1020:
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1658:, although Krasnikov also notes that when the spacetime is not flat from the outset, a similar result could be achieved without tachyons by placing in advance some devices along the travel path and programming them to come into operation at preassigned moments and to operate in a preassigned manner. Some suggested methods avoid the problem of tachyonic motion, but would probably generate a
1646:. The need for exotic matter raises questions about whether one can distribute the matter in an initial spacetime that lacks a warp bubble in such a way that the bubble is created at a later time, although some physicists have proposed models of dynamical warp-drive spacetimes in which a warp bubble is formed in a previously flat space. Moreover, according to
33:
671:
164:, 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
1787:(donut shape). However, as this less energetic warp bubble also thickens toward the interior region, it leaves less flat space to house the spacecraft, which has to be smaller. Furthermore, if the intensity of the space warp can be oscillated over time, the energy required is reduced even more. According to White, a modified
1821:
the necessary infrastructure. The pilot inside the bubble is causally disconnected from its walls and cannot carry out any action outside the bubble: the bubble cannot be used for the first trip to a distant star because the pilot cannot place infrastructure ahead of the bubble while "in transit". For example, traveling to
660:
1866:, and Philip O'Byrne have argued that were an Alcubierre-driven ship to decelerate from superluminal speed, the particles that its bubble had gathered in transit would be released in energetic outbursts akin to the infinitely-blueshifted radiation hypothesized to occur at the inner event horizon of a
1820:
matter cannot be found or used, then a solution might be to arrange for masses along the path of the vessel to be set in motion in such a way that the required field was produced. But in this case, the
Alcubierre drive vessel can only travel routes that, like a railroad, have first been equipped with
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spacecraft (c. 700 kg) or less, and stated their intent to perform small-scale experiments in constructing warp fields. White proposed to thicken the extremely thin wall of the warp bubble, so the energy is focused in a larger volume, but the overall peak energy density is actually smaller. In a
214:
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. Furthermore, Alexey Bobrick and Gianni Martire claim that, in principle, a class of subluminal, spherically symmetric warp drive
1758:
to a few milligrams. Van Den Broeck detailed this by saying that the total energy can be reduced dramatically by keeping the surface area of the warp bubble itself microscopically small, while at the same time expanding the spatial volume inside the bubble. However, Van Den Broeck concludes that the
1626:
to a certain family of inertial observers, but these observers are not really physically distinguished from other such families. Alcubierre interpreted his "warp bubble" in terms of a contraction of space ahead of the bubble and an expansion behind, but this interpretation could be misleading, since
198:
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
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These results suggest that any ship using an
Alcubierre warp drive carrying people would need shielding to protect them from potential dangerously blueshifted particles during the journey, and any people at the destination would be gamma-ray and high energy particle blasted into oblivion due to the
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could test the idea: one of the legs of the interferometer would appear to have a slightly different length when the test devices were energised. Alcubierre has expressed skepticism about the experiment, saying: "from my understanding there is no way it can be done, probably not for centuries if at
210:
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 Natårio. In his metric, spacetime contracts towards the prow of the ship and expands in the direction
1915:
hypothesizes that in all cases where the classical theory of general relativity allows them, quantum effects would intervene to eliminate the possibility, making these spacetimes impossible to realize. A possible type of effect that would accomplish this is a buildup of vacuum fluctuations on the
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meters. In
Alcubierre's original calculations, a bubble macroscopically large enough to enclose a ship of 200 meters would require a total amount of exotic matter greater than the mass of the observable universe, and straining the exotic matter to an extremely thin band of 10 meters is considered
1729:
conjectured by Ford and Roman hold, the energy requirements for some warp drives may be unfeasibly large as well as negative. For example, the energy equivalent of â10 kg might be required to transport a small spaceship across the Milky Wayâan amount orders of magnitude greater than the estimated
1603:, the Alcubierre metric has some apparently peculiar aspects. In particular, Alcubierre has shown that a ship using an Alcubierre drive travels on a free-fall geodesic even while the warp bubble is accelerating: its crew would be in free fall while accelerating without experiencing accelerational
1933:
and writes: "The conjecture has not been proven (it wouldn't be a conjecture if it had), but there are good arguments in its favor based on quantum field theory. The conjecture does not prohibit faster-than-light travel. It just states that if a method to travel faster than light exists, and one
1795:
In 2021, physicist Erik Lentz described a way warp drives sourced from known and familiar purely positive energy could existâwarp bubbles based on superluminal self-reinforcing "soliton" waves. The claim is controversial, with other physicists arguing that all physically reasonable warp drives
1745:
in
Belgium, in 1999, tried to address the potential issues. By contracting the 3+1-dimensional surface area of the bubble being transported by the drive, while at the same time expanding the three-dimensional volume contained inside, Van Den Broeck was able to reduce the total energy needed to
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1687:
A spaceship appropriately located with respect to the bubble trajectory could then choose to enter the bubble, rather like a passenger catching a passing trolley car, and thus make the superluminal journey ... as
Krasnikov points out, causality considerations do not prevent the crew of a
199:
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
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1928:
Alcubierre briefly discusses some of these issues in a series of lecture slides posted online, where he writes: "beware: in relativity, any method to travel faster than light can in principle be used to travel back in time (a time machine)". In the next slide, he brings up the
1015:{\displaystyle {\begin{aligned}v_{s}(t)&={\frac {dx_{s}(t)}{dt}},\\r_{s}(t)&={\sqrt {{\big (}x-x_{s}(t){\big )}^{2}+y^{2}+z^{2}}},\\f(r_{s})&={\frac {\tanh {\big (}\sigma (r_{s}+R){\big )}-\tanh {\big (}\sigma (r_{s}-R){\big )}}{2\tanh(\sigma R)}},\end{aligned}}}
425:
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As Farnes' theory allows a positive mass (i.e. a ship) to reach a speed equal to the speed of light, it has been dubbed "controversial". If the theory is correct, which has been highly debated in the scientific literature, it would explain dark energy, dark matter, allow
1670:
does not mean that
Alcubierre bubbles, if it were possible to create them, could not be used as a means of superluminal travel. It only means that the actions required to change the metric and create the bubble must be taken beforehand by some observer whose forward
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appear to support the conjecture, including a calculation dealing specifically with quantum effects in warp-drive spacetimes that suggested that warp bubbles would be semiclassically unstable, but ultimately the conjecture can only be decided by a full theory of
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of the intended path of a craft must be placed at superluminal speedâthat constructing an
Alcubierre drive requires an Alcubierre drive even if the metric that allows it is physically meaningful. Coule further argues that an analogous objection will apply to
1952:
television series and films use the term "warp drive" to describe their method of faster-than-light travel. Neither the Alcubierre theory, nor anything similar, existed when the series was conceivedâthe term "warp drive" and general concept originated with
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to travel more quickly than the speed of light. The existence of exotic matter is not theoretically ruled out; however, generating and sustaining enough exotic matter to perform feats such as faster-than-light travel (and to keep open the "throat" of a
462:
1853:
would destroy anything inside the bubble at superluminal velocities and destabilize the bubble itself; the article also argues that these problems are absent if the bubble velocity is subluminal, although the drive still requires exotic matter.
1611:, however, would be present near the edges of the flat-space volume because of the large space curvature there, but a suitable specification of the metric would keep the tidal forces very small within the volume occupied by the ship.
117:. If exotic matter with the correct properties cannot 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
1848:
A 2009 article by Carlos BarcelĂł, Stefano Finazzi, and Stefano Liberati uses quantum theory to argue that the Alcubierre drive at faster-than-light velocities is impossible mostly because extremely high temperatures caused by
1683:(2,600 light-years away) and arrive less than 2,600 years in the future according to external clocks, it would be required that someone had already begun work on warping the space from Earth to Deneb at least 2,600 years ago:
1045:
104:
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
1916:
border of the region of spacetime where time travel would first become possible, causing the energy density to become high enough to destroy the system that would otherwise become a time machine. Some results in
2384:
Alcubierre, following the lead of wormhole theorists, argues that quantum field theory permits the existence of regions of negative energy density under special circumstances, and cites the Casimir effect as an
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1825:(which is 25 light-years from Earth) requires arranging everything so that the bubble moving toward Vega with a superluminal velocity would appear; such arrangements will always take more than 25 years.
