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We construct solutions of plane symmetric wormholes in the presence of anegative cosmological constant by matching an interior spacetime to theexterior anti-de Sitter vacuum solution. The spatial topology of this planesymmetric wormhole can be planar, cylindrical and toroidal. As usual the nullenergy condition is necessarily violated at the throat. At the junctionsurface, the surface stresses are determined. By expressing the tangentialsurface pressure as a function of several parameters, namely, that of thematching radius, the radial derivative of the redshift function and of thesurface energy density, the sign of the tangential surface pressure isanalyzed. We then study four specific equations of state at the junction: zerosurface energy density, constant redshift function, domain wall equation ofstate, and traceless surface stress-energy tensor. The equation governing thebehavior of the radial pressure, in terms of the surface stresses and theextrinsic curvatures, is also displayed. Finally, we construct a model of aplane symmetric traversable wormhole which minimizes the usage of the exoticmatter at the throat, i.e., the null energy condition is made arbitrarily smallat the wormhole throat, while the surface stresses on the junction surfacesatisfy the weak energy condition, and consequently the null energy condition.The construction of these wormholes does not alter the topology of thebackground spacetime (i.e., spacetime is not multiply-connected), so that thesesolutions can instead be considered domain walls. Thus, in general, thesewormhole solutions do not allow time travel.Comment: 14 pages, 8 figures, Revtex4. Two references adde

Plane symmetric traversable wormholes in an anti–de Sitter background