The null geodesic equations in the Alcubierre warp drive spacetime are numerically integrated to determine the angular deflection and redshift of photons which propagate through the distortion of the "warp drive" bubble to reach an observer at the origin of the warp effect. We find that for a starship with an effective warp speed exceeding the speed of light, stars in the forward hemisphere will appear closer to the direction of motion than they would to an observer at rest. This aberration is qualitatively similar to that caused by special relativity. Behind the starship, a conical region forms from within which no signal can reach the starship, an effective "horizon". Conversely, there is also an horizon-like structure in a conical region in front of the starship, into which the starship cannot send a signal. These causal structures are somewhat analogous to the Mach cones associated with supersonic fluid flow. * e-mail: chadc@orion.physics.montana.edu † e-mail: hiscock@montana.edu ‡ e-mail: shane@orion.physics.montana.edu 1The existence of these structures suggests that the divergence of quantum vacuum energy when the starship effectively exceeds the speed of light, first discovered in two dimensions, will likely be present in four dimensions also, and prevent any warp-drive starship from ever exceeding the effective speed of light.Typeset using REVT E X 2 Alcubierre [1] has described a spacetime which has features reminiscent of the "warp drive" common in science fiction lore. The Alcubierre solution allows a "starship" to have an apparent speed relative to distant observers which is much greater than the speed of light, an effect caused by the spacetime expanding behind and contracting in front of the starship.In such a spacetime, passengers on the starship can travel arbitrarily large distances in small amounts of proper time; further, there is no time dilation effect between the starship and clocks outside the region affected by the warp drive.If a technology based on such a spacetime could be realized, space travel to distant points in our Universe could seem almost plausible. The Alcubierre warp drive spacetime has properties, however, which make it unlikely to be physical. As Alcubierre himself pointed out, in order to create the distortion of spacetime which produces the warp drive effect, "exotic" matter is required, which violates the weak, strong, and dominant energy conditions. Although quantized fields can locally violate the energy conditions, an analysis by Pfenning and Ford [2] has shown that the distribution of exotic matter needed to generate the warp 'bubble' around the starship appears quite implausible. Additional work has shown that any spacetime that permits apparent superluminal travel will inevitably violate the weak and averaged null energy conditions [3][4][5]. On the other hand, Van Den Broeck has recently shown how to significantly reduce the amount of negative energy density matter required for the warp drive to the order of grams [6].Even if one could somehow obtain the ...

There exists a class of contractible open 3-manifolds W p which are topologically distinct from OB3. They have the property that Wp x OB is diffeomorphic to R4. A spacetime with a Cauchy surface diffeomorphic to some W p therefore has a spacetime manifold diffeomorphic to R4. A theorem is established to the effect that any asymptotically simple and empty spacetime has a spacetime manifold diffeomorphic to R4, but can only have R3 Cauchy surfaces. Also f' and 9must be diffeomorphic to 5 ' x R. These results supersede an argument of Geroch in support of similar conclusions.