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In general relativity, one often first specifies a plausible distribution of matter and energy, and then finds the geometry of the spacetime associated with it; but it is also possible to run the
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1895:. Chris Van den Broeck constructed a modification of Alcubierre's model that requires much less exotic matter but places the ship in a curved spacetime "bottle" whose neck is about 10 meters.
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1845:
An article by José Natårio (2002) argues that crew members could not control, steer or stop the ship in its warp bubble because the ship could not send signals to the front of the bubble.
97:; 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
655:{\displaystyle {\begin{aligned}\alpha &=1,\\\beta ^{x}&=-v_{s}(t)f{\big (}r_{s}(t){\big )},\\\beta ^{y}&=\beta ^{z}=0,\\\gamma _{ij}&=\delta _{ij},\end{aligned}}}
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With this particular form of the metric, it can be shown that the energy density measured by observers whose 4-velocity is normal to the hypersurfaces is given by:
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1618:, which is often used in discussing the initial-value formulation of general relativity. This might explain the widespread misconception that this spacetime is a
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from Earth to a distant star and back in an arbitrarily short time, as measured by clocks on Earth, by altering the metric along the path of their outbound trip.
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3976:
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1734:. Counterarguments to these apparent problems have also been offered, although the energy requirements still generally require a Type III civilization on the
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Visser, Matt (December 1997). "The reliability horizon for semi-classical quantum gravity: Metric fluctuations are often more important than back-reaction".
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that behave identically to the physics of the Alcubierre drive, providing a natural solution for the current "crisis in cosmology" due to a time-variable
36:
Two-dimensional visualization of an Alcubierre drive, showing the opposing regions of expanding and contracting spacetime that displace the central region
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1293:{\displaystyle ds^{2}=\left(v_{s}(t)^{2}f{\big (}r_{s}(t){\big )}^{2}-1\right)\,dt^{2}-2v_{s}(t)f{\big (}r_{s}(t){\big )}\,dx\,dt+dx^{2}+dy^{2}+dz^{2}.}
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79:
194:, 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
1654:
faster-than-light trip requires forcing the exotic matter to move at local faster-than-light speeds, something that would require the existence of
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2109:
4150:
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Farnes, J. S. (2018). "A Unifying Theory of Dark Energy and Dark Matter: Negative Masses and Matter Creation within a Modified ÎCDM Framework".
128:
Another possible issue is that, although the Alcubierre metric is consistent with Einstein's equations, general relativity does not incorporate
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that his theory was directly inspired by the term used in the show and cites the "'warp drive' of science fiction" in his 1994 article. A USS
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Krasnikov (2003), p. 13, "Moreover, by analogy with the Casimir effect, it is reasonable to assume that Ï in such a wormhole will be large (~
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2010:
1710:. Nevertheless, an Alcubierre-type warp drive might be realized by exploiting certain experimentally verified quantum phenomena, such as the
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hold that a warp bubble traveling at 10-times the speed of light must have a wall thickness of no more than 10 metersâclose to the limiting
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136:(which would incorporate both theories) would eliminate those solutions in general relativity that allow for backward time travel (see the
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1473:{\displaystyle -{\frac {c^{4}}{8\pi G}}{\frac {v_{s}^{2}\left(y^{2}+z^{2}\right)}{4g^{2}r_{s}^{2}}}\left({\frac {df}{dr_{s}}}\right)^{2},}
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1503:) is thought to be impractical. According to writer Robert Low, within the context of general relativity it is impossible to construct a
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Ford and Roman (1995), p.5, "...the Casimir effect may be useful as an illustration. Here one has a constant negative energy density..."
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tries to use it to build a time machine, something will go wrong: the energy accumulated will explode, or it will create a black hole."
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series have made closer use of the theory behind the Alcubierre Drive incorporating warp bubbles/fields into the in-universe science.
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associated with it, and this is what Alcubierre did in building his metric. This practice means that the solution can violate various
83:
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3990:
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BarcelĂł, Carlos; Finazzi, Stefano; Liberati, Stefano (2010). "On the impossibility of superluminal travel: the warp drive lesson".
1870:; forward-facing particles would thereby be energetic enough to destroy anything at the destination directly in front of the ship.
420:{\displaystyle ds^{2}=-\left(\alpha ^{2}-\beta _{i}\beta ^{i}\right)\,dt^{2}+2\beta _{i}\,dx^{i}\,dt+\gamma _{ij}\,dx^{i}\,dx^{j},}
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Pfenning, Michael John (1998). "Quantum Inequality Restrictions on Negative Energy Densities in Curved Spacetimes". p. 1692.
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perpendicular to the motion, meaning that the bubble actually "slides" through space, roughly speaking by "pushing space aside".
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Agnew, J. (16 August 2019). "An Examination of Warp Theory and Technology to Determine the State of the Art and Feasibility".
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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
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McMonigal, Brendan; Lewis, Geraint F.; O'Byrne, Philip (20 March 2012). "Alcubierre warp drive: On the matter of matter".
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the contraction and expansion actually refer to the relative motion of nearby members of the family of ADM observers.
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The metric of this form has significant difficulties because all known warp-drive spacetime theories violate various
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5289:
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Finazzi, Stefano; Liberati, Stefano; BarcelĂł, Carlos (2009). "Semiclassical instability of dynamical warp drives".
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travel by contracting space in front of it and expanding space behind it, under the assumption that a configurable
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spacetimes can be constructed based on physical principles presently known to humanity, such as positive energy.
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flat 2D representation, the ring of positive and negative energy, initially very thin, becomes a larger, fuzzy
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The amount of negative energy required for such a propulsion is not yet known. Pfenning and Allen Everett of
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energy densities required are still unachievable, as are the small size (a few orders of magnitude above the
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Coule has argued that schemes, such as the one proposed by Alcubierre, are infeasible because matter placed
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could reduce the massâenergy requirements for a macroscopic space ship from the equivalent of the planet
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4017:"Star Trek Adventures: A Star Beyond the Stars â Modiphius | Star Trek Adventures | DriveThruRPG.com"
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Ford, L. H.; Roman, T. A. (1996). "Quantum field theory constrains traversable wormhole geometries".
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had explored the idea of gravitationally repulsive negative masses while developing the equations of
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1911:. While it is possible that the fundamental laws of physics might allow closed timelike curves, the
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Lobo, Francisco S. N.; Visser, Matt (2004). "Fundamental limitations on 'warp drive' spacetimes".
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between parallel plates could fulfill the negative-energy requirement for the Alcubierre drive.
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Van Den Broeck, Chris (1999). "A 'warp drive' with more reasonable total energy requirements".
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in general relativity, meaning that the theory predicts that they could be used for backwards
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2699:"Bringing balance to the universe: New theory could explain missing 95 percent of the cosmos"
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at the front of the bubble. Allen Everett and Thomas Roman comment on Krasnikov's finding (
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is the shift vector that relates the spatial coordinate systems on different hypersurfaces,
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Alcubierre, Miguel (1994). "The warp drive: hyper-fast travel within general relativity".
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is the lapse function that gives the interval of proper time between nearby hypersurfaces,
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Calculations by physicist Allen Everett show that warp bubbles could be used to create
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106:
59:
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Hiscock, William A. (1997). "Quantum effects in the Alcubierre warp drive spacetime".
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Van den Broeck, Christian (2000). "Alcubierre's warp drive: Problems and prospects".
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Krasnikov, S. (2003). "The quantum inequalities do not forbid spacetime shortcuts".
2110:"Scientists Are Starting to Take Warp Drives Seriously, Especially This One Concept"
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4086:
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Pfenning, Michael J.; Ford, L. H. (1997). "The unphysical nature of 'Warp Drive'".
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Everett, Allen; Roman, Thomas (1997). "A Superluminal Subway: The Krasnikov Tube".
2684:
2301:
2039:
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240:
3529:"Breaking the warp barrier: hyper-fast solitons in EinsteinâMaxwell-plasma theory"
3153:), which would relieve one of having to seek additional sources of exotic matter."
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3476:"Spacecraft in a 'warp bubble' could travel faster than light, claims physicist"
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has equal amounts of positive and negative qualities. Farnes' theory relies on
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would not apply as they would with conventional motion at near-light speeds.
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3503:"There's light-speed travel in 'Star Wars' and 'Star Trek.' Is it possible?"
