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The Alcubierre warp drive metric is a spacetime geometry featuring aspacetime distortion, called warp bubble, where a massive particle inside itacquires global superluminal velocities, or warp speeds. This work presentssolutions of the Einstein equations for the Alcubierre metric having fluidmatter as gravity source. The energy-momentum tensor considered two fluidcontents, the perfect fluid and the parametrized perfect fluid (PPF), atentative more flexible model whose aim is to explore the possibilities of warpdrive solutions with positive matter density content. Santos-Pereira et al.(2020; arXiv:2008.06560) have already showed that the Alcubierre metric havingdust as source connects this geometry to the Burgers equation, which describesshock waves moving through an inviscid fluid, but led the solutions back tovacuum. The same happened for two out of four solutions subcases for theperfect fluid. Other solutions for the perfect fluid indicate the possibilityof warp drive with positive matter density, but at the cost of a complexsolution for the warp drive regulating function. Regarding the PPF, solutionswere also obtained indicating that warp speeds could be created with positivematter density. Weak, dominant, strong and null energy conditions werecalculated for all studied subcases, being satisfied for the perfect fluid andcreating constraints in the PPF quantities such that positive matter density isalso possible for creating a warp bubble. Summing up allresults,energy-momentum tensors describing more complex forms of matter, orfield, distributions generate solutions for the Einstein equations with thewarp drive metric where negative matter density might not be a strictprecondition for attaining warp speeds.

Fluid dynamics in the warp drive spacetime geometry