Charged dust solutions for the warp drive spacetime

Abstract

The Alcubierre warp drive metric is a spacetime construction where a massive particle located inside a spacetime distortion, called warp bubble, travels at velocities arbitrarily higher than the velocity of light. This theoretically constructed spacetime geometry is a consequence of general relativity where global superluminal velocities, also known as warp speeds, are possible, whereas local speeds are limited to subluminal ones as required by special relativity. In this work we analyze the solutions of the Einstein equations having charged dust energy-momentum tensor as source for warp velocities. The Einstein equations with the cosmological constant are written and all solutions having energy-momentum tensor components for electromagnetic fields generated by charged dust are presented, as well as the respective energy conditions. The results show an interplay between the energy conditions and the electromagnetic field such that in some cases the former can be satisfied by both positive and negative matter density. In other cases the dominant and null energy conditions are violated. A result connecting the electric energy density with the cosmological constant is also presented, as well as the effects of the electromagnetic field on the bubble dynamics.