Defense Intelligence Reference Document Traversible Wormholes Stargates And Negative Energy

UNCLASSIFIED/;SflHl 8FFHil.t.k Wfili IH.k\f
II. A Brief Review of Transversable Wormholes and the
Stargate Solution
How does one study the physics of FTL spacetimes within the framework of general
relativity theory? When studying spacetime physics, the normal philosophy is to take
the general relativistic field equation, add some form of matter, make simplifying
assumptions, and then solve to deduce what the geometry of spacetime will be. 1 This is
very difficult to do because there are ten nonlinear second-order partial differential
equations with four redundancies (arbitrary choice of spacetime coordinates) and four
constraints (stress-energy conservation). There is a tremendous body of research that
takes exactly this approach, either analytically or numerically. However, this is not the
best strategy for understanding wormhole spacetimes. The appropriate strategy is to
decide beforehand on a definition of the traversable wormhole that you desire and
decide what the spacetime geometry should look like. Given the desired geometry, use
the general relativistic field equation to calculate the distribution of matter required to
set up this geometry. Then one needs to assess whether the required distribution of
matter is physically reasonable and whether it violates any basic rules of physics, etc.
The following sections briefly outline the key results for traversable wormholes.
A. TRAVERSABLE WORMHOLES
Traversable wormholes represent a class of exact metric solutions of the general
relativistic field equation. The solutions are "exact" in the sense that no approximations
requiring a plethora of physical assumptions have to be made to derive the appropriate
spacetime geometry. To define a stable traversable wormhole one needs to define the
desirable physical requirements it is to have in order to achieve the desired FTL travel
benefit. The desired requirements are the following (Reference 1, 3):
• Travel time through the wormhole tunnel or throat should bes; 1 year as seen by
both the travelers and outside static observers.
• Proper time as measured by travelers should not be dilated by relativistic effects.
• The gravitational acceleration and tidal-gravity accelerations between different parts
of the travelers' body should be s; 1 go (go is the acceleration of gravity near the
Earth's surface, 9.81 m/s2) when going through the wormhole.
• Travel speed through the tunnel/throat should be < c.
• Travelers (made of ordinary matter) must not couple strongly to the material that
generates the wormhole curvature; the wormhole must be threaded by a vacuum
tube through which the travelers can move.
• There is no event horizon at the wormhole throat.
1 The Einstein field equation is: G,,, =R, .. - [(1/2) g,,. R] = -(811G/c4)'f;,., where G,,, is the Einstein curvature tensor,
Rp, Is the Ricci curvature tensor, R - R",, (the trace of R,,.) is the Ricci scalar curvature, T,,, is the stress-energy-
rnornenturn tensor (a matrix quantity that encodes the density and flux of a matter source's energy and
momentum), G is Newton's universal gravitation constant (6.673 x 10-11 Nm'/kg7), and c is the speed of light. In
simplest terms, this relation states that gravity is a manifestation of the spacetime curvature (G,.,) induced by a
source of matter (T,.. ,). The Greek indices (11, v = 0 3) denote spacetime coordinates, xa .. x1, such that x, __ x, =
space coordinates and xo - time coordinate.
1
UNCLASSIFIED/ ;'F8R: 8FFI81.t.k Wliilii &Hbl:f