In one minute

José Rodal computes and visualises the scalar curvature invariants of the Alcubierre warp drive spacetime, from the Weyl and Ricci tensors. Writing the Ricci invariants through the Einstein tensor lets them be read directly in terms of the energy-momentum tensor. Detailed plots show that creating the warp bubble requires four distinct layers of anisotropic stress-energy. He also examines how the Kretschmann quadratic invariant decomposes. He finds that plots in earlier work by Mattingly and colleagues understated the curvature invariants by 8 to 16 orders of magnitude. He compares the drive's curvature with that of a black hole of Saturn's mass and confirms the Alcubierre spacetime is Petrov type I.

Visualization and analysis of the curvature invariants in the Alcubierre warp-drive spacetime