![]() ![]() His modification reduced the energy requirements to form the warp bubble to only a few solar masses and his geometry has more lenient violation of the NEC. Van Den Broeck reduced the amount of energy required by Alcubierre’s warp drive by positing a warp bubble with a microscopic surface area and a macroscopic volume inside. Krasnikov developed a non-tachyonic FTL warp bubble. Research into FTL warp drives has advanced tremendously since Alcubierre’s original proposal. Eighth, the passengers riding the FTL warp should not encounter a singularity inside or out of it. Seventh, the FTL warp should not generate an event horizon. Sixth, the matter of the passengers must not couple with any material used to generate the FTL space warp. Fifth, the local speed of any passengers should be less than c. Fourth, the magnitude of any tidal-gravity accelerations acting on the passengers will be less than g ⊕, which is the acceleration of gravity near the Earth’s surface. Third, the proper time measured by any passenger should not be dilated by relativistic effects. Second, the trip duration to a distant star may be reduced to be less than one year, as seen by both observers inside of the warp, which are called passengers, and by stationary observers outside of the warp. First, the rocket equation does not describe the portion of the flight undergoing FTL travel. He named the faster-than-light (FTL) propulsion mechanism based on this principle a “warp drive.”Ī spaceship using an FTL warp drive must obey eight prerequisites to carry a human to a distant star. Distant observers will perceive the ship to be moving at a global velocity greater than c, and the spaceship will be able to make a trip to a distant star in an arbitrarily short proper time. While the spaceship remains within its own light cone and its local velocity never exceeds c, the global velocity, which is defined as the proper spatial distance divided by proper time, may be much greater than c due to the contraction and expansion of spacetime. He proposed pairing a local contraction of spacetime in front of a spaceship with a local expansion of spacetime behind it. Alcubierre noticed that spacetime itself may expand and contract at arbitrary rates. However, general relativity (GR) allows a particle’s global velocity to exceed c while its local velocity obeys the prior statement. No particle may have a local velocity that exceeds the speed of light in vacuum, c, in Newtonian mechanics and special relativity. The curvature plots for the constant velocity Natário warp drive do not contain a wake or a constant curvature, indicating that these are unique features of the accelerating Natário warp drive. For each warp drive, this research shows a safe harbor and how the shape function forms the warp bubble. The warp drive parameters of velocity, skin depth and radius are varied individually and then plotted to see each parameter’s unique effect on the surrounding curvature. This paper uses the methods of computing and plotting the warp drive curvature invariants to reveal these spacetimes. While their mathematics is well established, the visualisation of such spacetimes is unexplored. Warp drives are the theoretical solutions to Einstein’s field equations that allow for the possibility for faster-than-light (FTL) travel. As a consequence, they provide a novel perspective into complex spacetimes, such as warp drives. Curvature invariants are independent of coordinate bases, so plotting these invariants will be free of coordinate mapping distortions. A process for using curvature invariants is applied to evaluate the metrics for the Alcubierre and the Natário warp drives at a constant velocity. ![]()
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