Alcubierre warp drive in spherical coordinates with some matter configurations
Gabriel Abellán (Departamento de Física, Facultad de Ciencias, Universidad Central de Venezuela, Av. Los Ilustres, Caracas, 1041-A, Venezuela, Astrum Drive Technologies, 13024 Dallas Pkwy Unit #120 B, Frisco, TX, 75034, USA); Nelson Bolivar (Departamento de Física, Facultad de Ciencias, Universidad Central de Venezuela, Av. Los Ilustres, Caracas, 1041-A, Venezuela, Astrum Drive Technologies, 13024 Dallas Pkwy Unit #120 B, Frisco, TX, 75034, USA, Instituto Balseiro, Centro Atómico Bariloche, Comisión Nacional de Energía Atómica (CNEA), Universidad Nacional de Cuyo (UNCUYO), Bariloche, 8400, Argentina); Ivaylo Vasilev (Astrum Drive Technologies, 13024 Dallas Pkwy Unit #120 B, Frisco, TX, 75034, USA, Technical University of Sofia, Sofia, 1000, Bulgaria)
In this work we introduce the Alcubierre warp metric using spherical symmetry. In this way we write the Einstein equations for a perfect fluid and for an anisotropic fluid with cosmological constant. Analysing the energy conditions for both cases, we find that these cases are flexible enough to allow them to be satisfied. We also find that in the time-independent case of the warp bubble, the metric admits a timelike Killing vector and all the energy conditions are satisfied except for the strong energy condition. Moreover, in the time-independent case a barotropic equation of state known from cosmological models naturally arises.