The Alcubierre drive is a speculative warp drive idea according to which a spacecraft could achieve apparent faster-than-light travel by contracting space in front of it and expanding space behind it, under the assumption that a configurable energy-density field lower than that of a vacuum (that is, negative mass) could be created. Proposed by theoretical physicist Miguel Alcubierre in 1994, the Alcubierre drive is based on a solution of Einstein's field equations. Since those solutions are metric tensors, the Alcubierre drive is also referred to as Alcubierre metric. Objects cannot accelerate to the speed of light within normal spacetime; instead, the Alcubierre drive shifts space around an object so that the object would arrive at its destination more quickly than light would in normal space without breaking any physical laws. Although the metric proposed by Alcubierre is consistent with the Einstein field equations, construction of such a drive is not necessarily possible. The proposed mechanism of the Alcubierre drive implies a negative energy density and therefore requires exotic matter or manipulation of dark energy. If exotic matter with the correct properties does not exist, then the drive cannot be constructed. At the close of his original article, however, Alcubierre argued (following an argument developed by physicists analyzing traversable wormholes) that the Casimir vacuum between parallel plates could fulfill the negative-energy requirement for the Alcubierre drive. Another possible issue is that, although the Alcubierre metric is consistent with Einstein's equations, general relativity does not incorporate quantum mechanics. Some physicists have presented arguments to suggest that a theory of quantum gravity (which would incorporate both theories) would eliminate those solutions in general relativity that allow for backward time travel (see the chronology protection conjecture) and thus make the Alcubierre drive invalid. Solitons offer a mathematical 'loophole' in general relativity to theoretically create a warp bubble with positive energy. They move through spacetime, while the bubble itself could move faster than the speed of light. In 1994, Miguel Alcubierre proposed a method for changing the geometry of space by creating a wave that would cause the fabric of space ahead of a spacecraft to contract and the space behind it to expand. The ship would then ride this wave inside a region of flat space, known as a warp bubble, and would not move within this bubble but instead be carried along as the region itself moves due to the actions of the drive. The local velocity relative to the deformed spacetime would be subluminal, but the speed at which a spacecraft could move would be superluminal, thereby rendering possible interstellar flight, such as a visit to Proxima Centauri within a few days. 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, although the amount of energy required is no longer thought to be unobtainably large. However, 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. Furthermore, a study by Remo Garattini and Kirill Zatrimaylov shows that the amount of negative energy density required to sustain a warp bubble can in principle be reduced if the bubble is moving in an external gravitational field, such as that of a black hole. Using the ADM formalism of general relativity, the spacetime is described by a foliation of space-like hypersurfaces of constant coordinate time t, with the metric taking the general form ds² = -(α² - βᵢβⁱ)dt² + 2βᵢdxⁱdt + γᵢⱼdxⁱdxʲ, where α is the lapse function, βⁱ is the shift vector, and γᵢⱼ is a positive-definite metric on each hypersurface. In Alcubierre's formulation: α = 1; βˣ = -vₛ(t)f(rₛ(t)); βʸ = βᶻ = 0; and γᵢⱼ = δᵢⱼ, where vₛ(t) = dxₛ(t)/dt, rₛ(t) = √((x - xₛ(t))² + y² + z²), and f(rₛ) = (tanh(σ(rₛ + R)) - tanh(σ(rₛ - R))) / (2 tanh(σR)) with arbitrary parameters R > 0 and σ > 0. Alcubierre's specific form of the metric is ds² = (vₛ(t)² f(rₛ(t))² - 1)dt² - 2vₛ(t)f(rₛ(t))dx dt + dx² + dy² + dz². From this metric, the energy density measured by observers normal to the hypersurfaces is negative: -(c⁴ / 8πG) * (vₛ²(y² + z²) / (4g²rₛ²)) * (df/drₛ)². Because the energy density is negative, exotic matter is required to travel faster than the speed of light. Astrophysicist Jamie Farnes from the University of Oxford proposed a theory unifying dark energy and dark matter into a single 'dark fluid'. Farnes noted that Albert Einstein explored gravitationally repulsive negative masses while developing general relativity. Farnes' theory relies on negative masses that behave identically to the physics of the Alcubierre drive, providing a potential solution for the cosmic