Defense Intelligence Reference Document Advanced Space Propulsion Based On Vacuum Engineering

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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 ds 2in
terms of the metric tensor g_,,v is given by
ds 2 = g dxPdx'·
·"'' ( 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)
where the identification dx0 = cdt, d-r1 = dx, dx:. = dy, dx' = dz is made, with metric
tensorcoefficients g(~1 =l, g 11 =g 22 =g_1_1=-l, x,,..=O for μ-::f::-v.
For spherical coordinates in ordinary Minkowski flat spacetime
where dx 11
= cdt dx 1
= dr clr 2
= dO d1/· = dr.p with metric tensor coefficients o -1' ' ' ' I'>{)() - '
g 11 =-l, g 22 =-r2, g_n=-r 2 sin 2 0, g.,,"=0 for jl-::f::-V.
(2)
(3)
As an example of spacetime alteration, in a spacetime altered by the presence of a
spherical mass distribution mat the origin (Schwarzschild-type solution), the above can
be transformed into (Reference 10)
ds- ~ ( I-Gm, re' )c'dt' -( I-Gm, re:)_, dr' -(I+ Gm/ re-) r- ( d0' +sin' 0dq,')
1+ Gm/ re- 1 + Gm: re (4)
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