Detailed study of null and time-like geodesics in the Alcubierre Warp spacetime

The Alcubierre warp spacetime yields a fascinating chance for comfortable interstellar travel between arbitrary distant places without the time dilation effect as in special relativistic flights. Even though the warp spacetime needs exotic matter for its construction and is thus far from being physically feasible, it offers a rich playground for studying geodesics in the general theory of relativity. This paper is addressed to graduate students who have finished a first course in general relativity to give them a deeper inside in the calculation of non-affinely parametrized null and time-like geodesics and a straightforward approach to determine the gravitational lensing effect due to curved spacetime by means of the Jacobi equation. Both topics are necessary for a thorough discussion of the visual effects as observed by a traveller inside the warp bubble or a person looking from outside. The visual effects of the traveller can be reproduced with an interactive Java application.