Warpdrive perturbed spacetimes

Abstract

In this final year project, we investigate the behavior of timelike trajectories in curved spacetimes - in particular, Schwarzschild and Kerr metrics that are perturbed by the Alcubierre or warp drive metric. The trajectories expectedly di er from the non-perturbed case and are more obvious in the case of Schwarzschild. Furthermore, we discover that time dilation effects are slightly tampered when travelling under the in uence of the perturbed spacetime. Subsequently, we study the case of the Kerr "Twin Paradox" by showing the difference in angular distance travelled and deriving the difference in proper times between their successive encounters. Finally, we show, by an approximation, that the counter rotating twin, orbiting using a warp drive, is able to mitigate the effects of time dilation due to frame dragging by the rotating black hole.