Traversable Wormholes in (2+1) and (3+1) Dimensions with a Cosmological Constant

TL;DR

This paper explores the existence and properties of traversable wormholes in (2+1) and (3+1) dimensions with a cosmological constant, focusing on matter constraints and stability considerations.

Contribution

It provides new solutions for traversable wormholes with a cosmological constant and analyzes their matter requirements and stability in lower and higher dimensions.

Findings

Traversable wormholes require exotic matter with radial tension exceeding energy density.

A positive cosmological constant allows for positive energy density in (2+1) dimensions.

Partial stability analysis indicates certain solutions can be stable under specific conditions.

Abstract

Macroscopic traversable wormhole solutions to Einstein's field equations in $(2+1)$ and $(3+1)$ dimensions with a cosmological constant are investigated. Ensuring traversability severely constrains the material used to generate the wormhole's spacetime curvature. Although the presence of a cosmological constant modifies to some extent the type of matter permitted (for example it is possible to have a positive energy density for the material threading the throat of the wormhole in $(2+1)$ dimensions), the material must still be ``exotic'', that is matter with a larger radial tension than total mass-energy density multiplied by $c^2$. Two specific solutions are applied to the general cases and a partial stability analysis of a $(2+1)$ dimensional solution is explored.