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The original warp-drive metric and simple variants of it happen to have the
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2772:"Astrophysicist claims "dark fluid" fills the missing 95% of the Universe"
2454:. Fundamental Theories of Physics. Vol. 189. Cham. pp. 257â279.
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has proposed a theory, published in the peer-reviewed scientific journal
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Van den Broeck, Chris (1999). "On the (im)possibility of warp bubbles".
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Alcubierre, Miguel; Lobo, Francisco S. N. (2017). "Warp Drive Basics".
2013:(for more on the sense in which the Alcubierre spacetime is a solution)
2005:
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in the other direction, first specifying a metric and then finding the
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With regard to certain specific effects of special relativity, such as
132:. Some physicists have presented arguments to suggest that a theory of
32:
4217:
4110:
4061:
3905:
3798:
3306:
3251:
3188:
3136:
3073:
2977:
2927:
2869:
2659:
2276:
2148:
4989:
4254:
1622:
of the field equation of general relativity. Metrics in ADM form are
1560:
1488:
63:
2793:"Can a negative-mass cosmology explain dark matter and dark energy?"
1583:), and suggest that an Alcubierre drive is physically possible with
3671:
3653:
Jessica Santiago; Sebastian Schuster; Mark Visser (15 March 2022).
3545:
2809:
2732:
2596:
2460:
156:
by creating a wave that would cause the fabric of space ahead of a
3876:
3749:
2210:
1784:
1750:. Later in 2003, by slightly modifying the Van den Broeck metric,
1680:
31:
4188:
A short video clip of the hypothetical effects of the warp drive.
2911:
Krasnikov, S. (1998). "Hyper-fast travel in general relativity".
4970:
1822:
1039:. Alcubierre's specific form of the metric can thus be written:
4554:
4271:
1722:, when described in the context of the quantum field theories.
4267:
4199:
GonzĂĄlez-DĂaz, Pedro (14 July 2000). "Warp Drive Space-Time".
3375:"Nasa physicist says warp drive is more feasible than thought"
3354:
2557:"Warp Drive May Be More Feasible Than Thought, Scientists Say"
1688:
spaceship from arranging, by their own actions, to complete a
93:
Objects cannot accelerate to the speed of light within normal
4550:
4172:"Can We Travel Faster Than Light? with Dr. Miguel Alcubierre"
2643:
Low, Robert J. (1999). "Speed Limits in General Relativity".
1559:, an idea which leads to a "beautiful" hypothesis where the
54:
idea according to which a spacecraft could achieve apparent
1770:
and collaborators announced that modifying the geometry of
456:
The particular form that Alcubierre studied is defined by:
452:
is a positive-definite metric on each of the hypersurfaces.
1718:
that also violate the energy conditions, such as negative
3975:
J. Gardiner, "Warp Drive â From Imagination to Reality",
2317:"Wormholes, Time Machines, and the Weak Energy Condition"
3628:"Breaking the warp barrier for faster-than-light travel"
2853:
Natario, Jose (2002). "Warp drive with zero expansion".
1494:
Thus, because the energy density is negative, one needs
74:
in 1994, the Alcubierre drive is based on a solution of
3655:"Generic warp drives violate the null energy condition"
3458:"2013 Starship Congress: Warp Field Physics, an Update"
1650:, generating a bubble in a previously flat space for a
70:) could be created. Proposed by theoretical physicist
1837:
proposed method of constructing an Alcubierre drive.
1312:
1048:
674:
465:
256:
247:, with the metric taking the following general form:
2315:
Thorne, Kip; Michael Morris; Ulvi Yurtsever (1988).
5222:
5087:
5059:
4928:
4877:
4839:
4818:
4807:
4765:
4709:
4693:
4635:
4599:
4588:
4480:
4437:
4401:
4378:
4341:
4305:
2578:Bobrick, Alexey; Martire, Gianni (20 April 2021).
1472:
1292:
1014:
654:
419:
3110:
3108:
2550:
2548:
2546:
2544:
1899:Causality violation and semiclassical instability
4255:"Skeptoid #922: Testing Alcubierre's Warp Drive"
3350:"How NASA might build its very first warp drive"
2906:
2904:
27:Hypothetical FTL transportation by warping space
2400:Fil'chenkov, M.; Laptev, Yu. (1 October 2017).
2127:
2125:
2123:
2065:AIAA Propulsion and Energy Forum and Exposition
2057:
2055:
4193:Marcelo B. Ribeiro's Page on Warp Drive Theory
3437:Miguel Alcubierre's Twitter feed, 29 July 2013
3052:
3050:
1547:, and which is expected to be testable by the
140:) and thus make the Alcubierre drive invalid.
86:, the Alcubierre drive is also referred to as
4566:
4283:
3977:Journal of the British Interplanetary Society
3712:"Warp Drives May Come With a Killer Downside"
3601:"Star Trek's Warp Drive Leads to New Physics"
3405:Journal of the British Interplanetary Society
2103:
2101:
1675:contains the entire trajectory of the bubble.
1220:
1194:
1128:
1101:
974:
942:
926:
894:
811:
778:
560:
534:
8:
2452:Wormholes, Warp Drives and Energy Conditions
2255:
2253:
2251:
2249:
2247:
2245:
3780:extreme blueshifts for P+ region particles.
2402:"Galaxy travel via Alcubierre's warp drive"
4815:
4596:
4573:
4559:
4551:
4290:
4276:
4268:
4167:It describes the concept in laymans terms.
4151:"Ideas Based on What We'd Like To Achieve"
2500:: CS1 maint: location missing publisher (
1891:impractical. Similar constraints apply to
4216:
4109:
4060:
3904:
3875:
3797:
3748:
3670:
3544:
3305:
3250:
3187:
3072:
2976:
2966:
2964:
2962:
2926:
2868:
2826:
2808:
2731:
2658:
2595:
2459:
2275:
2209:
2189:
2187:
2185:
2183:
2147:
1746:transport small atoms to less than three
1511:Connection to dark energy and dark matter
1461:
1448:
1430:
1416:
1411:
1401:
1381:
1368:
1353:
1348:
1341:
1322:
1316:
1311:
1281:
1265:
1249:
1232:
1225:
1219:
1218:
1203:
1193:
1192:
1174:
1158:
1150:
1133:
1127:
1126:
1110:
1100:
1099:
1090:
1074:
1056:
1047:
973:
972:
957:
941:
940:
925:
924:
909:
893:
892:
883:
867:
842:
829:
816:
810:
809:
793:
777:
776:
774:
752:
715:
705:
683:
675:
673:
636:
616:
593:
576:
559:
558:
543:
533:
532:
514:
494:
466:
464:
408:
400:
394:
386:
377:
363:
357:
349:
343:
327:
319:
308:
298:
285:
264:
255:
2990:
2988:
2382:from the original on 21 September 2012.
1679:For example, if one wanted to travel to
2051:
190:that, if interpreted in the context of
3724:from the original on 10 December 2012.
3464:from the original on 20 November 2013.
3343:
3341:
2555:Moskowitz, Clara (17 September 2012).
2525:10.7208/chicago/9780226225005.001.0001
2515:Everett, Allen; Roman, Thomas (2011).
2493:
2363:from the original on 23 February 2011.
1763:) of the spacetime structures needed.
1754:reduced the necessary total amount of
5447:Exact solutions in general relativity
3859:from the original on 12 October 2013.
3362:from the original on 10 January 2013.
2848:
2846:
2567:from the original on 13 January 2013.
2011:Exact solutions in general relativity
45:
7:
3426:from the original on 9 October 2022.
3348:Dvorsky, George (26 November 2012).
2445:
2443:
2395:
2393:
5145:TolmanâOppenheimerâVolkoff equation
5098:FriedmannâLemaĂźtreâRobertsonâWalker
1963:. Alcubierre stated in an email to
152:proposed a method for changing the
4323:Novikov self-consistency principle
3813:Everett, Allen E. (15 June 1996).
3632:Georg-August-UniversitÀt Göttingen
3385:from the original on 8 April 2016.
2580:"Introducing physical warp drives"
25:
4915:HamiltonâJacobiâEinstein equation
3710:Major, Jason (29 February 2012).
2791:Socas-Navarro, H. (30 May 2019).
2374:Cramer, John G. (15 April 1996).
1507:in the absence of exotic matter.
