Defense Intelligence Reference Document Antigravity For Aerospace Applications

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The exact relativistic strong-field condition that establishes the lower limit criterion for
Vrn1 to induce antigravity repulsion of a payload (as measured by distant inertial
observers in the rest frame of the source or in the initial rest frame of the payload) is
given by (Reference 15):
. , 3 [I L' ( 'I' GM )]y >-'1' --- ---0-
2 GMr 3 re- ( 6)
In this expression, y = ( 1 - f) 1t 112 is the standard relativistic Lorentz transformation factor
which is a function of the normalized relativistic velocity parameter[)= vie, \If= w(r) = I -
(2CM/rc1) is the goo (or time-time) component of the static Schwarzschild spacetime
metric 2 of a source (or central) body of mass M, Lis the constant specific angular
momentum of a ballistic payload of mass m, and r is the radial distance of the
approaching/receding payload from M. One can solve the inequality in Equation (6) for
j3 (or v) under the condition that a payload far from M, such that r>>b (bis the periapsis
distance of the payload from M) and r>> GMk2 , and find that the payload will become
gravitationally repelled by M whenever y2 > 3/2 or j3 > 3 112 . In order to derive an exact
solution, Felber considered the case for which M >> m so that the energy and momentum
delivered to the payload has a negligible back-reaction on the source body's motion.
And he found that a strong gravitational field is not required for antigravity propulsion
because a weak-field solution achieves the same results.
Felber discovered another interesting facet about this new relativistic antigravity effect.
He found that there is also an antigravity field that repels bodies in the backward
direction with a strength that is one-half the strength of the antigravity field in the
forward direction. Thus a stationary body will repel a test body that is radially receding
from it at any 11 > Fern- To delineate the propulsion benefit from this technique, Felber
determined that the maximum velocity (vp,L1ax-"1) that can be imparted to a payload
initially at rest by the weak (gravitational) field of a larger source mass moving toward
the payload at constant v > Vcri1 is v11ma,-wr<<dP-(3p)- 1]. For the strong-field case, the
maximum velocity (1·rm,,-,1) that can be imparted to the payload (initially at rest) by the
larger source mass moving toward the payload at any constant vis t'pm.n-,1 = fk. Felber's
analysis includes examples where he uses black holes for the large source mass.
This form of antigravity propulsion is not too surprising because Misner et al.
(Reference 16), Ohanian and Ruffini (Reference 17), and Ciufolini and Wheeler
(Reference 18) report that general relativistic calculations show that the time-
independent Kerr (spinning black hole) gravitational field exhibits an inertial frame
dragging effect similar to gravitational repulsive forces in the direction of a moving
mass at relativistic velocities. This and Felber's exact solution are among the genre of
Lense-Thirring type effects that produce antigravity forces. It is interesting to note that
even though general relativity theory admits the generation of antigravity forces at
relativistic velocities (Reference 19), they have not been seen in laboratory experiments
7 A spacetime metric (ds") is a Lorentz-invariant distance function between any two points in spacetime that is
defined by ds2 = g,,,dx"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 (r1,v = 0 ... 3)
denote spacetime coordinates, x 0 .x3 , such that x 1 .. x3 -= space coordinates and .0' = time coordinate. The
Schwarzschild metric is: ds7 = -(1 - 2GM/c7r)c7dt' + (1 - 2GMJc7rJ-'dr' + r'(d0 7 + sin 7Od,.p7). The corresponding
metric tensor is a diagonal matrix: g.,, = diag[-(1 - 2GM/c2r), (1 - 2GM/c2r) 1, r'-, r'-s,n 20]. (r,l::l,<Jl) are the usual
spherical polar coordinates in 3-dimensional space.
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