nos, namely, the vacuum solution of the Einstein equationsĬonnecting the warp drive to shock waves. Solution for this case is identical to the one we found in Ref. The zero pressure reduces the perfect fluid to the dust EMT, the The warp drive is connected to shock waves solutions. nos, except that now there isĪ cosmological constant coupled with the Burgers equation and, again, The other two sets of solutions are identical to each other and similar Vector to be a complex function in one case, depending on the ( t, y )Ĭoordinates, and in another case depending on the ( t, z ) coordinates. Two of them are very similar and raise the possibility for the shift The perfect fluid with the cosmological constant as source for theĪlcubierre warp drive results in four sets of differential equations, Of the energy momentum tensor together with the validity requirementsįor the energy conditions inequalities to be satisfied. We calculated the Einstein equations and analyzed the null divergence Whereas Mattingly matt discussed further curvature invariants for cleaver3 cleaver4 studied theĬurvature invariants characteristic of Natario and Alcubierre warp drives, TheyĪlso claimed that a warp field interferometer could not detect spacetimeĭistortions. Might affect the Alcubierre warp bubble to turn it unsustainable. LeeĪnd Cleaver cleaver1 cleaver2 analyzed how external radiation Observers when inside a region-delimited gravitational wave field. Quarra quarraĭiscussed null geodesics moving faster-than-light according to far away The mass of the spaceship inside the warp bubble. The energy stored in the warp fields must be a significant fraction of They proposed a linearized model for bothĪlcubierre and Natario proposals and demonstrated that for small speeds, Warp bubble proposed by Alcubierre needs to be massless (see also LoboVisser2004b LoboVisser2004 discussed that the center of the Hence, he designed a spacetime where no contraction orĮxpansion occurs for the warp drive bubble. Natario Natario2002 stated that the spacetime contraction andĮxpansion of the warp bubble is a peculiar consequence of the warpĭrive metric. Both the metric and the obtained EMT were thoroughly TheĮnergy-momentum tensor (EMT) for the Krasnikov metric is positive in Since the tube is designed to not possessĬlosed timelike curves, it would be theoretically possible to constructĪ two way non-overlapping system that could work as a time machine. The Krasnikov tube also requires huge amounts of Inside this tube, the spacetime isįlat and the lightcones are opened to allow the one direction Krasnikov by proposing a tube in the direction of the particle’s path,Ĭonnecting the start and end point. Everet and RomanĮveretRoman1997 coined the name for this spacetime topology as Velocities without the need for tachyons. Particles to travel between two points in space with superluminal He is the creator ofĪ specific spacetime topology with devices that would allow massive Properties with feasible physical assumptions. Not possible due to limitations on globally hyperbolic spacetimes Particle moving in space faster than a photon, arguing that this is Krasnikov Krasnikov1998 discussed the possibility of a massive Matter may not be a strict requirement to achieve global superluminal In addition, warp speeds seem to require moreĬomplex forms of matter than dust for stable solutions and that negative Spacetime geometry one may require a complex configuration andĭistribution of energy, matter and momentum as source in order to produceĪ warp drive bubble. That to achieve superluminal speeds by means of the Alcubierre warp drive Off-diagonal terms in the energy-momentum source. Motion creates a coupling in the Einstein equations that requires Results show that the shift vector in the direction of the warp bubble Which generalizes our previous dust solution (Santos-Pereira et al. 2020) and led to vacuum solutions connecting the warpĭrive with shock waves via the Burgers equation, as well as our perfectįluid solution without the cosmological constant (Santos-Pereira et al. 2021). We also consider the particular dust case with the cosmological constant, The Alcubierre warp drive metric having the perfect fluid as source. Solutions of the Einstein equations with the cosmological constant for To travel with superluminal global velocities. The Alcubierre metric describes a spacetime geometry that allowsĪ massive particle inside a spacetime distortion, called warp bubble,
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