From the "New Scientist" 12 Mar 2012
"Intergalactic subway: All aboard the wormhole express"
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You probably won't be surprised to learn that no one has yet come close to constructing such a wormhole. One reason is that they are notoriously unstable. Even on paper, they have a tendency to snap shut in the blink of an eye unless they are propped open by an exotic form of matter with negative energy, whose existence is itself in doubt.
Now, all that has changed. A team of physicists from Germany and Greece has shown that building wormholes may be possible without any input from negative energy at all. "You don't even need normal matter with positive energy," says Burkhard Kleihaus of the University of Oldenburg in Germany. "Wormholes can be propped open with nothing."
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Crucially, when space-time has more than four dimensions, the powerful theorems which forbid a wormhole unless it is propped open by negative energy may not apply. In 2002, Kirill Bronnikov at the Centre of Gravitation and Fundamental Metrology in Moscow, Russia, and Sung-Won Kim at Ewha Womans University in Seoul, South Korea, raised the possibility of a wormhole existing without exotic matter (Physical Review D, vol 67, p 064027). They uncovered a wealth of wormhole solutions in one of the popular versions of brane-world gravity, which describes our world as a 4D island or "brane" floating in higher dimensions. "No phantom matter is required, and the wormholes can have an arbitrary size," says Bronnikov.
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If the extra dimensions of higher dimensional theories are rolled up very small, or "compactified", that would explain why we do not experience them directly. The process of compactifying the extra six dimensions of string theory creates several new force fields, such as the so-called dilaton field. In the same way that general relativity describes gravity as the curvature of space, gravity in DEGB theory depends on the curvature plus the curvature raised to a higher power.
Using this extra term in the gravitational equations, Kleihaus and his colleagues have discovered a solution for a wormhole. It needs no stuff made of negative energy to prop it open, or, indeed, any matter at all (Physical Review Letters, vol 107, p 271101).