1487:is the determinant of the metric
5393:
5392:
4333:Quantum mechanics of time travel
4313:Chronology protection conjecture
3456:White, Harold (17 August 2013).
1931:chronology protection conjecture
1913:chronology protection conjecture
138:chronology protection conjecture
3527:Lentz, Erik W. (9 March 2021).
2519:. University of Chicago Press.
2426:10.1016/j.actaastro.2017.07.011
2108:Williams, Matt (1 March 2020).
1893:Krasnikov's superluminal subway
1841:Survivability inside the bubble
1789:MichelsonâMorley interferometer
1732:mass of the observable universe
1551:around 2030. Farnes found that
4722:Massâenergy equivalence (E=mc)
3979:, vol. 61, pp. 353â357 (2008).
3501:Dunham, Will (11 March 2021).
1986:Star Trek: The Original Series
1957:'s 1931 science fiction novel
1858:Damaging effect on destination
1743:Katholieke Universiteit Leuven
1215:
1209:
1186:
1180:
1122:
1116:
1087:
1080:
999:
990:
969:
950:
921:
902:
873:
860:
805:
799:
764:
758:
727:
721:
695:
689:
555:
549:
526:
520:
1:
4429:Parallel universes in fiction
4178:. Event Horizon. 6 June 2019.
4097:Classical and Quantum Gravity
4048:Classical and Quantum Gravity
3923:10.1016/S0370-2693(97)01226-4
3599:Gast, Robert (October 2021).
3533:Classical and Quantum Gravity
3293:Classical and Quantum Gravity
3238:Classical and Quantum Gravity
3005:Classical and Quantum Gravity
2856:Classical and Quantum Gravity
2646:Classical and Quantum Gravity
2584:Classical and Quantum Gravity
2263:Classical and Quantum Gravity
4439:Philosophy of space and time
2797:Astronomy & Astrophysics
2720:Astronomy & Astrophysics
2478:10.1007/978-3-319-55182-1_11
1741:Chris Van Den Broeck of the
1532:Astronomy & Astrophysics
243:of constant coordinate time
4737:Relativistic Doppler effect
4128:10.1088/0264-9381/21/24/011
4079:10.1088/0264-9381/14/11/002
3991:"The Physics of Warp Drive"
3689:10.1103/PhysRevD.105.064038
3324:10.1088/0264-9381/16/12/314
2828:10.1051/0004-6361/201935317
2750:10.1051/0004-6361/201832898
2517:Time Travel and Warp Drives
2376:"The Alcubierre Warp Drive"
2346:10.1103/PhysRevLett.61.1446
1816:Krasnikov proposed that if
5463:
5208:In computational physics:
4732:Relativity of simultaneity
4419:Many-worlds interpretation
4306:General terms and concepts
4235:10.1103/PhysRevD.62.044005
3815:"Warp drive and causality"
3767:10.1103/PhysRevD.85.064024
3398:"Warp Field Mechanics 101"
3269:10.1088/0264-9381/14/7/011
3117:AIP Conference Proceedings
3026:10.1088/0264-9381/15/8/026
2887:10.1088/0264-9381/19/6/308
2677:10.1088/0264-9381/16/2/016
2294:10.1088/0264-9381/11/5/001
2228:10.1103/PhysRevD.79.124017
2166:10.1103/PhysRevD.67.104013
1514:
1025:with arbitrary parameters
76:Einstein's field equations
5390:
5045:LenseâThirring precession
4627:Doubly special relativity
4209:American Physical Society
62:field lower than that of
4905:Post-Newtonian formalism
4895:Einstein field equations
4831:Mathematical formulation
4655:Hyperbolic orthogonality
4328:Self-fulfilling prophecy
3842:10.1103/PhysRevD.53.7365
3563:10.1088/1361-6382/abe692
3206:10.1103/PhysRevD.53.5496
3091:10.1103/PhysRevD.56.2100
2945:10.1103/PhysRevD.57.4760
2614:10.1088/1361-6382/abdf6e
1632:Einstein field equations
196:inertial reference frame
5437:Hypothetical technology
4616:Galilean transformation
4607:Principle of relativity
3460:. Icarus Interstellar.
2819:2019A&A...626A...5S
2742:2018A&A...620A..92F
2325:Physical Review Letters
2025:Quantum vacuum thruster
1983:. Since the release of
1702:Massâenergy requirement
182:defines the warp-drive
109:and therefore requires
5432:Science fiction themes
4701:Lorentz transformation
4492:closed timelike curves
4343:Time travel in fiction
4153:. NASA. Archived from
3442:9 January 2014 at the
3396:White, Harold (2013).
1905:closed timelike curves
1800:, as well as both the
1694:
1677:
1636:energyâmomentum tensor
1577:closed timelike curves
1549:Square Kilometre Array
1474:
1294:
1016:
656:
421:
37:
5169:WeylâLewisâPapapetrou
4910:Raychaudhuri equation
4849:Equivalence principle
4540:Traversable wormholes
4318:Closed timelike curve
2995:Coule, D. H. (1998).
2035:Spacecraft propulsion
1918:semiclassical gravity
1798:weak energy condition
1716:stressâenergy tensors
1685:
1668:
1475:
1295:
1017:
657:
422:
35:
5427:Lorentzian manifolds
5210:Numerical relativity
5051:pulsar timing arrays
4351:Timelines in fiction
4021:www.drivethrurpg.com
3665:(6) 064038: 064038.
1980:Star Trek Adventures
1727:quantum inequalities
1527:University of Oxford
1310:
1046:
672:
463:
254:
47:[alkuËÎČjere]
5417:Interstellar travel
5102:Friedmann equations
4996:HulseâTaylor binary
4958:Gravitational waves
4854:Riemannian geometry
4680:Proper acceleration
4665:Maxwell's equations
4611:Galilean relativity
4388:Grandfather paradox
4253:(6 February 2024).
4227:2000PhRvD..62d4005G
4182:John Michael Godier
4120:2004CQGra..21.5871L
4071:1997CQGra..14L.183H
3945:"Faster than light"
3915:1997PhLB..415....8V
3834:1996PhRvD..53.7365E
3759:2012PhRvD..85f4024M
3681:2022PhRvD.105f4038S
3606:Scientific American
3555:2021CQGra..38g5015L
3417:2013JBIS...66..242W
3316:1999CQGra..16.3973V
3261:1997CQGra..14.1743P
3198:1996PhRvD..53.5496F
3129:2000AIPC..504.1105V
3083:1997PhRvD..56.2100E
3018:1998CQGra..15.2523C
2937:1998PhRvD..57.4760K
2879:2002CQGra..19.1157N
2669:1999CQGra..16..543L
2606:2021CQGra..38j5009B
2470:2017FTP...189..257A
2418:2017AcAau.139..254F
2338:1988PhRvL..61.1446M
2286:1994CQGra..11L..73A
2220:2009PhRvD..79l4017F
2158:2003PhRvD..67j4013K
2074:10.2514/6.2019-4288
1862:Brendan McMonigal,
1812:Placement of matter
1808:energy conditions.
1766:In 2012, physicist
1597:Lorentz contraction
1421:
1358:
188:Lorentzian manifold
170:within a few days.
113:or manipulation of
50:) is a speculative
5442:1994 introductions
5151:ReissnerâNordström
5069:BransâDicke theory
4900:Linearized gravity
4727:Length contraction
4645:Frame of reference
4622:Special relativity
4486:general relativity
4409:Alternative future
4402:Parallel timelines
4380:Temporal paradoxes
4356:in science fiction
2780:. 29 October 2019.
2707:. 5 December 2018.
2030:Reactionless drive
1557:general relativity
1470:
1407:
1344:
1290:
1012:
1010:
652:
650:
417:
235:is described by a
229:general relativity
192:general relativity
38:
5422:Warp drive theory
5404:
5403:
5218:
5217:
5197:OzsvĂĄthâSchĂŒcking
4803:
4802:
4785:Minkowski diagram
4742:Thomas precession
4685:Relativistic mass
4548:
4547:
4500:Alcubierre metric
4414:Alternate history
4201:Physical Review D
4104:(24): 5871â5892.
4055:(11): L183âL188.
3893:Physics Letters B
3828:(12): 7365â7368.
3822:Physical Review D
3737:Physical Review D
3659:Physical Review D
3300:(12): 3973â3979.
