Morris-Thorne wormholes with a cosmological constant

TL;DR

This paper investigates Morris-Thorne wormholes within a universe with a cosmological constant, analyzing their physical properties, stability, and specific solutions, highlighting how the cosmological term influences wormhole characteristics.

Contribution

It provides a detailed analysis of spherically symmetric Morris-Thorne wormholes with a cosmological constant, including matching conditions and physical properties, which was not extensively studied before.

Findings

Surface tangential pressure varies with spacetime type and parameters.

Positive pressure at the boundary for asymptotically flat and anti-de Sitter spacetimes.

Negative or zero pressure depending on cosmological constant and wormhole size.

Abstract

First, the ideas introduced in the wormhole research field since the work of Morris and Thorne are briefly reviewed, namely, the issues of energy conditions, wormhole construction, stability, time machines and astrophysical signatures. Then, spherically symmetric and static traversable Morris-Thorne wormholes in the presence of a generic cosmological constant are analyzed. A matching of an interior solution to the unique exterior vacuum solution is done using directly the Einstein equations. The structure as well as several physical properties and characteristics of traversable wormholes due to the effects of the cosmological term are studied. Interesting equations appear in the process of matching. For instance, one finds that for asymptotically flat and anti-de Sitter spacetimes the surface tangential pressure of the thin-shell, at the boundary of the interior and exterior solutions, is always strictly positive, whereas for de Sitter spacetime it can take either sign as one could expect, being negative (tension) for relatively high cosmological constant and high wormhole radius, positive for relatively high mass and small wormhole radius, and zero in-between. Finally, some specific solutions with generic cosmological constant, based on the Morris-Thorne solutions, are provided.