Plane symmetric traversable wormholes in an anti-de Sitter background

TL;DR

This paper constructs plane symmetric traversable wormholes in anti-de Sitter space, analyzing energy conditions and junction conditions to minimize exotic matter, with solutions resembling domain walls that do not permit time travel.

Contribution

It introduces new solutions for plane symmetric wormholes in anti-de Sitter space with minimized exotic matter and detailed junction condition analysis.

Findings

Null energy condition is violated at the throat.

Surface stresses can satisfy the weak energy condition.

Constructed wormholes resemble domain walls without enabling time travel.

Abstract

We construct solutions of plane symmetric wormholes in the presence of a negative cosmological constant by matching an interior spacetime to the exterior anti-de Sitter vacuum solution. The spatial topology of this plane symmetric wormhole can be planar, cylindrical and toroidal. As usual the null energy condition is necessarily violated at the throat. At the junction surface, the surface stresses are determined. By expressing the tangential surface pressure as a function of several parameters, namely, that of the matching radius, the radial derivative of the redshift function and of the surface energy density, the sign of the tangential surface pressure is analyzed. We then study four specific equations of state at the junction: zero surface energy density, constant redshift function, domain wall equation of state, and traceless surface stress-energy tensor. The equation governing the behavior of the radial pressure, in terms of the surface stresses and the extrinsic curvatures, is also displayed. Finally, we construct a model of a plane symmetric traversable wormhole which minimizes the usage of the exotic matter at the throat, i.e., the null energy condition is made arbitrarily small at the wormhole throat, while the surface stresses on the junction surface satisfy the weak energy condition, and consequently the null energy condition. The construction of these wormholes does not alter the topology of the background spacetime (i.e., spacetime is not multiply-connected), so that these solutions can instead be considered domain walls. Thus, in general, these wormhole solutions do not allow time travel.