Fluid dynamics in the warp drive spacetime geometry

TL;DR

This paper explores solutions to Einstein's equations for the Alcubierre warp drive metric using fluid matter sources, demonstrating that positive matter density can support warp speeds without requiring negative energy conditions.

Contribution

It introduces new solutions with fluid matter sources, including a parametrized perfect fluid, showing positive matter density can sustain warp drives, expanding the theoretical possibilities beyond negative energy requirements.

Findings

Solutions with perfect fluid and PPF support warp speeds with positive matter density.

Energy conditions are satisfied in certain fluid configurations, allowing positive matter density for warp drives.

Complex matter distributions can generate warp drive solutions without negative matter density.

Abstract

The Alcubierre warp drive metric is a spacetime geometry featuring a spacetime distortion, called warp bubble, where a massive particle inside it acquires global superluminal velocities, or warp speeds. This work presents solutions of the Einstein equations for the Alcubierre metric having fluid matter as gravity source. The energy-momentum tensor considered two fluid contents, the perfect fluid and the parametrized perfect fluid (PPF), a tentative more flexible model whose aim is to explore the possibilities of warp drive solutions with positive matter density content. Santos-Pereira et al. (2020; arXiv:2008.06560) have already showed that the Alcubierre metric having dust as source connects this geometry to the Burgers equation, which describes shock waves moving through an inviscid fluid, but led the solutions back to vacuum. The same happened for two out of four solutions subcases for the perfect fluid. Other solutions for the perfect fluid indicate the possibility of warp drive with positive matter density, but at the cost of a complex solution for the warp drive regulating function. Regarding the PPF, solutions were also obtained indicating that warp speeds could be created with positive matter density. Weak, dominant, strong and null energy conditions were calculated for all studied subcases, being satisfied for the perfect fluid and creating constraints in the PPF quantities such that positive matter density is also possible for creating a warp bubble. Summing up all results,energy-momentum tensors describing more complex forms of matter, or field, distributions generate solutions for the Einstein equations with the warp drive metric where negative matter density might not be a strict precondition for attaining warp speeds.