3182:(10): 5496â5507.
3175:Physical Review D
3137:10.1063/1.1290913
3060:Physical Review D
2914:Physical Review D
2534:978-0-226-04548-1
2487:978-3-319-55181-4
2406:Acta Astronautica
2332:(13): 1446â1449.
2197:Physical Review D
2135:Physical Review D
2083:978-1-62410-590-6
1851:Hawking radiation
1752:Serguei Krasnikov
1708:energy conditions
1660:naked singularity
1648:Serguei Krasnikov
1640:energy conditions
1455:
1423:
1339:
1003:
848:
739:
174:Alcubierre metric
154:geometry of space
150:Miguel Alcubierre
130:quantum mechanics
88:Alcubierre metric
72:Miguel Alcubierre
56:faster-than-light
18:Alcubierre metric
16:(Redirected from
5454:
5396:
5395:
5179:van Stockum dust
4951:Two-body problem
4869:Mach's principle
4816:
4757:Terrell rotation
4597:
4575:
4568:
4561:
4552:
4535:van Stockum dust
4447:Butterfly effect
4292:
4285:
4278:
4269:
4264:
4246:
4220:
4179:
4166:
4164:
4162:
4139:
4113:
4090:
4064:
4032:
4031:
4029:
4027:
4013:
4007:
4006:
4004:
4002:
3997:on 24 April 2013
3993:. Archived from
3986:
3980:
3973:
3967:
3966:
3964:
3962:
3957:on 18 March 2016
3956:
3950:. Archived from
3949:
3941:
3935:
3934:
3908:
3888:
3882:
3881:
3879:
3867:
3861:
3860:
3858:
3819:
3810:
3804:
3803:
3801:
3789:
3783:
3782:
3752:
3732:
3726:
3725:
3707:
3701:
3700:
3674:
3650:
3644:
3643:
3641:
3639:
3624:
3618:
3617:
3615:
3613:
3596:
3590:
3589:
3587:
3585:
3548:
3524:
3518:
3517:
3515:
3513:
3498:
3492:
3491:
3489:
3487:
3472:
3466:
3465:
3453:
3447:
3434:
3428:
3427:
3425:
3402:
3393:
3387:
3386:
3370:
3364:
3363:
3345:
3336:
3335:
3309:
3287:
3281:
3280:
3254:
3245:(7): 1743â1751.
3232:
3226:
3225:
3191:
3169:
3163:
3160:
3154:
3147:
3141:
3140:
3112:
3103:
3102:
3076:
3067:(4): 2100â2108.
3054:
3045:
3044:
3043:on 27 June 2007.
3042:
3036:. Archived from
3012:(8): 2523â2537.
3001:
2992:
2983:
2982:
2980:
2968:
2957:
2956:
2930:
2921:(8): 4760â4766.
2908:
2899:
2898:
2872:
2863:(6): 1157â1166.
2850:
2841:
2840:
2830:
2812:
2788:
2782:
2781:
2768:
2762:
2761:
2735:
2715:
2709:
2708:
2695:
2689:
2688:
2662:
2640:
2634:
2633:
2599:
2575:
2569:
2568:
2552:
2539:
2538:
2512:
2506:
2505:
2499:
2491:
2463:
2447:
2438:
2437:
2397:
2388:
2387:
2371:
2365:
2364:
2362:
2321:
2312:
2306:
2305:
2279:
2257:
2240:
2239:
2213:
2191:
2178:
2177:
2151:
2129:
2118:
2117:
2114:ScienceAlert.com
2105:
2096:
2095:
2059:
1960:Islands of Space
1955:John W. Campbell
1889:
1864:Geraint F. Lewis
1569:Hubble parameter
1486:
1479:
1477:
1476:
1471:
1466:
1465:
1460:
1456:
1454:
1453:
1452:
1439:
1431:
1424:
1422:
1420:
1415:
1406:
1405:
1392:
1391:
1387:
1386:
1385:
1373:
1372:
1357:
1352:
1342:
1340:
1338:
1327:
1326:
1317:
1299:
1297:
1296:
1291:
1286:
1285:
1270:
1269:
1254:
1253:
1224:
1223:
1208:
1207:
1198:
1197:
1179:
1178:
1163:
1162:
1149:
1145:
1138:
1137:
1132:
1131:
1115:
1114:
1105:
1104:
1095:
1094:
1079:
1078:
1061:
1060:
1038:
1031:
1021:
1019:
1018:
1013:
1011:
1004:
1002:
979:
978:
977:
962:
961:
946:
945:
930:
929:
914:
913:
898:
897:
884:
872:
871:
849:
847:
846:
834:
833:
821:
820:
815:
814:
798:
797:
782:
781:
775:
757:
756:
740:
738:
730:
720:
719:
706:
688:
687:
661:
659:
658:
653:
651:
644:
643:
624:
623:
598:
597:
581:
580:
564:
563:
548:
547:
538:
537:
519:
518:
499:
498:
451:
442:
436:
426:
424:
423:
418:
413:
412:
399:
398:
385:
384:
362:
361:
348:
347:
332:
331:
318:
314:
313:
312:
303:
302:
290:
289:
269:
268:
246:
203:effects such as
167:Proxima Centauri
49:
42:Alcubierre drive
21:
5462:
5461:
5457:
5456:
5455:
5453:
5452:
5451:
5407:
5406:
5405:
5400:
5386:
5214:
5118:BKL singularity
5108:LemaĂźtreâTolman
5083:
5079:Quantum gravity
5061:
5055:
5041:geodetic effect
5015:(together with
4985:LISA Pathfinder
4924:
4873:
4859:Penrose diagram
4841:
4835:
4810:
4799:
4795:Minkowski space
4761:
4705:
4689:
4637:
4631:
4591:
4584:
4579:
4549:
4544:
4530:Tipler cylinder
4489:
4476:
4433:
4397:
4374:
4337:
4301:
4296:
4249:
4198:
4170:
4160:
4158:
4157:on 9 April 2013
4149:
4146:
4093:
4044:
4041:
4036:
4035:
4025:
4023:
4015:
4014:
4010:
4000:
3998:
3989:Shapiro, Alan.
3988:
3987:
3983:
3974:
3970:
3960:
3958:
3954:
3947:
3943:
3942:
3938:
3890:
3889:
3885:
3869:
3868:
3864:
3856:
3817:
3812:
3811:
3807:
3791:
3790:
3786:
3734:
3733:
3729:
3709:
3708:
3704:
3652:
3651:
3647:
3637:
3635:
3626:
3625:
3621:
3611:
3609:
3598:
3597:
3593:
3583:
3581:
3526:
3525:
3521:
3511:
3509:
3500:
3499:
3495:
3485:
3483:
3482:. 19 March 2021
3474:
3473:
3469:
3455:
3454:
3450:
3444:Wayback Machine
3435:
3431:
3423:
3400:
3395:
3394:
3390:
3373:Steadman, Ian.
