Using the concepts of general relativity relativistic interstellar travel to the stars approaching the speed of light can be computed for the general case of accelerated motion for half the journey and decelerated motion for the remaining half of the journey. According to general relativity a rocket and its passengers feel the effects of gravity when accelerating in flat spacetime where motion is described relative to a proper reference frame. Because of time dilation an astronaut can travel stellar distances, that is many light years within his/her own lifetime while many thousands of years will have elapsed on the planet of departure. This analysis determines the proper time dilation or elapsed time on a spaceship whose speed approaches the light speed and the instantaneous velocity or 4-velocity of a spaceship relative to the speed of light at some constant acceleration. As explained in general relativity the 4-velocity is the rate of change of the 4-vector with respect to the moving frames’ proper time. The results presented here are independent of the propulsion systems used. These results are equally valid for a spaceship powered by an advanced antimatter propelled photon rocket, or a spaceship powered by a VASIMR (Variable Specific Impulse Magnetoplasma Rocket) plasma rocket motor.