Spacewarp is one of three proposed methods of moving between events in spacetime faster than the speed of light. The idea was first proposed by Miguel Alcubierre, a doctoral candidate at the University of Wales.
The premise involves creating sufficient negative energy in front of a vessel to contract space while accumulating positive energy behind the vessel to expand space. This would theoretically create a wave to propel the vessel forward in a locally-stable region of spacetime.
Significant problems with the theoretical potential of this form of propulsion have been noted. Most significantly are the restrictions of quantum inequality (uncertainty principle-type inequalities that place limits on the magnitude and duration of negative energy fluxes due to quantum coherence), noted by Ford and Roman in 1995. Additionally, the rapid accumulation of large energy fluxes would appear to violate the strong, dominant and weak energy conditions.
Many of the problems with the Alcubierre drive were resolved by Chris Van Den Broeck in 1999 in a paper also published in Classical and Quantum Gravity. By contracting the 3+1 dimensional surface area of the 'bubble' being transported by the drive, while at the same time expanding 3 dimensional the volume contained inside, Van Den Broeck was able to reduce the total energy needed to transport small atoms to less than 3 solar masses.
Later work by González-Díaz resolved the problem of quantum instability; at least for 2 dimensions. In his paper published in Physical Review D, Vol. 62, González-Díaz proposed considering closed, time-like curves. This refinement allows for multiply-connected spaces, closing the geodesic incompletemeness and satisfying quantum instability requirements.
Recently Boris Vulfson applied for and was issued a patent for a device he claims works just like an alcubierre drive.