3372:
3371:
3367:
3347:
3346:
3339:
3289:
3288:
3284:
3234:
3233:
3229:
3171:
3170:
3166:
3161:
3157:
3148:
3144:
3114:
3113:
3106:
3056:
3055:
3048:
3040:
2999:
2997:"No warp drive"
2994:
2993:
2986:
2970:
2969:
2960:
2910:
2909:
2902:
2852:
2851:
2844:
2790:
2789:
2785:
2770:
2769:
2765:
2717:
2716:
2712:
2697:
2696:
2692:
2642:
2641:
2637:
2577:
2576:
2572:
2554:
2553:
2542:
2535:
2514:
2513:
2509:
2492:
2488:
2449:
2448:
2441:
2399:
2398:
2391:
2373:
2372:
2368:
2360:
2319:
2314:
2313:
2309:
2259:
2258:
2243:
2193:
2192:
2181:
2131:
2130:
2121:
2107:
2106:
2099:
2084:
2061:
2060:
2053:
2048:
2002:
1971:appears in the
1965:William Shatner
1944:
1923:quantum gravity
1901:
1887:
1876:
1868:Kerr black hole
1860:
1843:
1814:
1778:to that of the
1736:Kardashev scale
1714:, that lead to
1704:
1699:
1593:
1565:negative masses
1553:Albert Einstein
1535:, that unifies
1521:Astrophysicist
1519:
1513:
1484:
1444:
1440:
1432:
1426:
1425:
1397:
1393:
1377:
1364:
1363:
1359:
1343:
1328:
1318:
1308:
1307:
1277:
1261:
1245:
1199:
1170:
1154:
1125:
1106:
1086:
1070:
1069:
1065:
1052:
1044:
1043:
1033:
1026:
1009:
1008:
980:
953:
905:
885:
876:
863:
854:
853:
838:
825:
808:
789:
767:
748:
745:
744:
731:
711:
707:
698:
679:
670:
669:
649:
648:
632:
625:
612:
609:
608:
589:
582:
572:
569:
568:
539:
510:
500:
490:
487:
486:
473:
461:
460:
450:
446:
440:
434:
404:
390:
373:
353:
339:
323:
304:
294:
281:
280:
276:
260:
252:
251:
244:
221:
178:The Alcubierre
176:
146:
134:quantum gravity
28:
23:
22:
15:
12:
11:
5:
5460:
5458:
5450:
5449:
5444:
5439:
5434:
5429:
5424:
5419:
5409:
5408:
5402:
5401:
5391:
5388:
5387:
5385:
5384:
5377:
5372:
5367:
5362:
5357:
5352:
5347:
5342:
5337:
5332:
5327:
5322:
5317:
5312:
5307:
5305:Choquet-Bruhat
5302:
5297:
5292:
5287:
5282:
5277:
5272:
5267:
5262:
5257:
5252:
5247:
5242:
5237:
5232:
5226:
5224:
5220:
5219:
5216:
5215:
5213:
5212:
5205:
5204:
5199:
5194:
5187:
5186:
5181:
5176:
5171:
5166:
5157:Axisymmetric:
5154:
5153:
5148:
5142:
5131:
5130:
5125:
5120:
5115:
5110:
5105:
5096:Cosmological:
5093:
5091:
5085:
5084:
5082:
5081:
5076:
5071:
5065:
5063:
5057:
5056:
5054:
5053:
5048:
5037:frame-dragging
5034:
5029:
5024:
5021:Einstein rings
5017:Einstein cross
5010:
4999:
4998:
4993:
4987:
4982:
4977:
4964:
4954:
4953:
4948:
4943:
4938:
4932:
4930:
4926:
4925:
4923:
4922:
4920:Ernst equation
4917:
4912:
4907:
4902:
4897:
4892:
4890:BSSN formalism
4887:
4881:
4879:
4875:
4874:
4872:
4871:
4866:
4861:
4856:
4851:
4845:
4843:
4837:
4836:
4834:
4833:
4828:
4822:
4820:
4813:
4805:
4804:
4801:
4800:
4798:
4797:
4792:
4787:
4782:
4777:
4771:
4769:
4763:
4762:
4760:
4759:
4754:
4749:
4747:Ladder paradox
4744:
4739:
4734:
4729:
4724:
4719:
4713:
4711:
4707:
4706:
4704:
4703:
4697:
4695:
4691:
4690:
4688:
4687:
4682:
4677:
4672:
4667:
4662:
4657:
4652:
4650:Speed of light
4647:
4641:
4639:
4633:
4632:
4630:
4629:
4624:
4619:
4613:
4603:
4601:
4594:
4586:
4585:
4580:
4578:
4577:
4570:
4563:
4555:
4546:
4545:
4543:
4542:
4537:
4532:
4527:
4522:
4520:Krasnikov tube
4517:
4512:
4507:
4505:BTZ black hole
4502:
4496:
4494:
4478:
4477:
4475:
4474:
4472:Predestination
4469:
4464:
4459:
4454:
4449:
4443:
4441:
4435:
4434:
4432:
4431:
4426:
4421:
4416:
4411:
4405:
4403:
4399:
4398:
4396:
4395:
4390:
4384:
4382:
4376:
4375:
4373:
4372:
4371:
4370:
4360:
4359:
4358:
4347:
4345:
4339:
4338:
4336:
4335:
4330:
4325:
4320:
4315:
4309:
4307:
4303:
4302:
4297:
4295:
4294:
4287:
4280:
4272:
4266:
4265:
4251:Dunning, Brian
4247:
4196:
4190:
4185:
4168:
4145:
4144:External links
4142:
4141:
4140:
4091:
4040:
4037:
4034:
4033:
4008:
3981:
3968:
3936:
3883:
3862:
3805:
3784:
3727:
3717:Universe Today
3702:
3645:
3634:. 9 March 2021
3619:
3591:
3519:
3493:
3467:
3448:
3429:
3388:
3365:
3337:
3282:
3227:
3164:
3155:
3142:
3104:
3046:
2984:
2958:
2900:
2842:
2783:
2763:
2710:
2690:
2653:(2): 543â549.
2635:
2590:(10): 105009.
2570:
2540:
2533:
2507:
2486:
2439:
2389:
2366:
2307:
2270:(5): L73âL77.
2241:
2204:(12): 124017.
2179:
2142:(10): 104013.
2119:
2097:
2082:
2050:
2049:
2047:
2044:
2043:
2042:
2037:
2032:
2027:
2022:
2014:
2008:
2001:
1998:
1989:, more recent
1943:
1936:
1900:
1897:
1875:
1874:Wall thickness
1872:
1859:
1856:
1842:
1839:
1813:
1810:
1712:Casimir effect
1703:
1700:
1698:
1695:
1664:Krasnikov tube
1592:
1589:
1543:into a single
1512:
1509:
1481:
1480:
1469:
1464:
1459:
1451:
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1435:
1429:
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1103:
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989:
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619:
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611:
610:
607:
604:
601:
596:
592:
588:
585:
583:
579:
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571:
570:
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562:
557:
554:
551:
546:
542:
536:
531:
528:
525:
522:
517:
513:
509:
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503:
501:
497:
493:
489:
488:
485:
482:
479:
476:
474:
472:
469:
468:
454:
453:
448:
444:
438:
428:
427:
416:
411:
407:
403:
397:
393:
389:
383:
380:
376:
372:
369:
366:
360:
356:
352:
346:
342:
338:
335:
330:
326:
322:
317:
311:
307:
301:
297:
293:
288:
284:
279:
275:
272:
267:
263:
259:
239:of space-like
220:
217:
175:
172:
145:
142:
123:Casimir vacuum
107:energy density
84:metric tensors
78:. Since those
60:energy-density
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
5459:
5448:
5445:
5443:
5440:
5438:
5435:
5433:
5430:
5428:
5425:
5423:
5420:
5418:
5415:
5414:
5412:
5399:
5389:
5383:
5382:
5378:
5376:
5373:
5371:
5368:
5366:
5363:
5361:
5358:
5356:
5353:
5351:
5348:
5346:
5343:
5341:
5338:
5336:
5333:
5331:
5328:
5326:
5323:
5321:
5318:
5316:
5313:
5311:
5308:
5306:
5303:
5301:
5298:
5296:
5293:
5291:
5290:Chandrasekhar
5288:
5286:
5283:
5281:
5278:
5276:
5273:
5271:
5268:
5266:
5263:
5261:
5258:
5256:
5253:
5251:
5250:Schwarzschild
5248:
5246:
5243:
5241:
5238:
5236:
5233:
5231:
5228:
5227:
5225:
5221:
5211:
5207:
5206:
5203:
5200:
5198:
5195:
5193:
5189:
5188:
5185:
5182:
5180:
5177:
5175:
5172:
5170:
5167:
5164:
5160:
5156:
5155:
5152:
5149:
5146:
5143:
5141:
5137:
5136:Schwarzschild
5133:
5132:
5129:
5126:
5124:
5121:
5119:
5116:
5114:
5111:
5109:
5106:
5103:
5099:
5095:
5094:
5092:
5090:
5086:
5080:
5077:
5075:
5072:
5070:
5067:
5066:
5064:
5058:
5052:
5049:
5046:
5042:
5038:
5035:
5033:
5032:Shapiro delay
5030:
5028:
5025:
5022:
5018:
5014:
5011:
5008:
5004:
5001:
5000:
4997:
4994:
4991:
4988:
4986:
4983:
4981:
4978:
4976:
4975:collaboration
4972:
4968:
4965:
4963:
4959:
4956:
4955:
4952:
4949:
4947:
4944:
4942:
4941:Event horizon
4939:
4937:
4934:
4933:
4931:
4927:
4921:
4918:
4916:
4913:
4911:
4908:
4906:
4903:
4901:
4898:
4896:
4893:
4891:
4888:
4886:
4885:ADM formalism
4883:
4882:
4880:
4876:
4870:
4867:
4865:
4862:
4860:
4857:
4855:
4852:
4850:
4847:
4846:
4844:
4838:
4832:
4829:
4827:
4824:
4823:
4821:
4817:
4814:
4812:
4806:
4796:
4793:
4791:
4790:Biquaternions
4788:
4786:
4783:
4781:
4778:
4776:
4773:
4772:
4770:
4768:
4764:
4758:
4755:
4753:
4750:
4748:
4745:
4743:
4740:
4738:
4735:
4733:
4730:
4728:
4725:
