AAWSAP DIRD, Traversable Wormholes, Stargates, and Negative Energy, April 2010

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results that are similar to the static case.) This relation will help to decide if a
traversable wormhole having one throat, or two or more throats should be built and at
what energy cost this will incur.
The following is the result of our analysis for traversable wormholes having:
•
1-handle/throat (i.e., flat torus or spherical wormhole topology) giving g = 1, thus
Xe = 0, and so U s 0
•
2-handles/throats giving g = 2, thus xe = -2, and so U s -1/2
•
3-handles/throats giving g = 3, thus xe = -4, and so U s -1; and so on.
It is clear from this that as the number of wormhole handles/throats increases the
amount of negative energy required to create the wormhole will grow larger in
magnitude. This is an undesirable demand on any putative negative energy generator.
It is clear then that item (a) defines the most desirable engineering solution one can
hope for: a 1-handle/throat traversable wormhole that will require zero or (arbitrarily)
little negative energy to create. The magnitude of energy condition violations and the
amount of negative energy required to build a traversable wormhole will be addressed.
B. THE "STARGATE" SOLUTION
It is a straightforward exercise to design a real "stargate" from wormhole physics. A
stargate is essentially a traversable wormhole with a flat-face shape for the throat as
opposed to the spherical-shaped throat of the Morris and Thorne wormhole as discussed
in the previous section. A traveler going through a stargate will simply be shunted into
another remote spacetime region within our universe or into another universe.
The flat-face traversable wormhole solution is derived from the thin shell (a.k.a.
junction condition or surface layer) formalism of the Einstein field equation (Reference
6, 7). The procedure is to take two copies of flat Minkowski space and remove from
each identical regions of the form n x 1.R, where n is a three-dimensional compact
spacelike hypersurface and 9, is a timelike line (time axis). Then identify these two
incomplete spacetimes along the timelike boundaries an x ~H. The resulting spacetime is
geodesically complete and possesses two asymptotically flat regions connected by a
traversable wormhole. The throat of the wormhole is just the junction an, which is a
two-dimensional space-like hypersurface, at which the two original Minkowski spaces
are identified (see Figures 3 and 4) .
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