Warp drive dynamic solutions considering different fluid sources

Alcubierre proposed in 1994 that the well known special relativistic limitation that particles cannot travel with velocities bigger than the light speed can be bypassed when such trips are considered globally within specific general relativistic frameworks. Although initial results indicated this scenario as being unphysical, since it would seem to require negative mass-energy density, recent theoretical analyses suggest that such an unphysical situation may not always be necessarily true. In this paper we review some solutions of the Einstein equations using the original Alcubierre warp drive metric endowed with various matter-energy sources, namely dust, perfect fluid, anisotropic fluid, and perfect fluid with a cosmological constant. A connection of some of these solutions featuring shock waves described by the Burgers equation is also shown.