Abstract
The Alcubierre metric is a spacetime geometry where a massive particle inside a spacetime distortion, called warp bubble, is able to travel at velocities arbitrarily higher than the velocity of light, a feature known as the warp drive. This is a consequence of general relativity, which allows for global superluminal velocities but restricts local speeds to subluminal ones as required by special relativity. In this work we solved the Einstein equations for the Alcubierre warp drive spacetime geometry considering the dust matter distribution as source, since the Alcubierre metric was not originally advanced as a solution of the Einstein equations, but as a spacetime geometry proposed without a source gravity field. We found that all Einstein equations solutions of this geometry containing pressureless dust lead to vacuum solutions. We also concluded that these solutions connect the Alcubierre metric to the Burgers equation, which describes shock waves moving through an inviscid fluid. Our results also indicated that these shock waves behave as plane waves.
Highlights
Bubble guarantees that locally the particle’s speed remains subluminal
Further discussions of the metric proposed by Everett and Roman [5] were made by Lobo and Crawford [6,7], who discussed in detail the metric and energymomentum tensor (EMT) derived from it, and addressed if it is possible there exists superluminal travel without the weak energy condition violation
In this work we have analyzed the solutions of the Einstein equations for the Alcubierre warp drive spacetime with the choice of the dust energy–momentum tensor (EMT) as a possible source of global superluminal particle velocities, that is, warp speeds
Summary
Following Alcubierre’s original work, several efforts were made to understand the main caveats of the warp drive metric. Krasnikov [4] discussed the possibility of a massive particle making a round trip between two points in space faster than a photon, by arguing that this is not possible when reasonable assumptions for globally hyperbolic spacetimes are made He discussed in detail some specific spacetime topologies, assuming that, for some of them, they need tachyons for superluminal travel to occur. Since the Alcubierre metric was not originally advanced as a solution of the Einstein equations, but as an ad hoc proposal aimed at allowing for superluminal global speeds for particles, our aim here is to investigate if the dust energy–momentum tensor, the simplest source matter distribution for the Einstein equations, is able to create a superluminal warp field. We discuss in detail the dust matter distribution together with the Alcubierre warp drive metric For this matter source the solutions of the Einstein equations require a zero matter density, i.e., vacuum. Appendix I contains a brief description of the Burgers equation
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