Updated Math Model for Warp Drives and Classes of Future Warp Drives

There is an update of a mathematical and physical model for a warp drive.

The Alcubierre warp drive is an exotic solution in general relativity. It allows for superluminal travel at the cost of enormous amounts of matter with negative mass density. For this reason, the Alcubierre warp drive has been widely considered unphysical. In this study, we develop a model of a general warp drive spacetime in classical relativity that encloses all existing warp drive definitions and allows for new metrics without the most serious issues present in the Alcubierre solution. We present the first general model for subluminal positive-energy, spherically symmetric warp drives; construct superluminal warpdrive solutions which satisfy quantum inequalities; provide optimizations for the Alcubierre metric that decrease the negative energy requirements by two orders of magnitude; and introduce a warp drive spacetime in which space capacity and the rate of time can be chosen in a controlled manner. Conceptually, we demonstrate that any warp drive, including the Alcubierre drive, is a shell of regular or exotic material moving inertially with a certain velocity. Therefore, any warp drive requires propulsion. We show that a class of subluminal, spherically symmetric warp drive spacetimes, at least in principle, can be constructed based on the physical principles known to humanity today.

Miguel Alcubierre in 1994 require a Jupiter mass of negative energy. Negative energy might not exist and humans cannot produce any negative energy. Bobrick and Martire suggest using regular massive gravitational force to bend space time. They still need a planet-sized mass or something that warps space as much as a planet’s gravity. Planets exist but that level of warping of space is still far, far beyond capabilities and any reasonable development path.

Nextbigfuture reviewed this work in November, 2020.

The researchers propose classifications of future warp drives.

Class I: Mild subluminal warp drives: These would be less than the speed of light. Spacetimes of this class approach the flat Minkowski spacetime in the trivial limit. Non-trivial members of this class contain spacetimes with region Dwarp sufficiently curved, so that tetrads of observers Oin and Oout,co differ significantly from each other, i.e. the observers read off different rates of clocks and lengths of rulers. At the same time, such
spacetimes also contain weak-field solutions corresponding to classical shell-like objects moving with subluminal velocities and weakly modifying the state of the spacetime inside them. Such solutions are possible because the Dwarp region may be set arbitrarily close to being flat, rendering the whole spacetime arbitrarily close to Minkowski spacetime.

Class II: Mild superluminal warp drives: These spacetimes are characterized by the vector field ξ being spacelike or null everywhere. Consequently, such warp drives have luminal or superluminal velocities, i.e., vs ≥ c. These spacetimes also admit a trivial limit, wherein they reduce to flat Minkowski spacetime. Weak-field members of the class correspond to small amounts of ‘superluminal matter’ in the region Dwarp introducing small differences in the measurements of frames Oin, Oout,co. By ‘superluminal matter’ we understand the matter at rest with respect to a space-like reference frame. In the case of the stress-energy tensor for a perfect fluid, such matter violates the dominant energy condition. A general spacetime of this class introduces nontrivial differences between frames Oin and Oout,co. Since superluminal matter cannot be produced from physical matter, and since null or spacelike tetrads cannot be associated with physical observers, the spacetimes of this class have limited interest.

Class III: Extreme superluminal warp drives: These spacetimes are defined by the vector field ξ being timelike in the inner region Din, but null or spacelike in the asymptotic infinity of the outer region Dout. The remote comoving observers in such spacetimes move luminally or superluminally relative to the resting timelike observer Oout, i.e., vs ≥ c. This class of spacetimes does not contain trivial solutions and the warped region Dwarp is sufficiently curved to allow timelike observers Oin to be moving superluminally relative to the timelike observer Oout (and as a consequence, the timelike observer Oin will be travelling back in time from the point of view of yet another remote timelike observer O0 out). At the
same time, the comoving observer Oout,co is formally superluminal; in other words, remote timelike observers cannot be comoving with a warp drive of this class.

Class IV: ‘Extreme’ subluminal warp drives: Spacetimes of this class are defined by the vector field ξ being null or spacelike in the inner region Din, but timelike at the asymptotic infinity of the outer region Dout. Since the comoving observer Oout,co is timelike, such spacetimes are subluminal, i.e. vs < c. Since the Killing vector is spacelike in the inner region Din, no timelike internal observers can be at rest relative to the inner boundary of the drive ∂Din. This property bears similarity to black hole spacetimes, except for that the inner region Din for this class of spacetimes is flat everywhere. A necessary condition for spacetimes of this class to be physical is that the Killing horizon coincides with the boundary of the inner region, ∂Din. Otherwise, some fraction of matter in the region Dwarp will be superluminal.

For subluminal velocities, the Alcubierre drive belongs to Class I, mild subluminal warp drives. For superluminal velocities it belongs to Class III, extreme superluminal warp drives.

The math model suggest the most optimal way of reducing the total energy, as measured by Eulerian observers, is by flattening the shape of the warp drive.

The flattening of the warped region may be adjusted with velocity so that the drive preserves the same total energy.

Superluminal solutions can be constructed which satisfy the quantum inequalities.

Written by Brian Wang, Nextbigfuture.com