which a spacecraft could move would be superluminal, thereby rendering possible interstellar flight, such as a visit to Proxima Centauri within a few days. Alcubierre metric The Alcubierre metric defines the warp-drive spacetime. It is a Lorentzian manifold that, if interpreted in the context of general relativity, allows a warp bubble to appear in previously flat spacetime and move away at effectively faster-than-light speed. The interior of the bubble is an inertial reference frame and inhabitants experience no proper acceleration. This method of transport does not involve objects in motion at faster-than-light speeds with respect to the contents of the warp bubble; that is, a light beam within the warp bubble would still always move more quickly than the ship. Because objects within the bubble are not moving (locally) more quickly than light, the mathematical formulation of the Alcubierre metric is consistent with the conventional claims of the laws of relativity (namely, that an object with mass cannot attain or exceed the speed of light) and conventional relativistic effects such as time dilation would not apply as they would with conventional motion at near-light speeds. An extension of the Alcubierre metric that eliminates the expansion of the volume elements and instead relies on the change in distances along the direction of travel is that of mathematician José Natário. In his metric, spacetime contracts towards the prow of the ship and expands in the direction perpendicular to the motion, meaning that the bubble actually "slides" through space, roughly speaking by "pushing space aside". The Alcubierre drive remains a hypothetical concept with seemingly difficult problems, though the amount of energy required is no longer thought to be unobtainably large. Furthermore, Alexey Bobrick and Gianni Martire claim that, in principle, a class of subluminal, spherically symmetric warp drive spacetimes can be constructed based on physical principles presently known to humanity, such as positive energy. Mathematics Using the ADM formalism of general relativity, the spacetime is described by a foliation of space-like hypersurfaces of constant coordinate time , with the metric taking the following general form: where is the lapse function that gives the interval of proper time between nearby hypersurfaces, is the shift vector that relates the spatial coordinate systems on different hypersurfaces, is a positive-definite metric on each of the hypersurfaces. The particular form that Alcubierre studied is defined by: where with arbitrary parameters and . Alcubierre's specific form of the metric