also, if gravity is curvature in space-time, how does such curvature provide matter with energy just by being curves?