![]() This warp drive metric is such that a particle trapped inside this bubble would locally move at subluminal speeds, whereas the bubble with the particle inside acquires global superluminal velocities, or warp speeds. It creates a limited spacetime distortion, called warp bubble, such that the spacetime is contracted in front of it and expanded behind the bubble as it moves along a geodesic. The warp drive spacetime geometry advanced by Alcubierre uses these physical properties to propel material particles at superluminal speeds. It is well known that in general relativity particles can travel globally at superluminal speeds, whereas locally they cannot surpass the light speed. 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. 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. Regarding the PPF, solutions were also obtained indicating that warp speeds could be created with positive matter density. 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. The same happened for two out of four solutions subcases for the perfect fluid. ![]() (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 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. ![]() This work presents solutions of the Einstein equations for the Alcubierre metric having fluid matter as gravity source. 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.
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