4723:
4720:
4718:
4717:Time dilation
4715:
4714:
4712:
4708:
4702:
4699:
4698:
4696:
4692:
4686:
4683:
4681:
4678:
4676:
4673:
4671:
4670:Proper length
4668:
4666:
4663:
4661:
4658:
4656:
4653:
4651:
4648:
4646:
4643:
4642:
4640:
4634:
4628:
4625:
4623:
4620:
4617:
4614:
4612:
4608:
4605:
4604:
4602:
4598:
4595:
4593:
4587:
4583:
4576:
4571:
4569:
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4528:
4526:
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4521:
4518:
4516:
4513:
4511:
4508:
4506:
4503:
4501:
4498:
4497:
4495:
4493:
4487:
4483:
4479:
4473:
4470:
4468:
4465:
4463:
4460:
4458:
4455:
4453:
4450:
4448:
4445:
4444:
4442:
4440:
4436:
4430:
4427:
4425:
4422:
4420:
4417:
4415:
4412:
4410:
4407:
4406:
4404:
4400:
4394:
4391:
4389:
4386:
4385:
4383:
4381:
4377:
4369:
4366:
4365:
4364:
4361:
4357:
4354:
4353:
4352:
4349:
4348:
4346:
4344:
4340:
4334:
4331:
4329:
4326:
4324:
4321:
4319:
4316:
4314:
4311:
4310:
4308:
4304:
4300:
4293:
4288:
4286:
4281:
4279:
4274:
4273:
4270:
4262:
4261:
4256:
4252:
4248:
4244:
4240:
4236:
4232:
4228:
4224:
4219:
4218:gr-qc/9907026
4214:
4210:
4206:
4202:
4197:
4194:
4191:
4189:
4186:
4183:
4177:
4173:
4169:
4156:
4152:
4148:
4147:
4143:
4137:
4133:
4129:
4125:
4121:
4117:
4112:
4111:gr-qc/0406083
4107:
4103:
4099:
4098:
4092:
4088:
4084:
4080:
4076:
4072:
4068:
4063:
4062:gr-qc/9707024
4058:
4054:
4050:
4049:
4043:
4042:
4038:
4022:
4018:
4012:
4009:
3996:
3992:
3985:
3982:
3978:
3972:
3969:
3953:
3946:
3940:
3937:
3932:
3928:
3924:
3920:
3916:
3912:
3907:
3906:gr-qc/9702041
3902:
3898:
3894:
3887:
3884:
3878:
3873:
3866:
3863:
3855:
3851:
3847:
3843:
3839:
3835:
3831:
3827:
3823:
3816:
3809:
3806:
3800:
3799:gr-qc/9805037
3795:
3788:
3785:
3781:
3776:
3772:
3768:
3764:
3760:
3756:
3751:
3746:
3743:(6): 064024.
3742:
3738:
3731:
3728:
3723:
3719:
3718:
3713:
3706:
3703:
3698:
3694:
3690:
3686:
3682:
3678:
3673:
3668:
3664:
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3539:(7): 075015.
3538:
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3508:
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3494:
3481:
3480:Physics World
3477:
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3468:
3463:
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3452:
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3252:gr-qc/9702026
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3189:gr-qc/9510071
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3123:: 1105â1110.
3122:
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3074:gr-qc/9702049
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2928:gr-qc/9511068
2924:
2920:
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2907:
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2870:gr-qc/0110086
2866:
2862:
2858:
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2849:
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2843:
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2829:
2824:
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2802:
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2660:gr-qc/9812067
2656:
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2149:gr-qc/0207057
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2052:
2045:
2041:
2038:
2036:
2033:
2031:
2028:
2026:
2023:
2021:
2020:
2015:
2012:
2009:
2007:
2004:
2003:
1999:
1997:
1995:
1992:
1988:
1987:
1982:
1981:
1977:
1974:
1970:
1966:
1962:
1961:
1956:
1951:
1950:
1941:
1937:
1935:
1932:
1926:
1924:
1919:
1914:
1910:
1906:
1898:
1896:
1894:
1885:
1884:Planck length
1881:
1873:
1871:
1869:
1865:
1857:
1855:
1852:
1846:
1840:
1838:
1836:
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1809:
1807:
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1793:
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1777:
1773:
1772:exotic matter
1769:
1764:
1762:
1757:
1756:negative mass
1753:
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1641:
1637:
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1601:time dilation
1598:
1590:
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1586:
1585:exotic matter
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1517:Negative mass
1510:
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1497:
1496:exotic matter
1492:
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1467:
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1436:
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830:
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700:
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605:
602:
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594:
590:
586:
584:
577:
573:
565:
552:
544:
540:
529:
523:
515:
511:
507:
504:
502:
495:
491:
483:
480:
477:
475:
470:
459:
458:
457:
445:
439:
433:
432:
431:
414:
409:
405:
401:
395:
391:
387:
381:
378:
374:
370:
367:
364:
358:
354:
350:
344:
340:
336:
333:
328:
324:
320:
315:
309:
305:
299:
295:
291:
286:
282:
277:
273:
270:
265:
261:
257:
250:
249:
248:
242:
241:hypersurfaces
238:
234:
230:
226:
225:ADM formalism
218:
216:
212:
208:
206:
205:time dilation
202:
197:
193:
189:
185:
181:
173:
171:
169:
168:
163:
159:
155:
151:
143:
141:
139:
135:
131:
126:
124:
120:
116:
112:
111:exotic matter
108:
102:
100:
99:physical laws
96:
91:
89:
85:
81:
77:
73:
69:
68:negative mass
65:
61:
57:
53:
48:
43:
34:
30:
19:
5380:
5201:
5074:KaluzaâKlein
4826:Introduction
4752:Twin paradox
4525:Misner space
4510:Gödel metric
4499:
4490:can contain
4258:
4204:
4200:
4175:
4159:. Retrieved
4155:the original
4101:
4095:
4052:
4046:
4024:. Retrieved
4020:
4011:
3999:. Retrieved
3995:the original
3984:
3971:
3959:. Retrieved
3952:the original
3939:
3896:
3892:
3886:
3865:
3825:
3821:
3808:
3787:
3778:
3740:
3736:
3730:
3715:
3705:
3662:
3658:
3648:
3636:. Retrieved
3631:
3622:
3610:. Retrieved
3604:
3594:
3582:. Retrieved
3536:
3532:
3522:
3510:. Retrieved
3506:
3496:
3484:. Retrieved
3479:
3470:
3451:
3432:
3408:
3404:
3391:
3378:
3368:
3353:
3297:
3291:
3285:
3242:
3236:
3230:
3179:
3173:
3167:
3158:
3150:
3145:
3120:
3116:
3064:
3058:
3038:the original
3009:
3003:
2918:
2912:
2860:
2854:
2800:
2796:
2786:
2775:
2766:
2723:
2719:
2713:
2702:
2693:
2650:
2644:
2638:
2587:
2583:
2573:
2516:
2510:
2451:
2409:
2405:
2383:
2369:
2329:
2323:
2310:
2267:
2261:
2201:
2195:
2139:
2133:
2113:
2063:
2040:Unruh effect
2018:
1990:
1984:
1978:
1976:tabletop RPG
1972:
1968:
1958:
1947:
1945:
1939:
1938:Relation to
1927:
1902:
1877:
1861:
1847:
1844:
1834:
1829:
1827:
1815:
1796:violate the
1794:
1768:Harold White
1765:
1761:Planck scale
1748:solar masses
1740:
1724:
1705:
1697:Difficulties
1689:
1686:
1678:
1669:
1651:
1642:and require
1629:
1623:
1619:
1613:
1609:tidal forces
1594:
1573:
1530:
1523:Jamie Farnes
1520:
1493:
1482:
1302:
1034:
1027:
1024:
664:
455:
429:
222:
213:
209:
201:relativistic
177:
165:
161:
147:
127:
103:
92:
87:
41:
39:
29:
5163:KerrâNewman
5134:Spherical:
5003:Other tests
4946:Singularity
4878:Formulation
4840:Fundamental
4694:Formulation
4675:Proper time
4636:Fundamental
4515:Kerr metric
4452:Determinism
4393:Causal loop
4299:Time travel
4180:(hosted by
3899:(1): 8â14.
