Membrane models as a means of propulsion in general relativity: super-luminal warp-drive that satisfies the weak energy condition

Abstract

Presented are toy-models for sub-luminal and super-luminal warp-drives in 3+1 dimensions. The models are constructed in a chimeric manner—as different bulk space-times separated by thin membranes. The membranes contain perfect-fluid-like stress-energy tensors. The Israel junction conditions relate this stress-energy to a jump in extrinsic curvature across the brane, which in turn manifests as apparent acceleration in the bulk space-times. The acceleration on either side of the brane may be set individually by choice of model parameters. The Weak Energy Condition (WEC) is shown to be satisfied everywhere in both models. Although the branes in these toy models are not compact, it is demonstrated that super-luminal warp-drive is possible that satisfies the WEC. Additionally, the nature of these models provides framework for speculation on a mechanism for transition from sub-luminal to super-luminal warp. It is shown that the difference in extrinsic curvature across a thin membrane can yield a positive contribution to the Landau–Raychaudhuri equation, thus providing a means to evade some super-luminal warp-drive no-go theorems. Neither quantum effects nor stability of the models is considered.