Warp drive with zero expansion

Natário, José

doi:10.1088/0264-9381/19/6/308

Cited by 73 publications

(136 citation statements)

References 9 publications

(14 reference statements)

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“…Therefore, there will be points on the warp bubble wall where ∇ 2 φ < 0. At these points, one has R 00 < 0, and the strong energy condition is violated (as it we know it must be -see [Nat02]); in the corresponding Newtonian limit, this translates as the mass density generating the gravitational field being negative. is clearly a gradient, we immediately see that this corresponds to a Newtonian spacetime with potential…”

Section: Newtonian Warp Drivementioning

confidence: 99%

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Newtonian limits of warp drive spacetimes

Natário¹

2006

Gen Relativ Gravit

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Section: Newtonian Warp Drivementioning

confidence: 99%

“…if r > r 0 + ε where r 2 = x 1 2 + x 2 2 + x 3 2 and r 0 > ε > 0 (this is in the frame where the bubble is at rest; see [Nat02] for deatils). If v = ∇ψ, this will also be a Newtonian spacetime.…”

Section: Newtonian Warp Drivementioning

confidence: 99%

Newtonian limits of warp drive spacetimes

Natário¹

2006

Gen Relativ Gravit

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“…The alternative version of the warp bubble, due to José Natário demonstrates that the contraction/expansion referred to above is not always a feature of the warp drive [2]. In his construction a compression in the radial direction is exactly balanced by an expansion in the perpendicular direction, so that the shift vector is divergence-free ∇ · β = 0.…”

Section: B Natário Warp Drivementioning

confidence: 99%

“…In fact, numerous solutions to the Einstein field equations are now known that allow "effective" superluminal travel [2,3,4,5,6,7,8,9,10,11]. Despite the use of the term superluminal, it is not "really" possible to travel faster than light, in any local sense.…”

Section: Introductionmentioning

confidence: 99%

Fundamental limitations on ‘warp drive’ spacetimes

Lobo

Visser

2004

Class. Quantum Grav.

117

111

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"Warp drive" spacetimes are useful as "gedanken-experiments" that force us to confront the foundations of general relativity, and among other things, to precisely formulate the notion of "superluminal" communication. After carefully formulating the Alcubierre and Natário warp drive spacetimes, and verifying their non-perturbative violation of the classical energy conditions, we consider a more modest question and apply linearized gravity to the weak-field warp drive, testing the energy conditions to first and second order of the warp-bubble velocity, v. Since we take the warpbubble velocity to be non-relativistic, v ≪ c, we are not primarily interested in the "superluminal" features of the warp drive. Instead we focus on a secondary feature of the warp drive that has not previously been remarked upon -the warp drive (if it could be built) would be an example of a "reaction-less drive". For both the Alcubierre and Natário warp drives we find that the occurrence of significant energy condition violations is not just a high-speed effect, but that the violations persist even at arbitrarily low speeds.A particularly interesting feature of this construction is that it is now meaningful to think of placing a finite mass spaceship at the centre of the warp bubble, and then see how the energy in the warp field compares with the mass-energy of the spaceship. There is no hope of doing this in Alcubierre's original version of the warp-field, since by definition the point in the centre of the warp bubble moves on a geodesic and is "massless". That is, in Alcubierre's original formalism and in the Natário formalism the spaceship is always treated as a test particle, while in the linearized theory we can treat the spaceship as a finite mass object. For both the Alcubierre and Natário warp drives we find that even at low speeds the net (negative) energy stored in the warp fields must be a significant fraction of the mass of the spaceship.

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“…It was, however, recently shown by Natário [5] that Tr K=Tr D/c s = 0 is not a necessary prerequisite for the warp drive, so that the assumption of an incompressible background does not impede its construction. The nonvanishing components of the effective space-time Riemann tensor are (for an incompressible, vorticity-free background flow) [11],…”

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confidence: 99%

Warped space-time for phonons moving in a perfect nonrelativistic fluid

Fischer

Visser

2003

Europhys. Lett.

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Abstract. -We construct a kinematical analogue of superluminal travel in the "warped" space-times curved by gravitation, in the form of "super-phononic" travel in the curved effective space-times of perfect nonrelativistic fluids. These warp-field space-times are most easily generated by considering a solid object that is placed as an obstruction in an otherwise uniform flow. No violation of any condition on the positivity of energy is necessary, because the effective curved space-times for the phonons are ruled by the Euler and continuity equations, and not by the Einstein field equations.Introduction. -The concept of "warp fields", or faster than light (FTL) propagation/travel, is usually relegated into the realm of science fiction literature. Taking warp fields more seriously, when trying to develop physical realizations within the context of Einstein gravity, one has to face the difficulty that fulfilling the Einstein equations demands "exotic matter"; matter violating the null, weak, strong, and dominant conditions on the positivity of energy [1][2][3][4][5]. If, on the other hand, one allows for negative energy densities (which occur for example in the quantum vacuum of the Casimir effect) the energy densities (and to a lesser degree the total energies [6]) actually required to construct macroscopic warp drives are astronomical [7]. One way of side-stepping these problems, and developing a concrete physical model of what a warp field might look like, is to consider effective space-time theories originating in condensed matter [8,9]: A flowing hydrodynamical background governed by the nonrelativistic Euler and continuity equations represents a curved space-time for the quasiparticle excitations moving in the fluid. The role of the speed of light is played by the speed of sound, and superluminal travel turns into super-phononic propagation due to the effective space-time curvature. The necessity of violating the energy conditions is no longer given, because the effective pseudo-Riemannian space created by the laboratory flow in absolute Newtonian space is determined by the equations of nonrelativistic hydrodynamics, and not by the Einstein field equations.

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Warp drive with zero expansion

Cited by 73 publications

References 9 publications

Newtonian limits of warp drive spacetimes

Newtonian limits of warp drive spacetimes

Fundamental limitations on ‘warp drive’ spacetimes

Warped space-time for phonons moving in a perfect nonrelativistic fluid

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