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This Defense Intelligence Reference Document from the Defense Intelligence Agency is dated 2 April 2010 and was produced under the Advanced Aerospace Weapon System Applications (AAWSA) Program. It is one of a series of advanced technology reports from FY 2009. It reviews general relativistic warp drives, the cosmological constant, Casimir energy and extra space dimensions. It proposes that dark energy may come from higher dimensions and that controlling those dimensions could one day make a warp drive possible.
“The Advance”11 pages
UNCLASSIFIED/ ,'F8ft err1e1111t t!91! UICI! I 2. General Relativistic Warp Drives Alcubierre (Reference 1) derived a spacetime metric motivated by cosmological inflation that would allow arbitrarily short travel times between two distant points in space. The "warp drive" metric uses coordinates (t, x, y, z) and curve (or worldline) x = Xsh(t), y = 0, z = 0, lying in the t-x plane passing through the origin. Note that Xsh is the x-axis coordinate position of the moving spaceship (or warp bubble) frame. The metric 1 specifying this particular spacetime geometry is (Reference 1): (2.1) where c is the speed of light, Vsh(t) is the speed associated with the curve (or warp bubble speed), and rsh(t) is the Euclidean distance from the curve. The warp bubble shape function f (rsh) is any smooth positive function that satisfies f (0) = 1 and decreases away from the origin to vanish when rsh > R for some distance R. The geometry of each spatial slice is flat, and spacetime is flat where f (rsh) vanishes but is curved where it does not vanish. The driving mechanism of Equation (2.1) is the York extrinsic time, defined as (Reference 1): 8-. This quantity is The s behavior of the warp drive bubble provides for the simultaneous expansion of space behind the spacecraft and a corresponding contraction of space in front of the spacecraft. Figure 1 illustrates the s behavior of the warp drive bubble geometry. Thus the spacecraft is enveloped within a warp bubble and can be made to exhibit an arbitrarily large faster-than-light (FTL) speed (Vsh >> c) as viewed by external coordinate observers. Even though the worldlines inside the warp bubble region are spacelike for all external observers, the moving spaceship (warp bubble) frame itself never travels outside of its local comoving light cone and thus does not violate special relativity. (2.2) ' Figure 1. York Extrinsic Time (S) Plot 1 A spacetime metric (ds2), or line element, is a Lorentz-invariant distance function between any two points in spacetime that is defined by ds2 =- g,,,dxc dX'-', where g," is the metric tensor which is a 4x4 matrix that encodes the geometry of spacetime and dx,- is the infinitesimal coordinate separation between two points. The Greek indices(,,, v = 0 ... 3) denote spacetime coordinates, x 0 ... x 3, such that x 1... x 3 = space coordinates and .0 = time coordinate. 1 UNCLASSIFIED/ ,'P8"1 err1e1111t t!9! 8PIL¥
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