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This is an unclassified Defense Intelligence Reference Document (DIA-08-1003-015), dated 29 March 2010. The Defense Intelligence Agency prepared it under the Advanced Aerospace Weapon System Applications (AAWSA) Program, and Rep. Burchett entered it into the House committee record. The paper uses a general relativity metric tensor approach to look at how engineering spacetime might enable propulsion, including warp drives, apparent superluminal travel, reduced effective mass and antigravity. It finds these ideas consistent with physics but far beyond present engineering capability.
“The Advance”10 pages
UNCLASSIFIED/)TM'ell•PieNe&tle&OPSW I. Spacetime Modification - Metric Tensor Approach Despite the daunting energy requirements to restructure the spacetime metric to a significant degree, one can investigate the forms that such restructuring would take to be useful for spaceflight applications and determine their corollary attributes and consequences. Thus we embark on a "Blue Sky," general-relativity-for-engineers approach, as it were. As a mathematical evaluation tool, the metric tensor that describes the measurement of spacetime intervals is used. Such an approach, well known from studies in general relativity (GR), has the advantage of being model independent—that is, it does not depend on knowledge of the specific mechanisms or dynamics that result in spacetime alterations but rather only assumes that a technology exists that can control and manipulate (that is, engineer) the spacetime metric to advantage. Before discussing the predicted characteristics of such engineered spacetimes, beginning in Section III, a brief mathematical digression for those interested in the mathematical structure behind the discussion to follow is introduced. As a brief introduction, the expression for the four-dimensional line element di' in terms of the metric tensor g is given by (1) where summation over repeated indices is assumed unless otherwise indicated. In ordinary Minkowski flat spacetime, a (four-dimensional) infinitesimal interval ds is given by the expression (in Cartesian coordinates) ds2 =c2dt 2 —(dx 2 -Fdy 2 +dv 2 ) (2) where the identification dxa =cdt , =dy, dx 3 =dz is made, with metric tensor coefficients goo = 1, g ,g 2, = g„ ,—I, g„, =0 for pv . For spherical coordinates in ordinary Minkowski flat spacetime ors' ne'dt 2 - r'd02 -I' sin Odco2 (3) where (IX() = Cdt = dr r = CIO dy3 drp, with metric tensor coefficients go„ =I , g,, _ 1, r2 sin2 gpv 0 for p#v As an example of spacetime alteration, in a spacetime altered by the presence of a spherical mass distribution m at the origin (Schwarzschild-type solution), the above can be transformed into (Reference 10) 22 21 1-Gm/re' 1-Grn rc- ,\ , \ c72 dr 2 -(1+ OW rcir - v10- +sin 2 Ody 2 r (4) 1+Gm rc- 1 UNCLASSIFIED/r^^ ^"I^I" "11 fr.
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