"Negative curvature" isn't quite the right term. (For one thing, curvature in 4-dimensional spacetime cannot be described by a single number.) The Alcubierre dr

"Negative curvature" isn't quite the right term. (For one thing, curvature in 4-dimensional spacetime cannot be described by a single number.) The Alcubierre drive requires "exotic matter", i.e., matter that violates the weak energy condition. One way of phrasing that condition is that the matter will have negative average energy density as measured by certain observers.