Dust content solutions for the Alcubierre warp drive spacetime

TL;DR

This paper investigates the Einstein equations for the Alcubierre warp drive spacetime with dust matter, revealing that dust solutions lead to vacuum and connect to shock wave equations, providing insights into the physical plausibility of warp drives.

Contribution

It provides the first analysis of the Alcubierre metric as a solution of Einstein equations with dust matter, linking it to shock wave phenomena in fluid dynamics.

Findings

Dust solutions lead to vacuum solutions in the Alcubierre spacetime.

The geometry connects to the Burgers equation describing shock waves.

Shock waves behave as plane waves in this context.

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 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 out 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.