Space-Times with non-trivial topology.

Wormholes are essentially tunnels in spacetime. In the above figure the top and bottom sheets are connected via a wormhole. The two sheets may represent two different universes or two sections of the same universe which, if not for the wormhole's presence, would be separated by a very large distance. Wormholes are important in certain areas of quantum gravity and in the study of topology change in General Relativity.

If one wishes the wormhole to be static (that is, not evolve in time) then one must violate energy conditions to keep the wormhole open. Energy conditions are statements about the state that matter can be in. For example, energy density being positive is one energy condition although other energy conditions exist which involve other eigenvalues. We have attempted to construct a reasonably general class of wormholes which respect energy conditions as much as possible. We find that, in this class, it is possible to minimize the energy condition violating region near the throat. We can make this violating region arbitrarily small by introducing an energy condition respecting matter field which joins the violating matter at some point near the throat.

How is such a wormhole created? Well, if one exists, our models show how it can be supported by a type of star with two different pressures. An observer outside of this star will see a star with a regular mass and suspect that nothing is strange about this star. The models also allows for an arbitrary cosmological constant.

One final thing worth noting, many closed universes (an infinite number if you want) may be connected by many wormholes. In such a case the profile curve looks something like this:

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