>>12996933>>12996968>>12996997Make up any metric, and you can back-derive a stress-tensor which makes this metric. Now consider any geodesic in space-time. You can make it's length arbitrarily short by just making the metric small along this geodesic, and patch it on to the exterior solution smoothly in some way. If you derive the stress tensor for this, you have an "Alcubierre drive".
This is something everyone realizes when first learning GR. The reason this doesn't work is that there are physical conditions on stress-tensors, the energy conditons, that prevent causality violations such as this. These are only violated in quantum mechanics, and the violations preserve a weaker notion of causality, Mandelstam causality, on asymptotic boundaries.
The Mandelstam causality is enough to ensure no asymptotic signal can outrun light from one edge of space to another edge of space (thinking of infinity), this forbids any type of Alucbierre drive in any realistic quantum gravity. The drive is forbidden by energy conditions in ordinary GR, but people sometimes say quantum mechanics violates the energy conditions. It does in certain respects, but not in this gross way.
