Fluid dynamics in the warp drive spacetime geometry

Abstract

The Alcubierre warp drive metric is a spacetime geometry featuring a spacetime distortion, called a 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 has 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. (Eur Phys J C 80:786, 2020) 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 a 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 a negative matter density might not be a strict precondition for attaining warp speeds.

Hyper-Fast Positive Energy Warp Drives

“…There has been a recent uptick in interest regarding warp drives due to a set of papers made available in 2020 and 2021 claiming the construction of solutions that do not require sources with negative energy density [19][20][21][22] , obeying the weak energy condition (WEC). These increasingly physical warp drives were the focus of a mini-session at the 16 th Marcel Grossmann meeting that covered the history of warp drive research in academia, the recent positive energy warp drive research papers, and two articles regarding their reception 23,24 .…”

Obstacles from interstellar matter and distortion for warp drive travel

“…One of the main focuses of this field is to solve the above theoretical puzzles, see for example [16][17][18][19][20][21][22][23][24][25][26].…”

On the total energy conservation of the Alcubierre spacetime

“…Interestingly, in the latter case, an equation was obtained and that resembles the Burgers equation, which describes shock waves moving in a fluid. Latter, a perfect fluid and a charged dust were also considered as a source [11,12].…”