3638:23 December
3612:21 December
3411:: 242â247.
2704:EurekAlert!
2412:: 254â257.
1909:time travel
1725:If certain
1720:massâenergy
1607:. Enormous
1581:time travel
1541:dark matter
1537:dark energy
219:Mathematics
162:warp bubble
121:) that the
115:dark energy
5411:Categories
5315:Zel'dovich
5223:Scientists
5202:Alcubierre
5009:of Mercury
5007:precession
4936:Black hole
4819:Background
4811:relativity
4780:World line
4775:Light cone
4600:Background
4592:relativity
4582:Relativity
4482:Spacetimes
4457:Eternalism
4424:Multiverse
4211:: 044005.
4039:References
3961:25 January
3672:2105.03079
3546:2006.07125
2810:1902.08287
2733:1712.07962
2597:2102.06824
2461:2103.05610
2019:Enterprise
1969:Alcubierre
1942:warp drive
1690:round trip
1673:light cone
1545:dark fluid
1515:See also:
1505:warp drive
223:Using the
186:. It is a
158:spacecraft
66:(that is,
52:warp drive
5285:Robertson
5270:Friedmann
5265:Eddington
5255:de Sitter
5089:Solutions
4967:detectors
4962:astronomy
4929:Phenomena
4864:Geodesics
4767:Spacetime
4710:Phenomena
4467:Free will
4363:Time loop
4136:119010055
3931:118984236
3877:1001.4960
3750:1202.5708
3697:234095711
3579:219635854
3571:0264-9381
3034:250843331
2837:0004-6361
2777:Big Think
2630:231924903
2622:0264-9381
2561:Space.com
2496:cite book
2434:0094-5765
2211:0904.0141
2092:202443606
1991:Star Trek
1973:Star Trek
1949:Star Trek
1940:Star Trek
1818:tachyonic
1780:Voyager 1
1525:from the
1333:π
1314:−
1165:−
1140:−
994:σ
988:
964:−
948:σ
938:
932:−
900:σ
890:
787:−
634:δ
614:γ
591:β
574:β
508:−
492:β
471:α
375:γ
341:β
306:β
296:β
292:−
283:α
274:−
237:foliation
233:spacetime
184:spacetime
148:In 1994,
119:wormholes
95:spacetime
80:solutions
5398:Category
5275:LemaĂźtre
5240:Einstein
5230:Poincaré
5190:Others:
5174:TaubâNUT
5140:interior
5062:theories
5060:Advanced
5027:redshift
4842:concepts
4660:Rapidity
4638:concepts
4462:Fatalism
4260:Skeptoid
4243:59940462
4026:22 April
3854:Archived
3850:10020029
3722:Archived
3584:22 April
3512:22 April
3486:22 April
3462:Archived
3440:Archived
3421:Archived
3383:Archived
3379:Wired UK
3360:Archived
3332:15466313
3277:15279207
3222:18106362
3214:10019835
3099:19017879
2953:55825213
2895:15859984
2758:53600834
2565:Archived
2385:example.
2380:Archived
2358:Archived
2354:10038800
2236:59575856
2174:17498199
2000:See also
1994:spin-off
1888:1.6 Ă 10
1830:en route
1806:dominant
1656:tachyons
1620:solution
1616:ADM form
1605:g-forces
1501:wormhole
5340:Hawking
5335:Penrose
5320:Novikov
5300:Wheeler
5245:Hilbert
5235:Lorentz
5192:pp-wave
5013:lensing
4809:General
4590:Special
4368:in film
4223:Bibcode
4176:YouTube
4116:Bibcode
4087:1884428
4067:Bibcode
3911:Bibcode
3830:Bibcode
3775:3993148
3755:Bibcode
3677:Bibcode
3551:Bibcode
3507:Reuters
3413:Bibcode
3312:Bibcode
3257:Bibcode
3194:Bibcode
3125:Bibcode
3079:Bibcode
3014:Bibcode
2933:Bibcode
2875:Bibcode
2815:Bibcode
2738:Bibcode
2726:: A92.
2685:6540037
2665:Bibcode
2602:Bibcode
2466:Bibcode
2414:Bibcode
2334:Bibcode
2302:4797900
2282:Bibcode
2216:Bibcode
2154:Bibcode
2006:EmDrive
1776:Jupiter
1652:one-way
1624:adapted
1591:Physics
144:History
5381:others
5370:Thorne
5360:Misner
5345:Taylor
5330:Geroch
5325:Ehlers
5295:Zwicky
5113:Kasner
4241:
4161:2 July
4134:
4085:
4001:2 June
3929:
3848:
3773:
3695:
3577:
3569:
3330:
3275:
3220:
3212:
3097:
3032:
2951:
2893:
2835:
2803:: A5.
2756:
2683:
2628:
2620:
2531:
2484:
2432:
2352:
2300:
2234:
2172:
2090:
2080:
1802:strong
1792:all".
1561:cosmos
1489:tensor
1483:where
1037:> 0
1030:> 0
665:where
430:where
231:, the
180:metric
64:vacuum
5375:Weiss
5355:Bondi
5350:Hulse
5280:Milne
5184:discs
5128:Milne
5123:Gödel
4980:Virgo
4239:S2CID
4213:arXiv
4207:(4).
4132:S2CID
4106:arXiv
4083:S2CID
4057:arXiv
3955:(PDF)
3948:(PDF)
3927:S2CID
3901:arXiv
3872:arXiv
3857:(PDF)
3818:(PDF)
3794:arXiv
3771:S2CID
3745:arXiv
3693:S2CID
3667:arXiv
3575:S2CID
3541:arXiv
3424:(PDF)
3401:(PDF)
3328:S2CID
3302:arXiv
3273:S2CID
3247:arXiv
3218:S2CID
3184:arXiv
3095:S2CID
3069:arXiv
3041:(PDF)
3030:S2CID
3000:(PDF)
2973:arXiv
2949:S2CID
2923:arXiv
2891:S2CID
2865:arXiv
2805:arXiv
2754:S2CID
2728:arXiv
2681:S2CID
2655:arXiv
2626:S2CID
2592:arXiv
2456:arXiv
2361:(PDF)
2320:(PDF)
2298:S2CID
2272:arXiv
2232:S2CID
2206:arXiv
2170:S2CID
2144:arXiv
2088:S2CID
2046:Notes
1880:Tufts
1785:torus
1681:Deneb
1579:(see
5310:Kerr
5260:Weyl
5159:Kerr
5019:and
4973:and
4971:LIGO
4488:that
4163:2008
4028:2021
4003:2013
3963:2017
3846:PMID
3640:2021
3614:2021
3586:2021
3567:ISSN
3514:2021
3488:2021
3210:PMID
2833:ISSN
2618:ISSN
2529:ISBN
2502:link
2482:ISBN
2430:ISSN
2350:PMID
2078:ISBN
2017:IXS
1946:The
1823:Vega
1804:and
1599:and
1539:and
1032:and
985:tanh
935:tanh
887:tanh
82:are
40:The
5365:Yau
4990:GEO
4484:in
4231:doi
4124:doi
4075:doi
3919:doi
3897:415
3838:doi
3763:doi
3685:doi
3663:105
3559:doi
3355:io9
3320:doi
3265:doi
3202:doi
3133:doi
3121:504
3087:doi
3022:doi
2941:doi
2883:doi
2823:doi
2801:626
2746:doi
2724:620
2673:doi
2610:doi
2521:doi
2474:doi
2422:doi
2410:139
2342:doi
2290:doi
2224:doi
2162:doi
2070:doi
1835:any
1666:):
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