Dust content solutions for the Alcubierre warp drive spacetime

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.

Fluid dynamics in the warp drive spacetime geometry

“…In this paper we generalize the results obtained in Ref. [19] by following the next logical step, that is, investigating the perfect fluid as EMT source for the Alcubierre metric. We also propose a slightly generalized perfect fluid EMT, called here the parametrized perfect fluid (PPF), in order to produce a tentatively more flexible model such that the pressure may have different parameter values.…”

“…For the perfect fluid EMT solutions we found that two out of four subcases turn out to be the dust solution of Ref. [19] where both the matter density and the pressure vanish, but the Burgers equation also appears as a result of the solutions of the Einstein equations [29][30][31]. Two other subcases, however, indicate that warp speeds are possible with positive matter density, but at the cost of a complex solution for the warp metric regulating function.…”

“…Besides incoherent matter, or dust, already studied in Ref. [19], the simplest matter-energy distribution to be considered as a gravity source for the possible creation of a warp bubble, and then warp speeds, is the perfect fluid. Hence, this section will discuss matter content solutions of the Einstein equations considering a perfect fluid matter source EMT for the Alcubierre metric.…”

“…In a previous paper [19] we have considered some of these issues, but from a different angle. The Alcubierre metric was not advanced as a solution of the Einstein equations, as it was originally proposed simply as an ad hoc geometry designed to create a spacetime distortion such that a massive particle inside it travels at warp speeds, whereas locally it never exceeds the light speed.…”

Curvature Invariants for the Accelerating Natário Warp Drive

“…Loup expanded Natário's work to encompass a global acceleration [4,5]. Finally, recent research has investigated the Einstein equations for the Alcubierre spacetime with a dust matter distribution as its source [13].…”