Wormhole Solutions

Wormholes are solutions to the Einstein field equations for gravity that act as "tunnels," connecting points in space-time in such a way that the trip between the points through the wormhole could take much less time than the trip through normal space. The first wormhole-like solutions were found by studying the mathematical solution for black holes. There it was found that the solution lent itself to an extension whose geometric interpretation was that of two copies of the black hole geometry connected by a "throat" (known as an Einstein-Rosen bridge). The throat is a dynamical object attached to the two holes that pinches off extremely quickly into a narrow link between them. Wormhole geometries are inherently unstable. The only material that can be used to stabilize them against pinching off is material having negative energy density, at least in some reference frame. No classical matter can do this, but it is possible that quantum fluctuations in various fields might be able to. "Traversable" wormholes exist in wormhole space-times in which the wormhole is held open at least long enough for a signal or object (spaceship) to pass through. Interest in such wormhole solutions in general relativity was stimulated when Michael Morris and Kip Thorne of the California Institute of Technology examined the general properties necessary for a wormhole to remain open. They found that if a wormhole is static and unchanging in time, then it must contain "exotic" matter. Such matter has negative energy density and a large negative pressure (or tension)--larger in magnitude than the energy density. Such matter is called "exotic" because it so little resembles all forms of known matter. In following seminar the basics of wormhole physics are reviewed, where the interesting properties and characteristics of static spherically symmetric traversable wormholes are considered, such as, the mathematics of embedding, equations of structure for the wormhole, thetraversability conditions, the necessity of exoticmatter to support these geometries and wormhole solutions in modified gravity.