Hubble tension. If correct, this controversial theory could allow closed timelike curves and suggest that an Alcubierre drive is physically possible with exotic matter. Regarding special relativistic effects such as Lorentz contraction and time dilation, a ship using an Alcubierre drive travels on a free-fall geodesic even while accelerating: the crew experiences no g-forces. Severe tidal forces would be present near the edges of the flat-space volume due to high spacetime curvature, but proper metric engineering can keep tidal forces inside the passenger cabin negligible. Rather than deriving spacetime from a known distribution of mass-energy, Alcubierre worked backwards from a specified metric to find the required energy-momentum tensor, resulting in solutions requiring exotic matter and violating energy conditions. Furthermore, Serguei Krasnikov showed that generating a warp bubble in flat spacetime for a one-way superluminal trip requires exotic matter moving at local superluminal velocities (requiring tachyons), unless the required infrastructure is placed in advance along the path by an observer whose forward light cone contains the bubble's entire trajectory. All known warp-drive spacetime theories violate standard energy conditions. Ford and Roman calculated that quantum inequalities would make energy requirements extraordinarily large and negative—potentially equivalent to -10⁶⁴ kg for transporting a small craft across the Milky Way. In 1999, Chris Van Den Broeck modified the metric to contract the surface area while expanding the interior volume, reducing energy requirements to less than three solar masses. In 2003, Serguei Krasnikov reduced the negative mass requirement to a few milligrams. In 2012, Harold White proposed thickening the bubble wall to lower peak energy density, reducing requirements for a macroscopic craft to approximately 700 kg (comparable to Voyager 1). In 2021, Erik Lentz proposed positive-energy warp bubbles based on self-reinforcing solitons, though this remains debated. Because a pilot inside the bubble is causally disconnected from its outer walls, the crew cannot place infrastructure or configure spacetime ahead of the bubble while in transit. Krasnikov and Coule noted that pre-arranging infrastructure along a path requires subluminal placement beforehand, meaning establishing a warp route to Vega (25 light-years away) would take over 25 years before the first trip could be made. José Natário demonstrated that crew members could not steer, control, or stop the warp bubble because signals cannot be transmitted forward across the bubble's boundary. Additionally, a 2009 study by Carlos Barceló, Stefano Finazzi, and Stefano Liberati argued that extreme Hawking radiation at superluminal speeds would destroy everything inside the bubble and destabilize the bubble structure itself. Brendan McMonigal, Geraint F. Lewis, and Philip O'Byrne showed that as a warp bubble travels, it sweeps up interstellar particles. When decelerating upon arrival at the destination, these gathered particles would be released in an extremely energetic, highly blueshifted radiation blast (gamma rays and high-energy particles), potentially annihilating anything directly ahead of the craft. Pfenning and Allen Everett calculated that a warp bubble traveling at 10 times light speed would require an extraordinarily thin wall of approximately 10⁻³² meters (near the Planck length of 1.6 × 10⁻³⁵ meters). Creating and sustaining such extreme boundaries with exotic matter presents profound physical difficulties. Allen Everett demonstrated that warp bubbles can be configured to produce closed timelike curves, enabling backward time travel. The chronology protection conjecture (formulated by Stephen Hawking) suggests quantum back-reaction and vacuum fluctuations would build up uncontrollably at the boundary where time travel becomes possible, causing the system to explode or collapse into a black hole before a causality-violating time machine could operate. The concept and phrase 'warp drive' originated in science fiction, notably John W. Campbell's 1931 novel 'Islands of Space', and was popularized by 'Star Trek'. Miguel Alcubierre acknowledged that his 1994 theoretical paper was directly inspired by the Star Trek term. Subsequent Star Trek franchise media and spin-offs have since retroactively incorporated elements of Alcubierre's real-world spacetime metric theory and warp bubble concepts. Related concepts and physics topics include: EmDrive, Exact solutions in general relativity, IXS Enterprise, Quantum vacuum thruster, Reactionless drive, Spacecraft propulsion, Unruh effect, Closed timelike curves, Krasnikov tube, and Traversable wormholes.